Asma Gasmi

Vincent Augusto

Paul-Antoine Beaudet

Jenny Faucheu

Claire Morin

Xavier Serpaggi

Franck Vassel

Sleep stages classification using cardio-respiratory variables

Keywords: Sleep stages, machine learning, supervised classification, sleep architecture, polysomnography

Analysis of sleep is important in order to detect health issues and try to prevent them. In particular, sleep dysfunctions may be the first signs of cognitive frailties for elderly persons. The polysomnography (PSG) is considered the golden standard to perform a comprehensive sleep analysis, as it is based on several sensors placements. However, for longitudinal study of sleep that is required to prevent frailty for elderly persons, such medical equipment is not suitable since it is very invasive. Recent technological advances in sensors allow to gather data with a good precision with less intrusive equipment. The main objective of this study consists in developing a new algorithmic approach to analyse sleep using data from low intrusive sensors. In this study we focus on sleep phase detection, i.e. wake, Non-Rapid Eye Movement (NREM) and Rapid Eye Movement (REM). We consider the following sources of data: heart beat rate, as well as user data such as gender, age, etc. The problem is considered as a supervised classification machine learning problem. We propose a benchmark of several machine learning algorithms and compare their performances against the medical gold standard, the PSG. To do so, we use a data-set collected from a published clinical trial. Support Vector Machine (SVM) algorithm globally outperforms all other methods with a 76.5% agreement with the PSG. As a direct perspective of this study, we plan to add other sources of data using custom sensors to improve the performance of the prediction.

I. INTRODUCTION

Sleep analysis is a promising research field to delay frailty for elderly people and prevent serious health problems. Previous studies [START_REF] Ensrud | Stone, and for the Osteoporotic Fractures in Men Study Group. Sleep disturbances and frailty status in older community-dwelling men[END_REF] underline the good correlation existing between sleep disorders and cognitive frailty, the former being both a source and a consequence of the latter. In this context, polysomnography is acknowledged as the gold standard [START_REF] Allan | A manual for standardized terminology, techniques and scoring system for sleep stages in human subjects[END_REF] to assess sleep quality. It allows monitoring brain, heart, muscle, and breathing activity, and therefore deciphering the different sleep stages and the duration of sleep, as well as possible events of sleep disorder (apnea, restless legs syndrome, parasomnia...). However, PSG is a very intrusive and costly tool that cannot allow a longitudinal follow-up of patients. Different substitutes are currently developed and tested for a nonintrusive, accurate and inexpensive assessment of the sleep quality. Among them, ballistocardiograph is a promising tool. It allows a distant monitoring of the patient heart and breathing activity, since the sensor is placed under the mattress of the bed. Several studies report clinical studies and related post-processing to assess the sleep quality provided by the BCG against the gold standard. These studies can be classified depending on the number of raw data and derived parameters included to detect the sleep stages, as well as on the classification chosen for the sleep stages.

In this study, we chose the most common sleep classification, split in three stages [START_REF] Crawford | Physiological and pathological sleep: impact on successful aging and cognitive function[END_REF], [START_REF] Carskadon | Normal Human Sleep: An Overview[END_REF], defined as: 1) wake (representing less than 2% of the total sleep duration), characterised by slow muscle activity and slow eye movement. 2) NREM, characterised by a decreased heart rate, an absence of eye movement, muscle relaxation, and a slow breathing, as well as specific brain activities. It usually represents 75-80% of the total sleep duration; 3) REM, characterised by an intense brain activity, an absence of muscle activity, rapid and irregular breathing, increased heart and breathing rates, and quick eye movements. It represents 20-25% of the total sleep duration.

Table 1 summarises studies which aim at characterising the sleep using cardio-respiratory variables from the BCG or ECG and these three sleep stages. In past clinical trials, most of the methods were tested on a small number of subjects (less than twenty). Most of studies achieve around 75% precision comparing to PSG results. Only [START_REF] Yi | Non-Invasive In-Home Sleep Stage Classification Using a Ballistocardiography Bed Sensor[END_REF] has been able to reach a fairly good precision (85%) but it was only tested on 5 subjects while using as many as 78 features in their method. [START_REF] Migliorini | Automatic sleep staging based on ballistocardiographic signals recorded through bed sensors[END_REF] also performs well (76.10%) but the method could not be implemented within a commercial product. Similar conclusions can be drawn for [START_REF] Chen | Automatic sleep staging based on ECG signals using hidden Markov models[END_REF].

The main objective of this work is to design a noninvasive way of sleep stages classification that has a precision exceeding 70% while using the minimum number of features possible. We propose in this paper a supervised classification method in association with data that could be driven from ballistocardiograph (BCG).

This paper is organised as follows. We present in Section II the methods based on the use of cardio-respiratory variables that could be driven from BCG. Results are given and discussed in Section III. Section IV gives some conclusions perspectives.

II. SLEEP STAGES CLASSIFICATION

A. Empirical method approach

Each stage of sleep is characterised by a certain variation on the cardio-respiratory variables. From a medical point of view, the variation of the heart rate is observable from the distance between two R-peaks (also noted the RR interval). Different cardio-respiratory features can be derived from the RR interval, the heart beat and the respiration rate, as summarised in Table II. These features serve as basis for defining a series of conditions allowing the classification of sleep stages. The latter follows from an empirical algorithm that we developed based on the work of Kurihara and Watanabe [START_REF] Kurihara | Sleep-stage decision algorithm by using heartbeat and bodymovement signals[END_REF].

This algorithm is detailed in Figure 1. It combines the conditions of Table II to define the occurrence of each sleep stage, hence the importance of a correct determination of the a i coefficients of Table III. A sensitivity analysis was conducted, and revealed a limited influence of coefficients a 3 and a 5 , which were therefore set to the values reported in the literature. For the three other coefficients, a design of experiment was conducted where the sensitivity of each remaining coefficient was tested individually, since the coefficients are independent from each other. Finally, three sets of parameters were kept, and are reported. Note that the coefficients a i were determined from tests and results in the literature.

C 1 HBM < a 1 × HBmean C 2 R(k) ∈ [I REM ] C 3 RR < RRmean C 4 HRst ≤ a 2 × HBstmean C 5 RRst ≤ a 3 × RRstmean C 6 HBM < a 4 × HBmean C 7 RRst ≤ a 5 × RRstmean C 8 RRI ≥ RRImean
We consider that the NREM phase could be detected if the conditions C 1 , C 3 , C 4 and C 5 described in Tableé III are satisfied. Otherwise, if conditions C 2 , C 6 , C 7 and C 8 are satisfied, the REM phase is confirmed. We assume that every other state is wake. Finally three sets of parameters were kept and are reported:

• Set1: a 1 = 1.1, a 2 = 0.3, a 3 = 1.3, a 4 = 1.2, a 5 = 1.4 • Set2: a 1 = 0.8, a 2 = 0.3, a 3 = 1.3, a 4 = 1.4, a 5 = 1.4 • Set3: a 1 = 1.1, a 2 = 0.3, a 3 = 1.3, a 4 = 1.4, a 5 = 1.4
We have combined the results of the three algorithms by creating a vote system. This voting system respects the majority rule. In the case of a different result, the results from the one with the highest precision for detecting the REM phase (which is the less represented stage), is chosen. Since REM is the least detected phase, and since algo2 is the best one in detecting it, we added a condition in case of conflict, if algo2 recognises the epoch as a REM epoch then algo2 prevails.

B. Classification Method Using Machine Learning Approaches

Five classical machine learning algorithms were selected to improve the sleep stages determination, namely: support vector machine (SVM), Multinomial Logistic regression (Rlogic), k-nearest neighbours (KNN), Classification And Regression Trees (CART) and Naive Bayes (NB).

We considered that the features were the variables defined earlier in Table II. The target is the phase detected by the PSG for each epoch. Hence, the considered problem is a supervised classification problem with 3 outcomes (wake, NREM, REM). We use 80% of the collected data was used to train the machine learning algorithm. Figure 2 shows the steps of the classification algorithm we use in this paper.

The sleep algorithms resulting from these five machine learning processes were validated on the same set of data that they were trained in.

We built the concordance matrix to compare the classification between the PSG and the tested algorithm by counting the number of times each phase appeared for an epoch of 30s, compared to the ones of PSG. The percentage of agreement by phase i equal to numbers of epochs that the algorithm predicted that it is the phase i over the numbers of epochs that the phase i was given by the PSG. The percentage of Fig. 2. Classification method using Machine learning agreement is obtained by dividing the number of epochs that the algorithm was right, by the total number of epochs.

We consider the recall. We compute the F1-Score which is a measure that combines precision and recall with their harmonic mean, called F-measure or F-score such that the precision here is the percentage of agreement with PSG.

III. RESULTS AND DISCUSSION

A. Data

We used data collected from the clinical trial "St. Vincent's University Hospital / University College Dublin1 ". This database contains 25 full overnight polysomnograms from adult subjects with suspected sleep-disordered breathing. The subjects were all aged over 18 with no heart disease or dysfunction, and they did not take any kind of drug that could trouble the heart rate.

The first step consists in reassembling all the data collected to same sampling frequency (in this case we use 1Hz as frequency). Then a check on the data must be done to see if one of the main three variables is not available but could be calculated. In our case, the respiration was not available, so a calculation based on the thorax movements was performed. If all the 3 inputs are available, we proceed to the estimation of the derived parameters. The parameters are stored chronologically for every 30s epoch. We have chosen an epoch of 30s because the PSG that gave the classification divided the night into 30s epochs.

B. Results of tests using the empirical method

The results of the empirical algorithm detailed in Figure 1 together with each set of parameters (see Table II) are gathered in Table IV. One notes the poor global capacity of this algorithm to properly detect to NREM stage (only half of the NREM epochs are correctly classified), and the picture is even worse for the REM phase, with an agreement being far less than 25%.

A graphical representation is proposed in Figure 3. The occurrence of each sleep stage as detected by the PSG is plotted with black dots. Then, the results provided by each set of parameters is represented by one colour line of markers. The marker is a dot in case the sleep stage is correctly detected, a cross otherwise. One notices that this empirical algorithm tends to detect the NREM phase instead of the REM, while the wake stage is properly identified.

Due to the clinical importance of the REM phase, one chooses the second set of parameters as the option to be chosen in conflict cases for the classification method based on a voting system. Figure 3 shows that none of the three algorithms has succeeded in detecting the REM phase correctly. Most of them either detect it wrongly or detect nothing at all. By considering all the nights, the precision is 57.89% , 50.72% and 60.11% respectively for A1, A2 and A3. Although A1 and A3 have higher total precision in respect of A2, it was showed that the latter performs better in detecting REM phase.

Figure 4 shows the results of the Voting system algorithm. We outline some improvement regarding the detection of the REM phase. By using such Voting system, we have increased the total precision by 3%. Table IV summarises the precision of each algorithm per phase and the total one. to test the prediction algorithm. The aim was to find a better precision than existing works from the literature using less features.

Figure 5 shows that the best algorithm was SVM with 67.55%. To better understand this result, an agreement by phase matrix is given in Figure 10. This matrix presents the agreements between the PSG and the tested algorithm. Although this method performs well, especially for the NREM phase, we see that it failed to detect perfectly the minor classes. For instance, the total of REM phase did not exceed 12% of the total agreement. The precision, F1-score and recall resulting from the predicted classification are presented in Table V.

Against the previous works, our method is very satisfying since it has more than the average number of studied subjects and it has one of the best precision compared to the results given by PSG. We find out that [START_REF] Yi | Non-Invasive In-Home Sleep Stage Classification Using a Ballistocardiography Bed Sensor[END_REF] performs better for sleep stage classification. However, the latter was only tested on five subjects in contrast to our work that was tested on 25 subjects. This method used 78 features while we used only 17.

The total precision of the predicted classification is 76.50%. It is considered as an acceptable percentage comparing to the literature by practitioners. However, we aimed to improve our results by creating a voting system that considers the best three methods.

According to our tests, the three most precise algorithms are SVM (76,50%), CART (66,97%) and K-nearest neighbours (72.11%).

IV. CONCLUSIONS AND PERSPECTIVES

This article presents a new approach to estimate sleep stage classification using only cardio-respiratory variables that can be obtained from a contact-less BCG sensor. The method was tested using a collected data set of 25 subjects presenting symptoms of breathing sleep apnea. Inspired from the previous publications on this topic, a choice of parameters

Fig. 1 .

 1 Fig. 1. The 3 phases classification algorithm

Fig. 3 .

 3 Fig. 3. Hypnograms of different algorithm in comparison with the one got by the PSG based on the brain activities

Fig. 4 .

 4 Fig. 4. Hypnograms of the voting algorithm in comparison with the one got by the PSG based on the brain activities

Fig. 5 .

 5 Fig. 5. Precision of each method

Fig. 6 .Fig. 7 .

 67 Fig. 6. Confusion matrix without normalisation for the SVM

Fig. 8 .

 8 Fig. 8. Confusion matrix without normalisation for the KNN method

  As explained earlier, the data set was collected during a clinical trial done over 25 subjects having a high probability to suffer from breathing sleep issues. This data set counts 20,708 epochs of 30 seconds. Only 4,142 Epochs were kept

		TABLE IV
	AGREEMENT PERCENTAGE OF THE DIFFERENT ALGORITHMS
		Algo1	Algo2 Algo3 Voting
					Algorithm
	% of agreement on NREM 74,66	75,17	74,66	75,72
	% of agreement on WAKE	45,28	2,91	53,57	46,74
	% of agreement on REM	1,52	23,02	0,05	10,32
	% of total agreement	57,89	50,72	60,11	63,41
	C. Results of tests using Machine Learning methods

doi: https://doi.org/10.13026/C26C7D

was made. These parameters were driven from the cardiorespiratory variables.

We started by creating an empirical decision tree, based on the combination of conditions proven in previous research works. By modifying the coefficients in these conditions, we obtained three algorithms that achieved more than 50% of agreement with the results driven by the PSG using brain activities. A system of vote was designed between these three algorithm resulting in a better score agreement (up to 63.41%).

By using five machine learning methods, we found that SVM is the most precise technique in this application with a total agreement of 76.50%, compared to the classification given by the PSG.

In our future works we aim to improve this method by including other parameters such as body movements and mass distribution. We plan to conduct tests on healthier subjects: an upcoming clinical trial, whose main aim is to place a BCG sensor in a medical bed alongside with scaling sensors, will to help us reach better results. This trial is part of a project aiming to link the sleep disorders with issues on cognitive impairment and deterioration in memory quality.


Mohannad Ismail
email: mohannad.ismail1@gmail.com

Margot B Brooks

Joan Van Baaren

Loulou Albittar

Synergistic effects of temperature and plant quality, on development time, size and lipid in Eccritotarsus eichhorniae

Keywords: absolute energy demand, dispersal, interaction, mirid, size

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The capacity of ectothermic insects to establish in specific environments depends on their abundance and distribution, and this is to some extent governed by the abiotic and biotic factors of the environment, and to a large extent by phenotypic plasticity with respect to life history traits and fitness of the insect individuals [START_REF] Gaston | Patterns in the distribution and abundance of insect populations[END_REF][START_REF] Chown | Physiological Diversity in Insects: Ecological and Evolutionary Contexts[END_REF][START_REF] Beukeboom | Size matters in insectsan introduction[END_REF]. The fitness of an insect is a function of individual survivorship and fecundity in the environment in which it lives [START_REF] Mitchell | Insect Behavior, Resource Exploitation, and Fitness[END_REF]. Fitness traits have been positively linked to the size of individuals under normal, non-stressful conditions, implying that bigger individuals have higher reproductive outputs (Stearns, 1992;[START_REF] Chown | Body size variation in insects: a macroecological perspective[END_REF].

Examples of this relationship have been demonstrated in insect parasitoids for both females [START_REF] Ellers | A field study of size-fitness relationships in the parasitoid Asobara tabida[END_REF] and males [START_REF] Lacoume | Effect of host size on male fitness in the parasitoid wasp Dinarmus basalis[END_REF]. Body size affects all aspects of physiology and biological processes (Stearns, 1992;[START_REF] Honek | Intraspecific variation in body size and fecundity in insects -a general relationship[END_REF][START_REF] Kingsolver | Size, temperature, and fitness: three rules[END_REF], thus it is a key consideration in ecology and evolutionary theories [START_REF] Kraushaar | Population variation in sexual selection and its effect on size allometry in two dung fly species with contrasting sexual size dimorphism[END_REF][START_REF] Angilletta | Temperature, growth rate, and body size in ectotherms: Fitting pieces of a life-history puzzle[END_REF]. Larger body size is known to be associated with greater protein and lipid reserves [START_REF] Roff | The evolution of life histories: theory and analysis[END_REF]Visser, 1994;[START_REF] Rivero | The physiological costs of being small in a parasitic wasp[END_REF]. In insects, lipids are necessary to sustain all biological functions [START_REF] Arrese | Insect fat body: energy, metabolism, and regulation[END_REF] including reproductive processes [START_REF] Blanckenhorn | Size-dependent energy reserves, energy utilization and longevity in the yellow dung fly[END_REF][START_REF] Ismail | Physiological costs of cold exposure on the parasitoid Aphidius ervi, without selection pressure and under constant or fluctuating temperatures[END_REF] and flight activities [START_REF] Haunerland | Transport and utilization in insect flight muscles[END_REF], therefore lipid availability is a major factor affecting insect viability.

Temperature is considered as the most important abiotic factor affecting growth, development and nutritional content of hosts and thus determining body size in ectothermic insects (Stamp, 1993;[START_REF] Kingsolver | Plasticity of size and growth in fluctuating thermal environments: Comparing reaction norms and performance curves[END_REF]Stillwell et al., 2007;[START_REF] Mega | The adult body size variation of Dryas iulia (Lepidoptera, Nymphalidae, Heliconiinae) in different populations is more influenced by temperature variation than by hostplant availability during the seasons[END_REF]. Temperature is also known to affect the relationship between lipid and insect size, thus affecting fitness (de [START_REF] Kogel | Effect of host plant on body size of Frankliniella occidentalis (Thysanoptera : Thripidae) and its correlation with reproductive capacity[END_REF][START_REF] Ismail | What are the possible benefits of small size for energy-constrained ectotherms in cold stress conditions?[END_REF]. The relationship between body size and temperature leads to an important premise in insect biology, referred to as the temperature-size rule (TSR). Individuals reared at lower temperature present longer development time and larger body size at maturity A c c e p t e d M a n u s c r i p t [START_REF] Atkinson | Temperature and organism size -a biological law for ectotherms[END_REF][START_REF] Atkinson | Why are organisms usually bigger in colder environments? Making sense of a life history puzzle[END_REF][START_REF] Blanckenhorn | Different growth responses to temperature and resource limitation in three fly species with similar life histories[END_REF][START_REF] Angilletta | The temperature-size rule in ectotherms: Simple evolutionary explanations may not be general[END_REF].

In addition, temperature may have a significant effect on the overall wing loading (the pressure exerted by the wings on the surrounding air) of individuals [START_REF] Marden | Aerial predation and butterfly design: how palatability, mimicry and the need for evasive flight constrain mass allocation[END_REF][START_REF] Gilchrist | Plastic and genetic variation in wing loading as a function of temperature within and among parallel clines in Drosophila subobscura[END_REF]. This index is important because wing loading has been shown to be correlated to flight capacity in some insect species [START_REF] Moiroux | Local adaptations of life-history traits of a Drosophila parasitoid, Leptopilina boulardi: does climate drive evolution[END_REF][START_REF] Gilchrist | Plastic and genetic variation in wing loading as a function of temperature within and among parallel clines in Drosophila subobscura[END_REF].

However, in the environment, several factors interact together to affect the development of organisms (Sulmon et al., 2015). For example the availability, as well as the quality, of food are considered to be determinant for several biological parameters of insects [START_REF] Nylin | Plasticity in life-history traits[END_REF][START_REF] Awmack | Host plant quality and fecundity in herbivorous insects[END_REF][START_REF] Ismail | Interaction between temperature and water nutrient levels on the fitness of Eccritotarsus catarinensis (Hemiptera: Miridae), a biological control agent of water hyacinth[END_REF], including adult body size [START_REF] Blanckenhorn | Adaptive phenotypic plasticity in growth, development, and body size in the yellow dung fly[END_REF][START_REF] Bownes | Nutrient-mediated effects on Cornops aquaticum Bruner (Orthoptera: Acrididae), a potential biological control agent of water hyacinth, Eichhornia crassipes (Mart.) Solms (Pontederiaceae)[END_REF]. [START_REF] Bownes | Nutrient-mediated effects on Cornops aquaticum Bruner (Orthoptera: Acrididae), a potential biological control agent of water hyacinth, Eichhornia crassipes (Mart.) Solms (Pontederiaceae)[END_REF] showed by measuring body mass that body size of the grasshopper Cornops aquaticum (Orthoptera: Acrididae) was bigger when fed on Eichhornia crassipes (Pontederiaceae) plants of higher quality, but did not investigate the effect of temperature. Plant quality is dependent on the levels of available nitrogen [START_REF] Hogendorp | Effect of nitrogen fertility on reproduction and development of citrus mealybug, Planococcus citri Risso (Homoptera : Pseudococcidae), feeding on two colors of coleus, Solenostemon scutellarioides L. Codd[END_REF][START_REF] Burke | Effect of nutrient quality and leaf age of water hyacinth, Eichhornia crassipesEichhornia crassipes, on the development of its co-evolved herbivore, Eccritotarsus catarinensis (Hemiptera: Miridae)[END_REF], but this can also be modified by the temperature of the environment [START_REF] Bauerfeind | Increased temperature reduces herbivore host-plant quality[END_REF]. The interaction between temperature and plant quality has previously been considered in the attempt to understand the impact of plant quality on modulating the relationship between temperature and body size in ectothermic insects and other organisms. For instance, Mascalux et al. (2009) demonstrated the significant effects of temperature and food quality on the clutch size and growth rate of two freshwater cladocerans, Daphnia magna and Simocephalus vetulus (Cladocera: Daphniidae). [START_REF] Lee | Macronutrient balance modulates the temperature-size rule in an ectotherm[END_REF] found that the reaction norm between temperature and body size of Spodoptera litura (Lepidoptera:

Noctuidae) was altered because of changes in food nutrients.

However, most of the studies on the effect of plant quality on TSR have been conducted using different species of plants rather than by varying the quality of the same plant. For instance, [START_REF] Diamond | Environmental Dependence of Thermal Reaction Norms: Host Plant Quality Can Reverse the Temperature-Size Rule[END_REF] evaluated the impact of plant quality on the TSR using the A c c e p t e d M a n u s c r i p t

insect Manduca sexta (Lepidoptera: Sphingidae) on tobacco and devil's claw. In their study, the two proposed plants might not have had the same relative suitability as resources for the particular herbivore insect, despite being of similar quality [START_REF] Musundire | Host plant effects on morphometric characteristics of Liriomyza huidobrensis, L. sativae and L. trifolii (Diptera: Agromyzidae)[END_REF]. To our knowledge, no previous study investigated using differing qualities of the same plant species.

In this study, we used the leaf sap-sucking mirid insect Eccritotarsus eichhorniae (Hemiptera:

Miridae) as a research model. This insect is native to Peru and was previously named

Eccritotarsus catarinensis [START_REF] Hill | The performance of the water hyacinth mirid, Eccritotarsus catarinensis, on water hyacinth and pickerel weed: a comparison of laboratory and field results[END_REF], as it was originally considered to be one of two populations (the other originating from Brazil) of the species E. catarinensis (Hill et al., 1999), due to their almost undistinguishable morphologies. However, [START_REF] Paterson | Two in one: cryptic species discovered in biological control agent populations using molecular data and crossbreeding experiments[END_REF] confirmed that they are cryptic species and more recently, [START_REF] Henry | Description of a cryptic new species of the plant bug genus Eccritotarsus (Heteroptera: Miridae: Bryocorinae) from Peru, a new biocontrol agent of water hyacinth, Eichhornia crassipes (Pontederiaceae)[END_REF] described the Peruvian population as E. eichhorniae. The two species were released in South Africa to control the invasive aquatic weed, E. crassipes, commonly known as the water hyacinth (Hill et al., 1999[START_REF] Hill | The performance of the water hyacinth mirid, Eccritotarsus catarinensis, on water hyacinth and pickerel weed: a comparison of laboratory and field results[END_REF]. Adults and nymphs of Eccritotarsus feed gregariously on the leaves of water hyacinth, but [START_REF] Paterson | Cryptic species of a water hyacinth biological control agent revealed in South Africa: host specificity, impact, and thermal tolerance[END_REF].

The objective in the present study was to evaluate the impact of temperature and plant quality, and their interaction, on morphological and physiological traits of E. eichhorniae. In order to understand what impact plant quality would have on the relationship between temperature and size, plant quality was manipulated to provide high, medium and low nutritional status. We predicted that: 1) According to the TSR, individuals exposed to low temperature should present a larger body size at maturity and would have greater lipid content than those raised at high A c c e p t e d M a n u s c r i p t temperatures. 2) Individuals raised on high quality food would be bigger, accumulate more lipids and have higher wing loading compared to those reared on low quality plants.

3) The insect size would decrease linearly with increasing temperature and reduced plant quality. 4)

The combination of increased temperature with reduced plant quality would be more detrimental and negative effects would be synergetic, lipid content would be lower and insect body size would be smaller than when exposed to one of these factors alone. 5) Changes in relative size would subsequently affect the overall wing loading.

MATERIALS AND METHODS

Eccritotarsus eichhorniae used in this study were from a stock culture originally collected from a tropical area in the upper Amazonian basin of the Yarapa River, near Iquitos in Peru [START_REF] Hill | The performance of the water hyacinth mirid, Eccritotarsus catarinensis, on water hyacinth and pickerel weed: a comparison of laboratory and field results[END_REF]. oligotrophic (low quality, tap water only), mesotrophic (medium quality: 1.5 mg l -1 ), and eutrophic (high quality: 6.25 mg l -1 ) waters, based on nitrogen concentrations [START_REF] Reddy | Influence of nitrogen supply rates on growth and nutrient storage by water hyacinth (Eichhornia crassipes) plants[END_REF]. A water-soluble commercial fertilizer (Multifeed Classic Fertilizer, 19N: 8P: 16K) was used in combination with a commercial iron chelate (33 mg l -1 ) to prevent chlorosis. The selected concentrations are the averages of nitrogen levels reflecting the range present in South

African water bodies [START_REF] Coetzee | The role of eutrophication in the biological control of water hyacinth, Eichhornia crassipesEichhornia crassipes, in South Africa[END_REF]. Water in the tubs with high, medium and low nutrient levels was replaced every two weeks. Plants grown under high nutrient levels had large green leaves of good quality and were judged to be eutrophic. Plants that were grown under medium nutrient levels had smaller leaves just starting to yellow, and were considered to be mesotrophic. Oligotrophic conditions produced plants of poor quality with small, yellow leaves (Figure 1) [START_REF] Ismail | Interaction between temperature and water nutrient levels on the fitness of Eccritotarsus catarinensis (Hemiptera: Miridae), a biological control agent of water hyacinth[END_REF].

Experimental design

For the experiments, nymphs at the last stage were taken randomly from the insect culture and placed individually in small plastic Petri dishes (20 mm) with moist filter paper and a fresh water hyacinth leaf (replaced if necessary) until the adult stage.

The insects were exposed to 9 treatments, varying temperature against plant quality. Insects were kept at 3 different temperatures (20°, 25° and 30°C) and were fed on 3 qualities of plants (high, medium and low) produced from mother plants. 30°C was considered a stressful temperature since fitness traits were decreased significantly compared to 25 and 20°C [START_REF] Ismail | The impact of geographical origin of two strains of the herbivore, Eccritotarsus catarinensis, on several fitness traits in response to temperature[END_REF].

One-day-old adult male and female E. eichhorniae were placed in pairs for two days at 25°C in small plastic Petri dishes (20 mm) with moist filter paper and a small fresh water hyacinth leaf from each of the three water nutrient levels from the tub cultures, in order to become reproductively mature. Sexual male and female pairs (the parental generation) were then Germany) with a thermal precision of ± 1°C, under a photoperiod of 14L: 10D, and humidity 75 ± 10%. There were 9 replicates for each treatment, totaling 81 altogether. Fresh plants of the respective plant quality were provided regularly to the nymphs resulting from these adult pairings until they reached the adult stage.

Development time and Body indices

The development time of the progeny was calculated from the day the eggs were laid until the individuals became adults.

In this study two morphological traits representing body size, tibia length and wing length, were measured. Tibia length is the most common indicator of body size in insect parasitoids [START_REF] Godfray | Parasitoids: behavioral and evolutionary ecology[END_REF] and the forewing length is the most commonly used measure of body size in Lepidoptera [START_REF] Miller | Wing measure as a size index in lepidoptera -family Olethreutidae[END_REF], damselfly [START_REF] Hassall | Latitudinal variation in morphology in two sympatric damselfly species with contrasting range dynamics (Odonata: Coenagrionidae)[END_REF], mosquitoes [START_REF] Siegel | Relationship between wing length and dry weight of mosquitoes[END_REF] and Drosophila species [START_REF] Liefting | Plasticity versus environmental canalization: population differences in thermal responses along a latitudinal gradient in Drosophila serrata[END_REF]. A previous study of E. eichhorniae (then referred to as E. catarinensis) showed that tibia length was similar in females and males, while in females the wings were longer than in males [START_REF] Ismail | Male mating preference of two cryptic species of the herbivorous insect Eccritotarsus catarinensis[END_REF].

Measurements for body indices were from 10 individuals (five males and five females) taken randomly from the bottles at each replicate of the 9 combinations (temperature * food quality), totaling 45 individuals of each sex for each combination. Body size was measured using the numeric image analysis software Olympus Stream Motion 1.9 (Olympus Soft Imaging Systems) under a binocular microscope (Olympus SZX-16) linked to a video camera (Olympus DP 72), as follows: the length of the hind tibia (from the femur-tibia joint to the tibia-tarsus A c c e p t e d M a n u s c r i p t joint) and the length of the forewing (from base to the apex). The wing loading index was calculated as the ratio of total body fresh mass to squared wing length [START_REF] Gilchrist | Plastic and genetic variation in wing loading as a function of temperature within and among parallel clines in Drosophila subobscura[END_REF].

The physiological traits (dry body mass and lipid content)

A total of 135 females and 135 males aged < 04 hours (15 female and 15 male individuals from each of the nine treatments) were killed using liquid nitrogen, in order to immediately halt all metabolic processes. Individuals were then frozen at -20 °C until all replicates were processed.

Lipid content was determined based on the method explained in Visser and Ellers, (2012) and Visser et al., (2010). Fresh mass of each mirid was recorded, after which they were freeze-dried for 2 days (VirTis Benchtop 2 K freeze drier: SP Industries, USA) before measuring dry body mass (DBM) of each mirid. Freeze-dried mirids were then placed individually in glass tubes containing 5 ml of ether. After one day the ether was removed, individuals were washed with a fresh batch of ether and freeze-dried for 2 days, after which final dry weight (lean dry mass LDM) was recorded. Body fat mass (FM) was derived by subtracting LDM from DBM, and lipid content (LC) was calculated as a proportion (LC=FM/LDM). All mass measurements were taken using a micro-electrobalance (Sartorius MC 598648-003-48, sensitivity 0.001 mg;

Goettingen, Germany) located in an isolated balance room.

Statistical analysis

Statistical analyses were conducted using the statistical software R version 4.0.2 (2020-06-22) (R Core [START_REF] Team | R: A language and environment for statistical computing[END_REF]. Development times for males and females were analysed using generalised linear model (GLM) with temperature and plant quality as fixed factors (Gamma distribution with time data). GLM with temperature and plant quality as fixed factors, was also used to analyse the other parameters: hind and wing length for females and males (Gamma distribution), wing loading of males (quasibinomial distribution), wing loading of females,

A c c e p t e d M a n u s c r i p t

DBM for females and males (Gaussian distribution). We used ANCOVA to test the differences in LC in males and females (data were square root transformed), with temperature and food quality as the main factors and incorporating DBM as a covariate. Finally, the previous parameters were further analysed to test the differences between females and males using GLM with sex as a fixed factor. Significant results at p < 0.05 were followed by the use of Tukey's honest significant difference test for multiple comparison using the multcomp package and glht function [START_REF] Hothorn | Simultaneous Inference in General Parametric Models[END_REF].

RESULTS

Development time

The development time from egg to the adult stage increased significantly with the combination of low plant quality and high temperatures at 25° and 30°C, compared to the combination of medium and high qualities of plant for both sexes (Table 1, Figure 2). Development time decreased significantly with increasing temperature (Table 1) and with high plant quality for both sexes (Table 1). Development time did not vary between females and males (Table 2).

Hind tibia length

A significant interaction was found between temperature and plant quality for both females and males (Table 1). Individuals reared on low quality food under 30°C had the smallest tibia length (Figure 3 A,B). Individuals grew significantly larger as judged by tibia length at low temperature than at high temperature for both sexes (Table 1). Individuals of both sexes were significantly bigger when reared on high quality plants than on low quality plants (Table 1).

Females and males had almost the same length of tibia (Table 2).

Wing length

A c c e p t e d M a n u s c r i p t

A significant interaction was found between temperature and plant quality on wing length especially for females only (Table 1). Female individuals fed on low quality plants under 30°C presented the smallest wings and those fed on high quality plants at 20°C had the longest wing (Figure 3 C). Wing length decreased significantly in response to high temperature and to low plant quality for both females and males (Table 1, Figure 3 C,D). Females had significantly longer wings than males (Table 2).

Wing loading

A significant interaction was found between the two factors for females, but not for males (Table 1). While females had greater wing loading when feeding on high quality plants at 30°C, they had lower wing loading when feeding on low quality plants at the same temperature (Figure 4). Temperature had no significant effect on wing loading of E. eichhorniae for both sexes (Table 1). Plant quality had a significant impact on wing loading for females and males (Table 1), with greater wing loading when feeding on high quality food compared to low quality food (Figure 4). No significant difference was found between females and males (Table 2).

Dry body mass

No significant interaction was found between temperature and plant quality in females (Table 1), whereas a significant interaction was found between the two factors in males (Table 1). Male individuals feeding on high quality plants at 20°C had larger DBM (Figure 5 B). Dry body mass of individuals decreased significantly with increasing temperature for both sexes (Table 1, Figure 5 A, B). Greater DBM was recorded in individuals fed on good quality food compared to those with poor food quality for both females and males (Table 1, Figure 5 A,B). Dry body mass of females was significantly higher than that of males (Table 2).

A c c e p t e d M a n u s c r i p t

Lipids

There was no interaction between temperature and plant quality on LC in females or males (Table 3). A positive correlation was detected between DBM and LC in females, but not in males (Table 3). Individuals of both sexes presented significantly greater LC at low temperature compared to high temperature (Table 3, Figure 5 C, D). Females tended to contain significantly more LC when fed on high quality plants than on plants of poor quality, but this was not the case for males (Figure 5 C, D). No difference in LC was observed between males and females (Table 2).

DISCUSSION

In this study, individuals of E. eichhorniae were exposed to contrasting abiotic and biotic factors: different temperatures and plant qualities. Development time was affected by temperature and plant quality. Tibia and wing length, dry body mass and lipid content decreased significantly with increasing temperature and reduced food quality in both sexes. Wing loading, in contrast, decreased significantly with low plant quality, and this response was more marked in females than in male individuals. In addition, the combined factors presented two types of synergistic effects on the same traits. When optimal factors were combined (ie. high plant quality and low temperature), positive synergistic effects were demonstrated on development time and tibia length of both females and males, wing length of females as well as dry body mass of males. On the other hand, when the stressor factors were combined (ie. low plant quality and high temperature), negative synergistic effects operated on the aforementioned traits.

Consistent with the typical pattern in ectothermic animals, the results, which follow prediction 1, support the TSR [START_REF] Atkinson | Temperature and organism size -a biological law for ectotherms[END_REF][START_REF] Atkinson | Why are organisms usually bigger in colder environments? Making sense of a life history puzzle[END_REF][START_REF] Angilletta | The temperature-size rule in ectotherms: Simple evolutionary explanations may not be general[END_REF]. The smaller size at high temperature in our study might be related to the greater consumption of plant material [START_REF] Niesenbaum | When studying the effects of light on herbivory, should one consider temperature? The case of Epimecis hortaria F. (Lepidoptera: Geometridae) feeding on Lindera benzoin L. (Lauraceae)[END_REF], resulting in decreased efficiency A c c e p t e d M a n u s c r i p t of conversion of food into body matter, because of higher metabolic losses [START_REF] Kingsolver | Interactions of temperature and dietary protein concentration in growth and feeding of Manduca sexta caterpillars[END_REF]. It can be argued that small size might be an adaptive attribute to cope with the effect of high temperatures, reducing the surface area of the insect, and hence the rate of evaporation from the body. In addition, the reduction of evaporation from individual bodies is considered to be a consequence of decreased cell size [START_REF] Partridge | Evolution and development of body size and cell size in Drosophila melanogaster in response to temperature[END_REF][START_REF] Partridge | Thermal evolution of ectotherm body size: why get big in the cold? In Animals and temperature: phenotypic and evolutionary adaptation[END_REF]. These arguments are also consistent with the absolute energy demand hypothesis, which predicts that smaller individuals are at an advantage under stressful conditions [START_REF] Blanckenhorn | Time and energy constraints and the evolution of sexual size dimorphism -to eat or to mate[END_REF][START_REF] Ismail | What are the possible benefits of small size for energy-constrained ectotherms in cold stress conditions?[END_REF]. Smaller individuals may be able to withstand environmental stress because they require less energy to sustain their biological functions. Weldon et al. (2019) showed that smaller individuals of the marula fruit fly Ceratitis cosyra (Diptera: Tephritidae) had higher desiccation and starvation resistance than bigger ones.

As foreseen in prediction 2, we found that individuals feeding on high quality plants developed faster and matured at larger size than those feeding on low quality plants. Body size for both sexes followed a linear pattern according to the quality of the plant at each tested temperature, confirming prediction 3. Thus, it appears that food of high quality is a major factor as a prerequisite for larger individuals, operating in a similar way to insect response to temperature in TSR. According to these results, we propose that further study may justify a food-size rule (FSR) equivalent to the TSR. A similar response of faster development time was found when nymphs of the Brazilian species E. catarinensis fed on high nutrient leaves comparing with those fed on low nutrient leaves [START_REF] Burke | Effect of nutrient quality and leaf age of water hyacinth, Eichhornia crassipesEichhornia crassipes, on the development of its co-evolved herbivore, Eccritotarsus catarinensis (Hemiptera: Miridae)[END_REF]. [START_REF] Mukarugwiro | The effect of water nutrients on the feeding intensity and development of larvae of Neochetina eichhorniae (Warner) (Coleoptera: Curculionidae), a biocontrol agent of the invasive water hyacinth[END_REF] demonstrated that larvae of Neochetina eichhorniae (Coleoptera: Curculionidae) have larger body size and shorter larval developmental time when feeding on high quality plants of water hyacinth.

It is known that plant nutritional quality for insects is determined by the amino acid concentration and composition of the phloem sap, as well as the ratio of total sugars (Abisgold et al., 1994;Simpson et al., 1995;[START_REF] Albittar | Bottomup regulation of a tritrophic system by Beet yellows virus infection: consequences for aphidparasitoid foraging behaviour and development[END_REF]. Both amino acids and sugars are linked to nitrogen content in plants. Plant quality, however, varies during growth and development because of many abiotic and biotic factors. For instance, nutritional quality of plants decreased with increasing temperature [START_REF] Bauerfeind | Increased temperature reduces herbivore host-plant quality[END_REF] and depends on the levels of nutrients in the environment in which they grow [START_REF] Galloway | The nitrogen cascade[END_REF]. Thus, any change in the nutritional quality of plants can influence the efficiency of converting ingested food into body matter in insects. It has been shown that the efficiency of converting ingested food decreased with decreasing quality of diet (Timmins et al., 1988). Previous studies showed that nitrogen content of water hyacinth leaves increased with fertilizer treatments [START_REF] Reddy | Influence of nitrogen supply rates on growth and nutrient storage by water hyacinth (Eichhornia crassipes) plants[END_REF][START_REF] Center | Effects of host quality on flight muscle development in Neochetina eichhorniae and N. bruchi (Coleoptera: Curculionidae)[END_REF][START_REF] Burke | Effect of nutrient quality and leaf age of water hyacinth, Eichhornia crassipesEichhornia crassipes, on the development of its co-evolved herbivore, Eccritotarsus catarinensis (Hemiptera: Miridae)[END_REF][START_REF] Hill | Investigations of growth metrics and δ15N values of water hyacinth (Eichhornia crassipesEichhornia crassipes, (Mart.) Solms-Laub) in relation to biological control[END_REF]. It was also demonstrated that plant quality of water hyacinth increased with increasing nitrogen content and decreasing the carbon/nitrogen ratio [START_REF] Burke | Effect of nutrient quality and leaf age of water hyacinth, Eichhornia crassipesEichhornia crassipes, on the development of its co-evolved herbivore, Eccritotarsus catarinensis (Hemiptera: Miridae)[END_REF][START_REF] Hill | Investigations of growth metrics and δ15N values of water hyacinth (Eichhornia crassipesEichhornia crassipes, (Mart.) Solms-Laub) in relation to biological control[END_REF], justifying our assumption that nitrogen content, and consequently plant quality, of experimental plants increased with fertilizer treatments (Figure 1).

In this study, we present evidence that the combination of two stressor effects, high temperature and low plant quality, had greater synergistic negative effects, confirming prediction 4. Individuals reared at 30°C and fed on plants of differing quality, exhibited the smallest size on poor quality plants. A consequence of smaller body size of adults for successive generations continuing to feed on plants of lower quality, particularly at high temperature, would be the reduction in fitness traits of the individuals. Indeed, individuals of E. eichhorniae (then referred to as E. catarinensis) presented the lowest reproduction and survival rate of immature individuals when exposed to the combined effect of high temperature and low plant quality [START_REF] Ismail | Interaction between temperature and water nutrient levels on the fitness of Eccritotarsus catarinensis (Hemiptera: Miridae), a biological control agent of water hyacinth[END_REF]. This also confirms findings that a combination of multiple environmental factors had a greater negative impact on fitness traits of individuals as well as

A c c e p t e d M a n u s c r i p t populations, than one factor alone [START_REF] Scherber | Multi-factor climate change effects on insect herbivore performance[END_REF]Sulmon et al., 2015;[START_REF] Feehan | Synergistic negative effects of thermal stress and altered food resources on echinoid larvae[END_REF].

Furthermore, reduced plant quality may affect the TSR. The protracted development time of immature mirid individuals in our study in response to low quality plant when combined with higher temperature might be due to the requirement for greater quantities of food when it is of poor quality. This would necessitate more time spent on feeding, yet still yield a smaller size. Importantly, extended time taken to reach the adult stage may be necessary in order to maximize the rate of nutrient uptake from low quality plants (Taylor, 1988), due to decreased conversion efficiency of digestive enzymes [START_REF] Lindroth | Nutrient deficiencies and the gypsy moth, Lymantria dispar: effects on larval performance and detoxification enzyme activities[END_REF]. [START_REF] Diamond | Environmental Dependence of Thermal Reaction Norms: Host Plant Quality Can Reverse the Temperature-Size Rule[END_REF] found that a stressful combination of high temperature and low dietary quality could reverse the temperature-size rule. They found that the pupal mass of the moth M. sexta was higher when feeding on devil's claw than feeding on tobacco at 30°C. Our study is the first to make these comparisons by using different qualities of the same plant at three temperatures.

The slight increase in wing loading with higher temperature results in the need to increase wing beat frequency, and this may serve as an adaptation to a warmer environment, as it has the additional effect of reducing the impact of higher temperature by cooling the body [START_REF] Mani | Ecology and Biogeography of High Altitude Insects[END_REF][START_REF] Morin | Divergence of reaction norms of size characters between tropical and temperate populations of Drosophila melanogaster and D simulans[END_REF]. On the other hand, the individuals responded to lower quality plant by having lower wing loading, which is associated with superior flying ability [START_REF] Marden | Aerial predation and butterfly design: how palatability, mimicry and the need for evasive flight constrain mass allocation[END_REF][START_REF] Gilchrist | Plastic and genetic variation in wing loading as a function of temperature within and among parallel clines in Drosophila subobscura[END_REF][START_REF] Moiroux | Local adaptations of life-history traits of a Drosophila parasitoid, Leptopilina boulardi: does climate drive evolution[END_REF], conforming to prediction 5.

Having a low wing load would enable an insect to fly further. Ability to disperse over greater distances would enable individuals to migrate further in search of higher quality plant, which could have fitness consequences for themselves and their offspring. Smaller body size was directly linked with reduced lipid content for both sexes. While lipid content decreased with increasing temperature for both sexes, the response varied among females and males according to food quality. Females tended to accumulate significantly more lipids during immature stages when feeding on higher quality food rather than on poor quality food. Plant quality is an essential factor for accumulation of lipids in females, whereas for males, increased food quality does not necessarily result in increased lipid content. This may be related to the fact that females need more energy than males, to sustain biological activities such as egg production and maturation [START_REF] Bonduriansky | The evolution of male mate choice in insects: a synthesis of ideas and evidence[END_REF][START_REF] Ismail | What are the possible benefits of small size for energy-constrained ectotherms in cold stress conditions?[END_REF]. Insect body fat plays an essential role in energy storage and utilization, as well as in multiple metabolic activities [START_REF] Law | Insects as biochemical models[END_REF][START_REF] Arrese | Insect fat body: energy, metabolism, and regulation[END_REF]. Therefore, low quality leaves may not provide sufficient nutrition to allow females to accumulate the quantity of lipids required to sustain all of their metabolic and energetic functions, including successful reproduction.

In conclusion, individuals attained greater size at maturity by feeding on plants of high quality and this relationship was linear at each tested temperature. However further investigations including other insect species would be essential to justify a food-size rule. These results demonstrate that plant quality could influence the relationship between development time and the TSR, particularly at increased temperatures. Plant quality interacting with temperature had positive or negative synergetic effects on the insects depending on whether the combination was optimal or stressful, respectively. Based on our results, the potential dispersal of individuals may depend on plant quality rather than temperature. Larger individuals of E.

eichhorniae emerged when feeding on high quality plants at low temperature. However, since

A c c e p t e d M a n u s c r i p t

water hyacinth presents the biggest problem in eutrophic temperate areas, this may not necessarily mean successful biological control. Small individuals feeding on high quality plants at higher temperature may be more likely to stay, whereas smaller individuals emerging when feeding on low quality plants at higher temperature, may have greater flying capability, enabling them to disperse and thus limiting the population in the area of concern. In any of these circumstances, re-release of larger individuals with greater reproductive efficiency due to stored energy reserves may be advisable, as this would make the population more sustainable, and so help to assure the success of biological control.

A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t Small letters indicate the significant interaction between temperature and plant quality for both sexes.

  s c r i p t transferred to individual clear plastic bottles (1L) each containing a young, 5 leaved water hyacinth plant, with replicates for each of the three different qualities. Bottles were placed in 3 incubators at the 3 different temperatures (Binder GmbH, KBW 240 (E5.1), Tuttlingen,

  Our results indicate that both sexes of E. eichhorniae would respond to lower food quality with a theoretical increase in their flight capacity. This response has already been shown among aphids, where starvation due to low plant quality is a significant factor affecting flight initiation (Walters & Dixon, 1982; A c c e p t e d M a n u s c r i p t Parry, 2013). In contrast, Center & Dray (2010) demonstrated that flight ability of two weevil species N. eichhorniae and N. bruchi was at the expense of reproduction when feeding on high quality of water hyacinth.

Figure 1

 1 Figure 1

Figure 2

 2 Figure2

Figure 3

 3 Figure3

Figure 4

 4 Figure 4

  Figure 5

  Figure 1

  Figure 2

  Figure 4

Table 1 .

 1 Results of GLM for the effects of temperature and plant quality and their interaction 644 on the measured parameters of the herbivore Eccritotarsus eichhorniae. Significant effects are 645

	Table legends

Table 2 .

 2 Results of GLM for the effect of sex on the measured parameters of the herbivore Eccritotarsus eichhorniae. Significant effects are in bold.

		df	F	P
	Development time (Days)	1, 354	0	< 0.001
	Tibia length (mm) Wing length (mm) Wing loading DBM (mg) LC A c c e p t e d 1, 808 1, 643 1, 268 1, 268 1, 268	0.54 39.66 3.47 22.57 0.03 M a n u s c r i p t 0.46 < 0.001 0.06 < 0.001 0.86

Table 3 .

 3 ANCOVA with the effects of temperature and plant quality and their interaction (temperature x plant quality) and with dry body mass as a covariate, on lipid content of the herbivore Eccritotarsus eichhorniae. Significant effects are in bold.

	Females	Males

ACKNOWLEDGMENTS

This study was supported by funding from Rhodes University, as well as from the South African Research Chairs Initiative of the Department of Science and Technology, and the National Research Foundation of South Africa. We thank Shirley Pinchuck and Marvin Randall for facilitating work at the Electron Microscope Unit.

DATA AVAILABILITY STATEMENT

The data that support the finding of this study is available on Mendeley:

(http://dx.doi.org/10.17632/pnj7247t7n.1#file-742dd7fe-e22b-49fc-98b4-1f3ecc4db0c8)