Chapitre 1 Definition

Chapitre 2 Influence

Harmonia Axyridis Pallas

Chapitre

Effet De

Reponse Fonctionnelle Temperature

Dependante De

Harmonia Axy

Ridis Pallas

A My

Zus Persicae

ON THE DEMOGRAPHY AND INTRINSIC RATE OF POPULATION INCREASE OF

1 1.2 Harmonia axyridis 3 2. THE APPROACH 5 2.1 The approach to the evaluation of the effectiveness of the predator 5 2.2 The approach to the population modeling 8 3. OBJECTIVES 11

I wish to thank the members of the jury, Dr. Jérôme Casas, Dr. Joël Chadoeuf Dr. André Ferran, Dr. Jean-Marie Reidenbach, and Dr. Benoît Sauphanor, for reviewing this thesis and offering precious conunents, and for their lcindly being present at the defense. I am grateful to Dr.

Jérôme Casas and Dr. Jean-Sebastien Pierre for undertaking the task as reviewers of this thesis. I am indebted to my major professor, Dr. Jean-Marie Reidenbach, for accepting me to study under his presidence, and for supporting my study, without ail these the work for producing this thesis could flot have been realized. I thank Dr. Serge Poitout, the Director of INRA-Station de Recherches de Zoologie at Montfavet, for providing the opportunity for me to study in his laboratory and to benefit administrative and technical supports. Special thanks must be extended to Dr. Benoît Sauphanor (advisor, mentor, and friend) for helping me develop skills necessary to succeed in my career, for sharing with me his intellectual wits and cultural interests which have had a profound influence on my life, and for offering me friendliness which has been an important source of my courage and strength. I am grateful to Dr. André Kretszchmar, Dr. René Pieux, Mrs. Colette Pélissier, Mr. Francois Faivre D'arcier, Mr. Jacques Brun and Mr. Thierry Pascal for kindly providing advice, technique or materials for my research. My thanks should equally be extended to Mrs. Martine Fargier, Mrs. Andrée Tardy, Mrs. Conne Chêne and Mrs. Michele Aguila for their office support. I would also give my thanks to ail the people in the Station of Zoology for malcing the working atmosphere a pleasant one. I feel obliged to the following friends of mine for the spiritual support and friendship they have given me, which have made my staying in Avignon a more agreeable and unforgettable experience, Brigitte Sauphanor, Jean-Charles Bouvier, Christophe and Arme Lenfant, Abder Lyoussoufi, Mrs. Charmasson, Xingfa Gu, Yan Wang, Ping Du.

Finally, I want to thank my parents for having led me the way of life and encouraging me to improve myself unceasingly.

Résumé. Le puceron vert du pêcher, Myzus persicae Sulzer, est à l'origine de pertes croissantes dans les vergers commerciaux de pêchers du sud de la France. Des recherches sont entreprises à l'INRA sur la possibilité de contrôle biologique des populations de M persicae à l'aide d'une coccinelle prédatrice introduite, Harmonia cayridis Pallas. Nous analysons ici l'efficacité de H. axyridis comme agent de lutte biologique contre M persicae , par la modélisation de l'interaction proie-prédateur en fonction de la température. Les données de base pour la caractérisation de ces interactions et l'élaboration d'un modèle de simulation sont établies en laboratoire à la station de Zoologie de l'INRA d'Avignon. Le taux intrinsèque d'accroissement des populations de M persicae atteint son maximum à 24°C, alors que les températures procurant la consommation de proies maximale par la coccinelle se situent aux environs de 25-27.5°C. Le taux de développement des larves de H axyridis approche une valeur maximale lorsque la densité de proies augmente, et présente une réponse à la température typique des organismes poikilothermes. Le taux moyen de survie journalier âge -spécifique de H axyridis s'accroît avec la densité de proies selon une courbe sigmoïde, et répond également à la température. La simulation atteste que l'efficacité des jeunes larves (L 1-L3) de H. axyridis dans l'élimination de M persicae augmente avec la température.

Cette réponse ne se retrouve pas chez les larves de 4ème stade. Les larves âgées sont toujours plus efficaces que les jeunes larves à basses températures, et cet ordre s'inverse à l'autre extrémité de la gamme de températures efficaces (10-30°C), avec une série de transitions lorsque la température augmente. La simulation et les résultats d'expérimentations en conditions semi contrôlées n'établissent pas clairement les conditions de la maîtrise des populations de M persicae par lâchers inondatifs de H axyridis en vergers. L'efficacité du prédateur est moindre en conditions de basses températures, où la proie connaît au contraire un très fort taux d'accroissement de population. Des résultats satisfaisants sont obtenus sur arbres encagés où le lâcher d'un nombre approprié de larves de 3ème stade (50 par arbre) permet l'extinction de populations initiales de 20 pucerons par rameau. La simulation réalisée à partir des températures relevées au cours de l'expérimentation génère des résultats qualitativement conformes à l'observation.

ABSTRACT. Green peach aphid, Myzus persicae Sulzer, an important pest in the commercial peach orchards in the Rhone Valley of southem France, has been causing increasing econornic losses. Current control methods, are either ineffective or have drawbacks including increased pesticide resistance, destroying natural control mechanisms, contarninating of environment and fruits. To solve these problems, possibility of biological control using an introduced cocccinellid predator, Harmonia axyridis Pallas is investigated by researchers in INRA. As an integrated part of this effort, I investigated the effectiveness of H. axyridis as a biocontrol agent against M persicae, with the modeling and analysis of the temperature-dependent predator-prey interactions.

Background studies necessary for estimating parameters for describing the temperaturedependent predator-prey interactions and for building a simulation model were conducted by the author in the Zoology Station, INRA, Avignon. The intrinsic rate of population increase of M. persicae reaches its maximum value around 24 °C, while the optimal temperature for attaining the maximum prey consumption with a fixed prey density is about 25-27.5 °C. The developmental rate of larval H. axyridis approaches the maximum value as the prey density increases and the developmental rate of H. axyridis responds to temperature following a typical poikilothermal pattern. The average age-specific daily survival rate of H. axyridis increases with prey density following a sigmoid curve, and is also affected by temperature. Results from simulation analyses are presented suggesting that a major factor limiting the effectiveness of H. axyridis lies in the fact that this predator is flot very effective under low temperatures when the prey, green peach aphids can attain a fairly high rate of population increase. Simulation also suggested that the effectiveness of young larvae (L1-L3) of H. axyridis in eliminating green peach aphids augments as temperature increases, but this pattern does flot hold for the 4 th instar. From another perspective, older instar larvae are always more effective than the younger ones at low temperatures, but this pattern switches to the reverse order at the other end of the effective temperature range (I0-30°C), with a series of transitions in this pattern as temperatures increases within the range of the two extremes. Satisfactory results were obtained in suppressing the population of M. persicae using H. axyridis by releasing an acceptable number of 3 r1 instar larvae (50 larvae/tree) at an aphids density of average 20 aphids/shoot on caged trees. Simulation run with temperature data recorded during the experiment génerates results qualitatively consistent with the observation.

II

PREFACE

The potential use of Hannonia cibcyridis Pallas as a biological control agent for innundative release is exarnined for green peach aphids Myzus persicae, an insect pest in commercial peach orchards in southern France, using a simulation model. Chapter 1 describes M persicae as a pest in peach orchards and the history of study on H. axyridis in France, and introduces the objectives and approaches of this study with respect to the evaluation of H. axyridis as a biological control agent and the modeling of the predator- prey interactions between H. axyridis and M persicae.

In Chapter 2, models of the developmental rate and intrinsic rate of population increase of M. persicae as functions of temperature are developed upon data of age- specific life tables built for laboratory populations. Some other parameters of the life system of M. persicae are also presented in the chapter.

The temperature-dependent functional responses of ail the active immature stages of H. axyridis to M persicae are discussed in Chapter 3. The number of green peach aphids consumed by H. axyridis are modeled as function of both temperature and density of aphids exposed to the predator.

Chapter 4 deals with the developmental rate and survival rate of different larval stages of H. axyridis in relation to temperature and prey density. These relationships are described by models. The integration of the two aspects, developmental and survival rate, will account for the temperature-and density-dependence of the rate of change in the number of individual in the cohort of a given larvae stage.

Models described in the above chapter are incorporated in Chapter 5 into a computer simulation model. Simulation results are discussed concerning the effectiveness of H. axyridis as a predator of green peach aphids in relation to temperature, predator age, and prey density.

Chapter 6 presents the results of a release trial in the orchard using the experimental exclusion technique. The observation is compared with simulation that is conducted using temperature data recorded during the release trial.

Definition of the system and the approach

1. THE SYSTEM 1.1 The Green peach aphid Green peach aphid (Myzus persicae (Sulzer)) is a world-widely distributed species. It is outstanding in distribution and in host plant range (Van Emden, et al. 1969, Mackauer and[START_REF] Mackauer | Myzus persicae Sulz., an aphid of world importance[END_REF]. As a pest, green peach aphid flot only causes direct damage but is also able to transmit over 100 virus diseases of plants on about 50 different families including many important crops [START_REF] Kennedy | A Conspectus of Aphids as Vectors of Plant Viruses[END_REF][START_REF] Van Emden | The ecology of Myzus persicae[END_REF][START_REF] Swenson | Role of aphids in the ecology of plant viruses[END_REF][START_REF] Mackauer | Myzus persicae Sulz., an aphid of world importance[END_REF]. Perhaps because of its wide distribution and economic importance on several crops, M persicae has been extensively and intensively studied and was selected in 1967 as the key aphid species for an international collaborative research project under the IBP/UM (Use and Management of Natural Resources) program [START_REF] Mackauer | Myzus persicae Sulz., an aphid of world importance[END_REF]. It bas been an object in the study of physiology, biochemistry, nutrition [START_REF] Dadd | Dietary amino acid requirements of the aphid, Myzus persicae[END_REF][START_REF] Miles | Insect secretions in Plants[END_REF][START_REF] Parry | The artificial feeding of phosphamidon to Myzus persicae: II. The effects of phosphamidon on liquid uptake through a parafilm membrane[END_REF], genetics [START_REF] Ford | Ecological Genettes[END_REF][START_REF] Cognetti | Sexual genotypes of migratory tendencies in Myzus persicae Sulz[END_REF][START_REF] Blackman | The inheritance of life cycle differences in Myzus persicae (Sulz.)[END_REF]) insecticide resistance (Sudderuddins 1973[START_REF] Attia | Insecticide resistance in Myzus persicae in Australia[END_REF][START_REF] Sawicki | Stability of pesticide resistance in the peach-potato aphid, Myzus persicae (Sulzer)[END_REF], Weber 1985a, b, Devonshire 1989, Sauphanor et al, 1995) and plantaphid interactions [START_REF] Van Emden | The ecology of Myzus persicae[END_REF]. As an economically important pest, the biology, ecology and control of M persicae have been world-widely studied on potato and sugar beet, its secondary hosts. However, only a few researches (Tamacki 1973, Leclant 1986, 1988) were carried out on the aphid's primary host plant, peach trees, probably because this species.was previously flot, or was flot perceived as, an important pest in peach orchards. In fact, it was generally perceived, and it may still be perceived by some, that peach trees can tolerate a fairly high population of M. persicae without measurable economic damage [START_REF] Mackauer | Myzus persicae Sulz., an aphid of world importance[END_REF].

In southern France, green peach aphid has been drawing attentions for serious problems it is causing in peach orchards. It attacks the peach flowers and buds in the early spring, which may greatly reduce the production and quality of peach fruits [START_REF] Leclant | Etude biologique des aphides de la région Mediterranéenne: Implication agronomoques[END_REF]. The high population potentials of this pest allows frequent heavy infestations on peach trees which may seriously weaken the vitality of peach trees and affect the fruit production for the following years [START_REF] Leclant | Elements pour la prise en consideration des aphides dans la lutte integree en vergers de pechers[END_REF]. Moreover, two important factors has made green peach aphid become remarkable as a pest in peach orchard: 1) this aphid was once believed to be the major vector of Sharka, a vital virus disease of peach trees in Europe, which has destroyed some commercial orchards and has presented a major threat to the peach production (more recent researchs on epidemics of Sharka suggests that M persicae has a much less crucial role in the transmission of the viral disease than what had been believed (Sauphanor 1997, personal communication)); and 2) it has manifested an increased resistance to the major groups of insecticides which has resulted in failures of pesticide treatments in peach orchards (Craveti and Cervato 1993).

Few other approaches than chemical methods have been successful in maintaining the population density of green peach aphids at an acceptable low density, which was considered necessary for controlling the epidemics of the virus disease. The intensive use of chemical methods to reduce the economic losses due to this pest and to prevent the spread of virus diseases by controlling the aphid vector has resulted in the development of resistance of this species to major types of pesticides, which has often led to more frequent and more intensive use of pesticides (Weber 1985a, b, Sudderuddins 1973[START_REF] Attia | Insecticide resistance in Myzus persicae in Australia[END_REF], Savvicki et al. 1980[START_REF] Devonshire | Resistance of Aphids to Insecticides[END_REF]). The reliance on chemical methods in controlling green peach aphids has been in conflict with integrated control programs aiming at other orchard pests, and may eventually cause intolerable consequences to the environment of the. peach growing areas.

Thus, to free the peach production from the direct damage and threat of aphidmediated virus diseases, and to reduce the environmental risk from pesticide application, there is an urgent need for new and environmentally sound control approaches, including utilization of variety resistance of peach trees and biological control using natural enemies.

Research efforts have been 'made toward these directions in INRA-Research Station of

Zoology at Avignon for years (Sauphanor et al. 993). This research has been conducted within this context.

Harmonia aryridis

Harmonia axyridis is a predatory coccinellid originated in the East Asia. This species has a wide range of adaptation to various habitats and can prey on a wide range of aphid species (Shanderl 1986). For these reasons, it has been extensively studied and utilized in Japan, China, South Korea and Russia for biological control through conservation and enhancement of natural populations, as well as human augmentation of the natural population [START_REF] Niijima | Artificial diets for an aphidophagous coccinellid, Hannonia axyridis, and its nutrition[END_REF]. A great quantity of researches have been done concerning the biology [START_REF] Gotoh | Experimental transfer of abnormal "Sex-Ratio" in the ladybird beetle, Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae)[END_REF][START_REF] Takahashi | An experiment on the collecting method of eggs of the lady beetles, Coccinella septempunctata brucki Mulsant and Harmonia alyridis (Pallas) (Coleoptera: Coccinellidae)[END_REF][START_REF] Obata | Mating refusai and its significance in females of the ladybird beetle, Harmonia axyridis[END_REF][START_REF] Coderre | The occurance of Harmonia cncyridis (Pallas) (Coleoptera: Coccinellidae) in Canada[END_REF], ecology [START_REF] Shanderl | Les besoins trophiques et thermiques des larves de la coccinelle Harmonia axyridis Pallas[END_REF][START_REF] Obata | Mechanisms of prey finding in the aphidophagous ladybird beetle, Harmonia axyridis (Coleoptera: Coccinellidae)[END_REF][START_REF] Mcclure | Role of predators in regulation of endemic populations of Matsucoccus matsurnurae (Homoptera: Margarrodidae) in Japan[END_REF], 1987), behaviors [START_REF] Obata | Mechanisms of prey finding in the aphidophagous ladybird beetle, Harmonia axyridis (Coleoptera: Coccinellidae)[END_REF]Obata andHidaka 1987, Osawa 1994), physiology and biochemistry [START_REF] Ogawa | The purification and properties of trehalose from lady beetle, Harmonia axyridis[END_REF], population biology [START_REF] Hu | Matemally inherited "sonless" abnormal sex-ratio conditionn in the ladybeetle (Harmonia cocyridis)[END_REF], Bogdanov and Gage chii 1986[START_REF] Kholin | Stability of genetic polymorphism for wing sheath coloring in Harmonia axyridis (Pal!.) (Coleoptera: Coccinellidae) in the Primor'e region[END_REF][START_REF] Osawa | Seasonal variation in elytral color polymorphism in Harmonia axyridis (the ladybird beetle): the role of non-random mating[END_REF][START_REF] Ueno | Fluctuating asymmetry in relation to two fitness components, adult longevity and male mating success in a ladybird beetle, Harmonia cayridis (Coleoptera: Coccinellidae)[END_REF], nutrition and artificial mass rearing [START_REF] Niijima | Nutritional studies of an aphidophagous coccinellid, Harmonia axyridis. IV. Effects of chemically defined diet and some fractions of drone honeybee brood on the reproduction[END_REF][START_REF] Choi | Preliminary studies on the aphidivorous activity of coccinellid beetles (1-Jarmonia aryridis Pallas) and their artificial rearing [Potential biological control organisms[END_REF][START_REF] Choi | Mass rearing of a coccinellid beetle, Harmonia cayridis Pallas, on artificial dirts[END_REF][START_REF] Matsuka | Harmonia axyridis[END_REF], Shanderl et al. 1986[START_REF] Wang | Mass rearing and utilization in biological control of the lady beetle Leis axyridis (Pallas)[END_REF]), as well as the techniques for field application of this coccinellid species [START_REF] Niijima | Artificial diets for an aphidophagous coccinellid, Hannonia axyridis, and its nutrition[END_REF][START_REF] Wang | Mass rearing and utilization in biological control of the lady beetle Leis axyridis (Pallas)[END_REF]). In the United States, this species has been introduced

for controlling a variety of pests, mainly including aphids and scales [START_REF] Mcclure | Role of predators in regulation of endemic populations of Matsucoccus matsurnurae (Homoptera: Margarrodidae) in Japan[END_REF], 1987[START_REF] Bryan | Ladybugs take commercial flight to Texas[END_REF][START_REF] De Quattro | Gotcha! Tiny lady beetles have big biocontrol potential[END_REF]. Native populations have also been discovered in several locations in the North America [START_REF] Chapin | Harmonia axyridis (Pallas), the third species of the genus to be found in the United States (Coleoptera: Coccinellidae)[END_REF][START_REF] Dreistat | Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae), firstwestern United States record for this Asiatic lady beetle[END_REF][START_REF] Coderre | The occurance of Harmonia cncyridis (Pallas) (Coleoptera: Coccinellidae) in Canada[END_REF]). A very successful example of using this ladybug as an exotic species for classic biological control has been its being introduced into the USA for controlling the pecan aphids. It has been so successful that in several pecan growing states, the pecan aphid is no longer considered as a substantial pests (Bryan 1993, LaRock and[START_REF] Larock | An integrated pest management approach, emphasizing biologicaI control, for pecan aphids[END_REF]. But in many locations in the United States this coccinellid has becoming a nuisance to the residents, because they enter the houses in swarm for oversummering or overwintering [START_REF] Segelken | State residents asked to report "exotic" lady beetle[END_REF][START_REF] Robinson | Urban entomology: insect and mite pests in the human environment[END_REF]).

H. alyridis was introduced to France in the early 1980's by INRA-Laboratory of Population Biology at Antibes as a potential biological control agent. The fundamental aspects of the biology, ecology and behavior have been studied in details [START_REF] Shanderl | Les besoins trophiques et thermiques des larves de la coccinelle Harmonia axyridis Pallas[END_REF], Shanderl 1986, Ferran et al. 1985). Techniques for mass rearing with eggs of Ephestia kuehniella Zeller have been developed and commercial production was made possible [START_REF] Shanderl | Les besoins trophiques et thermiques des larves de la coccinelle Harmonia axyridis Pallas[END_REF], Shanderl 1986). Laboratory and field explorations of the possibility to use this species to control various pests, mostly aphids and scales, have been conducted on a number of crops (Ferran 1996, personal communication). Efforts have been made in trying to use this ladybug for inundative releases, and encouraging success bas been gained in biological control against Macrosiphum rosae (L.) on rose bushes (Ferran 1996, personal communication). However, there has been so far no other records or evidence showing any substantial success in using this ladybug in controlling insect pests in France. More detailed studies on the evaluation of the effectiveness of this coccinellid as a potential biological control agent against different pests should be conducted before valid conclusion could be made concerning the potential usefulness of this species as a biological control agent in France. In this study, we concentrate on the evaluation of the effectiveness of H. axyridis as a biological control agent against green peach aphid.

Two distinct categories for augmenting the use of biological control agent have been recognized [START_REF] Debach | Manipulation of entomophagous species[END_REF]: inoculative and inundative releases. The former refers to releasing relatively small number of beneficial insects as colonizing populations, with the purpose of providing relatively long-term pest regulation through in-field reproduction of the released species. Inundative releases, on the other hand, release large numbers to cause an immediate and direct mortality in the pest population [START_REF] Stinner | Efficacy of innundative releases[END_REF].

Due to the fact that green peach aphid colonizes peach trees as a primary host only for a rather short period in spring, and moves later on to a vast range of secondary hosts, the coccinellid is unlikely to establish close phenological and habitat with the aphid. Thus, inundative release is a natural choice for utilizing H. axyridis as a biological control agent against green peach aphid, that is, the coccinellid is used as an intervention agent for immediate suppression of the aphid population and need to be applied whenever the aphid population exceeded the tolerance threshold.

THE APPROACH

2.1 The approach to the evaluation of the effectiveness of the predator For biological control using inundative releases of biological control agent, the beneficial species is usually flot intended to be introduced as a long-term regulatory agent, but rather as a temporary suppressing force of the pest population [START_REF] Hoyt | The developing programs of integrated control of pests of apples in Washington and peaches in California[END_REF][START_REF] Debach | Biological Control by Natural Enemies[END_REF][START_REF] Stinner | Efficacy of innundative releases[END_REF]. Thus the long-term dynamics of the predator and the prey is of little concern in the evaluation of the effectiveness of the entomophaga. The evaluation of the effectiveness of a biocontrol agent for inundative release can be implemented using several different approaches or their combinations (Huffacker andKennett 1969, Luck et al. 1988). In the first case, direct field release trials can be conducted and gross cause-effect indication rather than proof is usually yielded based on observations and sampling data [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF]Dixon 1980, Luck et al. 1988). Altematively, life tables can be built for populations of the pest and the released biological control agent under natural or semi-controlled condition to assess the impacts of the natural enemy on the demography and the population trends of the pest, intensive inspections of marked aphid colonies or caged plants or plant parts, both with or without predators, are usually conducted for this methods. Strong proof of the impacts of the predator on the pest population may be obtained [START_REF] Dixon | An experimental study of the searching behaviour of the predatory coccinellid beetle, Adalia decepunctata (L.)[END_REF][START_REF] Varley | The use of models and life tables in assessing the role of natural enemies[END_REF], Frazer et al. 1981[START_REF] Bellows | Life-table construction and analysis in the evaluation of natural enemies[END_REF]). As a third alternative, laboratory or strictly controlled field populations can be manipulated by using experimental exclusion techniques to determine the quantitative relationships between the major component variables or processes of the system; the system is usually well defined, and simple measurable component processes or relations that contribute to the major behaviors of the system are identified from complex interactions; measured relationships between component variables are synthesized with a model [START_REF] Varley | The use of models and life tables in assessing the role of natural enemies[END_REF][START_REF] Ruesink | Status of the systems approach to pest management[END_REF][START_REF] Rabbinge | Systems analysis and simulation as an aid to the understanding of acarine predator-prey systems[END_REF]. The first approach is technically simple, but economically expensive and ecologically risky if the trial is to be conducted in a meaningfiffly large spatial scale and to include an inclusive range of release options (Pimentel et at. 1980); the results of the evaluation of the effectiveness with this approach are directly related to the real situation in practice, but on the other hand, they give little explanation for the consequence (success or failure) of the releases. For the second approach, convincing evidence can be obtained concerning impacts of introducing predators on prey population in a particular experimental setting, but the results are usually dependent on the particular situation and can in no sense be considered to apply to more general situations, since actual experiments are usually hindered by technical difficulties and limited in time and space. The third approach can result in the accumulation of a large amount of detailed information concerning quantitative relationships between various component variables, which is very useful for answering specific questions such as "Is temperature a critical factor that determines the effectiveness of the predator?". The data gathered with this approach can usually be considered as being more general than with the other two approaches, since the experiments for measuring those relationships are usually designed to be conducted, in the first place, under certain "ideal conditions" ---conditions that apply to most, if flot all, situations. Some system-specific and situation-specific factors, which were usually left out at the beginning, can be incorporated subsequently according to the need. This approach costs less research effort and resource, and can often provide insights into the mechanisms behind the phenomenal consequences, which is usually very valuable for subsequent researches such as the development of strategies for using the natural enemy in biological control, and even adds to the more general biological control theory [START_REF] Ruesink | Status of the systems approach to pest management[END_REF][START_REF] Rabbinge | Systems analysis and simulation as an aid to the understanding of acarine predator-prey systems[END_REF], Susan 1991). However, one inherent weakness of this approach, which results right from its being general, is its being less realistic than the other two approaches, since a lot of details that are regarded as being less relevant to the questions to be answered are dropped out of the model. The model prediction should be considered rather as hypotheses ta be tested than as faets to be accepted. The use of any single approach will face some limitations and constraints. In fact, each of the three approaches is better suitable ta address certain types of questions, ta fit to certain purpose or to be used in certain situation or certain phase of a research project than the others.

They should be regarded more as reciprocal approaches rather than competing ones, for example, the modeling approach can usually be used ta generate hypotheses that can be tested using the other two approaches; the field release trials can usually be used to test the predictions made by the model and/or the life table and arrive at the final judgment of the effectiveness of a natural enemy in the real situation. Information from the life table or the model can usually serve to eliminate a large number of options that should otherwise be considered, and raise better defined and more specific questions to be answered, or form more explicit statement to be proved by the field release trials.

The integration of the three approaches bas been accepted by the research group in INRA-Research Station of Zoology at Avignon. This thesis deals only with the part of study using the modeling approach. In this study, our major concern is whether H.

axyridis has the potentials to be used as a effective biological control agent for innundative release against the green peach aphid, in terms of the potential predatory pressure it may pose on the aphid population versus the potentials of aphid population growth, with both sides being dynamically modified by each other and by temperature. The potentials of population growth of the aphid is represented by the intrinsic rate of population increase which is a function of temperature and is subject to a multiplier representing the effect of intra-specific competition. The potential predatory pressure of the ladybeetle is regarded as an integral index of the attack rate, survival and developmental rates of the ladybug.

These elements are to be incorporated into a model which can be used to pose and answer questions such as whether this coccinellid can be an effective predator of green peach aphid at ail, or within which temperature range the coccinellid possesses the potentials to be a effective predator of green peach aphids.

The approach to the population modeling

A model is an intellectual construction or artificial analog of a physical system. The purpose for building a model of a system is always to obtain a representation of only the most important features of the system, so that we can study and use the model, instead of the physical system itself, which is more easy to understand and to handle than the real system for certain purposes [START_REF] Conway | Experience in pest modelling: a review of models, uses and future directions[END_REF]Murdie 1972, Curry and[START_REF] Curry | Mathematical foundations of population[END_REF]. It is in this sense that a perfect copy of the physical system is flot only impossible but also unnecessary, and thus, considerable simplifications are always needed, because an exact analog of the system will be as hard to understand, and behave as slowly as the physical system.

Different approaches to modeling population dynamics (no matter a single species or a multi-species system) can be distinguished [START_REF] Conway | Experience in pest modelling: a review of models, uses and future directions[END_REF][START_REF] May | Stability and Complexity in Mode! Ecosystems. r d Ed[END_REF], Guiterrez 1981[START_REF] Gets | Aperspective on systems analysis in crop production and insect management[END_REF], Dixon 1989, Arino et al.1991[START_REF] Berryman | Good theory and premature models[END_REF][START_REF] Renshaw | Modelling biological populations in space and lime[END_REF]).

Firstly, one can distinguish between analytical models and simulation models. Analytical models usually involve only a limited number of variables and parameters and the relationships between variables are mathematically explicit so that the model be kept simple enough to be analytically tractable. On the other hand, simulation models can incorporate a large number of variables and parameters and the relationships between variables do flot need to be mathematically explicit but can be implicitly embedded in the algorithm of computer programs [START_REF] De Wit | Simulation of ecological processes[END_REF]. In fact, there are hardly any models of a particular physical system that can be perfectly put into either of the categories; in most cases, simulation models use some analytical models as frameworks;

and analytical models need to incorporate some simulation techniques when being used to tackle specific problems with a specific system. Therefore, it is of little meaning or use to simply label one's model as an "analytical" or "simulation" model, as far as you want to model a specific system. It is perhaps more useful to distinguish a model based on how it is constructed; a model could be obtained by fitting population time series data to simple theoretical models which were built upon fundamental biological and ecological principles;

or otherwise, the model could be constructed using parameters measured directly from experiments or observations or derived from calibration or adjustment against the behavior of the system [START_REF] Berryman | On choosing models for describing and analyzing ecological time series[END_REF]. For the former apprbach, an adequate length of time series data need to be collected and compiled, and the model and system itself need to be pretty simple so as to allow feasible statistical analyses. This method requires that the population time series be stationary or at least be able to be transformed into an stationary time series, so it is most suitable to be used for studying long terni macroscopic population changes with one year as the time step. It is of limited use in studying microscopic population changes, or population with strong seasonality or subject to frequent violent perturbations, such as in many agricultural pest populations. This approach is obviously flot suitable for this study. For the latter approach, the system is usually structured reflecting certain biological details, and is thus possible to be reduced into some basic mechanistic sub-units of lower organization-levels which usually have a shorter time scale, so that the parameters in this kind of models are biologically explicit and can be measured directly or be estimated from other quantities. This kind of models are comparatively cheaper to build, and flexible in model complexity, but they often fail to describe and explain the overall long-term behaviors of a real system because of the involvement of different organization levels and different time or/and space scales. Thus, it is more suitable to be used to study specific microscopic behaviors of a system, rather than giving predictions of long-term macroscopic dynamic behaviors of a system. This study will accept this approach.

Another distinction can be made between models which describe population growth as a continuous process and those that describe change of populations with discrete generations or age classes [START_REF] May | Stability and Complexity in Mode! Ecosystems. r d Ed[END_REF]. The former includes models with the independent variable (time) being continuous, for which we have differential equations. The latter includes models with the independent variable (t) being discrete, for which we have difference equations. Because the life system of green peach aphid is characterized by high degree of generation overlaps, individuals are born and die at any moment, continuoustime model will be more appropriate and convenient in modeling the population changes.

Distinction can also be made between deterministic models and stochastic models. For deterministic models the population density (IV) changes uniquely and continuously by an infinitesimal amount dN in an infinitesimal time di. For stochastic models the population density is perceived to be a random variable with respect to every ET (Tis a specific real set). The classic stochastic population models are based on dikrete-state processes [START_REF] Bartlett | Stochastic population models[END_REF][START_REF] Pielou | An introduction of Mathematical Ecoloe[END_REF][START_REF] May | Stability and Complexity in Mode! Ecosystems. r d Ed[END_REF] where we have probability distribution function, f(n, t), which defines the probability to find the population to have n individuals at time t, thus the average population and the variance can be calculated at each time point t [START_REF] Bartlett | Stochastic population models[END_REF][START_REF] May | Stability and Complexity in Mode! Ecosystems. r d Ed[END_REF]. Obviously, this type of stochastic models gives a more realistic description of the population process, since in the deterministic model, each member of the population gives birth or dies to some fraction of an individual in each small interval of time, whereas in the stochastic model only whole animais are born and die with specified probabilities. While being more realistic, stochastic population models involve harder calculation and requires more information than their deterministic analogues. And more importantly, for very large populations, this distinction becomes unimportant, as [START_REF] May | Stability and Complexity in Mode! Ecosystems. r d Ed[END_REF] argued, the generalized central limit theorems of [START_REF] Mcneil | Central limit analogues for Markov population processes[END_REF] guarantees that for large value of N (or K, the carrying capacity, in case of logistic population growth) the mean of the population is identical to the deterministic population, and the statistical root-mean-square relative population fluctuation about the mean becomes trivial. This kind of stochasticity rooted in the fact that the population variables are fundamentally discrete ones is termed as "demographic stochasticity" [START_REF] Bartlett | Stochastic population models[END_REF].

Stochasticity also arise from the randomness of environmental elements of a population, for which a random variable of specified probability distribution is often added to the rate of population change [START_REF] Conway | Population models as a basis for pest control[END_REF], May 1972).

Another way to classify models is based on the model complexity, in the 70's and early 80's, the so called general-purpose large-scale system models was strongly advocated, they were characterized by involving a huge number of variables and parameters, and a wide range of interactions, being built for serving general purposes (Logan 1993). It turned out that those huge general-purpose large-scale model were even harder to understand and operate than the real system and were thus of little use. Recently, there has been sua a tendency that people are turning back to those small specific-purpose models which are characterized by incorporating only a minimum number of variables and parameters and serve certain well-defined specific purposes (Logan 1993). This study will accept the modeling approach with a very specific purpdse evaluating the effectiveness of H. axyridis as a predator ofM persicae, so the model will keep only the most relevant elements.

In this study, three major components will be incorporated in the model: the temperature-dependent population increase rate of M. persicae, the temperature- dependent functional response of H. axyridis to M persicae, and the temperature- dependent rates of development and survival of the larval stage of the predator. These elements are to be coupled in a dynamic simulation mode! (Fig. 1-1).

Population density of M. persicae N(t)

Intrinsic rate of population

OBJECTIVES

There are two major reasons for using the modeling approach to evaluate the effectiveness of H axyridis as a biological control agent against M persicae. Firstly, a model can serve to identify key factors that determine the effectiveness of the predator, increase our understanding of the consequence, which is critical in determining under what conditions the inundative releases would have the greatest or least chance of providing feasible control against the target pest. The model can also be used to direct field release trials and provide supplementary information on the field evaluations. Secondly, the model can provide a framework for more detailed system-specific or field-level tactic models in the following phase of researches for developing field application tactics and decision making conceming the optimum timing and numbers of the predator to release. The optimization of these two variables can greatly reduce costs as well as increase efficiency, particularly against highly vagile and fecund prey species like M persicae. Even in case that the predator turns out flot to be a effective predator of M persicae, the model can still be used in predicting the right kind of natural enemies that should be considered as potential biological control agents.

The objective of this study is to use the modeling approach to evaluate the potential effectiveness of H. axyridis as a biological control agent against M persicae within the limit of the population potentials of the prey, the searching efficiency of the predator and the sustainability of the predator in relation to the prey abundance, and the temperaturedependence of these processes, to enhance the understanding of the consequences of field release trials, to identify areas where more information is needed and provide guidelines for further field evaluations and application.

Introduction

In the context of developing more effective and rational approaches and strategies for controlling green peach aphid (Myzus persicae) in peach orchards, including evaluating the effectiveness of biological control agents and developing strategies for field application, which is the major concern of this study, information on the potentials of population increase of the aphid is critical. A classic approach to the study of insect population increase often include the intrinsic rate of population increase (r m) of the insect and the most important factors modifying this parameter. The intrinsic rate of population increase is a concept firstly developed by [START_REF] Lotka | f Physical Biolou[END_REF]. By definition it is the maximum rate of population increase attained under optimal environmental conditions representing the genetic and physiological characteristics of a species, which subjects to modifications of environmental conditions [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF][START_REF] Dean | Effect of temperature on the cereal aphids Metopolophium dirhodum (Wlk.), Rhopalosiphum padi (14 and Macrosiphum avenae (F.) (Hemiptera: Aphiddae)[END_REF][START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF]. The intrinsic rate of population increase has a number of component variables: the developmental rate of immature stages, the fecundity and age-specific reproductive profile and the survival rate of the immature and adult stages [START_REF] Birch | The intrinsic rate of natural increase of an insect population[END_REF][START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF][START_REF] Dixon | Parthenoginetic reproduction and the intrinsic rate of increase of aphids[END_REF]). These component variables can be measured by building life tables of the aphid under specific conditions. The modification of the intrinsic rate of population increase may result from: food quality, temperature, competition, and polymorphism, etc. (Frazer 1987). In this study, we will flot take into account the food quality of green peach aphid, which may result greatly from the seasonal variation in the physiological status of the host plants, as during most of the season from March, when the aphid eggs begin to hatch in the peach orchards, to May, when the aphids begin te move out of the peach orchards, the green peach aphid colonizes mainly the growing new shoots [START_REF] Davis | Life history of the green peach aphid on peach and its relation to the aphid problem on potatoes in Washington[END_REF], Leclant 1972, 1976[START_REF] Tamaki | Spring populations of the green peach aphid on peach trees and the role of natural enemies in their control[END_REF]. We may assume that the variation in the food quality for green peach aphids during the rising phase of the aphid population is bounded within a certain favorable range. The effects of morph determinations will flot be included in this study either, as our purpose is to investigate the aphid population of the parthenogenetic generations in peach orchards in Spring. The effects of intra-specific competition can be included by incorporating the value of carrying capacity in the model. For our purpose of this study evaluating the effectiveness of natural enemies, the temperature-dependent intrinsic rate of population increase is of major interest, because temperature has a regular annual seasonal trends and considerable random variation in the fields, and has been identified as an major factor causing the most detectable and predictable changes in the insect population increase rate [START_REF] Messenger | The influence of rhytlunetically fluctuating temperatures on the development and reproduction of the spotted alfalfa aphid, nerioaphis maculata[END_REF][START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF][START_REF] Goldman | A kinetic approach to the effect of temperature on algal growth[END_REF][START_REF] Eyring | Thermodynamics and chemical ldnetics[END_REF], Logan et al. 1976[START_REF] Sharpe | Reaction kinetics of poikilotherm development[END_REF][START_REF] Tamaki | Effective growth Units in population dynamics of the green peach aphid (Homoptera: Aphididae)[END_REF], and seaching efficiency [START_REF] Goldman | A kinetic approach to the effect of temperature on algal growth[END_REF][START_REF] Tamaki | Predator complex of the green peach aphid on sugarbeets: expansion of the predator power and efficacy model[END_REF][START_REF] Mack | Development of temperaturemediated functional response equation[END_REF]) and persistence of predators [START_REF] Mack | CMACSIM, a temperature-dependent predator-prey model simulating the impact of Cokomegilla maculata (DeGeer) on green peach aphids on potato plants[END_REF].

There have been researches published on the intrinsic rate of population increase of parthenogenetic generations of green 'peach aphid on secondary hosts such as potato [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF], tobacco (Harrison 969) and cabbage [START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF]), but we have found no published work on the intrinsic rate of population increase on peach trees.

The objective of this work is to measure the intrinsic rate of population increase of green peach aphid as modified by temperature under laboratory conditions, which can serve as a parameter for models to be used in evaluating the effects of extrinsic modifiers of the population dynamics of green peach aphid such as predators and variety resistance of host plants.

Material and Methods

Plants

Tm -T D (T ) =

[e PT -e Pr' AT [START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF][START_REF]Population growth rate of M. persicae as a function of temperature: ' dX/dt=r(Temp)*(Tave(t-z))*X-SX*X*Xm(t-z) (2) ' (Temp)=ADCX*((l+KaX.X*EXP(-RoX*[END_REF][START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF] where D(T) the temperature-dependent rate in question; T in the temperature ( °C); was define by Logan as the rate of the process concerned at some base temperature; p is a value for critical enzyme-catalyzed biochemical reactions; Tm the maximum temperature in degree above the bass temperature for the life process; AT the width of high temperature boundary layer.

T," -T

D(T) = a {[l + ke -e -e AT ) (2-5)
where a is a value representing the declining speed of the rate of the process in question at Tm ; K= (a -d( 7), p, Tm and AT have the same meaning as in the exponential outer expansion. A quasi-Newton's method was used to obtain estimations of the parameters in the above models. (days): characteristic return time (Tc, =1/ rm). Ail thesc parameters were measured from aphids maintained on peach seedlings cultivated in nutritive solution under laboratory conditions. Photoperiod is maintained at 14:10.

Results

Immature developmental rate

The data on the relationship between the rate of the immature development and temperature were well fitted to Logan et al's "exponential outer expansion" equation (Fig. 2-1). The estimated maximum temperature for the development of green peach aphids is 29.4770°C, and the estimates for the high temperature boundary layer AT is 5.3700°C (Table 2-2). The predicted value of temperature at which the maximum value for immature developmental rate is attained was calculated to be 24.0981 °C by seeking the maximum value of Eqn. 2-4. : the rate of the process concemed at some base temperature; p: a value for critical enzyme-catalyzed biochemical reactions; Tm : the maximum temperature in degree for the life process; AT: the width of high temperature boundary layer. A quasi-Newton's method vvas used to obtain estimations of the parameters in the above models.

Temperature (°C)

Fecundie of the apterous parthnogenetic females.

The fecundity of the aphids were described in terms of total fecundity and the age-specific fecundity profile. The total fecundity of the adults attains its maximum at 20°C. Below 20 °C, it showed a weak tendency to increase with temperature; above 20°C, the total fecundity declines rapidly as temperature increases, and the decline accelerates as the temperature augments (the slop of the curve becomes steeper toward the right) (Fig. 2-2, Table 2-1). The age-specific fecundity . profile (Fig. 23) showed that the reproduction of green peach aphids is more concentrated in early adult life under higher temperatures than under lôwer temperatures.

Below the optimal temperature (24 °C), as temperature increases, the peaks of age-specific fecundity becomes higher, but the duration of the reproduction becomes shorter. Beyond 24°C, as temperature increases, the peak of age-specific fecundity becomes lower and the duration of reproduction shorter. Age-specific survival rate. The life span of green peach aphids was observed to become shorter as temperature augments (Fig. 234). It is also shown in Fig. 2

Intrinsic rate of population increase.

The relationship between the intrinsic rate of population increase (r.) of green peach aphids and temperature turned to be similar to that between the developmental rate and temperature. The highest T m was observed at 24 °C (r.=0.3744). Below 24°C, the value of rn, increases with temperature, but beyond 24 °C, the Tm value decreases very rapidly as temperature augments (Fig. 2345). The maximum temperature threshold for non-negative population increase was estimated, by calculating T (C°) when I-. (as defined in Eqn. 2-5) is set to zero, to be 27.921°C, which is lower than the maximum temperature for immature development. Consequently, the width of high temperature boundary layer for r m is narrower than that for nymph development ( Temperature ("C) The curve is plotted using predicted values from equation [START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF][START_REF]Population growth rate of M. persicae as a function of temperature: ' dX/dt=r(Temp)*(Tave(t-z))*X-SX*X*Xm(t-z) (2) ' (Temp)=ADCX*((l+KaX.X*EXP(-RoX*[END_REF]; dots are values estimated using equation 2-1. A quasi-Newtons method was used to obtain estimations of the parameters in the above models.

Discussion

The local race of green peach aphids we studied at Montfavet exhibited an adaptation te low temperature on the primary host. Its highest developmental rate occurred at 24 °C.

it failed to complete development at 30 °C. This pattern is fundamentally consistent with that observed by [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF] on potato leaves and that by . [START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF] on cabbage plants where the aphid had the quickest development at 25°C (both studies were conducted under 5, 10, 15, 20, 25, and 30°C). However, in our experiment the developmental time from the first instar to adult under 10-30 °C is significantly longer than that in Barlow's while being shorter than that in Deloach's. Also, while our results is consistent with Barlow's concerning the fact that green peach aphid failed to complete its immature development at 30 °C, DeLoach's study (1974) showed that the aphid succeeded in developing into adult at the same temperature on cabbage plants. In this study, the fecundity of apterous viviparous adult females attained its upper bound (about 80 youngs/female, see [START_REF] Van Emden | The ecology of Myzus persicae[END_REF]) under temperatures below 20°C, and declined under temperatures above 20 °C. The peak net reproductive rate (Ro) occurred at 20 °C, which is consistent with DeLoach's observation but differs from Barlow's where it occurred at 15 °C. Although the maximum fecundity was observed to occur at 20 °C, a higher daily reproductive rate was attained at 24 °C because the reproduction of the female was much more concentrated . While the adult reproductive profile from our study is similar to those from Barlow's and DeLoach's, we recorded a much higher total fecundity than did Barlow and DeLoach. The age-specific survival profile of green peach aphid in relation to temperature observed in this study follows a pattern which is similar to that was demonstrated in Rhopalosiphum padi (Linnaeus) [START_REF] Leather | Aspects of the ecology of the bird cherry-oat aphid Rhopalosiphum padi (Linnaeus)[END_REF] as well as to those observed in green peach aphid by Barlow and DeLoach on potato and cabbage respectively. In ail these studies the aphid manifested a greater longevity and a higher immature survival rate under lower temperatures than under higher temperatures.

Nevertheless, the longevity we recorded is somewhat longer than that observed by Barlow but shorter than that by DeLoach; this difference in longevity between the three studies is in accordance with that in developmental time: the aphids in Barlow's system develop faster than that in ours and in DeLoach's, so it has a shorter longevity, and vice versa for the long longevity in Deloach's experiment. Similar to the developmental rate, the intrinsic rate of population increase (r",) of green peach aphids attained its peak value of 0.3744 at 24°C on peach plants. However, the limitation of temperature on population growth is more severe than that on individual development: the upper limit of temperature for a positive population growth is estimated at 27.555 °C in comparison to that for development, which is estimated at 29.477 °C. This difference was also exhibited by a bigger value of AT (width of the high temperature boundary layer) for the population growth rate (Tm) than that for the developmental rate (D) (Table 2,3). In the studies of [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF] and [START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF], the maximum value of r m of green peach aphid was attained at 25°C, approximately the same level as that in this study (considering their studies were earried out using temperatures 5, 10, 15, 20, 25 and 30 °C); both studies showed a negative value of rm at 30°C; however, the Tm value estimated in this experiment is smaller than that in Barlow's but greater than that in DeLoach's. From above it appears that the general patterns of the demographic characteristics and the intrinsic rate of population increase of green peach aphid in relation to temperature is similar in different studies carried out on different host plants, but the amplitude of specific values varies from one experimental system to another. The variation in the amplitude of specific values among the studies carried out by Barlow, DeLoach and the author seems to be rooted in the systematic innate variations in the properties of the systems studied instead of in random experimental errors. The difference may mainly result from the species and physiological status of host plants and geographical races of the aphid.

The utility of r,,, as a parameter to be used in insect population models has been questioned [START_REF] Cole | The population consequences of life history phenomena[END_REF] on the basis that it is flot a valid measure of population growth unless populations have attained a stable age structure, which is considered unlikely in nature by some author because of constantly fluctuating environmental conditions [START_REF] Birch | The intrinsic rate of natural increase of an insect population[END_REF][START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF], Dixon 1989). However, [START_REF] Hughes | A method for estimating the effects of mortality on aphid populations[END_REF] found that half of 109 distributions sampled from field aphid population had achieved a stable age structure. In fact, the high reproductive rate of green peach aphid and some density-dependent mechanism in natural populations is quite likely to make the age structure bounded within certain range.

The influences of temperature on biological processes have been an massively studied area. Nevertheless, several basic problems wait for fiwther exploration. A most obvious one is that higher rates of development occur with fluctuating temperatures than with constant temperatures [START_REF] Cloudsley-Thompson | The significance of fluctuating temperature on the physiology and ecology of insects[END_REF]. Messenger (1964b) and [START_REF] Siddiqui | Effects of some constant and alternating temperatures on population growth of the pea aphids, Acyrthosiphon pisum (Homoptera: Aphididae)[END_REF] have investigated this phenomenon in aphids and both obtained slightly faster development with fluctuating temperature. Questions remain concerning whether and how the shape of wave and amplitude of fluctuations of temperature may affect the developmental rate. Aphids usually have rapid development and assume parthenogenetic viviparous reproduction at least during part of their life history, the influences of temperature at certain time (or certain time interval) of life may be memorized or have delayed effects on the following life stages or even the following generation; or in other words, aphids that are currently living under the same temperature but had different history of temperature experience may manifest different development, survival and reproductive rates. This may be inherently related to the answer of the previous question.

Chapter 3.

Temperature-dependent functional response of Harmonia axyridis Pallas (Coleoptera: Coccinellidae) to Myzus persicae (Sulz.) (Homoptera: Aphididae)

Introduction

One of the most important variables determining the effectiveness of a predator is the predation rate, which usually varies with prey density and temperature (Frazer and Gilbert 1976, Gutierrez et al. 1981[START_REF] Mack | CMACSIM, a temperature-dependent predator-prey model simulating the impact of Cokomegilla maculata (DeGeer) on green peach aphids on potato plants[END_REF]. Information about the predation rate of the predator in relation to prey density and environmental temperature is essential to allow a valid evaluation of the potential effectiveness of Harmonia axyridis Pallas as a biological control agent against Myzus persicae (Sulz.) and the development of strategies for field releases.

The functional response describes the relationship between the number of prey attacked per predator per unit time and the number of prey present [START_REF] Solomon | The natural control of animal populations[END_REF][START_REF] Holling | Some characteristics of simple types of predation and parasitism[END_REF], Hassel] 1978). Three types of functional responses have been recognized, of which the type 11 response is primarily suitable for describing the predation of many invertebrate predators [START_REF] Holling | Some characteristics of simple types of predation and parasitism[END_REF], Hassell 1978;Hassell and Waage 1984). This type of response is characterized by the number of prey captured increasing rapidly with prey density and leveling off at high density of prey. One of the mathematical descriptions of the type II response is given by Holling's disk equation:

N = a.N (3-1) ° 1+a.Th.N
where Nis the number of prey offered to the predator, Na is the number of prey consumed per predator per unit time, a is the instantaneous attack rate of the predator, and Th is handling time, time that a predator spent in subduing, ingesting and digesting one prey item and the subsequent resting. Alternate models have been proposed by different authors based on different assumptions (see discussion by [START_REF] Royama | A comparative study of models of predation and parasitism[END_REF][START_REF] Williams | On understanding preçlator-prey interactions[END_REF], Williams and Julian° 1996). The most influential of these models are probably those of [START_REF] Royama | A comparative study of models of predation and parasitism[END_REF] and [START_REF] Rogers | Random search and insect population models[END_REF] who treated the functional response as the time integral rate of predation, taking into account declining prey density over time, in contrast to the instantaneous rate represented by Holling's disc equation. These models may be microscopically more realistic than Holling's equation. However, as [START_REF] Williams | On understanding preçlator-prey interactions[END_REF] pointed out, most of the models, including Holling's disc equation, are mathematically isomorphic forms of the Michaelis-Menten-Monod equation, which describes the rate of enzyme-catalyzed reactions in a saturation kinetic form. They make little, if any, qualitative difference in macroscopic dynamic structures of the predator-prey system.

Moreover, the implicit form of the mathematical expression of the Royama-Rogers model make it difficult to be incorporated into an explicitly defined mathematical model of predator-prey dynamics and add to the cost of computation. Therefore, Holling's disc equation remains the most commonly used model.

As poikilothermic animais, insects have their metabolic rate and other biological rates varying with surrounding temperature. Temperature has additional differential effects on an insect species and its predators. As was demonstrated in the previous chapter, M. persicae adapts well to low temperature in terms of its population growth rate (Chapter 2). Determining the effects of temperature on the predation rate and developmental and survival rates (sec Chapter 4) of H. axyridis is thus critical in detennining within what temperature range the predator is likely to be a effective biological control agent and in developing field release strategies concerning the timing and numbers of the releases.

Several approaches have been used to describe the temperature-dependent functional response [START_REF] Messenger | Bioclimatic studies of the aphid parasite Praon exsoletum[END_REF][START_REF] Everson | The relative activity and functional response of Phytoseilus persimilis (Acarina: Phytoseiidae) and Tetranychus urticae (Acarina: Tetranycidae): the effect of temperature[END_REF][START_REF] Goldman | A kinetic approach to the effect of temperature on algal growth[END_REF], Frazer and Gilbert 1976, Tamalci and Long 1978, Guitirrez et al. 1981[START_REF] Flinn | Temperature-dependent functional response of the parasitoid Cephalonomia waterstoni (Gahan) (Hymenoptera: Bethylidae) attacking rusty grain beetle larvae (Coleoptera: Cucujidae)[END_REF]. A general temperature-mediated functional response model was developed by [START_REF] Mack | Development of temperaturemediated functional response equation[END_REF] by incorporating into Holling's type II response model (Eqn. 3-1) the enzyme lcinetics equations that had been used to describe the temperature dependence of growth or development [START_REF] Eyring | Thermodynamics and chemical ldnetics[END_REF]. This model describes the instantaneous attack rate a and the handling time Th as functions of temperature:

V. v 3. T • e T Th(T) = 1 + v I .e T (3-2b) (3-2a) a(T) 1+ u3 .e
where u i, u2, u3, u4 and v1 , v2, v3, v4 are curve fitting parameters.

The present chapter deals with the measurement of the predation rate of the larvae of H. axyridis in relation to the density of M. persicae and temperature, and we try to model the temperature-dependent functions using equation 3-1 and 3-2 a, b.

Materials and methods

The larvae of H. axyridis used in these experiments were obtained from the laboratory mass rearing using eggs of Ephestia kuehniella Zeller maintained in INRA-Laboratory of Population Biology in Antibes. The green peach aphid used as the prey came from laboratory colonies maintained on the peach seedlings of the variety 305 which were grown in nutritive solution (see Chapter 1). Cylindrical plastic jars (80x50 mm) were used for setting up the arenas. Three young peach leaves measuring about 12 cm long, with the tip of the stalks wrapped with a piece of filter paper saturated with nutritive solution (sec Chapter 1), were placed in each of the jars. Apterous nymphs ofM persicae in their 3 1-d or instars were distributed evenly on these peach leaves. Six aphid densities, depending on the stage of the predator larvae and experimental temperature, were used (Table 3-1), with each of the treatments replicated six times.

To keep the age of predators of a given stage roughly identical, we chose larvae of the instar prior to the instar to be observed, which appeared ready te molt, and placed them in the cylindrical jars. Freshly molted individuals, 4-8 heurs after the molting, were then used in observations. A single individual of H. cccyridis was placed in each of the arenas. Each set of arenas were placed in one of the incubators of different constant temperatures. The consumption of green peach aphids in each of the arenas was checked and the initial number of aphids was restored for each day until ail the larvae of the predator developed to the next stage. The larvae that had been used for the observation of a previous stage were flot used again in the observation of any of the following stages. The same procedure was repeated for ail the four larval instars of H. cayridis.

Experiments were conducted under 12. 5, 15, 18, 20, 25, 27.5, 30+0.5°C of constant temperatures respectively to measure the effepts of temperature on the fimctional response of each of the active stages of H. Axyridis to M. persicae. The humidity inside the incubators was maintained at approximately 70+5% RH and the photoperiod was set to 14:10 (L: D) for ail the observations. Light was provided by two 8 watt fluorescent tubes.

The air circulation of the incubators was made by an installed ventilator.

The average per-capita daily consumption of green peach aphids by each coccinellid larval stage was calculated from the total consumption of the predator during the specific larval stage divided by the length of that larval stage. If at certain low initial aphid density ail the aphids offered were consumed for most the experimental replicates, the data points were left out so as to avoid biased estimates of parameters. [START_REF] Holling | Some characteristics of simple types of predation and parasitism[END_REF] type II fimctional response model (Eqn. 3-1) was fitted to the data of the average daily consumption of M persicae by each larval stage of H. axyridis under each of the temperatures using Woolf linear transformation (Currie 1982):

N = Th.N + cri (3-3)
which was suggested to be a method that provides better parameter estimation than other linear transformations and nonlinear regression [START_REF] Fan | Parameter estimation of functional respOnse[END_REF].

The estimated parameters a and Th for different temperatures were then fitted to equations 3-2 a, b using the nonlinear regression procedure in SYSTAD (SYSTAD Inc. 1990-1993) to describe the effects of temperature on the predation rate.

Results

The data on the functional response for ail the larval instars of H. crtyridis under different temperatures were satisfactorily fitted to Holling's type II functional response model (Eqn. 3-1), which is characterized by the predation level increasing at a decreasing rate as prey density augments and approaches indefinitely a maximum predation level as prey density goes ta infinity (Fig. 3-1). 600 - Age-dependence of the functional response of H. axyridis to M. persicae. The predation rate of larval H. aryridis increases with their developmental stages, which is numerically manifested by the difference in the parameter values for different larval stages:

• : • • • : • e • : • • • • -"- r-.
the older instar larvae have a larger value of instantaneous attack rate a and a smaller value of handling time Th than the younger ones (Table 3-2). The instantaneous attack rate a determines the rate at which the number of prey attacked (Na) increases with the number of prey offered (N); and the handling time Th determines the voracity -the asymptote of Na as N increases ta infinity. From Table 3-2, we can see that the differences in the values of a between different instars are much smaller than the differences in the values of 771, which implies that the voracity has a bigger share than the instantaneous attack rate in the differences in the predation rates between different instars of the predator. a: the instantaneous attack rate; Th: the handling time. These two parameters are estimated by fitting experimental data to Eqn. 3-1, R 2 is the determination coefficient for the linear fit. LI, L2, L3, 1...4 denote the lai-val stage 1-4 respectively.

Temperature-dependence of the functional response of H. axyridis to M Persicae.

The maximum predation rate of larvae of H. alyridis occurred at about 25-27.5°C

depending on the developmental stages of the larvae. The estimated instantaneous attack rate a had the lowest values at 12.5 °C and increased with temperature until attaining its maximum value at the optimum temperature and then declined as temperature increased;

the optimum temperature at which the maximum instantaneous attack rate occurred was observed to be 27.5°C for the 1 e, 2ed and 3`d instars and 25 °C for the 4th instar (Table 3-2. Fig. 3-2). The estimates of handling time Th had its peak value at 12.5 °C and declined as temperature increased, attaining its lowest value at 25°C for ail the 4 instars (Table 3-2, Fig. 3-3). equation 3-2a, b (Table 3-3, Fig 3-2, 3-3). The predicted maximum values for the instantaneous attack rate a occur at a somewhat lower temperature than that measured directly from the experiment (Fig 3-2).

The parameters a(T) and 77i( 7) as temperature forcing functions could be plugged into equation 3-1, from which the temperature-dependent functional response of ail larval instars of H. axyridis to M. persicae were plotted in 3-D surfaces to illustrate the dependence of the predation rate on both temperature and prey density (Fig. 34)

Discussion

The experiment has shown that the functional responses of ail the four instars of H. axyridis to M. persicae conform Holling's type II response. The 3r d and 4th instar larvae of H. axyridis are significantly more effecient in prey searching and more voracious in prey consumption than the 1' and 2nd instars. The difference between the instantaneous attack rate a of different larval instars of the coccinellid is significantly smaller than that between the handling time Th (Table 3-2). According to Hollong (1959), Th signifies the time spent in subduing, ingesting and digesting a prey item and 77f4 is in fact the saturation value of prey consumption (Na); a signifies the searching ability and is the rate at which the saturation consumption is reached as the prey density increases. Therefore, the greater predation rate of the older instar larvae is more a result of being more v. oracious (having a shorter handling time or a bigger maximum prey consumption) than that of being more effecient in prey searching. Prey consumption of H. axyridis is highly dependent on temperature (Fig. 4-4).

The searching rate and the rate at which the prey are ingested and digested increase with temperature, but high temperature has inverse effects on predation rate. Moreover, the increase in developmental rate (see Chapter 4) as a result of increase in temperature naturally results in a higher daily requirement for food. However, we suspect that the total prey consumption might vary only slightly with varying temperature and prey density, because a bigger prey consumption due to the increase of temperature and prey density usually results in a shorter developmental time, thus a shorter period of consumption. It seems that there is such a tendency that the instantaneous attack rate a of the younger instar larvae is more sensitive to the variation in temperature than that of the older instars, but the handling time Th of the younger instars is less sensitive to the increase in temperature (Table 1).

In this experiment, the green peach aphids are quite evenly distributed in the arenas by the experimental manipulation. It would flot be the case for the field populations, which are usually characterized by clustered distribution (Leclant 1976, Tarnild 1973). We suspect that clustered prey distribution may promote the efficiency in the predator's intensive searching phase but reduce the efficiency in the extensive searching phase.

However, the overall searching efficiency is usually higher in the case of prey with clustered distribution (Hassell 1979). Even though, the data from trials using evenly distributed prey still do flot lose to be a bottom une for estimating the predator's prey consuming rate.

Introduction

The effectiveness of Harmonia axyridis Pallas as a biological control agent for inundative release against Myzus persicae (Sulz.) depends flot only on its predation rate in response to the density of prey, i.e., functional response, but also on the rate of change in its own density in response to the prey density, i.e., the numerical response. Though clearly defined in theoretical frameworks, the numerical response has been more or less neglected in the empirical studies of real-world predator-prey interactions because of the technical difficulties involved in the measurements of the response [START_REF] Readshaw | The numerical response of predator to prey density[END_REF], Hassell 1978[START_REF] Frazer | Coccinellidae[END_REF]). Two elements of numerical responses -aggregative and reproductive numerical responses have been recognized in the interactions of aphids and their natural enemies by [START_REF] Frazer | Coccinellidae[END_REF]. The aggregative numerical response is the spatial accumulation of predators in response to the prey density, which refers to the movement of predators into a field or patch with higher prey density or out of one with lower prey density [START_REF] Frazer | Coccinellidae[END_REF]. The reproductive numerical response is the relationship between the number of offspring reproduced by the predator and the prey density [START_REF] Frazer | Coccinellidae[END_REF]).

Biological theories and empirical studies (Guterriez 1981[START_REF] Mills | Some aspects of the rate of incraese of a coccinellid[END_REF], Hardman and Roger 1991, ) tell us that prey density also affects the developmental and survival rates of a predator, which have their shares in the population changes of the predator. This suggests that the developmental and survival numerical response, changes in developmental and survival rates of the predator in response to prey density, are also very important in evaluating the effectiveness of the predator. In the biological control using a predator as an intervention agent for inundative release, we usually do flot attempt to introduce the predator as a long-term regulatory factor of the target pest population as in the classical biological control, but rather want the predator to suppress the prey population instantly during certain critical periods. In the case with H. azyridis, we currently have no attempt to have the released predatory force to last for more than a single generation in peach orchards. Hence, in the evaluation of the effectiveness of H. cayridis as a biocontrol agent for inundative release against M. persicae, the aggregative and reproductive numerical response is of minor importance because the number of the coccinellid larvae is determined by the initial number at release, the survival rate and duration of active stages, instead of being a result of spatial accumulation from other localities or the reproduction of the parent generation. Therefore, the developmental and survival numerical responses of the predator are more important components to study, in the case of using the predator for innundative releases, because they determine how the released predatory force changes in relation to prey density and environmental factors.

As with functional response, numerical response of a predator is affected by temperature, in addition to prey density. While the effect of temperature on numerical response is one of the major factors determining the effectiveness of a predator in suppressing the prey population (Frazer 1976[START_REF] Barlow | Simulation .of Lime Aphid Population Dynamics[END_REF], Guiterrez et al. 1981), empirical studies in this aspect have been rare. Some remarkable studies as to this point have been done on the temperature-dependent numerical responses of Typhlodromus pyri to the European red mite (Hayes and McArdle 1987, Hayes 1988, Hardman and Rogers 1991). As for the interactions between aphids and their coccinellid predators, [START_REF] Mills | Some aspects of the rate of incraese of a coccinellid[END_REF] studied the effects of temperature on the growth, development and fecundity of Adalia. bipunctata when feeding on pea aphids provided at different densities, and found that temperature has some non-linear effects on the adult fecundity and development of the predator. [START_REF] Hardman | Effects of temperature and prey density on survival, development, and feeding rates of immature Typhlodromus pyri (Acari: Phytoseiidae)[END_REF] studied the effects of temperature and prey density on survival and development of immature Typhlodromus pyri and found that both the survival and developmental rate of this phytoseiid increase with temperature as well as prey density following nonlinear responses.

We conducted this study because information about the effects of temperature and density of M persicae on the developmental and survival rates of H. axyridis is required in depicting the change in the predation force following a release, which is directly related ta the effectiveness of the predator, and in determining the appropriate predator stages, numbers and timing of releases with respect to temperature and prey density for controlling the aphid population. The information is also helpful in providing a better understanding of the consequenses of releases of this ladybug in orchards. Our objective of this study was to develop models describing the temperature-dependent developmental and survival numerical responses of H. axyridis to M. persicae based on laboratory experiments.

Materials and Methods

The coccinellid larvae used in this study came from the laboratory population reared on the eggs of Ephestia kuehniella Zeller maintained in INRA-Laboratory of Population Biology at Antibes. The green peach aphids used as the prey were from laboratory colonies maintained on peach seedlings (see chapter 1) in the laboratory of INRA-Research Station of Zoology at Avignon. Three young peach leaves measuring 12 cm in length or so, with the end of stalks wrapped with a piece of filter paper saturated with nutritive solution ta keep the leaves from desiccation, were placed in each of the 80x50 mm cylindrical plastic jars. Apterous aphid nymph of instar 3-4 were placed evenly on these peach leaves. Six aphid densities, namely 10, 20, 40, 80, 160, 200 aphids/jar were offered each to one individual of the predator respectively. The feeding regime had six replicates.

The larvae of the instar prior to the one to be observed, those which appeared close to malt, were kept in round jars. Freshly molted individuals were then separated and moved to the arenas. A single larva was placed in each of the arenas. Each set of arenas (6 treatments x 6 replicates) were placed in one of the incubators in which a constant temperature was maintained. The number of larvae survived and molted to the next stage were recorded for each day. The initial number of aphids was restored after the observation. The larvae that had been used for the observation of a previous stage were flot used again in the observation of any of the following stages. The same procedure was repeated for ail the four larval instars of H. axyridis.

The experiments described above were conducted under 12. 5, 15, 18, 20, 25, 27.5, 30+0.5°C of constant temperatures respectively to measure the impacts of temperature on the numerical responses of each of the larval stages of A. axyridis. The humidity inside the incubators was maintained at 70 + 5% RH and the photoperiod was set to 14:10 (L:D) for ail the observations. The average rate of development used in this paper was calculatted as

1 n D = = d d i
where D is the average rate of development, n is the sample size, d is the average duration of development of individual i of the .ith instar, ces are observed developmental duration (in days) of individual i.

We used the geometrical average of the survival rate over the number of days required to complete the development of the stadium as the measure of the daily survival rate:

ir

S = ( 11 S,)d 1=1 E d because ay = i=i 1 and `T S = X , we have D /= 1 X . I X. =( 3 )D A. 1 (4-2)
where S is the average daily survival rate; S t is the survival rate of the jth instar on day t; is the number of survival larvae at the beginning of the!' instar; d, di and D have the Ail the parameter estimation involved in the modeling process was conducted using the Quasi-Newton nonlinear regression procedure provided by SYSTAD (SYSTAD Inc. 1990-1993)

Results

Developmental rate of H. axyridis as a function of the number of prey offered. As might be expected, the rate of development of H. axyridis increased with bath temperature and the number of M. persicae offered (Table 4-1, Fig. 4-1). Here, we used the analytical strategy that firstly defined the average developmental rate as a function of the number of prey offered, and then incorporate the effect of temperature into the parameters of the density dependent models.

At ail the temperatures used for the experiment, the relationship between the rate of development and the number of prey offered followed a saturation curve (Fig. 4-1): a rapid increase with the number of prey offered at beginning and leveling off as the number of prey offered getting larger. This developmental response to the number of prey present is more sensitive at higher temperatures than is at lower ones (Fig. 4-1), i.e. at higher temperatures the development is more food effective. This relationship was modeled using the following formula (see appendix 1 for derivation):

D(N)= (4-3)
where D(N) is the rate of development as a function of prey density N, Dm the maximum rate of development, fl is a parameter with it reciprocal signifying the rate at which the developmental rate approaching the maximum value Dm as more prey are present, i.e. the sensitivity of developmental rate ta prey density, a smaller fl value implies a greater sensitivity. The parameters Dm and 13 for each of the larval stadiums were estimated for different temperatures and for different larval stages (Table 4-2). Developmental rate of H. axyridis as a function of temperature. When the number of prey offered was fixed, the developmental rate of H. axyridis varied with temperatures (Table 4-1) which can be characterized by the variation of parameters in the preydenpendent developmental rate model as functions of temperatures. From Table 4-2 it can be seen that as temperatures increase the value of maximum developmental rate Dm increases, and the value of parameter fi decreases. The relationship between the maximum developmental rate Dm and temperature T is basically of the same form as that of the typical developmental response of poilcilothermal animais to temperature (Fig. 4-2). Here it was described using Logan et al 's model (1976): Dm(T). v, HA (e P H4 _ e Ar," ) where DA is the rate of physiological process at some base temperature; pH A is a value for critical enzyme-catalyzed biochemical reactions; Tm HA is the maximum temperature in degree above the base temperature for the life process; z1TH A is the width of high temperature boundary layer. Table 4-3 listed the parameters estimated for ail the larval stadiums. The maximum temperatures for development (Tin fiA) were approximately 29-30 °C; the optimal temperatures for development were about 25-27 °C; and the width of high temperature boundary layers (4T11A) were around 3-4°C depending on larval stages. The 3rd instar had the highest maximum developmental rate and the 4 th instar had the lowest.

The value of parameter reciprocal to the sensitivity of developmental rate to the number of prey offered, decreased with temperature T (Fig. 4-3), i.e. the higher the temperature, the more sensitive the developmental rate of H. axyridis to the food availability, or, each food item is likely to trigger a greater developmental effects under higher temperatures. This relationship was described using an empirical exponential mode!. fl(T) = Bd 1 .e -.Ed [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF](5) where Bd, and Bd2 are constants. The estimated values for Bdi and Bd2 is listed in Table 4-3. The average developmental rate can thus be described as a fiinction of both temperature and number of prey offered by substituting for Dm and fi in equation (4-1)

with Dm(7) and /3(T), i.e.:

D(T ,N)= Dm(T).[1

-e -1)( D ie (4-6)
The general feature of this model is geometrically sketched as Fig. 4-4. Dm: the maximum developmental rate; b: the rate by which the average developmental rate approaches Dm as the number of prey present increases; the parameters are presented as mean with standard error; R2: determination coefficient of the nonlinear correlation. Newton's method vas used in estimating the parameters. LI , L2, L3, La: the larval instar 1-4. : the rate of physiological process at some base temperature; pHA : a value for critical enzymecatalyzed biochemical reactions; Tm im : the maximum temperature in degree above the bass temperature for the life process; ATH4 : the width of high temperature boundary layer; le: the detertnination coefficient for the nonlincar correlation. Newton's method was used in estimating paramcters. L I , L2, L3 and L4 dcnote the larval stadium 1-4 respectively. Fig. 4-4 Developmental rate of H. axyridis in relation to temperature and the density of M persicae. Graphes were generated from Eqn. 4-6, and parameters in table 3.

Average daily survival rate of H. axyridis as a function of the initial number of prey.

Here the average daily stage-specific survival rate (equation 4-2), instead of the integral stage-specific survival rate, was used. It is conceptually more legitimate and practically more convenient for this study because in the natural condition the major factors affecting the predator's survival rate, i.e., the prey density and temperature, are changing constantly, and in the simulation model the time-unit for defining the change of temperature, density of prey and predator is one day. Also, the daily age-specific survival rate enables a more direct comparison of the temperature-and prey-dependence of survival between different larval stages, for the effect of duration of development on the survival rate is removed. As with the average developmental rate, the average daily survival rate of H. axyridis increased with both temperature and the number of M. persicae offered (Table 4-4). We used the same analytical approach as was used for modeling the developmental rate: the average survival rate was defined as a function of the number of prey offered in the first place, and then incorporate the effect of temperature into the parameters of the density-dependent survival mode!.

The average daily survival rates S of ail the larval stages increased with the number of prey available (Fig. 45). The survival rates increased as prey densities increased and approached asymptotically the maximum survival rate as the prey density became higher and higher (Fig. 45). In general, at the same prey density, older instar larvae had lower daily survival rates than younger ones (Fig. 45), which may reflects the trophic requirement increases with age of the larvae. The response of daily survival rate to the number of prey offered was fitted to a sigmoid curve used by Chen (1990) (equation 4-5, see appendix for derivation).

S(N) --,-

1 (4-7)

1+ Sci.e -sc = ..iv

where S(N) is the average daily survival rate of the predator in relation to the number of prey offered 1V, SC 1 is a parameter whose reciprocal is related to the average daily survival rate 'when no prey available, and Sc2 is a parameter signifying the rate at which S(N)

approaches its maximum value (=1 in this case). This model gave a fairly good depict of the prey-dependence of the average daily survival rate of H. axyridis (Fig. 4-4, Table 45) Survival rate of IL axyridis as a function of temperature. At any fixed density of aphids exposed to the ladybeetle larvae, the daily survival rate of the larvae is dependent on the environmental temperature. The parameters Sc ' and Sc2 could, in turn, be defined as functions of temperature (Fig. [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF][5][START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF][5][6]. The following empirical models were used :

Sci ( n=

Sc12 .e -sc " .T) (4-8)

Sc2 (T)= Sc21-( 1-Sc22.e -&-.T ) (4-9)
where Scii, Sc12, Sco, Sc21, Sc22, and Sc23 are parameters from the curve fitting and do flot have explicit biological meaning. The values of these constants were estimated and given in Table 4-6. N: the number of prey offered; Sc ' : a parameter whose reciprocal is related to the average daily survival rate when no prey available; Sc2: a parameter signifying the rate at which S(N) approaches its maximum value (=1 in this case); R 2 : the determination coefficient for the nonlinear correlation. Newton's method was used in estimating parameters. L I , L2, L3 and L4 denote the larval stadium 1-4 respectively.

The survival rate of larvae of H. cayridis as a function of both temperature and prey density was then described by incorporating Sc i (T) and Sc2(7) into the equation 4-5 :

1 (4-10)

S(T,N)= 1 + Sc i (T).e -Sc ' (7).N

The feature of this model within the biologically defined interval was illustrated geometrically as in Fig. 4567. estimating the developmental and survival rate of the predator in the field conditions.

In this study, we used the average daily survival rate, calculated by taking the geometric average of the stage-specific survival rate of a larval stadium. This measure of survival rate allows us to incorporate the survival rate directly into the simulation model, which is usually run with one day as the time step, and thus the survival rate of any specific day can be calculated from the temperature and prey density of the day. We should be aware that the averaged daily survival rate is only an simplified approximation, because the daily survival rate may depend on the developmental progression within the given instar, rather than a uniform value throughout the whole length of the instar. We adopted the present approach because no data concerning the age-specific survival rate is unavailable and experiments measuring that requires a large quantity of individuals. As with the developmental rate (S), we relate the survival rate directly to the number of prey (N) present. Let zIS be the increment of S as N increases by 4/V, we derive the S as a function of N from the relationship between AS and AN. Firstly, we assume that: (1) The daily survival rate approaches its maximum value (Sm=i) as the number of prey present increases infinitely; [START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF] the magnitude of tIS with respect to z1N is proportional to the product of S with 1-S (the deference between the maximum survival rate and the actual survival rate). Thus, we have:

= Sc, . S. (1 -S). AN (A-2-1) dN (A-2-3) dS = Sc2 S.(1-S) AS or = Sc i .S.(1-S) AN - (A-2-2)
where Sc2 is a proportional coefficient The interactions between H. axyridis (Pallas) and M persicae (Sulz.) are dynamic, so it is impossible to evalu" ate the effectiveness of the predator by evaluating the static characteristics of the predator and the aphid. The predator and green peach aphid interacting with each other comprise a dynamic system which possesses the attribute of behavior, i.e. the evolution of population densities of the predator and the prey as a result of complex inter-specific interactions. In the biological control of green peach aphid we wish to manage certain portion of the behavior by releasing the predator with appropriate timing and numbers so as to minimize the losses to the damage of the aphid at a profitable price. The understanding of the dynamic behavior of the predator-prey interactions is thus the basis for the evaluation of the effectiveness of the predator and the development of optimal release strategies. Models are required toward this end. The form of the model should be determined by the purpose for which it is needed. This chapter is to discuss the general approach and technical details of the simulation model developed for assessing the potentials of H. axyridis (Pallas) as a biological control agent against Myzus persicae (Sulz.), and to present some results from the sample simulations.

Modeling is an open-ended task, one can never obtain a perfect model. However, one advantage of the modeling approach to problem solving is that sometimes even if the stated objective is flot immediately achieved, weakness in our understanding of the system will be exposed, thus suggesting new research projects. In this sense, this study represent an initial step toward an strategy supporting system of the biological control of green peach aphids.

The general framework of the simulation model

The appropriate model for this study is one which incorporates an adequate amount of biological realism concerning temperature-and density-dependence of the interaction between Myzus persicae and Harrnonia axyridis, while keeping a considerable degree of tractability. There is little point in having a model that is too complex to manipulate and to understand. Deterministic model was chosen since stochastic model usually require additional information about the variation and probability distribution of each parameter, and add additional complexity in the model structure and computation.

This model includes three major component submodels: 1) the population increase of M persicae; 2) the functional response of H. axyridis to M persicae; and 3) the numerical response of H. axyridis to M persicae.

Aphid population dynamics can be modeled using two different approaches. One approach assumes that an aphid population has a stable age structure and complete overlapping generations [START_REF] Hughes | A model of an aphid population ---A general statement[END_REF]) and can thus be modeled as a homogenous entity. The population change is characterized by the rate of population change. The other approach takes into account the population age structure and the population is modeled as an assembly of different age-classes and the population change is characterized by age-specific demographic parameters [START_REF] Barlow | Simulation .of Lime Aphid Population Dynamics[END_REF]. The choice of approach depends on the system, data available and the purpose of the mode!. In this study, our purpose of modeling the population dynamics of green peach aphid is to use the model as a component model to be coupled with the fiinctional response and numerical response mode! of H. axyridis to study the effects of temperature on the predator-prey interactions. For this purpose, we accepted the holistic approach since it is much easier to handle and its behavior is more tractable. Also, a more complex and detailed age-structured green peach aphid population model will flot be of great help to the overall performance of the simulation mode!, since there has been no information available concerning the predator's attack rate on different age-classes of the aphids and the predator's preference for prey age-classes, which is necessary when an age-structured prey model is used. Because we modeled the green peach aphid population as an homogeneous entity in which each average "individual" ma.kes an equal contribution to the population, we as well approximate the aphid consumption by the lady beetle larvae as the loss of average "individuals" due to the predation.

A simple Holling's type II functional response was used to model the attack rate of H. axyridis on M persicae as a fimction of temperature. Complex interactions such as predator interference, predator's choice for prey size and the response in the predator's searching efficiency to the aggregation of the aphids are ignored. In practice, we do flot want to release and usually can flot afford releasing a predator cohort that is so big as to cause significant predator interference.

For the purpose of evaluating the effectiveness of H. axyridis as a biocontrol agent for inundative release, no population recruitment of H. axyridis was incorporated in the model. The change of the released cohorts of H. axyridis was modeled using an ageclassed model -the members of one age-class are shifted bodily to the next after a certain amount of thermal time, corresponding to the duration of the age-class, is accumulated.

The duration of age-class of H. axyridà is dependent on the temperature and abundance of its prey, green peach aphids. A age-specific daily survival rate was applied to the cohort. The age-specific daily survival rate is again a function of temperature and aphid population density.

The green peach aphid model

The population course of green peach aphids is simulated with the following approach: We modeled the green peach aphid population using a delayed logistic model under the assumption that the current value of the intrinsic rate of population increase is determined by the average value of temperature over a period from the oerrent time bacicward to a previous time t-r. Here r is the elapse of time between the current time and the previous time.

dN _ re (T r ). N 7T r.N (5-1)
where N is the population density of the aphid, r",(i'r) is the intrinsic rate of population increase driven by T , the average temperature over a period from the current time t backward to a delayed time t-r. In chapter 2, we have characterized the intrinsic rate of population increase of green peach aphid as a function of temperature using Logan's sigmoid outer expansion (Eqn. [START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF][START_REF]Population growth rate of M. persicae as a function of temperature: ' dX/dt=r(Temp)*(Tave(t-z))*X-SX*X*Xm(t-z) (2) ' (Temp)=ADCX*((l+KaX.X*EXP(-RoX*[END_REF][START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF][5]. That model and parameter will be used here for describing = a{r] ke -P t-] -1 -e

(5-2)

The parameters here have the same meaning as those in Eqn. 2-5. The independent variable 7, is an average of temperature over the time interval [t-r, t]. The more realistic and more general form of should be some kind of weighed average with a characteristic weight function. Because of the Jack of information concerning this aspect, here we just use the simplest average, the simple arithmetic average, which.is defined by

T = fs.T(s)ds

(5-3)

t-s N in Eqn. 5-1 is the average population over a period from the current time t backward to the delayed time r. Again, it can be a weighed average. Here we use the simple arithmetic average as an approximation:

NT = fs.N(s)ds

(5-4) r-r ( -T ) b in Eqn. 5-1 is the intra-specific competition coefficient and r T represents the carrying capacity which is driven by , the average temperature over a period from the current time t backward to a delayed lime 1-r.

In practice, it is impossisible to obtain continuous-time measurement of temperature and population density. Consequently, we sample the state of these continuous-time variables at certain time interval to obtain a discrete-time approximation, such as the average daily temperature, instead of the continuous-time measurement of temperature, and a discrete-time measurement of population, such as daily population count, so that -T or -Kr, is approximated with the mean of the respective discrete measurements over

I f T (s) T 1 r =-EN (s) s=i-r
In

ai (T). N = 1+ a,(T).Thi (T).N

(5-9) (5-10) (5)(6)(7)(8)(9)(10)(11) where the subscript i represents the ith instar larvae of H. axyridis, ail the other parameters and variables have the same meaning as the in Eqn. 3-1, 3-2a, b.

The total prey consumption of the ail the four larval stages of the ladybug is then:

N a Developmental rate. The developmental progress of ladybug larvae were modeled as a function of the current daily temperature and prey density using Eqn. 4-3, 4-4, 4-5: Di (T,N)= Dm, (7)11-Ciun-e ]

(5-12)

Dm,(T)= YI HA (e P' T (5)(6)(7)(8)(9)(10)(11)(12)(13) ,6,(T). (5)(6)(7)(8)(9)(10)(11)(12)(13)(14) here i signifies the ith instar of larvae. Ail the other parameters and variables have the same meaning as those in Eqn. 4-3, 4-4, 4-5. The time when larvae enter the next instar was calculated by

= E D (T (s), N (s))

( [5][6][7][8][9][10][11][12][13][14][15] where DiOis the developmental rate of the t e' instar larvae as a function of temperature T(s) and prey density N(s) on day s. In the computer program, the time when the . ith instar larvae enter the next instar is calculated by computing the ± i (T (s), N (s)) forward starting from ta, the time when the larvae entered the i d' instar from the previous instar, until r is satisfied and then ail the individuals that entered the ith D,(T(s),N (s)) k 1 r.

instar get to the i+ /th instar.

Survival rate. The average daily stage-specific survival rate (Eqn. 4-7, 4-8, 4-9, 4-10) is used for the survival rate of the i th instar ladybug larvae as a function of the current daily temperature and prey density:

(5-16) sci2 (r).N

1 + ( 7). e-Sc i , (T) = .

(1 -Sci . 2 .e -s`" T ) (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) Sc, (T)=Sc, 1 .(1-Sc22 .e T ) (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where ail the parameters and variables have the same meaning as those in Eqn. 4-7, 4-8, 4-9, 4-10. The change in the density of the t h instar ladybug larvae was then modeled as (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) where Pi is the density of the ith instar ladybug larvae, Ui(t) is the number of the t e' instar larvae released at time t, Li_1 and Li are logic variables, they assume only two values (0 or 1), when larvae remain in the ith stage, Li assumes the value 1, when the larvae finished the development of the ith stage and enter the next stage, Li assumes the value 0.

dl (T , N). P,_ 1 -[1 -L i .S,(T,N)].P, +U(r)

if ED,(T(s),N(s)

)< 1 Li = o if ED1 (T(s),N(s))1
( [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] where Di() is the developmental rate of the ith instar larvae as a function of temperature T(s) and prey density N(s) on day s.

The framework for the overall simulation model is then expressed as:

(5-21a)

dl'

(5-21 b)

The computer simulation program.

The state variables, driving variable, initial conditions, input and output.

Temperature is the only driving variable in the model, the temperature data used in the simulation are generated using CLIMGEN, a climate data generating software developed by USDA-ARS, and parameters derived from the Avignon local meteorological record.

The only initial condition in this model is the number of overwintering eggs, which can be given by a random number generator or an predetermined estimate. When the aphid population exceeds the level of tolerance, the stage and number of lady beetle larvae are prompted for input. The program outputs the population trajectories of green peach aphids and the ladybeetles.

Time and space scale of the simulation. A Julian day is used as the time scale in this simulation model, considering that it is a most natural and convenient time scale and, also, ail the parameters used in the model were measured in this time scale in the experiments.

In cases that thermal time is used to account for the time required to complete certain biological processes, such as the completion of development of given stages, day-degree is used in actual calculations, but it is then converted to Julian days. As a model aiming at addressing fundamental qualitative properties of temperature-and density-dependence of predator-prey interactions, we try to avoid involving spatial complexity such as habitat heterogeneity and predator displacement among aphid colonies, etc., in the simulation. A single aphid colony is used as the spatial scale. We assume that the intra-specific competition coefficient b, the impact of an individual on other individuals in the same colony, is a constant independent of temperature. The carrying capacity, represented by rin.(T)/b, is then varying with temperature. In natural conditions, aphids may move into or out of a colony by walking (the apterous forms) or flying (allate forms). This process of within-habitat movement may be density-dependent or/and temperature-dependent, but no sufficient data available as to give a valid pattern that characterizes this process. In this study, we use a random variable of uniform distribution to generate the number of aphids moving into or out of a colony, which is independent of aphid density and temperature.

The bias in the results using this method may be viewed as enormous in microscopie scale, but could be considered as being tolerable in macroscopic scale, since the effects of intercolony movement on population dynamics is much more important under low population density then under high population density of aphids. As the season approaching the end, green peach aphids produce allate forms that emigrate out of the peach orchard to secondary hosts. The proportion of aphids moving out of the orchard is shown to increase as the end of the season is approached (Tamacici 1973[START_REF] Leclant | Etude biologique des aphides de la région Mediterranéenne: Implication agronomoques[END_REF]. Here the number of aphids moving out of the peach orchard is modeled as the product of aphid population density, a uniformly distributed random variable and the proportion of the accumulated day-degree over the total day-degree required to complete the phase of life history of aphids in the peach orchard with an power of x (x is a value to be chosen to obtain expected results):

(T ( 1 ) Tb) N en? m (I) = N (1).RND .( ° DDtotal (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) where Nc,.(t) is the number of aphids moving out of the orchard, N(t) is the current aphid population density, RND is a random variable of uniform distribution, T(t) is the temperature of time 1, Tb is the base temperature for the development of aphids, DDtoui is the total day-degree required to complete the phase of life history of the aphid in the peach orchard, x is a value to be chosen.

The main program. The Main program consists 5 major sections. The first section defines subroutines, fiinctions, arrays and parameter values. The second section reads the temperature data from a data file generated with CLIMGEN and calculates the date when the aphids appears in the orchards. The aphids are supposed to appear in the peach orchards at the point of time when certain effective thermal accumulated above the threshold (4.5 °C, Tamacki et al. 1982). Section three initializes the system by assigning initial values to state variables ---populations of green peach aphids and ladybeetle larvae.

The initial population of green peach aphids is given by the truncation of number multiplied by a random variable of uniform distribution. A zero is given to the initial population of ladybeetle larvae since the aphid population is supposed to be below the threshold of tolerance. Sections 4-6 include various procedures doing the numerical computations of the simulation, which begins on the date when green peach aphids appear in the orchards and terminates when a thermal time total of 1912 day-degree is accumulated above 4.5 °C. Section four calls the subroutine RmLag for calculating the intrinsic rate of population increase of green peach aphids as a function of temperature with integral time delay and the delayed density-dependence due to intra-specific competition (see "section 2. Green peach aphid model" of this chapter). Section five checks whether the aphid population exceeded the threshold of tolerance, if so, a certain number of lady beetle larvae of a chosen larval stage is released. The subroutine ComputY is called to calculate the developmental rate, daily survival rate and prey consumption of the lady beetle larvae as a function of current daily temperature and aphid population. Subroutine RungeKutta. This subroutine is a simple ordinary differential equation solver using the fourth order Runge-Kutta algorithm. The state system to solved is defined as in aphids and Harmonia axyrids (Fig. 5-1 L l , L2, L3). For the 3 1" g instar, the minimum number of larvae required at 18 oc is somewhat less than those at 21 °C and 24 °C (Fig. 5-1 L3).

For the 4g' instar, the minimum number of larvae required to bring the aphid population eventually down to zero does flot quite follow the pattern of a monotonous decrease along with the increase in temperature (Fig. 5-1 L4). Within the temperature range between 15

and 24 °C the minimum number of the 4`h instar larvae required actually increases with temperature, a scheme reverse to that for the l and 2" instars (Fig. 5-1 L4, 5-2). The simulation also showed that with the same final consequence of the aphid population eliminated by releasing a minimum number of ladybeetle larvae required to eventually eliminate the aphids, the length of the course of aphid population collapse can be quite different depending on temperatures. The aphid population collapses in a much greater speed under higher temperatures than does under lower temperature (Fig. . Also, younger instar larvae display a greater extent of change in the length of time it takes to eliminate the aphids as temperature increases than do older instars, for example, at 12°C it takes more than 50 days longer for the 1 st instar larvae released in the minimum required number te elirninate the aphids than it does at 24 or 27 °C, while this change for the 4th instar is only less than 10 days (Fig. . Sec that more days are required to completely eliminate the aphids under low temperature than under high temperature, and that the difference in the days required to completely eliminate the aphids is much smaller for the older instar larvae than for the younger instar larvae. The data are generated with the computer simulation program. Li, L2, L3, L4 represent the larvae or 1" 2 nd, 3rd and 42' instars.

Difference in the effectiveness between different larval stages of Harmonia axyridis.

The simulation procedure used here is the same as was described in the above paragraph.

The

Population /colony

aphid population level at which the ladybeetles are released. We illustrate some observed patterns concerning this issue with the results from the simulation using a single constant temperature of 15 °C. For the first three larval instars of H. cocyrids, at the left part of the x-axis representing the aphid population level, the minimum number of individuals required to ensure a complete elimination of the aphids on a single colony increases sharply as the aphid population level at which the ladybeetle larvae are released increases.

Then this value slowly decreases as the aphid population level increases (Fig. 567). For the fourth instar, the minimum number of individuals required to ensure a complete elimination of the aphids increases continually as the aphid population level increases (Fig. 567). to . This pattern conforms somewhat the common sense. However, no field data is available at the moment to perform valid comparison. If the aphid population level at which the predator is released is set at 250 per colony, the three times releases of 3rd instar larvae with each at 1.5, 1, 1 larvae /colony, the total number of predator to release is much biger than that released at lower prey population levels results in a less satisfactory control over the aphid population (Fig. 56789). If the predator is released at 500 aphids per colony, the three releases of the 3r d instar larvae with each at 2.5, 2, 2 larvae /colony, an almost unrealistic number, gives an almost unacceptable result (Fig. 56789). These simulations also shows that a biger number of predator need to be released at a early time of the season when the temperature is low, than at a late time of the season. Now we can ask the question that whether a better result, in the sense of reducing the releases and the total number of predator released, can be obtained by releasing for the first release a greater number of predator. Two aspects, i.e. the minimum number of predator required to ensure an eventual depletion of aphids and the length of the elapse of time from the day when the predator are released to that when the aphids are completely depleted from the colony, are used to measure the relative effectiveness of larvae of H. axyridis in suppressing population ofM persicae, since for innundative release, we do flot expect the predator to act as a longterm regulator of the prey population, but, in most cases, as depletor of the prey. For ail the four larval instars of H. axyridis, the minimum number of predator required to ensure an eventual depletion of aphids approaches to zero as temperature approaches the highest extreme for the population growth of the aphids, and it increases to the highest quantity at the other extreme of the range of effective temperature. Within the range of suitable temperature for both species (for example, 15-24°C), the minimum number of the 1g, and 2nd instar larvae of H. axyridis required to eventually eliminate the aphids decrease monotonously as temperature increases. Within the same range of temperature, this pattern flattened out for the 3n 1 instar. For the zeh instar, within the temperature range of 15-24 °C the effectiveness decreases as temperature increases, just the reverse order of that for the l e and 2"" instars. Within this scenario, the relative order of the effectiveness of different stages of H. axyridis switches from L I <L2<L3<1.4 under 12°C to 1,4<L3<1,2<Li under 27°C, with a series of transition at temperatures in between. The elapse of time from the time when the predator is released to the time when the aphids are depleted from the colony also depends on temperature and the age of the predator. For all the four larval stages of the ladybeetle, the length of this elapse of time decreases as temperature increases, and the decrease in the length of this lime elapse as temperature increases is sharper for the younger instar larvae than for the older instar larvae. The length of this time elapse is longer for younger instar larvae than for older instar larvae, and the difference is much greater at lower temperatures than at higher temperatures. Based on above, it is suggested that at lower temperatures, older instar larvae (L 3 and L4) are more effective because the number of larvae required to release is smaller and they can eliminate the aphids in a much shorter time, and thus are more preferable when the release of predator is required at low temperature. At higher temperature, younger instar larvae (L 1 and L2) are usually at least flot less effective than the older instar larvae since the number of the younger instar larvae that are required to be released is similar (compared with L3)

Days Days

or smaller (compared with L 4) number and they spend only a little longer time to wipe out the aphids, and thus are more preferable when the release of predator is required at high temperatures. These suggestion may reinforced by practical considerations. At low temperatures, it takes a much longer time for the young instar larvae to wipe out the aphids, which allows a greater chance for the aphids, being frequently disrupted by the predator, to move around and transmit virus diseases. Also, a longer course gives greater probability of predator loss due to dropping on the ground, being died of wind or rai, or being preyed on by general predators, so the risk of failure is greater and in practice a larger number of larvae than that is expected may need to be released. Under high temperature, the older instar larvae can usually quickly end up their development of active stage(s) before wiping out the aphids.

The minimum quantity of ladybeetle larvae required to be released also depends on the population level at which the larvae are released. In most cases, the minimum number of individuals required to ensure a complete elimination of the aphids on a single colony increases sharply as the aphid population level at which the ladybeetle larvae are released increases before it reaches a peak value. Then this value slowly decreases as the aphid population level increases (Fig. 567). The left part of the curves Fig. 5-7 describing a sharp increase in the minimum number of larvae that need to be released is most relevant to our practical problem since we expect to suppress the aphid population before it gets very high, and thus, it will be more effective and more economy to release the ladybeetle larvae at a low aphid population level. However, thi condition may be limited by two factors: 1)

The temperature dependence of the effectiveness may conflict with this condition ---fo release the predator at low aphid density usually implies to conduct the first release at low temperature which usually requires a large number of predator.

2) The behavioral constraints may put limit on the condition. As with many other predators, the ladybeetle may need a minimum rewardable density of prey to initialize and then concentrate its predation on this prey, it is especially true for the ladybeetle larvae like H. axyridis from mass production which has grown on food different from the prey.

The left part of the curve in Fig. 5-7 describing a sharp increase in the minimum number of predator required for L I -L3 is fairly easy to understand. However, the right part of the curve in Fig. 5-7 describing a slight decrease in the minimum number of predator required for L I -L3 may be in contradiction with our intuition. The mechanism underlying this is that when aphid population size is beyond K/2, the half of the maximum population size, the rate of population change dN/dt of the aphids actually decreases as Nincreases, .

The simulation also shows that the number of releases of larvae of H. axyridis required to ensure the aphid population under check throughout the season may be reduced by increasing the number of individuals released each time, but the total number of larvae that need to be released throughout the season is flot reduced by doing this way. In any case, the number of releases of larvae of H. axyridis required to ensure the aphid population under check throughout the season is flot likely to be reduced to less than two releases.

The feasibility of biological control of green peach aphids using H. axyridis depends highly on the level of tolerance to aphid infestation. If the tolerance level is low, once the infestation get intolerablely high, interventions with immediate aphid elimination are usually required. When H. axyridis is to be used as a biocontrol agent against the green peach aphids in this case, a large number of 3rd or zeh instar larvae will be required for the release, which may be economically unfeasible. In addition to this, behavioral limits, such as the fact that a considerably high aphid population density may be required for initializing and maintaining a concentrated searching for the aphids by the ladybeetle, or risks of failure due to the randomness and stochasticity of the events that happens after the release may deny the possibility of using H. myridis as a control agent for innundative release if the level of tolerance to aphid infestation is low. In case that the level of tolerance to green peach aphids is high, the utilization of H. cayridis as a biocontrol agent for innundative release seems a feasible alternative to the current control methods.

The most important factor among those which are flot incorporated into the model is probably the searching behavior of the ladybeetle larvae. A significant loss of the larvae released was usually the explanation for the failure of almost ail of the open-air field release trials that have been conducted. The most satisfactory result of release came probably from the experiment carried out under semi-controlled condition for which full sized peach trees were each caged with fine screen, and the ladybeetle larvae released were confined in the cages (see Chapter 6). The behavioral and demographic fate of the ladybeetle larvae are still greatly unknown at the moment. In this case, we expect our results from the simulation model represent an upper bounds of the effectiveness of H.

ax-yridis as a biocontrol agent against M. persicae.

Introduction

Experimental exclusion techniques have been widely used to assess the effectiveness, especially the short-term performance, of a natural enemy in suppressing a target pest population (Valley andGradwell 1971, Luck et al. 1988). In the early stage of developing a biological control program, these techniques are particularly useful, for they usually yield a larger amount of useful information because the fate of both the predator and the prey can be traced in details; they may bring to end researches on a species that is unlikely to be a effective natural enemy before much effort and expense are devoted; they may narrow the range of options for large-scale open-air field release trials; and most importantly, some specifically designed experiment can answer specific questions. In our study of evaluating Harmonia axyridis as a biocontrol agent against Myzu.s persicae, this kind of experiment was found to be required in several places. Our simulation model predicted that under a suitable temperature and at a relatively low aphid population level, the larvae of H. axyridis could be more or less quite effective in eliminating the green peach aphids, even though the overall evaluation of the predator is flot quite encouraging. For example, suppose that intervention is carried out whenever the aphid population reaches an average of 25 aphids/shoot, complete depletion of aphids can be obtained by releasing as few as 0.25 ladybeetle larvae of the third instar per shoot, corresponding to 75 individuals/tree for a peach tree with 300 shoots (Chapter 5, Fig. 56789). However, none of the large-scale open-air field releases carried out by us at several locations demonstrated the predicted consequence, in spite of the fact that sometimes as many as 300 larvae of the r i instar were released to each tree. Actually little obvious effects on the aphid population were witnessed in open orchard releases, and little was known concerning what happened to the predator released, since it was extremely difficult to follow the fate of the released cohort of the predator in the open field conditions. In this case, it is suggested that either the model prediction is totally nonsensical, which implies that some serious mistakes were made during the model construction or numerical computation, or some factors that resulted in an significant loss of the released ladybeetle larvae, other than the normal temperature-and prey density-dependent mortality, existed in open fields. Some suspected causes are: 1) a large number of the ladybeetle larvae were preyed upon by some generalist predators such as birds, ants, etc.; 2) the larvae dropped down the trees passively because they cannot hold on the foliage of the peach tree very well; 3) the larvae fell down the tree in search of more suitable habitats or food because the larvae reared on eggs of Ephestia kuehniella Zeller cannot adjust well to the new habitat and food. The objectives of this experiment are two folds: a) to compare qualitatively the observed pattern of population change of M. persicae resulting from releasing larvae of H. axyridis with the pattern from simulations; b) to acquire some hints about the cause of the loss of released larvae of the predator.

Materials and Methods

Eight peach trees of similar size were selected and pruned to leave approximately the same number of shoots (approximately 250 new shoots/tree). Each of these trees were encaged in a 2.5x2.5x2.5 m fine screen (1 mm) cage. The cages were well closed to prevent insects outside the cages from getting in and the insects inside the cages from getting out. Each tree was infested with green peach aphids from laboratory colonies on the 17th of May. Fifty new shoots from each tree were marked as samples for observation.

On the next day, four of the encaged trees were randomly chosen, and onto each of them were released 50 third instar larvae of H. axyridis, corresponding to an average of 0.2 larvae per shoots. The larvae of H. cayridis came from the mass-rearing with eggs of Ephesiia maintained by INRA-Laboratory of Population Biology at Antibes. The 50 larvae were put in a petri dish which were placed at the major branching site of the tree.

Monitoring the populations of green peach aphids and the released cohort of H. aryridis on the marked shoots vas carried out every or every other day. For the ladybeetle larvae, the number of individuals found on the marked shoots was counted. For the aphids, the degree of aphid infestation of each shoot was used as an index of aphid population level. Leclant's classification (Leclant 1967) of tree-level aphid infestation degrees was adapted to colony-level infestation degrees here: degree 0: no aphids at ail, N = 0; degree 1: slightly infested, number of aphids 0 <N < 5'; degree 2: obviously infested, 5' <N<5 2; degree 3: top 2-3 leaves become curled, 5 2 <N<53 ; degree 4: 3-5 leaves curled, aphids crowd the top of the shoot 5 3 <N<54 ; degree 5: aphids crowd ail over the top of the shoot and more than 5 leaves, 5 4 <N.

An index of relative infestation was calculated for each tree using the following formulas: The data on aphid infestation degree can also be used to estimate the average population density of the aphids on a colony:

v 5 <cl 1.-s 0 J. d E ) 0 f d (6-2)
where K is the estimated average of population density of green peach aphids per colony; ,2,3,4,5] is the degree of infestation; Id : is the frequency of shoots with a (6-1) degree of infestation d. Here, for each degree of infestation, we used the upper limits of the range of population density, since we found that in actual observation, the upper limits usually gave much more weight in determining the degree of infestation, for example, 150 aphids/colony is a density falls in the range represented by degree 4 (5 3<150<54), but this density may often be judged as degree 3 since it is doser te 5 3 . Moreover, according to our classification of the degree of infestation, for the degree 5, the corresponding range of population density has only a lower limit (N>5 4). We just simply used d=5 in the estimation of population, a survey we carried out indicated that this value (5 5) does set an upper limit for the aphid population on a single colony. The estimated aphid populations for both control and treatment were then compared with simulation conducted using temperature data recorded in one of the cages using a self-recording thermometer which was placed in a wooden box. Average daily temperature was calculated from temperatures recorded at 0, 6, 12, 18, and 24 o'clock (see table I for data on average daily temperature).

d: d € [0,1

Results

The Index of aphid infestation of ail the four peach trees onto which the 3r d instar larvae of H. cocyridis were released was observed to have a continuous decline following the release of the predator on May 18 and eventually fell down to zero in about 8-10 days aller the release of the predator (Fig. 6-1), while that of the four trees without the ladybeetle larvae kept increasing (except for one tree on which the IF had a slight decline) (Fig. 6-2). The comparison of the average value of IF for the treatment with that for the control demonstrated more clearly the effect of the released predator on the population change of green peach aphids (Fig. 6-3). On the day prior to the release of predator, both the two group of trees had basically the same average degree of infestation of green peach aphids. And the rate of increase in the average degree of infestation from the first day to the second day had almost the same slop for the two group of trees (Fig. 6-3). Even the frequency distribution of the infestation degree was basically the saine for both the treatment and control prior to (May 17) and on the day (May 18) of the release (Fig. 6-4).

After the release, for the treatment, the frequency of high degree of infestation declined continuously until ail shoots fell into zero degree of infestation, while for the control, the frequency of high degree of infestation kept increasing (Fig. 6-4). The overall average infestation, as was measured by the index of relative infestation, diverged between the treatment and control after the predator was released (Fig. 6-3). The impacts of the predator on the population of the aphids was well manifested by this method.

The fact that the green peach aphids on the trees with ladybeetle larvae were eliminated while those on the trees without the ladybeetle larvae kept increasing suggests that an effective number of active ladybeetle larvae must have well persisted to the moment of the aphid depletion, otherwise there might have been chance for the recovery of the aphid population. The data form observation showed that the larvae of H. oecyridis had persisted even after the aphids were depleted. Although the relative density of the ladybeetle larvae declined with aphid population (Fig. 6-5), some 4 th instar larvae still survived and remained active when green peach aphids had been effectively wiped out from the trees (Fig. 6-6). The average per-colony population density of green peach aphids were estimated from the degree of infestation for both control and treatment and plotted against time (Fig. 6-7 a). The observed population changes for both control and treatment were then compared with results from computer simulation using temperature data recorded in one of the cages. The pattern of population change due to the release of the ladybeetle larvae is qualitatively identical for the simulated populations and real populations (Fig. 67). The observed population of green peach aphids for the control did flot reach as high as the corresponding simulated population (Fig. 6-8 a). The observed declining of aphid population alter the release of 3"1 instar larvae was much slower than that in the simulation (Fig. 6-8 b), which may partly be owing to the fact that the predator survival rate in the real system is lower than that in the simulation system through most of the course (Fig 6- aphid population in the real system is more obvious at the beginning (Fig. 6-8 b) when the survival rate of the predator was even higher than that in the simulation (Fig. 6789).

Infes

Conclusion and Discussion

The results from the exclusion experiment showed that a complete depletion of green peach aphids was obtained by releasing 50 third instar larvae and H. axyridis at the aphid population level of average 20 aphids/shoot, which is qualitatively coincident with the simulation results. However, the simulation results deviated numerically from the observations to a considerable extent, which shows again that the prediction of the model has only qualitative significance and is meaningful only under certain restricted conditions.

The model population of green peach aphids at the absence of H. oecyridis increased to a much higher level than did the real population. The difference may result from factors limiting the population growth of green peach aphids existing in the real system, such as generalist predators, physiological state of the peach trees, etc. The elimination of aphids is much slower in the real situation than that predicted by the simulation, which may partially be owing to the lower survival rate of the ladybeetle larvae in the real system than in the simulation, but it is suspected that the major reason may lies in the fact that the ladybeetle larvae must disperse onto the shoots and adapt to the new prey, M Persicae, and may spend a large amount of time traveling around along branches of the tree. That behavioral element was flot incorporated into the mode!. Spatial patchiness and heterogeneity can also result in great deviation of the behavior of the real system from that of the simulation. Even for the best case as was displayed in the results of this chapter, the prediction, even in the qualitative sense, can only be acceptable for short-term time scale, since the deviation may be magnified by orders as time proceeds.

In fact, it will certainly be naive to try to verify a model built mostly upon general biological principles and laboratory experiments by seeking numerical conformities between the model outputs and the trajectories of the field population, since the model system involves much less complexity than the real system. Because of this, here we do flot even bother trying to make such numerical comparisons or to daim any credibility for the predictive capacity of this model in predicting field populations. However, a model is useful only if it can reveal at least some properties of the real system or represent, in certain aspects, the characteristics of behaviors of the system. From the results presented above, we can see that the qualitative compatibility of the model output with the behavior of the real system is satisfactory. What was expressed above should flot be mistak-en as a statement that the validation of a mode! by comparing the numerical trajectories of the model system with those of the real system is unnecessary or impossible. What is meant here is that delicately designed experiments or observations should be carried out under strictly controlled conditions to test well-defined specific predictions or hypotheses.

Another matter that malces the experiment significant is that the results showed that the ladybeetle larvae reared on eggs of Ephestia kuehniella Zeller can indeed get adjusted to their new habitat and food, even though one may argue that this adjustment is the results of being confined within the cage. One critical question is how greater is the probability for a larva dropped on the ground to relocate and get back onto the tree in a cage than that in an open orchard, and whether this probability is sufficiently greater to account fiilly for the difference between the consequence of releasing the ladybeetle larvae in the cage and that in the open orchard. We may suspect a greater probability for a larvae HO dropped on the ground to get back onto the tree, because the larvae were witnessed several times to remount the tree from the sides of the cages which are usually touched by branches of the trees. But the exclusion of general predators of the ladybeetle larvae such as birds by using the cages, may also contribute tci the fact that ladybeetle larvae released in the cages wiped green peach aphids while that released in open orchards did flot, although a usually much greater number of ladybeetles are released. More experiments need to be carried out concerning this point.

The experiment was carried out in late May, when the aphid population growth rate usually drops down because the peach foliage is becoming less favorable for aphid population growth than that at an earlier time, and a large number of aphids develop into allate forms to move out of the orchard. At this time of the year, naturally occurred enemies of green peach aphids also become more abundant. Under the same condition, the ladybeetle larvae can be very active and voracious. Ail those contribute to the elimination of the green peach aphids by the ladybeetle. This kind of consequence may have not been obtained if the release was carried out early in the season when the temperature is lower.

It will be of great significance to make such an experiment early in the season.

CONCLUDING REMARKS

This study is a part of the research effort on the potential use Of Harmonia axyridis

Pallas for biological control against Myzus persicae (Sulz.). Our emphasis is on the evaluation of the effectiveness of H. axyridis as a predator of M persicae. Modeling and simulation were used in the attempt to improve the understanding of the basic processes in the predator-prey interactions of this system, and to reveal general qualitative patterns concerning the temperature-and density dependence of the effectiveness of the predator.

From the laboratory and field experiments as well as the simulation and analysis of the model system, the following information were extracted:

1. The intrinsic rate of population increase of M persicae augments as temperature increases before a maximum value is attained at 24 °C. Then a phase of declining in this value follows. It was also shown that the maximum values for the intrinsic rate of population increase, the developmental rate, the net reproductive rate, and age-specific survival rate, are reached at somewhat different temperatures. The optimal temperature for a maximum survival and net reproduction (20°C) is lower than that for maximum development and population increase (24°C).

/. The number of green peach aphids consumed per individual of H. axyridis increases monotonously with prey density following Holling's type II functional response. With a fixed prey density, the prey consumption also increase with temperature until an optimal temperature, beyond which the prey consumption decreases, is reached. The optimal temperature for gaining the maximum prey consumption with a fixed prey density is about 25-27.5 °C. Larvae of an older instar are more voracious than those of a younger instar.

3. The developmental rate of larvae of H. axyridis augments with the number of prey (green peach aphids) present following a saturation curve -a maximum value is asymptotically approached as the prey density increases. With a fixed prey density, the developmental rate of H. axyridis responds to temperature following a typical pattern of developmental response of poilcilothermal animals to temperature. The average agespecific daily survival rate of H. axyridis increases with prey density following a sigmoid curve with the asymptote -maximum survival rate being 1. With a fixed prey density, this rate increases with temperature following approximately a saturation curve.

4. Simulation suggested that the effectiveness of young larvae (L 1-L3) of H. axyridis in eliminating green peach aphids augments as temperature increases, but this pattern does flot hold for the 4 th instar. From another angle, older instar larvae are always more effective than the younger ones under low temperatures, but this pattern switches to the reverse order at the other end of the effective temperature range,. with a series of transition in this patter as temperatures increases within the range of then two extremes.

5. The simulation also suggested that the number of larvae of H. axyridis required to eliminate the green peach aphids augments with the aphid population level at which the predator are released, which implies that better results can be obtained by releasing the ladybeetle larvae at a lower prey density. The overall evaluation of the potentials of using H. axyridis for the biological control of green peach aphids is flot conclusive before the economic cost of releasing such coccinellid and the tolerance level to green peach aphid infestation are defined. However, it appears that the inundative release of this coccinellid is unlikely to be used singly for controlling green peach aphids, at leasi not so for controlling the aphids in commercial gardens, based on the following facts: 1) H. axyridis is flot very effective under low temperatures, and thus the green peach aphids that appear early in the Spring cannot.be controlled very quickly by releasing an feasible number of the predator. 2) the tolerance level for green peach aphids is perceived to be low at present time, so a quick and ensured depletion of aphids is usually desired. At the present lime, this predator may be usede in backyard gardens or as an alternate method to be incorporated into an integrated pest management program, for example, using pesticide spray at the early season, and release the ladybeetle when the aphids resurge later under a higher temperature, so as to minirnize the use of spray which may conflict with the integrated control of the other orchard pests, and as a consequence, to reduce the development of pesticide resistance of green peach aphids.

As was emphasized in earlier chapters, the model prediction in Chapter 5 and

Chapter 6 has mainly qualitative implication, it should flot be surprised if a considerable quantitative deviation from the observation appeared. In fact, it is flot our main purpose to build a quantitative predictive model, because it requires more empirical data, which are flot available, and by gaining quantitative preciseness and predictability of specific processes, the model's ability in revealing general explanatory, qualitative patterns or properties may be sacrificed. However, this model can serve as a framework for more realistic models. The most required elements to enhance the realism of the model are probably the beliavior of H. axyridis in responding spatial patchiness and heterogeneity and the mortality of both the predator and aphids due to generalist predators and other non-random events.

valeur de ses populations naturelles ou par lâchers. Les recherches ont porté sur la biologie, l'écologie, la physiologie, la biologie des populations, les besoins nutritionnels et l'élevage de masse en laboratoire, ainsi que sur les techniques d'application. Aux U.S.A., cette espèce a été introduite pour le contrôle d'espèces variées, dont principalement les pucerons et les cochenilles. Des populations indigènes ont également été découvertes dans plusieurs localités de l'Amérique du Nord.

Un exemple réussi de l'utilisation de cette coccinelle comme espèce exotique pour la lutte biologique classique a été son introduction aux USA pour lutter contre le puceron du pacanier. Le succès de cette introduction fut tel que dans des régions comme le Kentucky ou la Géorgie, cette espèce de puceron n'est plus considérée comme un ennemi majeur. Notre étude se replace dans une approche de modélisation d'un objectif très spécifique -évaluer l'efficacité de H. axyridis comme prédateur de M. persicae -ne conservant que les éléments les plus importants.

H. axyridis a été introduit en

Trois composants majeurs seront incorporés dans le modèle : le taux d'accroissement des populations de M. persicae en fonction de la température, la réponse fonctionnelle de H. axyridis à M. persicae en fonction de la température, et les taux de survie et de développement de H. axyridis en fonction de la température. Ces éléments seront couplés à un modèle de simulation de dynamique.

INFLUENCE DE LA TEMPERATURE SUR LA DEMOGRAPHIE ET LE TAUX DE CROISSANCE INTRINSEQUE DE MY ZUS PERSICAE (SULZER)

INTRODUCTION

Dans le contexte du développement de stratégies rationnelles pour contrôler M. persicae en vergers de pêchers, et en particulier pour évaluer l'efficacité des ennemis naturels, une bonne connaissance de la dynamique de population des pucerons est indispensable. La réalisation de cet objectif requiert l'utilisation de modèles, dont le plus fréquemment utilisé dans la description de la croissance des populations de pucerons est le taux de croissance intrinsèque (r m). Il inclut des variables constitutives telles que le taux de développement des stades immatures, la fécondité en fonction de l'âge et le taux de survie des stades immatures et adultes [START_REF] Dixon | Parthenoginetic reproduction and the intrinsic rate of increase of aphids[END_REF]. Ces variables peuvent être mesurées en établissant les tables de vie des pucerons en conditions spécifiques. Le taux de croissance intrinsèque peut être modifié par la qualité de nutrition, la température, la compétition intraspécifique, la détermination des morphes, etc. (Frazer, 1987). Dans cette étude, nous ne prendrons pas en compte la qualité de nutrition, qui peut dépendre principalement de variations saisonnières chez la plante-hôte.

Depuis les premières éclosions en mars en vergers de pêchers, jusqu'en mai, où les pucerons commencent à quitter les pêchers, les pucerons colonisent principalement des pousses en croissance.

Cette phase de croissance des populations de M. persicae s'effectue donc probablement sur un milieu qui reste favorable. L'effet de la détermination des morphes ne sera pas pris en compte du fait de l'étude exclusive de générations parthénogénétiques de printemps sur pêchers. Les effets de la compétition intraspécifique peuvent être pris en compte en incorporant la valeur de la densité maximum dans le modèle. Pour notre étude, l'effet de la température sur le taux de croissance intrinsèque de la population est d'un intérêt primordial. Les températures ont en effet une tendance saisonnière régulière et de fortes variations aux champs. Elles ont été identifiées comme principal facteur de changement dans l'accroissement des populations de pucerons, ainsi que dans les réponses fonctionnelles et numériques des prédateurs.

Les taux de croissance intrinsèques des populations de M. persicae ont été calculés sur des hôtes secondaires de cette espèce tels que la pomme de terre [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF] et le chou [START_REF] Deloach | Rate of increase of populations of cabbage, green peach, and turnip aphids at constant temperatures[END_REF], mais n'ont fait l'objet d'aucune étude sur pêchers.

Notre objectif est de mesurer ce taux de croissance intrinsèque chez M. persicae et ses variations en fonction de la température, en conditions de laboratoire. Sa connaissance est requise pour établir des modèles d'évaluation des facteurs de modification extrinsèques de la dynamique de population de M.

persicae, tels que la prédation ou la résistance variétale de la plante-hôte. Le taux de survie par âge de M. persicae en fonction de la température est proche de celui de Rhopalosiphunz padi L. [START_REF] Leather | Aspects of the ecology of the bird cherry-oat aphid Rhopalosiphum padi (Linnaeus)[END_REF]. Les basses températures procurent à M. persicae une plus grande longévité et un plus fort taux de survie aux stades immatures et chez les adultes jeunes que les températures élevées.

Le taux de croissance intrinsèque est également optimal à 24°C mais l'effet limitant des températures sur la croissance des populations est moins fort qu'il ne l'est sur le développement individuel. Cette différence est également exprimée par une valeur plus forte de DT pour la croissance de la population que pour le taux de développement (Tableau 2-3). [START_REF] Barlow | The influence of temperature on the growth of experimental population of Myzms persicae (Sulzer) and Macrossiphum euphorbiae (Thomas) (Aphididae)[END_REF] H. axyridis à toutes les températures s'ajustent bien au modèle de réponse fonctionnelle défini précédemment, caractérisé par un niveau de prédation qui s'accroît avec la densité de proie puis se stabilise lorsque cette densité de proie tend vers l'infini (Fig 3-1).

L'efficacité prédatrice des larves de H. axyridis s'accroît avec l'âge, ce qui se traduit par une augmentation du taux d'attaque instantané et par une diminution du temps de prédation (Tableau 3-1).

Le maximum d'efficacité prédatrice des larves est atteint expérimentalement à 25 -27.5°C. La valeur du taux d'attaque instantané a est la plus basse à 12.5 et 30°C pour les larves des quatre stades, la plus haute à 27.5°C pour les trois premiers stades et à 25°C pour le quatrième (Tableau 3-1, Fig. 3-2). Pour les quatre stades, le temps de prédation Th est le plus long à 12.5 et 30°C, le plus court à 25°C (Tableau 3-1, Fig. 3).

Les valeurs calculées pour les paramètres a et Th indiquent pour le taux d'attaque instantané a une valeur maximale à une température inférieure à celle estimée directement par les données expérimentales. La représentation 3-D de la réponse fonctionnelle en fonction de la température pour chaque stade larvaire indique que la consommation de proie par H. axyridis est hautement corrélée à la densité de proie et à la température (Fig. 34).

DISCUSSION

Les larves des troisième et quatrième stades consomment significativement plus que les premiers et deuxièmes stades. Cette différence entre les stades résulte moins du taux d'attaque instantané que du temps de prédation, ce qui peut expliquer une plus grande différence de consommation entre les stades aux fortes densités de proies qu'aux faibles densités (Fig. 3-1).

La consommation de proies est fortement liée à la température (Fig. 4 Le taux de survie journalier a été estimé comme la moyenne géométrique calculée sur le nombre de jours nécessités pour compléter le développement du stade :

X • D S = .17 ) i (4-2)
où S est le taux moyen de survie journalier, Xi-1 et Xi le nombre de larves survivantes au début et à la fin du ième stade, D le taux de développement moyen.

Toutes les estimations paramétriques rencontrées dans la phase de modélisation sont réalisées par une procédure de régression non linéaire de quasi-Newton.

RESULTATS

Taux de développement de H. axyridis en fonction du nombre de proies offertes. Comme on pouvait s'y attendre, le taux de développement de H. axyridis augmente à la fois avec la température et avec le nombre de M. persicae offert (Tableau 1). Nous avons utilisé une stratégie analytique modélisant tout d'abord le taux moyen de développement comme une fonction du nombre de proies offertes. Les paramètres de ces modèles sont ensuite modélisés comme fonction de la température. A toutes les températures testées, la relation entre taux de développement et nombre de proies offertes journellement suit une courbe de saturation (Fig 1), modélisée selon :

ID( IV) = Drrt.[1 -e-AN]
(4-3) où D(N) est le taux de développement en fonction de la densité de proies N, Din le taux maximal de développement, p un paramètre dont l'inverse correspond à la vitesse à laquelle le taux de développement approche Dm quand le nombre de proies augmente (sensibilité du taux de développement au nombre de proies offertes). Une valeur de 13 plus faible correspond à une plus grande sensibilité. Les paramètres Dm et p ont été estimés pour tous les stades larvaires et pour les différentes températures (Tableau 2). Le paramètre p, (l'inverse de la sensibilité du taux de développement à la densité de proies) décroît avec la température T (Fig. 3). Plus la température est élevée, plus le taux de développement est sensible à la disponibilité en nourriture : chaque portion de nourriture induit un effet sur le développement plus important quand la température augmente. Cette relation est modélisée empiriquement via un modèle exponentiel :

Taux de développement

)3(T) = Bd i .e •''2 (4-5) où Bdi et Bd2 sont deux constantes. Les estimations de Bd, et Bd 2 sont données dans le Tableau 3. Le taux moyen de développement peut donc être décrit comme une fonction de la température et de la densité de proies en introduisant D/7/(T) et ,5(T) dans l'équation (1) :

(7-, N) = rom(T) 1 -e 13(7" ).' [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF](5)(6) L'allure générale de ce modèle est donnée en Fig. 4. Ce modèle incorpore trois sous-modèles principaux :

• Le modèle de dynamique des populations de M persicae.

• Le modèle de réponse fonctionnelle de H. 1,T( s) s=t-'r

(5-5)

N (s)

(5-6)

= ±,D(T (s))

(5 -7) dans le programme, t-T est estimé en calculant ED(T(s)) en partant de t jusqu'à ce que Taux de survie. Le taux de survie spécifique journalier dépendant de l'âge [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF](5)(6)(7)(8)[START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF](5)(6)(7)(8)(9)[START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF](5)(6)(7)(8)(9)(10) est modélisé comme le taux de survie journalier de la larve de coccinelle au ième stade, fonction de la température instantanée et de la densité de proies :

S i (T , N)

1 ±Sc (T) (T).N (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) S 1 (T) = Sc, 1 . ( 1 -Sc, 2. e -sq 33-) (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) Sci 2 ( T) = Sc21 .(1-S c 22 .e -s'T ) (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) Tous les paramètres et variables ont la même signification que dans les équations 4-7, 4-8, 4-9, 4-10.

L'évolution de la densité de coccinelle du ième stade larvaire est alors modélisé par :

dPi = (1--[1 -L i i (T,N)].P; + U. (t) (5-19) dt

où Pi est la densité de larves de coccinelles au ième stade larvaire, U 1(t) le nombre de larves du ième stade lâchées au temps t, Li et Li deux variables logiques prenant deux valeurs (0 ou 1). Si une larve reste au ième stade, L i vaut 1. Quand une larve a fini son développement au stade i et entre dans le stade suivant, L i vaut 0.

prédateur parmi les colonies de pucerons, etc., dans la simulation. Une seule colonie de pucerons est utilisée comme échelle d'espace. Nous supposons que b, le coefficient de compétition intraspécifique (l'impact d'un individu sur les autres individus de la même colonie) est une constante indépendante de la température. La capacité de déplacement représentée par r,,,.(7')/b, dépend alors de la température.

En conditions naturelles, les pucerons peuvent se déplacer en marchant ou, pour les formes ailées, en volant. Ce processus de déplacement intra -habitat peut être dépendant de la densité ou de la température, mais aucune donnée n'est disponible pour nous permettre de dégager un cadre valide qui puisse caractériser ce processus. Nous avons utilisé dans cette étude un générateur de nombres aléatoires uniformes pour simuler le nombre de pucerons entrant ou sortant de la colonie, et ce de manière indépendante de la densité de pucerons et de la température. Le biais introduit par cette pratique peut paraître énorme à l'échelle microscopique, mais peut être considérée comme acceptable à l'échelle macroscopique, dans la mesure où les effets de déplacement intra-colonie sur la dynamique de population sont très nettement plus importants à faible densité de population qu'à forte densité. Quand la saison se termine, M persicae évolue vers des formes ailées qui émigrent des vergers de pêcher vers des hôtes secondaires. On montre que la proportion de pucerons sortant des vergers augmente quand la saison se termine. Le nombre de pucerons sortant du verger de pêchers est modélisé ici comme le produit de la densité de population de pucerons, de la proportion de degrés jours accumulés sur le nombre total de degrés jours nécessaires à l'accomplissement de la vie des pucerons dans le verger de pêchers à une puissance x (x valeur choisie pour obtenir les résultats attendus) et d'une variable aléatoire uniforme :

Et, (T (t) -Tb) N emm (t) = N (t) .RND.(

)..7c (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)) aptotal OÙ Nem",(t) est le nombre de pucerons sortant du verger, N(t) la densité de population actuelle, RND une variable aléatoire uniforme, T(0 la température le jour t, Tb le seuil inférieur de température pour le développement du puceron, DD,",,,/ la quantité de degrés jours nécessaire pour accomplir la phase de vie des pucerons dans le verger de pêcher, x une valeur à fixer.

Programme principal. Le programme principal est formé de 5 grandes parties. Dans la première partie sont définis les sous programmes, les fonctions, les tableaux et les valeurs des paramètres.

Dans la seconde partie, les données de température sont extraites d'un fichier de données créé par CLIMGEN, puis on calcule la date à partir de laquelle les pucerons apparaissent dans les vergers de pêcher, dans ce cas au moment où un total de 192 degrés jours est accumulé au dessus du seuil de 4.5°C. Dans la troisième partie, on initialise le système en affectant aux variables d'état (les populations de pucerons et les larves de coccinelles) leurs valeurs initiales. La population initiale de M persicae est obtenue par troncation d'une valeur aléatoire uniforme. La population initiale de larves de coccinelles est fixée à zéro tant que la population de pucerons est supposée au dessous du seuil de tolérance. Les parties 4 à 6 sont incluses dans la boucle principale du programme, qui démarre le jour où des pucerons apparaissent dans le verger et se termine quand 1912 degrés jours au dessus de 4.5°C ont été accumulés. Dans la quatrième partie, on appelle la subroutine RmLag pour calculer le taux d'accroissement intrinsèque de la population de pucerons qui est fonction de la température via une intégrale retard et une dépendance retard à la densité due à la compétition intraspécifique (voir partie 2, « modèle puceron vert » de ce chapitre). Dans la cinquième partie, on vérifie si la population de pucerons dépasse un seuil de tolérance auquel cas un certain nombre de larves d'un stade donné est lâché. Dans la subroutine ComputY on calcule le taux de développement, le taux de survie journalier et la consommation de proies des larves de coccinelles en fonction de la température instantanée et de la population de pucerons. Dans la sixième partie on appelle la subroutinc RungeKutta, qui donne la solution d'une équation différentielle ordinaire, pour calculer les densités de population de pucerons et de larves de coccinelles le jour suivant. Les résultats ainsi générés sont écrits dans un fichier dans une septième partie. Subroutine IttnLag. On appelle cette subroutine dans le programme principal pour calculer la température journalière et la population moyenne de pucerons sur un intervalle de temps (comme précisé dans l'équation qui est l'intervalle de temps entre une date passée et la date actuelle pendant lequel les degrés jours accumulés permettent le développement préimaginal des pucerons (ou le temps de génération moyen). Cet intervalle est calculé à partir de la date courante en reculant dans le temps jusqu'au moment où l'accumulation de taux de développement de pucerons (fonction de la température) atteint 1 (voir équation 5-7 et la discussion en section 2 de ce chapitre). La température moyenne sur un intervalle de temps est ensuite utilisée pour calculer le taux d'accroissement intrinsèque de la population moyenne de pucerons en utilisant l'équation 5-2. La valeurs du taux instantané d'attaque et du temps de manipulation, de même que la densité de population de pucerons et de coccinelles sont des entrées issues de la subroutine ComputY et du programme principal. La simulation montre également que la même extinction finale, de la population de pucerons, avec un nombre minimum de larves de coccinelles, est obtenue plus rapidement à hautes qu'à basses températures (Fig. . Ces variations de temps utile pour l'élimination des pucerons en fonction de la température sont plus fortes pour les jeunes stades larvaires que pour les stades âgés.

A 12°C, le temps nécessaire à l'extinction des pucerons par des larves de premier stade excède de 50 Le modèle de simulation est prévu pour révéler des propriétés qualitatives concernant la dépendance à la température et à la densité de l'interaction prédateur -proie entre H. axyridis et M persicae. Ce modèle n'est pas doté de grandes significations quantitatives dans la mesure où beaucoup de détails biologiques et physiques sont ignorés, soit pour conserver la tractabilité du modèle, soit par manque d'informations. Quoi qu'il en soit, ce type de modèle génère des propriétés qualitatives qui éclairent sur des composantes diverses de l'interaction prédateur -proie. Quelques unes des propriétés ont des implications générales dans un plus large contexte, peuvent servir à tester des hypothèses et éventuellement à accroître les connaissances scientifiques.

Deux aspects, à savoir le nombre minimum de prédateurs requis pour assurer une éventuelle extinction des pucerons et la durée de la période nécessaire à cette extinction après la date du lâcher, sont considérés pour estimer l'efficacité des larves de H axyridis pour éteindre les populations de

4 increaseofM.

 4 Fig. 1-1 Diagram of a conceptual model for the temperature-mediated predator-prey interactions between Harmonia axyridis and Myzus persicae.

. 3 .

 3 Peach seedlings in the stage of 15-20 leaves, which were obtained from the germination of peach cones of the variety 305, were used as the host plants of green peach aphid. These seedlings were cultured in 5x8.2 cm cylindrical plastic jars using a complete nutritive solution with the following composition in mol ni 3 The peach seedlings were watered with distilled water every three days, and the nutritive solution was supplemented every week. A sheet of paper in black color was put at the bottom of the peach seedlings, covering the plastic jars, with the stalk passing through a hole, so that the white-colored exuvia of the aphids could fall on this sheet of black paper and be easily found.Aphids. Laboratory colonies of parthenogenetic viviparous green peach aphids used inthis experiment were originated from the fimdatrix collected from the experimental orchard of INRA at Montfavet in March, 1992. These aphid colonies were maintained on peach seedlings cultured with nutritive solution in a climatized chamber with temperature being maintained at 21.0+0.5°C, relative humidity at approximately 60% and the photoperiod being the same with the natural photoperiod. For the experiments, adult aphids were put on each of the peach seedlings for producing viviparous nymphs, 4 hours later, these adults and excessive nymphs were removed from the seedlings, with only one nymph being left on each seedling. Observation. The peach seedlings carrying a aphid nymph which had been delivered for no longer than 4 hours were placed inside incubators in which temperature was kept at 12.5, 16, 18, 20, 24, 26, 27.5 or 30°C respectively. In each incubator were placed a rectangular plate filled with water and pieces of plastic sponge soaked in the water to raise the relative humidity. However, we failed to maintain the same level of relative .installed ventilator. Twenty replicates were used for each temperature treatment. The aphids were checked everyday, and the time of molting, dying of the nymphs and the number of new-born . nymphs reproduced each day by the adults were recorded. The young nymphs were removed each day after the observation.

Fig. 2 - 1

 21 Fig. 2-1 Developmental rate D (D=1 dayl ) of M persicae in relation to constant temperature (C). The ctin'e is plotted using predicted values (rom equation (2-2); the dots are observed values.

Fig. 2 - 2

 22 Fig.2-2 Relationship between the total fecundity of M. persicae and temperature ( °C) on peach seedlings cultivated vaith nutritive solution under laboratory conditions. Photo period 14:10.

Fig. 2 - 3

 23 Fig. 2-3 Age-specific fecundity profiles of M. persicae in relation to temperature (°C). Observation made under laboratory conditions. The aphids are reared on peach seedlings cultivated in nutritive solutions. Photoperiod is set at 14:10. The numbers in the legend boxes are temperatures in °C

Fig. 2 - 5 .

 25 Fig.2-5. Intrinsic population increase rate r m of M persicae in relation to constant temperatures ("C). The curve is plotted using predicted values from equation[START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF][START_REF]Population growth rate of M. persicae as a function of temperature: ' dX/dt=r(Temp)*(Tave(t-z))*X-SX*X*Xm(t-z) (2) ' (Temp)=ADCX*((l+KaX.X*EXP(-RoX*[END_REF]; dots are values estimated using equation 2-1.

Fig. 3 -

 3 Fig.3-1 Functional response of larvae of H. axyridis to M. persicae under 25 °C. The solid unes are generated from predicted values, the dots are observed values. The N in x-axis is the number of prey offered; 'The Na in y-axis is the number of prey consumed; L I , Li, L3, Le are larval instar 1-4 of the predator.

Fig. 3 - 2 Fig. 3 - 3

 3233 Fig. 3-2 The relationship betwcen instantaneous attack rate a of H. axyridis on M persicae and Temperature (°C). L1-4 denotes the larval stadium 1-4.

ere

  The estimated values of parameters a and Th under different temperatures for ail the larval instars were fitted to

Fig. 3 - 4 .

 34 Fig. 3-4. Daily consumption of M persicae by H axyridis in relation to temperature and density of the aphid. Values in plot are calculated from the mode!.

   same meaning as in Eqn. 4-1.

Fig. 4 -

 4 Fig. 4-1 Average developmental rate (da') of H. axyridis in relation to the number ofM persicae present. Values in the legend are temperatures in 'C. Lines are predictions from Eqn 4-3, marks are observed values. L I , L2, L3, and L4 denote the coccinellid larvae of instar 1-4 respectively.

Fig. 4 - 2 Fig. 4 - 3

 4243 Fig. 4-2 The maximum developmental rate Dm of H. axyridis in relation to temperature ( °C). Solid unes arc drawn using predicted values from Eqn. 4-4, marks are observed values. L I , LA, L3 and 1,4 denote the larval instar 1-4 respectively.

Fig. 4 - 5

 45 Fig.4-5The average daily survival rate of H. axyridis in relation to the number of M persicae prescrit. Unes are predicted value computed from. Eqn 4-7, marks are observed values. Values in the legend are temperatures in °C. LI , Li, L3 and L4 denote the larval stadium 1-4 respectively.

Fig. 4 -Fig. 4 -

 44 Fig. 4-6 Relationship between the parameter Sc i from Eqn. 4-3 and temperature (T). Solid unes are drawn using predicted values from Eqn. 4-8, marks arc observed values.

  [START_REF] Beddington | The components of arthropod predation. II. The predator rate of increase[END_REF] suggested that the survival rate of a predator in relation to the prey density follow a sigmoid curie, based on a normal distribution of the mean number of prey consumed. His model has net been used very widely to fit experimental data because it is basically suitable for describing survival rate of a generation fits much less well the survival rate data on a daily or stage basis. In addition, the meaning and biological mechanisms of parameters in his model is quite vague. In their study of the predator-prey interactions between Typhlodronnts pyri and its prey -European red mite,[START_REF] Hardman | Effects of temperature and prey density on survival, development, and feeding rates of immature Typhlodromus pyri (Acari: Phytoseiidae)[END_REF] proposed a saturation curie te describe the survival rate in response te the prey density. Our results supported a sigmoid curie, which has basically the same features as that used byChen et al. (1985) in his study of the numerical responses of Chlysopa septenpunctaia to Myzus persicae. We derived a model which is different from Beddington's in the underlying mechanism to describe the survival rate of H. cccyridis in response te the density ofMpersicae. we have D=0, which lead to C'=Dm. Hence, D = Dm (1 -" ) (A-1 -5) Derivation of the equation describing the relationship between the survival rate and number of prey present (equation 4-7).

As

  the overwintering eggs of green peach aphids hatch in the peach orchards in the early spring when a certain amount of effective thermal time, meaning the accumulation of temperature above the base temperature (4.5°C) is accumulated(Tamacki 1988, Mack and[START_REF] Mack | CMACSIM, a temperature-dependent predator-prey model simulating the impact of Cokomegilla maculata (DeGeer) on green peach aphids on potato plants[END_REF]. The parthenogenetic viviparous population will grow through the season, until June when a certain amount of thermal time is accumulated and then ail the individuals emigrate out of the peach orchards. The in-orchard migration between colonies during the course of population change was simulated with a random number of uniform distribution. The ladybeetle larvae can be released at any point of time of the season.

3 .

 3 ail the equations z-represents the time-lag for the integral time-delay. The average generation time and the duration for immature development can be considered as two of the candidates for r. Here we accepted the duration for the immature development as r Because the duration for immature development is dependent on the temperature, which changes with time, thermal time is used in determining the time-lag for the integral timedelay. Here ris calculated from the relation program, t-r is determined by computing the 2: D (T (s)) backward tstarting from the current time t until D (T ( s)) 1 is satisfied and then the value of s was taken as t-r. D(T(s)) the immature developmental rate is calculated fiom Eqn. 2parameters and variables have the same meaning as those in Eqn. 2-4. We use the immature developmental time as the length of time over which the integral time delay of temperature-and density-dependence is accounted for by assuming that the current rate of population change is affected by the integral effects of temperature and population density over the immature developmental time. The average generation time or the characteristic return time may also be used as the length of time accounted for integral time delay under different assumptions. The simple average of temperature or population density that is used here is only the simplest case for the integral lime delay of temperature-and density-dependence. Weighed averages upon certain patterns of wéight distribution over the delayed time period is be expected to be more realistic representations of time delay effect. The ladybeetle model Functional response. The fimctional response of the ladybeetle larvae was modeled as a function of the instantaneous temperature and population density of green peach aphid using Holding's type II response (Eqn. 3-1, 3-2a, b).

  Section six calls the subroutine RungeKutta, a solver of ordinary differential equation, to compute the population density of aphids and lady beetle larvae of the next day. Section seven writes the data generated by the simulation to a data file.Subroutine RmLag. This subroutine is called by the main program to calculate the average of daily temperature and the average of aphid population over a delayed time period (as specified by equation, which is the time interval between a time point in the past and the current time during which a thermal time accumulation sufficient for the aphids to complete their immature development (or average generation time) is attained. This time lag is calculated form the current time point backward to a time point in the past at which the accumulation of developmental rate of the aphids, which is a function of temperature, reaches one (see equation 5-7 and the discussion in "Section 2. Green peach aphid model" of this chapter). The average of daily temperature over the delayed time period is then used to calculate the intrinsic rate of population increase Tm(T) using equation 5-2, and the average of aphid population over the same time period is used to account for the delayed density-dependence of the aphid population (see equation 5-1). The daily temperature, aphid population density, relevant parameters and time counter are passed to this subroutine and the intrinsic rate of population change and the average of aphid population over a delayed time period are output as globally shared values. Subroutine ComputY. This subroutine is called fo calculate the prey consumption, developmental rate and survival rate of the lady beetle larvae as functions of temperature and aphid population density. The first part of the subroutine computes the developmental rate of the larvae and the developmental progress in terms of accumulation of developmental rate using equations 5-12 to 5-14. The latter is passed to the subroutine RungeKutta and is used ta determine whether the larvae enter the next stage on the next day according to the relation defined in Eqn. 5-15. The second part compute the survival rate which is used in the subroutine RungeKutta as the rate of change of the ladybeetle larvae. The third part of the subroutine compute the instantaneous attack rate and handling time in relation to temperature and is passed ta the subroutine RungeKutta for calculating the total consumption of aphids by the ladybeetles.

Fig. 5 -Fig. 5 - 2 .

 552 Fig.5-1. Estimated values of the minimum number of larvae of Harmonia axyridis required to eventually eliminate the green peach aphids on a single colony in relation to temperature. The predator are released at the aphid population level of 250 aphids/colony. These data are generated with the computer simulation program. Li, L2, L3, L4 represent the larvae or 1 e 2nd 3rd and ei instars.

Fig. 5 - 3 .

 53 Fig.5-3. Simulated population change of green peach aphid after larvac of Harmonia axyridis are released in the minimum number required to eventually eliminate the green peach aphids on a single colon'. The predator are released at the aphid population level of 250 aphids/colony. The value of the minimum number of larvae required to eliminate green peach aphids on a single colony is the same as used in Fig5-1 and Gig. 5-. Sec that more days are required to completely eliminate the aphids under low temperature than under high temperature, and that the difference in the days required to completely eliminate the aphids is much smaller for the older instar larvae than for the younger instar larvae. The data are generated with the computer simulation program. Li, L2, L3, L4 represent the larvae or 1" 2 nd, 3rd and 42' instars.

Fig. 5 - 4 .Fig. 5 - 5 .

 5455 Fig.5-4. Estimates of number of days it take for the aphid population to be brought down to zero by larvae of Harmonia axyridis released in the minimum number required to eventually eliminate the green peach aphids on a single colony. Sec that this value decreases as temperature increases. The data are generated with the computer simulation program. The predator arc released at the aphid population level of 250 aphids/colony. The value of the minimum number of larvae required te eliminate green peach aphids on a single colony is the sanie as used in Fig 5-1 and Fig. 5-. LI, L2, L3, L4 represent the larvae or I 2nd , 3rd and 4 th instars.

Fig. 5 -

 5 Fig .5-6. Simulated population change of green peach aphid after larvae of Harmonia axyridis are rcleased in the minimum number required to eventually eliminate the green peach aphids on a sin gle colony. The predator are released at the aphid population level of 250 aphids/colon y. The value of the minimum number of larvae re quired to eliminate green peach aphids on a sin gle colony is the same as used in Fig 5-1 and Gig. 5-. See that more cla ys are required to completel y eliminate the aphids by the younger instar larvae than b y the older instar larvae, and that the difference in the days required to completely eliminate the aphids by different instars is much smaller under hi gh temperature than under low temperature. The data are generated with the computer simulation program. Li, L2, L3, L4 represent the larvae or I' z 3-and 4th instars.

Fig. 5 -

 5 Fig.5-8. Simulated population change of green peach aphid under varible temperature when no Harmonia axyridis are released throughout the season. Temperature data are generated using CLIMGEN, a climate data generator developed by USDA-ARS, with parameters calculated from the local meteo record maintained by INRA-Station de Agroclimatologie at Montfavet.

Fig. 5 -

 5 Fig. 5-9 shows simulation results concerning the consequence of releasing larvae of H. a:cyrids for biological control against M persicae. The number of larvae required to be released increases with the aphid population level at which the ladybeetle larvae are released. When the predator is released once the aphid population reaches 25 per colony, a very satisfactory result is obtained by releasing the 3 rd instar larvae three times each at 0.25 larvae /colony (Fig. 5-9 a). When the predator is released once the aphid population reaches 100 per colony, a similar result is obtained by releasing the 3' d instar larvae three times with each at 1, 0.5, 0.5 larvae /colony respectively (Fig. 5-9 b). If the aphid

Fig. 5 -Fig. 5 -

 55 Fig.5-10. Simulated population change of green peach aphid under varying temperature when increasing the number of larvae of Harmonia axyridis for the first release at the the aphid population density of 25 0/colony. The Instar and quantity of larvae of Harmonia axyridis released ---a: l e instar 5-1; b: 2 nd instar 4-1, c: 3 rd instar 3-1, d: 4 th instar 3-1. Temperature data are generated using CLIMGEN, a climate data generator developed by USDA-ARS, with parameters calculated from the local meteo record maintained by INRA-Station de Agroclimatologie at Montfavet.

FOR'

  RungeKutta to solve differential equations.CALL RungeKutta(i, Xave#, r#. SX#, AR#0, Th#0, Totsum, TotThermReq) 'Write output to the screen:PRINT USING a$; i + U Temp(i + 1); X(i + 1); Y(1, i + 1); Y(2, i + I); Y(3, i-i-1); Y(4, i + 1) i = i + 1 LOOP Dayend% = i -1 End of main loop. 'Write output to a data file. OPEN "c:Ixiii.bas\data\SV4-.dat " FOR OUTPUT AS #2 FOR i = DayEmern/0 TO Davend% PRINT #2, i, Temp(i), X(i); Y(1. i); Y(2, i); Y(3, i); Y(4Compute intermediate parameter values related to the ladybeetle. ....................................................................... END SUB 'End of subprogram RungeKutta FUNCTION TotalConsum __________________________________________________________________________ FUNCTION TotalConsum (AR(), Th(), Xk, Yk()) SHARED ColonSize Imp = 0 FOR Stage% = 1 TO 4 IF Yk(Stagc%) > 0 AND Xk > 0 THEN ConsumY = AR(Stage%) * ColonSize * Xlc * Yk(Stage%) / (Yk(Stage%) + AR(Stage%)

  where IF is the index of relativeinfestation, d: d e [0 ,l,2 ,3,4,5] is the degree of infestation; fd : is the frequency of d.It is obvious that the maximum value of IF is one, and the minimum zero. The IF value was calculated for each of the trees either with or without ladybeetle larvae. The average IF of the trees vvith ladybeetle larvae and the trees without were compared.

Fig. 6 - 2 3

 623 Fig. 6-1 Evolution of index of relative infestation of green peach aphids on encaged peach trees with larvae of Harmonia axyridis.

  9). But this is probably flot the only cause, since the retardation in the declining of the

Fig. 6 - 4 5

 645 Fig. 6-4 Comparason of frequency of degree of infestation green peach aphids on pcach trees with 3rd instar larvae of Harmonia axyridis released with that on trees without lady beetle larvae. a: on 17-May; b: on I8-May; c: on 19-May; d: on 21-May; e: on 24-May; f on 28-May. For the treatment, 50 3rd instar larvae of Harmonia axyridis were released on the 18 May.

6.

  Satisfactory results was obtained in suppressing the population of M. persicae using H. axyridis by releasing an acceptable number of 3r d instar larvae (50 larvae/tree) at an aphids density of average 20 aphids/shoot. Simulation mn with temperature data recorded during the experiment generates results qualitatively consistent with the observation. But the cause underlying the failure of most of the release trials in openair orchards is flot explained by anything from the exclusion experiment as well as the simulation.

  de H. axyridis en fonction de la température. La relation entre le taux maximum de développement et la température (Fig2) est de même forme que la réponse typique des animaux poikilothermes à la température, décrite ici selon le modèle de Logan : vinA est le taux du processus physiologique à une température de base donnée; pllA est une valeur correspondant aux réactions biochimiques critiques catalysées par les enzymes; Tm n" est la température maximale (en °C) au dessus de la température de base du processus de vie; ilT im la largeur de la marge supérieure de températures. Les estimations de ces paramètres pour tous les stades larvaires sont données en tableau 4 . La température maximale de développement (Tmim ) est d'environ 29-30 °C, l'épaisseur de la marge supérieure de températures (4THA ) d'environ 3-4 °C pour les 4 stades larvaires.

  . D(T(s)) le taux de développement des immatures, est calculé à et les variables ont la même signification qu'en équation 2-4. Nous utilisons la durée de développement larvaire comme longueur de temps sur lequel est calculée l'intégrale effectuée par rapport au temps de la dépendance à la température et à la densité. On suppose pour cela que le taux instantané d'évolution de la population est influencé par l'intégrale des effets de la température et de la densité de population sur la durée de développement larvaire. La durée moyenne d'une génération ou le temps de retour caractéristique peuvent être également utilisés comme base de temps sur laquelle calculer les intégrales effectuées par rapport au temps si l'on fait d'autres hypothèses. Les simples moyennes de température ou de densité de population que nous où i représente le ième stade de la larve. Tous les autres paramètres et variables ont la même signification que dans les équations4-3, 4-4, 4-5. Le temps de passage d'une larve dans le stade suivant est calculé en utilisant1=Di (7' (s) ,N(s))(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15) où A() est le taux de développement du I'me stade larvaire fonction de la température T(s) et de la densité de proie N(s) au jour s. Dans le programme, le temps de passage du ième stade larvaire au suivant est estimé en calculant E (T (s) ,N(s)) en partant de 4,, le temps d'entrée dans le Io I iéme stade, jusqu'à ce que soit vérifiée l'inégalité (T(s),N(s)) ?_ 1 A ce moment, tous les ro individus du ième stade passent dans le i+1 ième stade.

5 .

 5 PROPRIETES DU SYSTEME PROIE-PREDATEUR GENERE PAR LE MODELE DE SIMULATION Influence de la température sur l'efficacité de H. aryridis. L'efficacité des coccinelles est évaluée en terme de nombre minimum de larves requis pour l'extinction de la population de pucerons, à partir d'un niveau de population initial donné. Plus le stade larvaire est efficace, plus le nombre d'individus nécessaires à l'élimination des pucerons est réduit. Cette valeur est estimée par une procédure numérique, dans laquelle le nombre de pucerons qui entre ou sort du verger est établi comme nul. L'observation ne porte ainsi que sur l'extinction des pucerons liée à la prédation par les larves de coccinelles. Le niveau de population de pucerons auquel les larves de coccinelles sont lâchées est fixé à 250. En général, pour les trois premiers stades larvaires de H. axyridis , un plus grand nombre d'individus est requis à basse température qu'à température élevée pour éteindre une colonie. La décroissance du nombre minimum de larves requises lorsque la température augmente est plus rapide aux deux extrêmes de la gamme de températures favorables, de 12°C à 27°C, qu'aux températures favorables à la fois à H axyridis et M persicae, de 15 à 24°C (Fig. 5-1 L I , L2, L3). Pour le troisième stade, le nombre de larves minimum requis au-dessous de 18°C est plus faible qu'à 21 et 24°C (Fig. 5-1 L3). Pour le quatrième stade, le nombre minimum de larves requis pour l'extinction de la population de pucerons ne suit pas exactement une décroissance monotone avec l'augmentation des températures (Fig 5-1 L4). Dans la gamme de température 15-24°C, le nombre minimum de larves du quatrième stade requis augmente avec la température, schéma inverse de celui des stades 1 et 2 (Fig 5-1 L4, 5-2).

M

  persicae. Dans le cas de lâchers inondatifs, le prédateur n'est pas attendu comme un agent de régulation à long terme, mais plus souvent comme un agent d'élimination de la proie. Pour les quatre stades larvaires du prédateur, le nombre d'individus nécessaire à l'extinction des pucerons tend vers zéro quand la température tend vers l'extrême supérieur pour la croissance de la population de pucerons, et il tend vers les valeurs les plus élevées à l'autre extrémité de la gamme des températures efficaces. Dans la gamme des températures favorables aux deux espèces (15 -24°C), le nombre minimum efficace de larves 1 et 2 du prédateur décroît de façon monotone quand la température augmente. Pour le quatrième stade, dans cette même gamme de températures, l'efficacité décroît quand la température augmente dans l'ordre inverse par rapport aux premier et deuxième stades. Avec ce scénario, l'ordre relatif d'efficacité des différents stades de H axyridis passent de L1<L2<L3<L4 à 12°C à L4<L3<L2<L1 à 27°C, avec une série de transitions aux températures intermédiaires. Le temps d'élimination des pucerons à partir du lâcher du prédateur dépend également de la température et de l'âge du prédateur. Pour les quatre stades de la coccinelle, la durée de cette période décroît quand la température augmente, et cette décroissance en relation avec la température est plus forte pour les jeunes stades que pour les stades âgés. Il est donc suggéré qu'a basse température, les stades âgés sont plus performants car ils sont efficaces plus rapidement et à effectifs inférieurs. Leur utilisation doit être préférée lorsqu'une intervention est nécessitée à basse est très bas pour prévenir la transmission du virus. Cela implique des interventions très précoces et efficaces rapidement. Un grand nombre de larves 3 ou 4 de H. axyridis serait alors requis, ce qui est économiquement irréaliste. Par ailleurs, des limites comportementales, comme la forte population initiale de pucerons pour fixer le prédateur sur ses colonies, sont en contradiction avec les objectifs de la lutte dans les zones infestées par la Sharka. En dehors de ces zones, l'utilisation de H. axyridis est techniquement possible, mais sa faisabilité économique dépend du coût de production et de lâcher et du bénéfice attendu des interventions. Parmi les facteurs non incorporés dans le modèle, le plus important est sans doute le comportement de recherche des larves de coccinelle. Une perte significative de prédateurs explique l'échec de nombre d'essais de lâchers en plein champ. Le résultat de lâchers le plus satisfaisant vient probablement d'essais conduits en conditions semi-contrôlées, par lâchers de coccinelles sur des arbres encagés. Dans ce cas, nous attendons du modèle une représentation du maximum d'efficacité de H axyridis comme agent de lutte biologique contre M persicae. EVALUATION DE L'EFFICACITE DE HARMONIA AXYRIDIS COMME AGENT DE LUTTE BIOLOGIQUE CONTRE MYZUS PERSICAE PAR ESSAI SUR ARBRES ENCAGES AU CHAMP INTRODUCTION La technique d'exclusion a été largement expérimentée pour évaluer l'efficacité, particulièrement à court terme, d'un ennemi naturel pour supprimer les populations d'un ravageur. Dans les premiers stades de développement d'un programme de lutte biologique, cette technique est particulièrement utile car elle permet généralement de collecter un grand nombre d'informations sur le ravageur et sur la plante. Elle peut permettre de conclure rapidement à l'inadéquation d'un prédateur au contrôle d'un ravageur donné. Elle peut réduire le nombre d'options pour des essais à grande échelle en plein champ. Dans notre étude de l'évaluation de H axyridis pour le contrôle de M persicae, ce type d'expérimentation a été jugé utile pour plusieurs raisons. Notre modèle de simulation prédisait qu'à température adéquate et à relativement faible niveau de population de pucerons, les larves de la coccinelle pouvaient être plus ou moins efficaces dans l'élimination des populations de la proie. A titre d'exemple, une intervention sur des populations de pucerons atteignant en moyenne 25 individus par rameau nécessiterait pour une extinction complète des populations un lâcher de 0.25 coccinelles du troisième stade larvaire par rameau, soit 75 individus pour un arbre de 300 rameaux. Cependant, aucun des essais que nous avons conduits en plein champ n'a permis la vérification de cette hypothèse, malgré des lâchers parfois supérieurs à 300 larves du troisième stade par arbre. L'effet des prédateurs sur les populations de pucerons n'a pu être précisé, le devenir des insectes lâchés étant par ailleurs très difficile à suivre dans ces conditions de plein champ. Il est supposé dans ce cas que la prédiction du modèle est totalement fausse, ce qui implique quelques erreurs sérieuses dans sa conception, ou que des facteurs autres que la dépendance à la température et à la densité de proie influent significativement sur les insectes lâchés en plein champ. Plusieurs raisons peuvent être évoquées :• un grand nombre de larves de coccinelles est la proie de prédateurs généralistes tels les oiseaux et les fourmis.

  oùIF est l'indice d'infestation relative, d: d e [0,1,2,3,4 ,5] le degré d'infestation; fd : la fréquence de d. Il est clair que la valeur maximum de IF est 1, et le minimum 0. La valeur de IF est calculée pour chaque arbre avec ou sans larve de coccinelle. On compare la moyenne des IF des arbres avec et sans larve de coccinelles.Les données sur le degré d'infestation des pucerons peuvent aussi être utilisées pour estimer la densité moyenne des pucerons sur une colonie : N. est la densité moyenne estimée de la population de pucerons par colonie; d:d e [0,1,[START_REF]comme H. axyridis provenant d'un élevage de masse sur proies de substitution. La partie gauche de la courbe en Fig. 5-7, décrivant un fort accroissement du nombre de prédateurs requis aux stades Ll -L3 est facile à comprendre. Mais la partie droite de cette courbe, décrivant une légère diminution de l'effectif minimum de lâchers pour ces mêmes stades est inattendue. Le mécanisme sous-jacent est que lorsque la population de pucerons est supérieure à K/2, la moitié de la taille maximale de population, le taux de changement de population dN/dt de pucerons décroît quand N augmente. La simulation indique également que le nombre de lâchers de prédateurs nécessaire peut être réduit en augmentant l'effectif de chaque lâcher, mais l'effectif total de prédateurs nécessaire s'en trouverait augmenté[END_REF][START_REF]Population growth rate of M. persicae as a function of temperature: ' dX/dt=r(Temp)*(Tave(t-z))*X-SX*X*Xm(t-z) (2) ' (Temp)=ADCX*((l+KaX.X*EXP(-RoX*[END_REF][START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF]5] le degré d'infrstation; fa : la fréquence de d.Ici, pour chaque degré d'infestation, nous utilisons la limite supérieure de la classe de densité de population qui donne habituellement une meilleure estimation de l'infestation : une colonie de 150 pucerons devrait être classée au degré 4, mais sera le plus souvent estimée comme degré 3, car plus proche de 5 3 ; qui plus est, le degré 5 n'a qu'une limite inférieure. Les populations de pucerons des deux traitements sont ensuite comparées à la simulation conduite en utilisant les températures enregistrées dans une des cages. La température moyenne d'une journée est calculée par la moyenne des températures à 0, 6, 12, 18, et 24 heures.R ES U LTATSL'infestation des 4 arbres sans coccinelles s'accroît, sauf un arbre dont le IF connaît une légère décroissance (Fig.6-1). L'indice d'infestation des 4 pêchers sur lesquels les larves de coccinelles sont lâchées décroît de manière continue à partir de la date du lâcher, le 18 mai, et tombe à zéro après 8 -10 jours (Fig.6-2). La comparaison des valeurs moyennes de IF pour les arbres traités et témoins démontrent plus clairement l'effet du lâcher du prédateur sur l'évolution des populations de pucerons (Fig.6-3). Le jour précédant le lâcher, l'évolution du degré d'infestation est la même dans (6-1) les deux groupes d'arbres, de même que la distribution de fréquence des degrés d'infestation (Fig.6-4). Après le lâcher, la fréquence des hauts degrés d'infestation décroît de manière continue jusqu'à ce que toutes les pousses soient ramenées au degré d'infestation zéro, tandis que la fréquence des hauts degrés d'infestation continue à croître sur les arbres témoins (Fig.6-4).Le fait que les populations de pucerons des arbres traités soient éliminées tandis que les populations des arbres témoins poursuivent leur accroissement suggère qu'un nombre efficace de larves actives de coccinelles s'est maintenu jusqu'à l'extinction des populations de pucerons. Les observations montrent que c'est effectivement le cas. Bien que la densité relative des larves de coccinelles décroisse avec la population de pucerons (Fig.6-5), quelques larves de quatrième stade survivent et restent actives après la disparition de la proie (Fig.6-6). La densité moyenne de population de pucerons par colonie est estimée et suivie dans le temps par le degré d'infestation des arbres traités et témoins (Fig.6-7a). La population observée dans les deux cas diffère des résultats de la simulation. Le changement de population dû au lâcher de coccinelles est qualitativement identique dans la simulation et dans les populations réelles (Fig.6-7), contrairement à la population de pucerons dans les témoins, inférieure aux populations prévues par le modèle de simulation (Fig.6-8a). Le déclin effectif des pucerons après le lâcher est moins rapide que dans la prédiction du modèle de simulation (Fig.6-8b), peut-être en raison d'une plus faible survie du prédateur en situation réelle que dans la simulation (Fig.6-9). Ce n'est peut-être pas la cause principale, le retard par rapport à la simulation du déclin de l'infestation étant plus évident juste après le lâcher, à un moment où la survie du prédateur est plus forte dans la réalité que dans le modèle de simulation (Fig.6-9). CONCLUSION ET DISCUSSION Les résultats des tests d'exclusion indiquent qu'une complète élimination de M persicae à la population initiale de 20 individus par rameau est obtenue en lâchant 50 L3 de H. axyridis, ce qui correspond qualitativement aux résultats de la simulation. La simulation dévie numériquement des observations d'une manière très sensible, indiquant à nouveau que la prédiction du modèle a une signification essentiellement qualitative et sous certaines conditions. La population simulée de pucerons en l'absence du prédateur s'accroît plus fortement que la population réelle. Cette différence peut résulter de facteurs limitant la croissance de la population, tels que des prédateurs par la coccinelle. Ce type de conséquence aurait pu ne pas être obtenu par un lâcher plus précoce dans la saison, à température moins élevée. Il serait d'un grand intérêt de reproduire cette expérimentation plus tôt en saison.

Analysis of data. The demographic data obtained for each temperature from above observations were used to build age-specific life tables. The average duration of development for each nymph stages, age-specific survival rate and average age-specific reproductive rate were calculated. The average duration of development and the average daily fecundity were calculated using the arithmetic mean. The average rate of development used in this paper was computed as: fl (2-1) where D is the average rate of development, n is the sample size, dis are observed developmental duration (in days). The age-specific survival rate was calculated as: (2-2) where 4 is the age-specific survival rate of day x, Arx and Arx_, are the number of survival aphids of two consecutive days. Based on information from the life tables, the intrinsic rate of population increase rn, , a comprehensive parameter that summarizes the developmental rate, survival rate and fecundity of green peach aphids, was calculated using Birch's approximation (Birch 1948): -r x L e .1x m x =1 (2-3) where rm is the intrinsic rate of population increase; x is the age in days; 4 is the age specific survival rate; m" is the age temperature and that between the intrinsic rate of population increase and temperature were fitted to Logan et al.'s two models (Logan et al. 1976): the model of exponential outer expansion (see Eqn. 2-4) and the sigmoid outer expansion (see Eqn. 2-5).

Within the range of temperature studied, the immature stage of the apterous parthnogenetic viviparous form of M persicae attained

	its highest
	developmental rate at 24°C, it took in average 5.3333+0.1421 days for the aphid to finish
	the development of its immature stages. Below 24 °C, the developmental rate of the
	immature stage increases with temperature, it took as long as 15.1667+0.1741 days for
	the aphids to finish the nymph development at 12.5°C; above 24 °C, the immature
	developmental rate decreases as temperature increases, it took 7.6667+0.1421 days for the
	aphids to finish their nymph development at 27.5°C. At 30°C, all the 20 aphids died before
	finishing the development of the second nymph stage (Table 2-1).

Table 2 -

 2 1 Parameter estimates (M+SE) of the life table ofM persicae under laboratory conditions.

	(1992, Montfavet)

Developmen tal rate (dah

	0.2
	0.18 -
	0.16 -
	0.14 -
	0.12
	0.1 -
	0.08
	0.06
	0.04
	0.02 -
	0
	10	12	14	16	18	20	22	24	26	28

Table 2 -

 2 2 Parameter estimates for the developmental rate as a function of temperature of M

			T., -T
	persicae, using: D (T) = [ePr e -Ar (Logan' exponential outer expansion).
					(1992, Montfavet)
						R2
	Mean	0.6730	0.1856	29.4770	5.3700	0.995
	SE	2.5631	0.4335	12.1324	1.2342
	D(T): the developmental rate; T is the temperature ( °C);

-4 that under lower temperatures, most of the death happened during the late adult life and the survival curve appeared more of Deevey's type I, while under higher temperatures, most of the death occurred during the immature stages and the survival curve appeared more close to Deevey's type III.

											125C
											-16.0C
											-6-1aoc
											__e__ 20.0C
											24.0 C
											o 26.0 C
											--27.5C
	0	10	20	30	40	50	60	70	80	90	1(X)
					'rime (days)
	Fig. 2-4 Age-specific survival rate of.ilf. persicae in relation to temperature(t). Observation made under
	laboratory conditions. 4=Na..//N., is the age specilic survival rate of age x. The aphids are reared on peach
	seedlings cultivated in nutritive solutions. Photoperiod is set ai 14:10.

Table 2

 2

	-

Table 2 -

 2 3 Parameter estimates for the intrinsic population growth rate as a function of temperature

	T.-T

Table 3 -

 3 1 Number of M. persicae offered to each larva of H. axyridis of different larval stage at different temperatures. Values in the table are numbers of green peach aphids offered to H. axyridis. LI ,

	(Montfavet, 1993)

L2, L3, L4 denote

  the larval stage 1-4 respectively.

Table 3 -

 3 2. Parameter estimates for functional responses of Lai -val H. wyridis to M persicae under constant temperatures ( °C).

	(1992, Montfavet)

Table 3 -

 3

	Parametcrs	L,	L2	L3	L4
	a (T)=	u T e I-• 1 +	_ r	.		()
	1 11		0.1982+0.1162 31.778 +9.8700	0.1022 +0.0567 16.236 +8.228	I\ 0.0867 9.1798	+0.0362 +6.2851	0.0489 +0.0172 -2.6996 +4.9397
	/13		1370.3+2150.1	2139.3 +3454	..."..., _ e-33191.5	12636 +2921.1
	714		202.04+54.578	255.28 +83.30	210.14	+74.989	284.56 +66.739
	R2		0.9818	0.9648	0.9457	0.8691
		1+v e
			V.
		v 3 .T.e
	V I	3.3E+09 +3.6E+09	3.3E+09 +4.0E+09	3.3E+09	+6.2E+09	3.3E+09 +1.9E+09
	V 2		619.53 +97.192	603.44 +37.7064	610.04	+57.005	620.45 +20.565
	V 3		97.689 +47.770	215.47 +69.596	255.36	+109.26	636.06 +177.03
	V 4		55.658 +6.3184	59.198 +3.9735	53.001	+5.4351	52.142 +3.5801
	R2		0.9752	0.9968	0.9924	0.9967

3 Parameter estimates and goodness of fit of the models for the temperature -dependence of a and Th. (1992, Montfavet) a (7): the instantaneous attack rate as a fimction of temperature; Th(T): the handling time as a function of Temperature; u 1 , ui, u3, u4, y1, y2, y3, y4 are parameters for Eqn. 3-2a and 3-2b, their value are estimated by fitting the a and Th values listed in Table 1 to Eqn. 3-2a, b using Newton's nonlinear parameter estimation procedure. R 2 is the detennination coefficient of the nonlinear regression. LI , L2, L3, L4 denote the larval stage 1-4 respectively.

Table 4

 4

		-1 Average developmental rate (M+SE) of H. axyridis in relation to temperature and the
	number ofM aryridis offered.
						(1993, Monfavet)
		10	20	40	80	160	200
	L,
	12.5 °C 0.0968 +0.0048 0.1111 +0.0046 0.1200 +0.0029 0.1220 -1-0.0023 0.1250 ±0.0041 0.1250 ±0.0058
	15.0 °C 0.1600 +0.0060 0.1739 +0.0056 0.1818 +0.0075 0.1875 ±0.0070 0.1923 ±0.0054 0.1923 ±0.0054
	18.0 °C 0.1875 +0.0126 0.2222 +0.0112 0.2381 +0.0082 0.2500 ±0.0176 0.2500 ±0.0176 0.2500 ±0.0246
	20.0 °C 0.2105 +0.0084 0.3125 +0.0136 0.3846 +0.0334 0.4000 ±0.0372 0.4000 ±0.0372 0.4000 ±0.0375
	22.0 °C 0.4000 +0.0373 0.4286 +0.0351 0.4706 +0.0323 0.5000 ±0.0000 0.5000 ±0.0930 0.5000 ±0.0930
	25.0 °C 0.5000 +0.0000 0.5405 +0.0822 0.6000 +0.1054 0.6000 ±0.1054 0.6667 ±0.1118 0.6667 ±0.1118
	27.5 °C 0.5714 +0.0824 0.6667 +0.0824 0.8000 +0.0903 1.0000 ±0.0000 1.0000 ±0.0000 1.0000 ±0.0000
	L2
	12.5 °c 0.1176±0.0031 0.1379 +0.0031 0.1481 +0.0040 0.1538 +0.0053 0.1579 ±0.0050 0.1579 ±0.0050
	15.0 °C 0.1765 +0.0070 0.2353 +0.0087 0.2667 +0.0140 0.3077 +0.0146 0.3333 ±0.0366 0.3333 ±0.0335
	18.0 aC 0.2667 +0.0140 0.3125 +0.0136 0.3333 +0.0334 0.3333 +0.0465 0.3636 +0.0278 0.3636 +0.0278
	20.0 °C 0.3077 +0.0146 0.3846 +0.0351 0.4444 +0.0294 0.4762 +0.0192 0.5000 +0.0000 0.5000 +0.0000
	22.0 °C 0.3636 +0.0278 0.5000 +0.0930 0.6667 +0.1118 0.8333 +0.0824 1.0000 ±0.0000 1.0000 ±0.0000
	25.0 °C 0.4000 +0,0373 0.6667 +0.1118 0.8333 +0.0824 1.0000 +0.0000 1.0000 ±0.0000 1.0000 -1-0.0000
	27.5 °C 0.3636 +0.0278 0.5000 +0.0000 0.6667 +0.1118 0.8333 +0.0903 1.0000 +0.0000 1.0000 +0.0000
	L3
	12.5 aC 0.0667 +0.0026 0.0833 +0.0026 0.0976 ±0.0058 0.1053 ±0.0049 0.1071 ±0.0047 0.1081 ±0.0019
	15.0 °C 0.0968 +0,0039 0.1053 +0.0025 0.1212 +0.0059 0.1739 ±0.0056 0.1818 ±0.0075 0.1818 ±0.0075
	l8.0 °	0.1481 +0.0066 0.2143 +0.0105 0.3125 +0.0136 0.3333 ±0.0334 0.3333 ±0.0334 0.3333 +0.0000
	20.0 °C 0.1550 +0.0107 0.2273 +0.0214 0.3333 +0.0334 0.3846 ±0.0339 0.4286 ±0.0351 0.4444 ±0.0360
	22.0 °C 0.1667 +0.0182 0.2500 +0.0176 0.4000 +0.0373 0.5000 ±0.0000 0.6000 ±0.1054 0.6667 ±0.1118
	25.0 oc 0.2000 +0.0109 0.2857 +0.0186 0.4286 +0.0351 0.6667 ±0.1118 1.0000 ±0.0000 1.0000 ±0.0000
	27.5 °C 0.2000 +0.0000 0.3077 +0.0146 0.5714 +0.0824 0.8000 ±0.0904 1.0000 ±0.0000 1.0000 ±0.0000
	L4
	12.5 °C 0.0351 +0.0021 0.0448 +0.0019 0.0523 +0.0021 0.0556 ±0.0017 0.0580 ±0.0017 0.0597 ±0.0013
	15.0 °C 0.0521 +0.0034 0.0702 +0.0025 0.0800 +0.0034 0.1111±0.0056 0.1143 ±0.0048 0.1176 ±0.0075
	18.0 °C 0.0727 +0.0033 0.1071 +0.0046 0.1538 +0.0132 0.1739+0.0068 0.1818+0.0182 0.1818+0.0091
	20.0 °C 0.0816 +0.0028 0.1250 +0.0050 0.1639 +0.0105 0.2000 ±0.0134 0.2105 ±0.0091 0.2105 ±0.0123
	22.0 °C 0.0952 +0.0090 0.1379 +0.0077 0.1739 +0.0111 0.2222 ±0.0137 0.2727 ±0.0215 0.2727 ±0.0215
	25.0 °C 0.1212 +0.0036 0.1667 +0.0091 0.2222 +0.0137 0.2500 ±0.0000 0.2727 ±0.0215 0.2857 ±0.0228
	27.5 °C 0.0606 +0.0023 0.0968 +0.0040 0.1500 +0.0061 0.1667+0.0091 0.2000 +0.0134 0.2222 +0.0137

N denotes the number of green peach aphid offered; values in the table are average developmental rate with standard errors; L 1 , L2, L3 and L4 denote the larval instar 1-4 respectively.

Table 4 -

 4 2. Parameter estimates for the average developmental rate (M+SE) of H. axyridis as a function of the number ofM persicae present:

	(1993, Montfavet)

Table 4 -

 4 3. Parameter estimates for equation 4-4 and 4-5, the maximum developmental rate Dm and the parameter b as fonctions of temperature.

	(1993, Montfavet)

' Do rs

Table 4 -

 4 4. Average daily survival rate (M+SE) of H. axyridis in relation to temperature and the number, ofM aryridis offered.

	(1993. Monfavet)

N denotes the number of green peach aphid offered.; values in the table are average dail y sunival rate; L I, L2, L3 and L4 denote the larval stadium 1-4 respectively.

Table 4 -

 4 5. Parameter estimates (M+SE) for the average survival rate of H. axyridis as a function of the number ofM persicae present: S ( N ) =11 (1+ Scl .e -s ca .N ) •

	(1993, Montfave)

Table 4 -

 4 6. Parameter estimates (M+SE) for equation 4-8 and 4-9, the parameter Sc, and Sc2 as functions of temperature.

	(1993, Montfavet)

SC11

, & LI Sc 13, Sc21 , Sc22, Sc23 are constants from the curve fitting; R 2 is the deterrnination coefficient for the nonlincar correlation; Newtons method vas used in estimating parameters. L1 L2, L3 and L4 dcnote the larval stadium 1-4 respectively. Fig.

4

-8 Daily sunival rate of H. axyridis in relation to temperature (oC) and the density of M. persicae. Graphes were generated from Eqn. 4-6, and parameters in table 6.

Table 1 .

 1 Air temperature measured using a self-recording thermometer placed at the height of 76 cm under the tree in the cage.

	Date	Temperature ( °C)
	17-May	19.4
	18-May	19.2
	19-May	18.8
	20-May	18.6
	21-May	16.2
	22-May	16.5
	23-May	17.6
	24-May	19.4
	25-May	22.8
	26-May	23.0
	27-May	23.2
	28-May	21.3
	29-May	21.9
	30-May	21.1
	31-May	22.6

  France au début des années 1980 par le Laboratoire de Biologie des Invertébrés de l'INRA d'Antibes, comme agent potentiel de lutte biologique. Les aspects fondamentaux de la biologie, de l'écologie et du comportement ont été étudiés en détail(Schandler & Ferran 1985, 1988). Les techniques d'élevage de masse à partir d'oeufs d'Ephestia ont été développées permettant la production commerciale. Des études de laboratoire et de terrain ont été conduites sur les possibilités d'utilisation de cette espèce pour lutter contre divers ravageurs, principalement les pucerons, de nombreuses cultures. Un effort a été fait pour tenter d'utiliser cette coccinelle que ce soit par la lutte biologique classique ou par des lâchers abondants. Cependant, à ce jour, nous n'avons connaissance d'aucun document ou démonstration manifeste prouvant le succès substantiel de l'utilisation de cette coccinelle dans la lutte contre les insectes ravageurs en France. Des études plus détaillées sur l'évaluation de son efficacité en tant qu'agent potentiel de lutte biologique contre différents ravageurs devraient être entreprises avant qu'une conclusion valable ne soit formulée sur l'utilité potentielle de cette espèce comme agent de lutte biologique en France. La présente étude portera plus particulièrement sur l'évaluation de l'efficacité d'H. axyridis comme agent de lutte biologique, par lâchers inondatifs, contre le puceron vert du pêcher.Comme alternative, des tables de vie peuvent être établies pour les populations du ravageur et du prédateur lâché en conditions naturelles ou semi contrôlées pour évaluer l'impact du prédateur sur l'évolution démographique du ravageur. Dans ce cas, une surveillance intensive des colonies de pucerons marqués, éventuellement sur plantes ou parties de plantes encagées avec/sans prédateur atteste plus formellement de l'impact du prédateur sur les populations du ravageur. En troisième alternative des populations peuvent être manipulées en laboratoire ou en conditions extérieures strictement contrôlées par des techniques d'exclusion pour déterminer les relations quantitatives pour déterminer les composantes variables majeures du système ; le système est habituellement bien défini et des composantes facilement mesurables et contribuant fortement au comportement du système sont identifiées au sein d'interactions complexes ; les relations mesurées entre les variables constitutives sont synthétisées par un modèle. La première approche est techniquement simple, mais économiquement coûteuse et écologiquement dangereuse si l'essai doit être conduit à très grande échelle en incluant plusieurs options de lâcher ; les résultats de l'évaluation d'efficacité de cette méthode sont directement liés à la situation réelle en pratique, mais permettent peu l'interprétation des conséquences (succès ou échec) du lâcher. La deuxième approche indique clairement l'effet de l'introduction de prédateurs sur la population proie dans un environnement expérimental particulier, niais les résultats dépendent souvent de la situation particulière et ne peuvent être généralisés, de telles expérimentations rencontrant fréquemment des contraintes techniques fortes et étant limitées dans le temps et l'espace. La troisième approche peut permettre l'accumulation d'un grand nombre d'informations concernant les relations quantitatives entre les différentes variables, ce qui est très utile pour répondre à des questions spécifiques telles que "La température est-elle un facteur clé pour l'efficacité du prédateur ?". Les données recueillies par cette méthode peuvent être considérées comme plus générales que celles obtenues d'après les deux précédentes approches, puisque habituellement obtenues sous "conditions idéales" transposables à (presque) toutes les situations. Quelques facteurs spécifiques du système ou de la situation, pouvant ne pas être considérés dans un premier temps, peuvent l'être par la suite selon la nécessité. Cette approche dont le coût est moindre permet souvent une meilleure interprétation des phénomènes observés, ce qui est souvent très utile aux recherches sur le développement des stratégies d'utilisation d'un prédateur comme agent de lutte biologique, et peut conforter la théorie générale de la lutte biologique. Elle présente un défaut qui découle de sa vocation générale, à savoir un moindre réalisme que les deux autres approches, nombre d'éléments considérés comme moins fondamentaux n'étant pas pris en compte dans le modèle. L'utilisation d'une seule approche impose des contraintes et des limitations. Chaque approche est en fait plus appropriée pour répondre à un type de question, pour être utilisée dans telle situation ou à telle étape du projet de recherche. Elles sont plus complémentaires que concurrentes, l'approche modélisation pouvant générer des hypothèses validées ultérieurement par les autres approches. Les lâchers sur le terrain permettront une appréciation finale de l'efficacité du prédateur en conditions naturelles. Les information données par les tables de vie ou le modèle permettent généralement d'éliminer des options de lâcher qui pourraient être retenues bien que sans intérêt, et mieux définir les problèmes posés, ou d'expliciter plus clairement les options à vérifier par les lâchers de terrain. L'intégration des 3 approches a été adoptée par l'équipe de recherche de la Station de Zoologie de l'INRA d'Avignon. Cette thèse traitera seulement de la partie de l'étude concernant l'approche modélisation. Seront considérées plus particulièrement les capacités de H. cayridis comme agent de contrôle biologique contre le puceron vert du pêcher par lâchers inondatifs, en terme de pression potentielle exercée par le prédateur sur le potentiel de croissance de la population d'aphides, chaque population étant réciproquement modifiée par l'autre et par la température. Le potentiel de croissance des populations de pucerons est représenté par le taux intrinsèque d'accroissement de population, fonction de la température et est soumis à l'effet de la compétition intra-spécifique. Le potentiel de pression prédatrice est exprimé comme indice global du taux d'attaque, de survie et de développement de la coccinelle. Ces éléments sont intégrés dans un modèle pouvant servir à poser ou répondre à des questions quant à l'efficacité de la coccinelle comme prédateur du puceron, ou quant à la gamme de températures permettant l'expression du potentiel de prédation de la coccinelle sur le puceron vert. APPROCHE DU MODELE DE POPULATION Un modèle est une construction intellectuelle ou analogue artificiel d'un système physique. Le but de la modélisation d'un système est toujours d'obtenir une représentation de ses éléments constitutifs les plus importants. Le modèle, plus facile à appréhender, sera utilisé en lieu et place du système pour certaines études. C'est dans ce sens qu'une copie parfaite du système est non seulement impossible mais également non nécessaire. De ce fait des simplifications considérables sont toujours requises, En fait presqu'aucun modèle ne s'insère parfaitement dans aucune des catégories. La plupart des modèles de simulation utilisent comme cadre des modèles analytiques, et les modèles analytiques nécessitent également l'intégration de techniques de simulation. La distinction entre modèle analytique particulier. Il peut être plus utile de caractériser un modèle par sa construction. Un modèle peut être obtenu en ajustant le développement de population à des modèles théoriques simples basés sur des principes biologiques et écologiques fondamentaux. Le modèle peut également être construit directement à partir d'observations ou dérivé d'un ajustement du comportement du système. Pour la première approche, des séries chronologiques adéquates doivent être compilées et collectées, et le modèle et le système lui-même doivent être assez simples pour être analysables statistiquement. Cette méthode requiert des séries chronologiques stationnaires, ou au moins transformables en séries stationnaires, pour permettre l'étude de changements macroscopiques à long terme des populations sur des pas de temps d'une année. Elle est d'un intérêt limité pour l'étude de changements microscopiques des populations, de populations à fortes variations saisonnières ou soumises à de violentes perturbations, comme chez la plupart des insectes ravageurs. Pour la seconde approche, le système est structuré pour refléter certains détails biologiques. Il peut être décomposé en sous-unités à plus faible niveau d'organisation et à échelle de temps généralement plus courte. Les paramètres sont dans ce cas biologiquement explicites et peuvent être mesurés directement ou estimés à partir d'autres quantités. Ce type de modèle est comparativement plus simple à construire mais ne permet généralement pas d'expliquer le comportement à long terme d'un système en raison de l'intervention de plusieurs niveaux d'organisation et de différentes échelles de temps et d'espace. Il doit pour cela être utilisé plus spécifiquement sur des échelles limitées, qui constitueront le contexte de notre étude.

	un analogue exact du système étant aussi difficile à comprendre et se comportant aussi lentement que Les modèles peuvent également être classés selon leur complexité. Les modèles généralistes à large
	le système original. échelle étaient développés dans les années 70 et au début des années 80. Destinés à une
	compréhension générale du système, ils incorporaient un très grand nombre de paramètres et de
	Différentes approches de la modélisation de la dynamique des populations (qu'il s'agisse d'une nombreuses interactions. Ils sont apparus plus difficiles à comprendre et à manipuler que les systèmes
	espèce seule ou d'un système pluri spécifique) peuvent être distinguées. On distingue tout d'abord les réels et sont d'un intérêt limité. La tendance actuelle est de revenir à des modèles à objectifs
	L'APPROCHE modèles analytiques et les modèles de simulation. spécifiques caractérisés par un nombre minimum de paramètres.
	Les modèles analytiques mettent en jeu un nombre limité de variables et de paramètres. Les relations
	EVALUATION DE LI EFFICACITE DU PREDATEUR entre les variables y sont mathématiquement explicitées de manière à ce que le modèle soit assez
	Dans la lutte biologique utilisant des lâchers inondatifs de prédateur, le prédateur n'est habituellement simple pour être utilisable.
	pas destiné à être introduit en tant qu'agent régulateur à long 'terme de la population de ravageurs, Les modèles de simulation peuvent intégrer un grand nombre de variables et de paramètres. Les
	mais plutôt en tant qu'agent de suppression temporaire. Donc la dynamique à long terme du prédateur relations entre variables n'ont pas besoin d'être mathématiquement explicitées, mais peuvent être
	et de la proie n'est pas d'un grand intérêt pour l'évaluation de l'efficacité du prédateur. La mesure de intégrées implicitement dans l'algorithme du programme informatique.
	l'efficacité d'un prédateur utilisé dans la lutte biologique par lâchers inondatifs peut être réalisée selon
	différentes approches ou associations. Dans le cas de lâchers tentés directement sur le terrain, les
	résultats obtenus à partir d'échantillonnage seront des indications de cause à effet plutôt que des
	preuves flagrantes.

  'infestation de chaque plant pour l'expérimentation est réalisée par dépôt d'une femelle adulte pour la production de jeunes larves. Ces adultes et les larves excédentaires sont retirés au bout de quatre heures, une seule jeune larve étant laissée sur chaque plant. Le développement des insectes est suivi dans des cellules incubatrices à 12.5, 16, 20, 24, 26, 27.5 ou 30°C, à raison de 20 répétitions par température. Les mues, la mortalité, et la production de nouvelles larves par les adultes sont enregistrées journellement.Ces données démographiques pour chaque température sont utilisées pour la réalisation de tables de vie. La durée moyenne de développement de chaque stade larvaire, le taux de survie par âge et le taux de reproduction par âge sont calculés. La durée moyenne de développement et la fécondité journalière moyenne sont estimées en utilisant des moyennes arithmétiques.Le taux intrinsèque d'accroissement de la population r rn, est un paramètre qui synthétise le taux de développement, le taux de survie et la fécondité du puceron vert du pêcher. Il est calculé à partir des tables de vie en utilisant l'approximation de Birch : est le taux étudié en fonction de la température; T la température (en°C); tif est défini par Logan comme le taux du processus étudié à une température de base déterminée; p correspond à une valeur critique associée aux réactions biochimiques catalysées par les enzymes ; T n, la température maximale (en °C) au dessus de la température de base du processus de vie; AT la largeur de la marge limite supérieure de température. Dans le cadre des températures étudiées, le taux de développement le plus élevé des larves parthénogénétiques de M. persicae est atteint à 24°C avec une durée de développement de 5,33 ± 0,14 jours. En dessous de cette température, le taux de croissance décroît avec la température, le développement larvaire nécessitant 15,17 ± 0,17 jours à la température de 12,5°C. La durée de développement s'accroît également au-dessus de 24°C (16,67 + 0,14 jours à 27,5°C). A 30°C les 20 pucerons meurent avant la fin du deuxième stade larvaire (Tableau 2-1). La relation entre températures et taux de développement des stades immatures est bien ajustée à l'équation de Logan (Fig.2-1). Le seuil supérieur de développement de M. persicae est La durée de développement de M. persicae diminue lorsque la température augmente (Fig.2-4). Aux températures basses, la mortalité intervient majoritairement au stade adulte, contrairement aux températures élevées où de fortes mortalités sont enregistrées sur stades larvaires.La race locale de M. persicae étudiée à Montfavet présente une adaptation à basse température sur son hôte primaire. Son taux de développement le plus élevé est atteint à 24°C et son développement ne peut s'achever à 30 0 , ce qui est conforme aux résultats obtenus par Barlow sur betterave.

	MATERIEL ET METHODES estimé à 29,48°C, la marge supérieure de température AT de 5,3700°C (Tableau 2-2) et la température (2-3) E e''.x.lx .nix =1 L'expérimentation est conduite en laboratoire sur des jeunes plants de pêchers (stade 15-20 feuilles, à laquelle le taux de développement maximal est atteint à 24,0981°C. La fécondité des femelles vivipares atteint son maximum (80 larves par femelle, Van Emden et al., issus de semis de la variété GF 305) servant de plante-hôte aux pucerons. Les colonies de femelles parthénogénétiques vivipares de M. persicae proviennent de fondatrices prélevées en mars 1992 dans le verger expérimental de l'INRA de Montfavet. Elles sont maintenues en élevage en chambre climatisée à la température de 21±0,5°C, humidité relative de 60% et photopériode naturelle. où rm est le taux intrinsèque d'accroissement de la population; x l'âge en jours; lx le taux de survie âge spécifique; mx le taux de reproduction âge spécifique. Le rin est estimé par maximum de vraisemblance. Les deux modèles de Logan (1976) sont ajustés sur 1969) à des températures inférieures à 20°C et décline au-delà de cette température. Un fort taux de Fécondité des femelles parthénogénétiques. Elle est décrite en termes de fécondité totale et de reproduction journalier est cependant atteint en dessous de 24°, la reproduction des femelles étant profil de fécondité par âge. Elle s'accroît avec la température jusqu'à 20°C, puis décroît rapidement lorsque la température s'élève (Fig. 2-2, Tableau 2-1). A température élevée, la reproduction se alors plus concentrée dans le temps (Fig 4-3).
	les données reliant le taux de développement et la température d'une part, le taux d'accroissement concentre pendant les premiers jours de vie des adultes (Fig. 2-3). Jusqu'à la température optimale de
	intrinsèque de la population et la température d'autre part. Le modèle d'expansion exponentielle est 24°C, l'augmentation de la température se traduit par un raccourcissement de la période de
	exprimé par : reproduction et par une augmentation du pic de fécondité. Au-delà de 24°C, l'augmentation de la
	= v_er &PT. -e fe;" température entraîne toujours un raccourcissement de la période de reproduction mais la valeur du pic 7-", -7-A'r (2-4) de fécondité décroît.
	Le taux moyen de développement utilisé ici est calculé selon la formule: Taux de survie par âge. Taux de croissance intrinsèque des populations. La relation entre le taux de croissance intrinsèque r", et la température est analogue à celle qui relie taux de développement et température. La où D(T) Le dernier modèle est le modèle d'expansion sigmoïde: valeur la plus élevée du r," est observée à 24°C = 0,3744). En dessous de 24°C, la valeur de r n,
	d augmente avec la température et au-delà, elle décroît très rapidement lorsque la température augmente. (2-1) ID; T Le seuil maximum de température pour un accroissement non-négatif de la population est estimé à
	i=1 11)(T) 27,92°C, température inférieure au seuil maximum de développement larvaire. En conséquence la cxf[14-ke-efr 1 --e ./17-(2-5)
	largeur de la marge supérieure de température est plus faible pour rm que pour le développement où d est le taux moyen de développement, n la taille de l'échantillon, D i 's les durées de développement observées (en jours). où a est une constante représentant la vitesse de décroissance du taux du processus étudié à Tm ; ic = larvaire (Tableau 2-2).
	Le taux de survie âge spécifique est calculé comme suit : (a-tAl r, d(T), p, T m et AT ont la même signification que ci -dessus. Une méthode de quasi-La température procurant le plus fort taux d'accroissement intrinsèque est estimée à 23,79°C. En
	Newton est utilisée dans les deux cas. comparaison, le taux net de reproduction qui représente la multiplication de la population par
	génération atteint son maximum (82,15 par génération) à 20°C (Tableau 2-2). Un autre paramètre utile (2-2) N pour la compréhension de la dynamique de population est la durée moyenne d'une génération. Elle est
	la plus courte (10,81 jours) à 24°C et s'accroît lorsque la température diminue. Le temps de
	où I. est le taux de survie âge spécifique du jour x, N A et Nx., les nombres de pucerons survivants doublement de la population est un indice plus immédiat pour estimer la vitesse de développement de
	aux jours x-1 et X. population. Il est inférieur à 2 jours à 24°C, et s'établit respectivement à 4.8, 3.5, 3.1 et 2.1 jours à
	12.5, 16, 18, 20°C.

L

RESULTATS

Taux de développement des stades immatures.

DISCUSSION

  de l'efficacité de H. axyridis comme agent de contrôle biologique de M. persicae et la détermination des stratégies de lâchers requièrent des informations sur l'efficacité du prédateur en relation avec la densité de proie et les températures environnantes. La réponse fonctionnelle décrit la relation entre le nombre de proies attaquées par prédateur par unité de temps de recherche et la densité de proie imposée au prédateur. Trois principaux types de réponses fonctionnelles ont été reconnus parmi lesquels la réponse de type II est la plus utilisée pour modéliser la prédation des invertébrés.L'équation de Holling fournit la description la plus courante de la réponse de type II: axyridis à M. persicae en fonction de la température, et nous essayons de modéliser le taux d'attaque instantané et le temps de prédation en fonction de la température selon l'équation 3-2 a,b.Les larves de H. axyridis sont produites dans un élevage de masse au Laboratoire de Biologie des Invertébrés d'Antibes, et M. persicae provient des ilevages conduits sur plants de pêchers au Laboratoire d'Avignon. Les observations sont réalisées dans des enceintes en plastique de 80 mm de diamètre et 50 mm de haut, contenant chacune trois jeunes feuilles de pêchers alimentées par une solution nutritive. Des aptères du 3-4ème stade de M. persicae sont introduits tous les soirs dans le dispositif, à six densités différentes. Chacun de ces traitements est répété six fois. Pour homogénéiser l'âge des prédateurs, les larves du stade précédent prêtes à muer sont isolées, et les stades d'observation prélevés 4 à 8 heures après la mue. Une larve de H. axyridis est introduite par enceinte.La consommation est contrôlée journellement dans chaque enceinte et le nombre initial de pucerons restauré chaque jour jusqu'à la fin du stade de H. axyridis. La même procédure est reproduite pour les quatre stades larvaires et les adultes de H. axyridis.

		MATERIELS ET METHODES
		N a =	a.N h.N		(3-1)
	Chaque essai est réalisé aux températures de 12.5, 15, 18, 20, 25, 27.5 et 30 ± 0.5°C, à 70%
	d'humidité, en photopériode 16:8 (jour:nuit).
	L'équation de type II de Holling de la réponse fonctionnelle est appliquée aux données de
	consommation journalière de chaque stade du prédateur aux différentes températures, en utilisant la
	transformation de Woolf :
	N =Th.N + cr l				(3-3)
	Elle assure de meilleurs paramètres d'estimation que les autres transformations linéaires ou la
	régression non linéaire.		_u
		cz(	u.T.e 1	144	(3-2a)
		RESULTATS	1 -I-u 3 . e
	Les	données	de	la	réponse	fonctionnelle	de	tous	les	stades	de
						V2
				1 -I--v1
			-			1, 4.	(3-2b)

et De Loach (1974)

étudièrent le taux de croissance intrinsèque de M. persicae sur betteraves et pommes de terre respectivement. La température optimale qu'ils établissent à 25°C pour le taux de croissance intrinsèque est plus élevée que celle que nous observons (24°C) ou que nous calculons (23,79°C). La différence peut provenir de l'effet de la plante-hôte ou de la variabilité entre races géographiques de M. persicae. INTRODUCTION L'évaluation où N est le nombre de proies imposées au prédateur, Na le nombre de proies consommées par unité de temps de recherche, a le taux d'attaque instantané du prédateur, et Th le temps nécessaire à l'ingestion et à la digestion d'une proie. Organismes poïkilothermes, les insectes ont un métabolisme dépendant des conditions thermiques. M. persicae est apparu bien adapté aux basses températures en terme de taux de croissance de population. Les informations sur la liaison entre température et efficacité prédatrice et taux de développement de H. axyridis sont fondamentales pour l'évaluation de cette espèce comme agent de lutte biologique. Un modèle général de réponse fonctionnelle liée à la température incorpore à la réponse de type II de Holling les équations de cinétique enzymatique utilisées pour décrire la relation entre température et croissance ou développement. Ce modèle, que nous utiliserons, décrit le taux d'attaque instantanée a et le temps de prédation Th comme fonctions de la température : 3 Ce chapitre décrit la réponse fonctionnelle de H.

LA TEMPERATURE ET DE LA DENSITE DE PROIE SUR LES TAUX DE SURVIE ET DE DEVELOPPEMENT DES STADES IMMATURES DE H. A XY RIDIS INTRODUCTION L

  Th est moins sensible à un accroissement de température chez les jeunes stades que chez les stades âgés.Dans le cadre de cette expérimentation, les larves de M. persicae sont dispersées chaque jour dans l'enceinte. Ce n'est pas le cas des populations naturelles caractérisées par une distribution agrégative, qui peut favoriser la phase de recherche intensive du prédateur mais réduire l'efficacité de la phase de recherche extensive. L'efficacité de recherche reste généralement supérieure en cas de distribution agrégative de la proie. Cette contrainte expérimentale appliquée à la proie ne doit cependant pas modifier fondamentalement le taux de prédation. 'efficacité de H. axyridis comme agent de lutte biologique contre M. persicae par lâchers inondatifs ne dépend pas uniquement de la réponse fonctionnelle mais également de la réponse numérique, à savoir le changement de densité du prédateur en réponse à la densité de la proie. Bien que clairement définie, la réponse numérique a été peu étudiée en raison des problèmes techniques posés par son évaluation. Dans le cadre des interactions entre les pucerons et leurs ennemis naturels, deux éléments de réponse numérique sont généralement distingués, la réponse numérique agrégative et reproductive.La réponse numérique agrégative correspond à la concentration du prédateur en réponse à la densité de proies. La réponse numérique reproductive est la relation entre le taux de reproduction du prédateur et la densité de proie. On doit ajouter à ces deux principaux éléments les changements de taux de développement et de survie en fonction de la densité de proie qui sont également importants 'objet de notre analyse, qui vise à déterminer les effets de la température et de la densité de M. persicae sur les taux de survie et de développement de H. axyridis, est de définir le stade et la densité de prédateur appropriés à la maîtrise des populations de pucerons. Cette étude doit également permettre la compréhension des performances de la coccinelle après des lâchers en vergers. , aux températures constantes de 12.5, 15, 18, 20, 25, 27.5, 30 ± 0.5°C. Le taux moyen de développement est calculé comme Suit:

	d=	7Z E	(4-1)
		i=1
	où d est le taux moyen de développement, n la taille de l'échantillon, D i's les durées de
	développement observées (en jours).
	MATERIELS ET METHODES
	Le dispositif ainsi que les modalités concernant la proie et le prédateur sont identiques à ceux utilisés

-4), son accroissement influençant directement l'activité de recherche et la vitesse à laquelle les proies sont ingérées et digérées. Par ailleurs, l'accroissement de taux de développement accompagnant un accroissement de température se traduit par une exigence alimentaire accrue. On peut cependant s'attendre à ce que la consommation totale ne varie que faiblement avec la température et la densité de proie, une consommation accrue liée à ces deux facteurs résultant habituellement en un temps de développement plus court et par là même à une période de consommation réduite.

Le taux d'attaque instantané des jeunes stades est plus sensible à l'accroissement de la température que celui des stades âgés, mais le temps de prédation CHAPITRE 4 EFFET DE pour évaluer l'efficacité du prédateur. Dans le cas de lâchers inondatifs, le but n'est pas d'établir un équilibre entre la proie et le prédateur mais de supprimer momentanément la proie pendant certaines périodes critiques. Les populations introduites de H. axyridis ne se maintenant pas plus d'une génération dans les vergers, les réponses numériques agrégatives et reproductives sont d'un intérêt limité. Le nombre initial de larves du prédateur dans les vergers est déterminé par la date du lâcher et non par l'effet du déplacement ou de la reproduction des générations précédantes. Comme pour la réponse fonctionnelle, la réponse numérique d'un prédateur est affectée par la température et la densité de proie. Bien que l'effet de la température sur la réponse numérique soit considéré comme un élément majeur pour déterminer la capacité du prédateur à supprimer la population de proie, peu d'études expérimentales concernent cet aspect. Lpour l'étude de la réponse fonctionnelle. Les nombres de larves survivantes et ayant évolué au stade suivant sont relevés chaque jour, et le nombre de pucerons restauré comme précédemment après chaque observation. Cette procédure est reproduite six fois pour chacun des quatre stades de H.

axyridis

Taux de survie journalier moyen de H. axyridis en fonction du nombre initial de proies.

  Comme pour le taux de développement moyen, le taux moyen de survie journalier augmente avec la température et avec le nombre de proies offertes (Tableau 4). De même que précédemment

nous définissons ce paramètre comme une fonction du nombre de proies offertes et incorporant l'effet de la température dans les paramètres du modèle. Le taux journalier de survie s'accroît avec la disponibilité en proie selon une courbe sigmoïde :

LE MODELE

DE SIMULATION 1. CADRE GENERAL DU MODELE DE SIMULATION Le

  modèle approprié pour cette étude doit comporter une part adéquate de réalisme biologique dans la description de la dépendance à la température et à la densité de proie de l'interaction entre M persicae e: H. axyridis, tout en conservant un bon degré de tractabilité. Il y a peu à gagner avec un modèle trop complexe à manipuler et à comprendre. Un modèle déterministe est retenu de préférence à un modèle stochastique, qui requiert habituellement des informations complémentaires sur la van i don et la distribution de chaque paramètre, et augmente la complexité de la structure et du calcul du iiodèle.

LE MODELE PUCERON VERT DU PECHER L

  La seconde approche prend en compte la structure d'âge de la population, qui est alors modélisée comme un assemblage de différentes classes d'âge; l'évolution de la population est caractérisée par des paramètres démographiques dépendant de l'âge.Le choix de l'approche dépend du système étudié, des données disponibles et du but du modèle. , aucune information n'étant disponible quant au taux d'attaque ou à la préférence du prédateur pour une classe d'âge de la proie.Un modèle de réponse fonctionnelle du type II de Holling est utilisée pour modéliser le taux d'attaque de H. cvcyridis sur M persicae en fonction de la température. Les interactions complexes comme les interférences entre prédateurs, la préférence du prédateur pour une taille de proie et l'efficacité de recherche du prédateur en fonction de l'agrégation du puceron sont ignorées. En pratique, le nombre de prédateurs qu'il est possible ou souhaitable de lâcher est rarement suffisant pour créer une interférence entre prédateurs. Puisque nous modélisons les populations de pucerons comme une entité homogène dans laquelle chaque individu moyen contribue de manière égale à la population, la perte d'individus moyens due à la prédation peut constituer une approximation de la consommation des pucerons par les larves de H. 'évolution de la population de puceron vert du pêcher est simulée ainsi : les oeufs de pucerons ayant passé l'hiver éclosent en verger de pêcher au début du printemps quand une certaine valeur de degrés-jours (365 degrés jours dans le modèle) est atteinte, le calcul n'étant fait qu'au dessus du seuil de température de 4,5°C. La population se développe durant la saison selon un mode parthénogénétique vivipare jusqu'en juin, après 1740 degrés jours. Tous les individus émigrent alors hors des vergers de pêcher. La migration entre colonies pendant la période étudiée est simulée par

	Dans cette étude, notre but est de coupler la modélisation des populations du puceron à la
	modélisation des réponses fonctionnelles et numériques de H axyridis afin d'évaluer les effets de la
	température sur leurs interactions. A cette fin, nous adoptons l'approche holistique, plus facile à

axyridis • Le modèle de réponse numérique de H. axyridis La dynamique de population des pucerons est modélisée en utilisant deux approches. Une approche suppose qu'une population de pucerons a une structure d'âge stable et un chevauchement complet des générations, et peut être modélisée comme une entité homogène. L'évolution de la population est caractérisée par son taux d'accroissement. manipuler et dont le comportement est plus facile à appréhender. Un modèle de population plus complexe et détaillant la structure d'âge du puceron n'améliorerait pas la performance globale du modèle de simulationaxyridis Pour évaluer l'efficacité de H. axyridis comme agent de contrôle biologique par lâchers inondatifs, aucun recrutement de population de H. axyridis n'est incorporé dans le modèle. L'évolution des cohortes de coccinelles lâchées est modélisée avec un modèle de classe d'âge, le contenu de la classe d'âge étant transféré globalement dans la suivante après un certain nombre de degrés-jours, correspondant à la durée de la classe d'âge. La durée d'une classe d'âge de H. axyridis dépend de la température et de l'abondance des pucerons. Un taux de survie journalier âge-spécifique, également fonction de la température et de la densité de proie, est appliqué à la cohorte. 2. tirage aléatoire uniforme. Les larves de coccinelles peuvent être lâchées à n'importe quel moment dans la saison.

En pratique, le modèle de simulation est basé sur des pas de temps journaliers. En conséquence certaines variables, à priori estimées continûement dans le temps, seront remplacées par leur version discrète. On aura en particulier :

  Dans toutes les équations, it /représente l'intervalle de temps utilisé lors des intégrations. La durée moyenne d'une génération et la durée de développement préimaginal sont généralement considérées comme les deux candidats pour t. Nous retenons ici pour t la durée du développement préimaginal.Dans la mesure où cette durée de développement dépend de la température, qui varie dans le temps, une notion de degrés-jours sera utilisée pour déterminer l'intervalle de temps sur lequel sont calculées les intégrations sur le temps. t est calculé à partir de la relation :

	s= t-

Sc ,

Acknowledgment

Discussion

In our models developed here to describe the developmental and survival rates of H. axyridis as functions of prey density and temperature, one of the independent variables is the number of prey present instead of the number of prey consumed as was used in many similar studies. Many studies indicated that the relationship between the developmental rate and the prey consumption follows a saturation curve (Chen et al. 1985[START_REF] Hayes | A laboratory study of the predatory mite, Typhlodromus pyri (Acarina: Phytoseiidae). I. The effect of temperature and food consumption on the rate of development of the eggs and immature stages[END_REF][START_REF] Hayes | A laboratory study of the predatory mite, Typhlodromus pyri (Acarina: Phytoseiidae). II. The effect of temperature and prey consumption on the numerical response of adult females[END_REF][START_REF] Hardman | Effects of temperature and prey density on survival, development, and feeding rates of immature Typhlodromus pyri (Acari: Phytoseiidae)[END_REF]. The number of prey consumed, in the case of Holling's type II functional response, is itself a function of the number of prey present following a saturation equation. In fact, if we use Na in the place of N in with Na as the independent variable may probably be more accurate than those estimated for equation 4-3 because the developmental rate D is more directly related to the number of prey consumed than to the number of prey present and the stochasticity and randomness existing in the relationship between N and Na. However, equation 4-3 has some advantages: firstly, this loss of accuracy can be partly compensated by reducing experimental error from the manipulation of the system for obtaining the data on Na, the error involved in the estimation of parameters in equation 4-12, and the amount of calculation (and thus the round-off en -or) in the eValuation of the function; secondly, a big amount of trial work load for counting the real Na can be saved, in addition, the model with prey density instead of the number of prey attacked can be more readily used for

Appendix

Derivation of the equation describing the relationship between the developmental rate and number of prey present (equation 4-3).

Consider that the developmental rate (D) of a predator is a ffinction with the number of prey consumed (Na). Since Na is a continuous, differentiable function of N (the number of prey present) in [0, according to equation 4-12, we can define D as a function of N.

let AD be the increment of D as N increases by AN, we start our derivation from considering the relationship between AD and DI'!, which is a simpler case than the relationship between D and N. Firstly, we assume that: (1) a maximum developmental rate Dm can be attained as the number of prey present increases infinitely;

(2) the magnitude of AD with respect to AN is proportional to Dm-D (the deference between the maximum developmental rate and the actual developmental rate), i.e. an increase in prey density can trigger a larger increase in the developmental rate of the predator when the deference between the . maximum developmental rate and the actual developmental rate is bigger. [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF]300). Temp(366), Ynew(4) DIM DevRatY(4), SurRotY(4), AR(4), Th(4), DmY(4), B1(4) DIM FiY [START_REF] Diny | Temp)=FiY*(EXP(RoY*Temp)-EXP(RoY*T1nY-(TmY-Temp)/D1Y)[END_REF]. RoY(4), TinY(4), D1Y(4), Bt1(4). 812(4) DIM Sc11(4), Sc12(4). Sc13(4), Sc21(4). Sc22(4), Sc23(4) D1M Aul(4). Au2(4). Au3(4). Au4(4), Av1(4), Av2(4), Av3(4), Av4( 4 2) Survival rate as a function of temperature and density of prcy L'objectif de l'étude est d'utiliser la modélisation pour évaluer le potentiel de H. axyridis comme prédateur de M. persicae dans les limites du potentiel de développement de la proie, de la faculté de prospection du prédateur, du maintien du prédateur en fonction de l'abondance de la proie, de la dépendance de ces aspects vis-à-vis de la température, et de fournir des directives pour des évaluations ultérieures en plein champ.

S(N) =--

(4-7)

1+ SC1 .e -Sc2 N où S(N) est le taux de survie journalier moyen du prédateur fonction du nombre de proies offertes N; Sc 1 un paramètre dont l'inverse est relié au taux de survie journalier moyen quand il n'y a pas de proie disponible, Sc2 un paramètre décrivant la vitesse à laquelle S(N) s'approche de sa valeur maximale. Ce modèle décrit bien la dépendance à la proie du taux de survie journalier moyen de H. axyridis (Fig. 4, Tableau 5).

Taux de survie de H. axyridis en fonction de la température. Pour un nombre de proies disponibles donné, le taux de survie de H. axyridis dépend de la température (Fig. 5,6) de son environnement. Les paramètres Sc 1 et Sc2 peuvent également être modélisés en fonction de la température (Fig 5,6). Les modèles empiriques suivants ont été utilisés :

où Sc, 1 , Sc 12 , Sc 13 , Sc 21 , Sc22 , et Sc23 sont des paramètres calés lors de l'ajustement de la courbe sans signification biologique explicite (Tableau 6).

Le taux de survie des larves de H. axyridis en fonction de la température et de la densité de proies est modélisé en introduisant Sc 1 (T) et Sc2(T) dans l'équation 5 :

1 1-i-Scl (T) .e -S c'2 (T).N Le comportement de ce modèle dans les intervalles définis biologiquement est illustré en Fig. 7 DISCUSSION Dans les modèles développés ici pour décrire les taux de développement et de survie de H. axyridis en fonction de la densité de proie et de la température, une des variables indépendantes est le nombre de proies présentes, plutôt que le nombre de proies consommées utilisé dans plusieurs études similaires. La relation entre taux de développement et consommation de proies suit habituellement une courbe de saturation. Dans le cas de la réponse fonctionnelle de Holling de type II, le nombre de proies consommées est lui-même une fonction du nombre de proies présentes suivant une équation de directement relié au nombre de proies consommées qu'au nombre de proies présentes. L'équation 4-3 a cependant quelques avantages : la perte de précision peut être partiellement compensée en réduisant l'erreur expérimentale liée à la manipulation du système pour obtenir les valeurs de Na, l'erreur liée à l'estimation des paramètres de l'équation 4-12, et le nombre de calculs dans l'évaluation de la fonction. De plus, une large part de la charge expérimentale liée à l'évaluation de Na peut être économisée et le modèle considérant la densité de proie plutôt que le nombre de proies attaquées peut être utilisé plus rapidement pour l'évaluation des taux de survie et de développement du prédateur en conditions de plein champ.

Dans cette étude, nous utilisons le taux de survie journalier moyen calculé par la moyenne géométrique des taux de survie spécifiques de chaque stade larvaire. Cette mesure nous permet d'incorporer directement le taux de survie dans le modèle de simulation, habituellement résolu sur un pas de temps de 1 jour, le taux de survie étant calculé selon la température et la densité de proie du jour correspondant. Nous devons porter attention au fait que le taux de survie journalier moyen n'est qu'une approximation, car il peut être spécifique de l'âge physiologique plutôt qu'une valeur unique pour le stade. Nous adoptons cette approche simplifiée en raison de l'absence de données sur le taux de survie par âge, et de l'impossibilité de les acquérir sans un dispositif contraignant. Beddington (1976) suggère que le taux de survie du prédateur en fonction de la densité de proie suit une courbe sigmoïde basée sur une distribution normale du nombre moyen de proies consommées.

Ce modèle n'a pas fait l'objet de nombreuses validations par des données expérimentales, la signification des paramètres du modèle étant imprécise. Dans leur étude sur les interactions prédateur/proies entre Typhlodromus pyri et sa proie, Panonychus uhni, [START_REF] Hardman | Effects of temperature and prey density on survival, development, and feeding rates of immature Typhlodromus pyri (Acari: Phytoseiidae)[END_REF] proposent une courbe de saturation pour décrire le taux de survie en réponse à la densité de proie.

Nos résultats se conforment à une courbe sigmoïde, et nous en déduisons un modèle qui diffère du modèle de Beddington pour l'interprétation des mécanismes décrivant le taux de survie de H. axyridis en réponse à la densité de M. persicae.

La population de M persicae est modélisée par un modèle logistique à effet retard, en supposant que la valeur actuelle du taux intrinsèque d'accroissement de la population est dépendant de la température moyenne calculée sur un intervalle de temps de largeur T finissant à la date actuelle. = f T.T(s)ds

(5-3)

/ -T

N dans l'équation 5-1 correspond à l'effectif moyen de la population entre t-oer et t. Une fois de plus, on pourrait utiliser une moyenne pondérée. En approximation, nous utilisons ici une simple moyenne arithmétique.:

= f 'r. N(s)ds '" la température moyenne entre t et t-t.

utilisons ici sont les formes les plus simples d'intégration par rapport au temps de la dépendance de la température ou de la densité. On pourrait s'attendre à ce qu'une moyenne pondérée utilisant une distribution de poids donnée soit une représentation plus réaliste.

LE MODELE COCCINELLE

Réponse fonctionnelle. La réponse fonctionnelle du ième stade larvaire est modélisée comme une fonction de la température instantanée et de la densité de population de pucerons verts du pêcher via une réponse de Holling de type II (Equations 3-1, 3-2a,b).

ai (T).N Na i = 1 I-ai(T).Thi(T).N

(5-9)

(7")

(5-10) (T,N) = Drrzi (T) e-P` (7. )-N (5)(6)(7)(8)(9)(10)(11)(12) DM i ( T)

7-1-z; (7-) -

vf HA (ePHA' T e PHA UMHA -T) I ATHA (5)(6)(7)(8)(9)(10)(11)(12)(13) P i (T) = Bd 1 . e -Bd2

( [5][6][7][8][9][10][11][12][13][14] dN -rin (77,).1V .(1r,"(Tr)

if EDi (T(s),N(s)) k 1 (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) où Do ) est le taux de développement du ième stade larvaire fonction de la température T(s) et de la densité de proie N(s) le jour s.

Le cadre général du modèle de simulation peut alors s'écrire: Pas de temps, d'espace et simulation. Le pas de temps de ce modèle de simulation est le jour circadien, le plus naturel et le plus pratique, et constituant également l'échelle à laquelle ont été mesurés tous les paramètres du modèle. Dans le cas où des degrés jours ont été utilisés pour mesurer le temps nécessaire à l'accomplissement de certains processus biologiques, comme par exemple l'ensemble du développement de certains stades, les degrés jours sont utilisés dans les calculs mais sont ensuite convertis en jours circadiens. Comme modèle s'intéressant aux propriétés qualitatives de base de la dépendance à la température et à la densité des interactions hôte-prédateur, nous chercherons à éviter la complexité spatiale, telle que l'hétérogénéité de l'habitat et le déplacement du population moyenne de pucerons sur la même période est utilisée pour prendre en compte la dépendance retard à la densité de population de pucerons (voir équation 5-1). La température journalière, la densité de population de pucerons, les paramètres utiles et le compteur de temps sont des entrées de cette subroutine. Le taux intrinsèque d'évolution de la population, la population moyenne de pucerons sur un intervalle de temps sont des sorties ainsi que des valeurs globales partagées. Comportement dynamique du modèle de simulation. Le modèle de simulation génère les comportements dynamiques suivants : en l'absence de lâcher de coccinelle, les populations du puceron vert du pêcher apparaissent en vergers fin février -début mars et en disparaissent mi -juin.

Subroutine

Pendant toute cette période, la population de M persicae connaît des fluctuations avec 3 -4 pics et une plus forte abondance en avril -mai (Fig. 8). Ces résultats, quelque peu attendus, n'ont pu être comparés avec des données de terrain. La figure 5-9 montre les résultats de la simulation concernant les conséquences du lâcher de coccinelle pour contrôler M. persicae. Le nombre de larves requises augmente avec la population de pucerons au moment du lâcher. Si le prédateur est lâché lorsque la population de pucerons s'élève à 25 par colonie, un résultat très satisfaisant est obtenu avec le 3ème stade en effectuant trois lâchers de 0.25 larves de coccinelle par colonie. ( Fig. 5-9 a). Si le lâcher intervient quand l'effectif de pucerons s'élève à 100 par colonie, un résultat similaire est obtenu par trois lâchers à respectivement 1, 0.5 et 0.5 larves par colonie (Fig. 5-9 b). Si la population de pucerons atteint 250 par colonie, un résultat moins satisfaisant que précédemment est obtenu en portant l'effectif des trois lâchers de coccinelles à respectivement 1.5, 1 et 1 larve par colonie (Fig.

5-9 c).

A 500 pucerons par colonie, trois lâchers de 2.5, 2 et 2 larves du troisième stade, nombres presque irréalistes, donnent des résultats presque inacceptables (Fig. 56789). Ces simulations montrent également qu'un nombre plus élevé de prédateurs doit être lâché en début de saison à basse température que plus tard dans la saison. On peut se demander si un meilleur résultat serait obtenu en augmentant l'effectif de prédateurs du premier lâcher. Cette question est illustrée par la Fig. 5678910.

A 250 pucerons par colonie, le nombre de lâchers est ramené de 3 à 2 si un grand nombre de prédateurs est lâché la première fois. L'effectif du premier lâcher est de 5 Li, de 4 L2 ou de 3 L3 / L4 (Fig. 5-10 a,b,c,d). L'effectif du second lâcher est de 1 dans chaque cas. L'augmentation de l'effectif du premier lâcher ne réduit pas le nombre total de prédateurs lâchés mais réduit le nombre de lâchers. La réduction à 1 du nombre de lâchers impliquerait une trop forte augmentation de l'effectif lâché.

• les larves tombent du feuillage faute de pouvoir s'y fixer convenablement.

• en raison d'un conditionnement préalable sur oeufs d'Ephestia, les larves quittent les arbres à la recherche d'habitat ou de proies plus favorables.

Les objectifs de cette expérimentation sont de deux ordres :

• comparer qualitativement aux résultats de la simulation les changements de populations de M persicae induits par le lâcher de larves de H axyridis.

• acquérir quelques indications sur les causes de la disparition des prédateurs lâchés.

M ATERIELS ET METHODES

Huit pêchers de taille similaire sont sélectionnés et taillés pour conserver approximativement le même nombre de rameaux (250 par arbre). Chacun de ces arbres est enfermé dans une cage de 2.