Georgios Z Papadopoulos

Fabrice Theoleyre
email: theoleyre@unistra.fr

Pascal Thubert

Operations, Administration and Maintenance (OAM) features for Reliable and Available Wireless (RAW) Networks

Keywords: Industrial Internet of Things, IIoT, IoT, LLNs, Reliable and Available Wireless, RAW, Operations, Administration and Maintenance, OAM, Standardization, IETF

Though the requirements are well defined and

INTRODUCTION

The wireless medium is becoming more and more essential for critical applications. However, radio transmissions are known to be lossy, contrary to the transmissions in wired networks. Thus, controlling the congestion remains insufficient to provide high reliability. Even worse, radio link quality is time and space dependent [START_REF] Kotsiou | Is Local Blacklisting Relevant in Slow Channel Hopping Low-Power Wireless Networks[END_REF][START_REF] Pavkovic | Experimental Analysis and Characterization of a Wireless Sensor Network Environment[END_REF] . Thus, we expect to propose operations at the IP layer able to enable high reliability on top of these unreliable networks [START_REF] Thubert | Reliable and Available Wireless Problem Statement[END_REF] . To provide Quality of Service (QoS) along a multi-hop path that is composed of wired and wireless technologies, additional methods required to be considered to leverage the specific properties of wireless medium.

The newly-formed Reliable and Available Wireless (RAW) Working Group (WG) in the IETF extends Deterministic Networks (DetNet) WG to approach end-to-end deterministic performances over a network that comprises wireless segments. RAW must provision sufficient radio resources to provide high reliability, e.g., in terms of packet delivery ratio within delay constraints, and high availability, e.g., bounded number of consecutive losses. The capability to schedule the wireless transmissions appears critical to ensure a bounded latency; it is required not only to support the computation of the end-to-end schedule, but also to control the co-channel interference within the limits of a given technology and associated spectrum. In order to ensure delivery at all times, and yet avoid the overuse of constrained resources such as bandwidth and battery, RAW methods must dynamically monitor the network infrastructure and maintain the optimal amount of logical resources for each application [START_REF] Papadopoulos | RAW use cases[END_REF] . For this purpose, we need traceability, that belongs to Operations, Administration and Maintenance (OAM). We need to provide a toolset for fault detection and isolation, and for performance measurement. These OAM tools [START_REF] Mizrahi | An Overview of Operations, Administration, and Maintenance (OAM) Tools[END_REF] have to be tailored for the Low-power Lossy Network (LLN) world [START_REF] Kritsis | A Tutorial on Performance Evaluation and Validation Methodology for Low-Power and Lossy Networks[END_REF] . We propose here to detail the requirements of the OAM features recommended to construct a predictable communication infrastructure on top of a collection of wireless segments. We describe the benefits, problems, and trade-offs for using OAM in wireless networks to provide availability and predictability [START_REF] Theoleyre | Operations, Administration and Maintenance (OAM) features for RAW[END_REF] .

PROBLEM STATEMENT

RAW aims at making the communications more reliable and predictable over wireless network infrastructure. Most critical applications need to respect Service Level Objectives (SLO), defined in an end-to-end manner. Typically, an application needs a minimum reliability and a maximum latency to work properly.

We consider a typical scenario as illustrated in Fig. 1, where a wireless network is connected to a wired network via two different border routers. A source node needs to send a collection of packets (i.e., a data flow) to a destination. Since packets may be lost inside the radio network, the infrastructure selects multiple independent paths. Considering then for instance a broken link or external interference over one path, multiple different paths are established to forward the data flow to the final destination. Indeed, we have several flows (pairs of source / destination) in the heterogeneous network, that respect strict reliability and delay constraints.

In this letter, we aim at defining the OAM 8 operations that a RAW network must support:

• Operations correspond to the mechanisms to set-up to maintain the network operational. This part is also in charge of monitoring the network to identify possibly faults;

• Administration quantifies the resource that have already been allocated in the network;

• Maintenance focuses on repairing the network. This repair may be triggered after a fault has been detected, or preventively.

An OAM framework is required in RAW networks to maintain a real-time status of the network infrastructure. Thus, we can verify in real time that the SLOs are respected. Furthermore, to respect strict guarantees, RAW relies on an orchestrator (e.g., SDN controller) which will be responsible to schedule the transmissions in the deployed network. Thus, resources have to be provisioned a priori to handle any defect. OAM represents the core of the over provisioning process, and maintains the network operational by updating the schedule dynamically.

What makes RAW so specific is that the network infrastructure is based on heterogeneous technologies. We must gather enough information from the link layer to take the right decisions at the IP layer (e.g., packet replication, alternative paths). To make the network predictable, we must be able to capture these characteristics in real-time.

OPERATION FOR RAW NETWORKS

Radio resource allocation protocols have received much attention (e.g., 6P [START_REF] Wang | 6TiSCH Operation Sublayer (6top) Protocol (6P)[END_REF] ). However, we still need tools to make diagnostics, and to verify the network behavior. Hereafter, we detail the operations that a RAW network must support.

Connectivity Verification

In classical networks, ping packets help to verify that two end-hosts are well connected, i.e., a route exists in both directions. In RAW networks, resources are reserved per data flow to guarantee flow isolation properties. For the same reason, the control and data packets may not follow the same path. Thus, the ping packets must be labeled in the same way as the data packets of the flow to monitor. Moreover, ping packets should not "disturb" the actual data traffic. Thus, it is of primary importance to piggyback control information inside the data flows, instead of generating additional control packets.

Existing tools like traceroute help to identify the list of routers in the route. However, the network infrastructure provisions redundant resources for each flow, so that any fault can be handled without violating any SLA. Therefore, this means that multipath routing is the rule [START_REF] Koutsiamanis | From Best-Effort to Deterministic Packet Delivery for Wireless Industrial IoT Networks[END_REF] . Thus, to correctly identify unexpected behaviors, we have to implement per route tracing tools. All the possible paths between two maintenance endpoints should be retrieved. More importantly, the network infrastructure has to be able to reconstruct a priori the paths followed by a specific data packet. It might be that only one path is faulty, in such scenario the network infrastructure has to be able to identify the misbehaving subpart along the path.

Fault Detection and Identification

We need mechanisms able to detect faults, before they impact the network performance. By fault, we mean that the network has deviated from its expected behavior, so that it jeopardizes possibly its behavior.

In Low-power Lossy Networks (LLNs), we propose a two-steps process:

1. Fault detection: a misbehavior has been detected. For instance, the end-to-end reliability of a specific flow has decreased, or a buffer overflow occurred. While these events are the results of a fault, the infrastructure is not aware of the cause.

A device that detects a fault has to trigger an alarm;

2. Fault identification comes after the fault detection. After an alarm has been reported, the infrastructure has then to identify the causes of this deviation. For instance, the end-to-end reliability for a collection of data flows may decrease because of external interference along the path.

Typically, the level of monitoring increases to obtain more accurate information to identify the cause.

LLNs are specific, and make the fault detection and identification harder. Because of the energy-efficiency, we have to limit the volume of monitoring information since every bit consumes energy. Besides, the bandwidth is also significantly lower than in wired networks. In scheduled networks, we have to dedicate radio resources for the control traffic. Thus, localized and centralized mechanisms have to be combined together.

ADMINISTRATION FOR RAW NETWORKS

To take proper decisions, the network infrastructure has to be aware precisely of the state of each device and flow. This state helps the network to accept (or not) a novel flow (call admission), to reconfigure the network to reduce the energy consumption or to keep on respecting SLA contracts [START_REF] Gaillard | Service Level Agreements for Wireless Sensor Networks: A WSN operator's point of view[END_REF] .

Key Performance Indicators

Most Service Level Agreement (SLA) contracts mention end-to-end Key Performance Indicators (KPI), for each data flow. The end-to-end reliability is of primary importance, since most industrial applications stop working when large number of packets are lost. The reliability KPI is often expressed at the application level, while the packets may be fragmented. Thus, reliability constraints per fragment are even higher to be able to reassembly the packets at the destination.

The end-to-end delay is also particularly sensitive: after a given deadline, the packet becomes obsolete and does not need to be delivered. Typically, control command applications [START_REF] Park | Wireless Network Design for Control Systems: A Survey[END_REF] are interactive, and need to react in real time after having received physical measurements.

Thus, we need a per-flow monitoring approach, and we have to measure the SLA for each virtual circuit.

Individual Performance Metrics

Administrators of mission-critical networks need to know in real-time the performance of the network infrastructure. Thus, the we need to measure the link quality to provision enough resources for the flows forwarded through such link. Many link quality metrics exist in the literature, from the Packet Delivery Ratio (link-level) to RSSI, LQI and SNR (PHY level).

The link quality should be monitored i) per channel, ii) per neighbor, iii) per flow, iv) per scheduled transmission. Indeed, counter-measures deeply depend on the phenomena which impacts the reliability. For instance, a low link quality for a specific channel may come from external interference, while a low packet delivery ratio for a given transmission opportunity may denote a collision in the schedule.

Furthermore, we have to collect also network-layer statistics. The buffer occupancy denotes the congestion along the path, and should be sufficiently low to buffer the packets when a fault occurs. Besides, a high buffer occupancy implies also a larger medium access delay, which may jeopardize the respect of the end-to-end SLAs.

Worst-case Metrics

Since low-power lossy networks exhibit time-dependent characteristics, we need to predict the future performances. Thus, we have to pay attention on the measurement method. A Window Mean Exponential Weighted Moving Average (WME-WMA) is very common to obtain smoothed values for stochastic metrics. However, the estimator has to be sufficiently reactive to detect anomalies.

Since wireless networks are known to be lossy, we have have to implement strategies to improve the reliability on top of unreliable links. Hybrid Automatic Repeat reQuest (ARQ) has typically to enable retransmissions based on the end-to-end reliability and latency requirements. To take correct decisions, the controller requires to be aware of the distribution of packet losses for each flow, and for each hop of the paths. In other words, average end-to-end statistics are not enough. They must allow the controller to predict the worst-case.

Energy Efficient Collect

RAW targets also low-power wireless networks, where energy represents a key constraint. Thus, we have to take care of the energy and bandwidth consumption.

A first technique consists in piggybacking control packets in data packets. Indeed, inserting additional bits in an existing packet is often much less expensive as transmitting another dedicated control packet. The transmitter may buffer control packets and piggyback them in data packets if the combination does not exceeds the Maximum Transmission Unit (MTU) [START_REF] Gaillard | Monitoring KPIs in synchronized FTDMA multi-hop wireless networks[END_REF] . Alternatively, we may create additional flags/fields for retrieving control information. Typically, path inference tools [START_REF] Dong | Understanding Path Reconstruction Algorithms in Multihop Wireless Networks[END_REF] insert additional information in the headers so that the destination can identify the path followed by a given packet. With multipath routing in scheduled networks, some mechanisms help to reduce the volume of information to include in the headers 15 16 .

MAINTENANCE FOR RAW NETWORKS

While the administration and operation features aim to provide the state of the network, and to detect faults, the maintenance aims to reconfigure the network to be able to respect the SLA.

Fault Tolerance

To be fault-tolerant, several paths can be reserved between two maintenance endpoints. They must be Node-Disjoint and avoid Shared-Risk Link Groups (SRLG), in order to guarantee that a single problem cannot interrupt the communication. In wireless,

TABLE 1 OAM features and their specificities in RAW networks

Feature

Mechanisms and Challenges Operation Each flow has its own dedicated ressources to monitor and to check, and multipath routing is the rule; Faults are very common in wireless networks (external interference, obstacle); Identifying the faults requires to collect and aggregate different metrics / events. Administration Metrics have to be monitored per flow, and also per radio ressource (e.g., radio channel);

We need to identify worst case metrics, and thus to know their distribution; Energy is the key for autonomous devices, and the volume of information to collect must be limited.

Management

We have a trade-off between resource badly used by the network, and the cost to reconfigure the network;

The network must be able to detect and predict the evolution, with an efficient over-provisioning scheme.

avoiding SRLG means employing as much diversity as possible, including channel diversity, time diversity, code diversity, and possibly different PHY techniques (e.g., narrowband vs; spread spectrum) to defeat the various interferences that after the medium. In Fig. 1, the green and orange paths pass through different routing devices, and border routers.

When multiple paths are reserved between two maintenance endpoints, they may decide to replicate the packets to introduce redundancy, and thus to alleviate transmission errors and collisions [START_REF] Papadopoulos | Exploiting Packet Replication and Elimination in Complex Tracks in LLNs[END_REF] . In Fig. 1, the green set of paths on the right of the figure are meshed, so that packets are replicated among all these links. Such technique is particularly efficient to deliver data packets even if the links are very unreliable [START_REF] Koutsiamanis | Meet the PAREO Functions: Towards Reliable and Available Wireless Networks[END_REF] .

Reconfiguration

A wireless network exhibits time-variable characteristics, that may come from e.g., obstacles, external interference, devices running out of energy. In these conditions, we must implement self-healing and self-optimization mechanisms. The network must continuously retrieve the state of the network, to judge about the relevance of a reconfiguration Reconfiguration may only be triggered if the gain is significant, and we need to quantify: the cost of the sub-optimality: resources may not be used optimally (e.g., a better path exists); the reconfiguration cost: the controller needs to trigger some reconfigurations. For this transient period, resources may be twice reserved, and control packets have to be transmitted.

Since RAW expects to support real-time flows, we have to support soft-reconfiguration, where the novel ressources are reserved before the ancient ones are released. Some mechanisms have to be proposed so that packets are forwarded through the novel track only when the resources are ready to be used, while maintaining the global state consistent (no packet re-ordering, replication, etc.)

Efficient Provisioning

Because the QoS criteria associated to a path may degrade, the network has to provision additional resources along the path. We need to provide mechanisms to patch a schedule (changing the channel to use, allocating more timeslots, changing the path, etc.).

Based on the information retrieved through the administration feature, the network must be able to predict the evolution. If the network is also able to quantify a priori the impact of one reconfiguration, it is also able to trigger a change to optimize the cost (e.g., energy, bandwidth).

CONCLUSIONS

In this letter, we presented the Operation, Administration and Management (OAM) features to enable wireless infrastructure to support critical applications. We regrouped in Table 1 the challenges specific to RAW networks. We need to provide OAM mechanisms to be able to provision enough ressources in order to respect reliability and delay guarantees.

In the future, we expect to implement all the mechanisms presented here to assess their performance in vivo. We need also to define standardized methods to measure each of the metrics described here. We have to define efficient mechanisms based on lossless compression techniques to reduce the volume of control packets to maintain an accurate view of the infrastructure.

FIGURE 1

 1 FIGURE 1Network Infrastructure of a typical Industrial Low-Power Network.

Funding Information

This research was supported by the French National Research Agency (ANR) project Nano-Net under contract ANR-18-CE25-0003 Summary established, the adoption of radios for


domain: sdv sde

text:
Marie-Hélène Sauge
email: marie-helene.sauge@avignon.inra.fr

Jean-Luc Poëssel

Thomas Guillemaud

Laurent Lapchin

Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach

Keywords: Adaptation, Density dependence, Gene-for-gene plant-insect interactions, Induced resistance, Prunus persica, Timing of induction

In gene-for-gene host-enemy interactions, monogenic plant resistance results from pathogen recognition that initiates the induction of plant defense responses. Schematically, as the result of the on/off process of recognition, phenotypic variability in enemy virulence is expected to be qualitative, with either a failure or a success of host colonization. We focussed on a major gene from peach conferring avoidance resistance against the green peach aphid Myzus persicae. Measurements of herbivore density and time-dependent aspects of resistance induction were examined, as well as variability in the aphid's ability to exploit the resistant host. Varying densities of infestation did not provoke differences in the aphid's tendency to leave a plant, and a single aphid was sufficient to elicit a response. Similarly, the duration of infestation did not affect the aphid response. A brief aphid feeding time of 3 h triggered induced resistance, which became effective between 24 and 48 h after the initial attack. Induced resistance decayed over time in the absence of additional infestation. Thirty aphid genotypes collected from natural populations were tested in the laboratory. No clone could colonize the resistant host, suggesting that all of them triggered the induction of effective plant defense responses. However, we detected significant quantitative variation among clones in the tendency of aphids to leave plants. These results improve our understanding of induced resistance as a dynamic phenomenon and suggest that the potential for aphids to adapt to a major plant resistance gene may depend on factors other than the mere capacity to evade recognition.

Introduction

Models of antagonistic coevolution between host plants and their enemies have been largely based around two major hypotheses. [START_REF] Ehrlich | Butterflies and plants: a study in coevolution[END_REF] theory was that the evolution of insect specialisation on host plants is constrained by the diversity of the plant secondary metabolites involved in the relationship. In this arms race metaphor, plants accumulate constitutive chemicals, regarded as biochemical defenses if they have negative effects on the herbivores (Wittstock and Gershenzon Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8

Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript 2002). Herbivores have in turn evolved behavioural or biochemical strategies for avoiding plant toxins [START_REF] Després | The evolutionary ecology of insect resistance to plant chemicals[END_REF]. Host defense chemicals and herbivore ability to metabolize plant defensive compounds (virulence) across populations may display continuous heritable variation with a high degree of correspondence between host and herbivore phenotypes [START_REF] Berenbaum | Chemical phenotype matching between a plant and its insect herbivore[END_REF].

The gene-for-gene concept proposed by Flor (1955) states that a pathogen is able to infect a host unless the host carries a specific resistance (R) gene that matches a specific pathogen avirulence (Avr)

gene. Major R genes act at the earliest stages of pathogen detection by triggering a signaling cascade that culminates in activation of strong defenses. Schematically, pathogens adapt to an R gene because altered or deleted Avr genes allows them to evade recognition [START_REF] Bent | Elicitors, effectors, and the R genes: the new paradigm and a lifetime supply of questions[END_REF]. Gene-forgene coevolution, first defined in plant-pathogen associations, was also an inspiration for several interactions between plant and piercing-sucking insects [START_REF] Kaloshian | Hemipterans as plant pathogens[END_REF][START_REF] Smith | The molecular bases of plant resistance and defense responses to aphid feeding: current status[END_REF]. The genetics of the interaction between wheat and the Hessian fly, Mayetiola destructor (Say) (Diptera: Cecidomyiidae), have been generally recognized to fit this model. The interaction is typically manifested as a binary response, i.e. either a resistant plant and dead fly larvae or a susceptible plant and living larvae [START_REF] Harris | Grasses and gall midges: plant defense and insect adaptation[END_REF]. In many interactions between plants and aphids, resistance is controlled by major genes, some of which encode or show tight linkage with plant R proteins conferring resistance to microbial pathogens [START_REF] Rossi | The nematode resistance gene Mi of tomato confers resistance against the potato aphid[END_REF][START_REF] Klingler | Aphid resistance in Medicago truncatula involves antixenosis and phloem-specific, inducible antibiosis, and maps to a single locus flanked by NBS-LRR resistance gene analogs[END_REF][START_REF] Dogimont | Gene resistant to Aphis gossypii[END_REF]). Aphid biotypes that can overcome these forms of resistance have appeared commonly among populations and have been designed on the basis of their qualitative pattern of virulence with respect to these genes (e.g. [START_REF] Alston | Resistance genes in apple and biotypes of Dysaphis devecta[END_REF][START_REF] Porter | Greenbug (Homoptera: Aphididae) biotypes: selected by resistant cultivars or preadapted opportunists?[END_REF][START_REF] Burd | Biotypic variation among North American Russian wheat aphid (Homoptera: Aphididae) populations[END_REF]).

The distinction between Ehrlich and Raven's hypothesis and the gene-for-gene concept has proven to be useful to understand ecological and evolutionary patterns of variation in resistance and virulence at the population level. In particular, the gene-for-gene concept may help explain the nature of the local adaptation of enemy to host that is difficult to reconcile with the arms race view of coevolution [START_REF] Kniskern | Two modes of host-enemy coevolution[END_REF]. Considering the mode of host-enemy coevolution can also have practical ramifications in agricultural systems, insofar as the type of genetic constraints exerted by resistant crop varieties affects the manner in which herbivorous insects evolve and thus impact [START_REF] Gassmann | Evolutionary analysis of herbivorous insects in natural and agricultural environments[END_REF]. It was recently demonstrated that the breakdown of monogenic plant resistance occurred less frequently when the R gene was combined to partial resistance quantitative trait loci [START_REF] Palloix | Durability of plant major resistance genes to pathogens depends on the genetic background: experimental evidence and consequences for breeding strategies[END_REF][START_REF] Brun | Quantitative resistance increases the durability of qualitative resistance to Leptosphaeria maculans in Brassica napus[END_REF].

We previously found within the genus Prunus (Rosaceae) genetic variation in induced resistance to the green peach aphid Myzus persicae (Sulzer) (Hemiptera: Aphididae), a polyphagous aphid species, which represents a threat for many crops in the world [START_REF] Sauge | Genotypic variation in induced resistance and induced susceptibility in the peach-Myzus persicae aphid system[END_REF]). This genetic system establishes a useful framework for ecological studies of plant-aphid relationships. Moreover, some of these peach [Prunus persica (L.) Batsch] genotypes are used in breeding programmes. This is the case for the cultivar Rubira, which confers strong avoidance resistance causing aphids to leave the plant within a few days [START_REF] Sauge | Induced resistance by Myzus persicae in the peach cultivar 'Rubira[END_REF]. The question of resistance durability represents a critical issue in cultivated fruit trees, since the management of resistance genes in time and space remains limited.

Thus, we aim to produce information that could help determining to which of the two modes of coevolution the Rubira-M. persicae interaction approximates.

Resistance in Rubira is known to be controlled by a major dominant gene [START_REF] Pascal | Inheritance of green peach aphid resistance in the peach cultivar 'Rubira[END_REF]. This gene, named Rm2, maps at the bottom end of linkage group 1 of an F 2 genetic map derived from Rubira and anchored to the "Texas" × "Earlygold" reference map for Prunus [START_REF] Lambert | Mapping Rm2 gene conferring resistance to the green peach aphid (Myzus persicae Sulzer) in the peach cultivar "Rubira®[END_REF]. During the last decade, much has been discovered about the biochemical interactions that specifically occur during gene-for-gene interactions [START_REF] Stahl | Plant-pathogen arms race at the molecular level[END_REF][START_REF] Kaloshian | Hemipterans as plant pathogens[END_REF][START_REF] Bent | Elicitors, effectors, and the R genes: the new paradigm and a lifetime supply of questions[END_REF][START_REF] Smith | The molecular bases of plant resistance and defense responses to aphid feeding: current status[END_REF]. By contrast, only a few data are available about Rm2-mediated plant responses to M. persicae infestation [START_REF] Poëssel | Metabolic profiling of shoot apices infested by the peach-potato aphid in susceptible and resistant peach cultivars[END_REF] the prediction that qualitative differences in the expression of virulence occur among aphid genotypes.

Materials and Methods

Plants and aphids

Prunus persica cv. Rubira (clone S2605) is a cultivar used as peach rootstock. It was selected in 1980 at the Institut National de la Recherche Agronomique, France, in a red-leaf peach progeny from USA.

It is considered to be homozygous at most loci, including the Rm2 locus, and is usually seedpropagated. For all experiments, seedlings were grown in a greenhouse, and surveyed to keep them free of enemies. Plants were tested when six weeks (42 d) old.

Under temperate climate, M. persicae host-alternates between the peach where sexual reproduction occurs (primary host) and many herbaceous host plants (secondary hosts). In early spring 2002, thirty aphid colonies were collected in three locations of southern France, in peach orchards planted with susceptible varieties (Table 1) (Guillemaud et al. 2003b). Aphids from each sample were assumed to belong to the clonal progeny of a fundatrix, hatched from sexually-produced eggs. We believed that each colony represented a distinct genotype, an hypothesis that was verified by genotyping a subset of samples using eight microsatellite loci (result not shown). An avirulent laboratory clone (Mp03) used in previous work [START_REF] Pascal | Inheritance of green peach aphid resistance in the peach cultivar 'Rubira[END_REF][START_REF] Sauge | Induced resistance by Myzus persicae in the peach cultivar 'Rubira[END_REF][START_REF] Sauge | Genotypic variation in induced resistance and induced susceptibility in the peach-Myzus persicae aphid system[END_REF] was added to the set of field clones and used as a reference. We used one parthenogenetic female from each sample to initiate the rearing of 30 new colonies on individual peach seedlings in a growth chamber with a 16-h day length at 19°C.

Plant resistance in response to varying densities and timing of aphid infestation

To characterize the induced phenotype of resistance in relation to (i) the intensity and (ii) the timing of aphid feeding stimuli, we carried out four experiments where the two factors were manipulated independently (see Table 2 for experimental designs). We asked several questions. What is the We conducted the experiments on plants that had been preinfested by M. persicae (clone Mp03) or not (control). Inducing adult aphids were placed on their preferred feeding site (the terminal growing shoot) of each plant of the preinfested group; they were not restricted from dispersing. At the end of the preinfestation period, we removed all aphids. In experiment a, we fixed the duration of preinfestation at 48 hours, a sufficient duration to trigger induced resistance. In experiments b, c, and d, we fixed the number of inducing aphids at 20 to ensure a reasonable aphid density [START_REF] Sauge | Induced resistance by Myzus persicae in the peach cultivar 'Rubira[END_REF]. To measure the level of induced resistance, we placed 10 test adult aphids (clone Mp03) on each control and preinfested plant. In the case of preinfested plants, we installed test aphids on the same shoot as the one used for preinfestation. The number of aphids remaining on plants was counted 6 times during the first 48 hours after their installation. The few offspring produced were removed at each inspection. We adopted a short counting period because the longer this period, the higher the probability for an induction by test aphids to occur on control plants. We performed 6 to 10 plant replicates for each treatment.

Genotypic variation in aphid virulence

To determine whether there was variation in the response of M. persicae to plant resistance among natural populations and, if so, whether the level of virulence differed qualitatively or quantitatively, we exposed clones collected from several orchards (planted with susceptible peach varieties) to Rubira plants. We placed 25 synchronized adult aphids on each caged plant. Aphids remaining on plants were counted twice a day at 9.00 and 17.00 hours until no more aphids were left. The few offspring produced were not taken into account as a parameter of virulence since they all died on plants before

Statistical analysis

All statistical analyses were performed using the R software (R Development Core Team 2010). Since avoidance resistance can be characterized by the time at which the aphid leaves the plant, we used survival analysis, a statistical method to study time-to-event variables. It is commonly utilized in biomedical research and is also applied in ecological entomology to predicting the foraging behaviour of parasitoids (e.g. [START_REF] Haccou | Information-processing by foragers -Effects of intra-patch experience on the leaving tendency of Leptopilina heterotoma[END_REF] or modelling population dynamics [START_REF] Ma | A survival-analysis-based simulation model for Russian wheat aphid population dynamics[END_REF].

We adopted a Cox's proportional hazards model [START_REF] Cox | Regression models and life-tables[END_REF] to quantify the plant-leaving tendency of aphids. The model describes the influence of covariates on the instantaneous probability that the aphid leaves the plant, given that it is still on it, according to the equation:

h(t) = h o (t) exp β x ,
in which h(t) is the plant-leaving tendency (hazard function) after a time t spent on the plant, h o (t) is the baseline hazard at time t (representing the hazard for an individual with the value 0 for all the covariates) and β is the regression coefficient of the covariate x. If a coefficient β is such that the exponential term (the hazard ratio) is greater than one, then the corresponding covariate x has an increasing effect on the plant-leaving tendency. A coefficient β leading to a hazard ratio smaller than one reduces this tendency.

We estimated the time taken by an individual aphid to leave the plant as the mean time between the last inspection where it was checked and the first inspection where it was missing. We estimated the coefficient β by maximizing a partial likelihood, and we tested the significant effect of the covariates Cox model are regarded as additional sources of variation that must be accounted for the estimation of the coefficients, but whose effects are not considered of particular interest. In a second step we tested for differences in the survival curves of aphids across groups of preinfestation or aphid genotypes using the log-rank test, one of a family of test procedures with parameter ρ defined by [START_REF] Harrington | A class of rank test procedures for censored survival data[END_REF].

Results

Plant resistance in response to aphid infestation

The tendency of M. persicae to leave plants of Rubira was affected by preinfestation (Table 3). The amount of damage needed to elicit induced resistance was extremely low. A preinfestation by a single aphid significantly increased the hazard for subsequent individuals to leave the plant, by a factor of exp (β) = 6.31 on average, that is, by 531% (Table 3a). Higher numbers of inducing aphids did not lead to an increased level of induced resistance within the tested range (log-rank test: χ 2 = 0.5, d.f. = 3, P = 0.908), showing that induced resistance was not aphid density-dependent.

Varying timing of preinfestation differentially affected the plant-leaving tendency of aphids. In experiment b where the aphid behaviour was studied immediately after removing inducing aphids (Table 3b), we found that induced resistance became effective between 24 and 48 h of aphid feeding, since the minimum duration necessary to detect induced resistance was 48 hours. At this stage, it was not possible to assess if induction required 24 h or 48 h of feeding, or some combination. Experiment c indicated that very short feeding times (as short as 3 hours) were sufficient to elicit induced resistance, provided induction was measured 48 hours after the beginning of preinfestation (Table 3c). In addition, when the time since the onset of preinfestation was held constant to 48 hours, there was no significant effect of the duration of preinfestation on the level of plant avoidance (log-rank test: 3d). However, estimated hazard ratios decayed as the time elapsed between the end of preinfestation and the measure of induced resistance increased. The hazard to leave the plant was increased by 317% when induced resistance was measured immediately after removing the aphids, but only by 241% and 64% when induced resistance was measured respectively 24 and 48 hours after the end of the preinfestation. Differences among groups were highly significant (log-rank test: χ 2 = 27.8, d.f. = 2, P < 0.0001).

Genotypic variation in aphid virulence

No aphid genotype sampled in the orchard could establish colonies on Rubira plants. In addition, when looking at the aphid tendency to leave the plant (Table 4), all the clones had a higher estimated hazard ratio than Mp03, the laboratory reference clone which is known to trigger effective induced resistance [START_REF] Sauge | Induced resistance by Myzus persicae in the peach cultivar 'Rubira[END_REF]. Taken together, these results suggest that all clones are avirulent. The fact that Mp03 had the lowest hazard ratio possibly reflects the effects of conditioning (maternal effects), since this laboratory clone was reared continuously on peach without host plant alternation. Excluding these possible conditioning effects would require to rear Mp03 on a secondary host, such as pepper or potato, before to test it on Rubira. Anyhow, since Mp03 has always been maintained on a susceptible peach variety, it is unlikely to have undergone any selective adaptation to Rubira.

Despite the fact that all the field clones were avirulent, we detected highly significant variation among them in plant avoidance (log-rank test: χ 2 = 122, d.f. = 29, P < 0.0001). Under identical conditions, the hazard ratio estimated for clone Car 1 was on average four times higher than for clone Car 16 (Table 4). We did not detect any influence of the geographical origin of the genotypes on the estimated aphid plant-leaving tendency (Kruskal-Wallis rank sum test : χ 2 = 0.940, d.f. = 2, P = 0.62).

Comment gene-mediated resistance. A similar behavioural approach was adopted for example in the work by Gómez et al. (2010), where inducible change in leaf palatability measured by means of choice tests with the cabbage army moth, Mamestra brassicae (L.), was interpreted as a sign of defense activation in white clover, Trifolium repens L.. We suggest that induced resistance in Rubira is called an all-ornothing trait, given that its level depends neither on the amount nor on the duration of the aphid feeding stimuli. This qualitative response supports the idea that aphid adaptation might occur because of the loss of pathogen recognition by the plant.

Irrespective of the genetic context of our study, the absence of aphid density-dependence in induction contrats with results from research with arthropods with chewing mouthparts, in which the intensity of herbivory was found to influence the magnitude of induced resistance or defense induction [START_REF] Agrawal | Specificity of constitutive and induced resistance: pigment glands influence mites and caterpillars on cotton plants[END_REF][START_REF] Underwood | Density dependence in induced plant resistance to herbivore damage: threshold, strength and genetic variation[END_REF][START_REF] Massey | Herbivore specific induction of silica-based defences[END_REF]. This difference may be due to the fact that phloem-feeders do not remove leaf tissue per se. For example Zehnder and Hunter (2007) found that in milkweed (Asclepias) species infested by the oleander aphid, Aphis nerii (Boyer de Fonscolombe) (Hemiptera: Aphididae), aphid density did not lead to increased induction of plant defensive cardenolides.

The speed of responses to enemy attacks may be critical in determining whether the plant or the pest prevails. The time course of M. persicae-induced resistance showed a pattern similar to the dynamics of plant defense responses in other well-characterized plant-aphid systems that involve resistance derived from major genes (e.g., [START_REF] Gao | Involvement of the octadecanoid pathway in Bluegreen aphid resistance in Medicago truncatula[END_REF][START_REF] Li | Soybean defense responses of the soybean aphid[END_REF]. In these systems, plant responses were activated as soon as 6 hours after infestation and extended periods of aphid probing activated more genes, whose number could be finally doubled at 36 or 48 hours after infestation. Then, the induction of defense-related genes declined after 24 or 48 hours. In Rubira, a very brief aphid Field data suggest that all M. persicae genotypes tested could be reasonably assigned to a discrete class of avirulence, since no progeny could establish on the plant. It is likely that the matching class of virulence, if it exists, has remained undetected in our sampling scheme because of a low or spatially heterogeneous frequency of virulent genotypes in natural populations. Today, predicting the evolution of resistance conferred by Rm2 is difficult. On the one hand, a previous microsatellite analysis exposed a large spatial and temporal genetic variability in French populations of M. persicae (Guillemaud et al. 2003a), theoretically necessary to allow adaptive genes to evolve (but see [START_REF] Lombaert | Response of the melon aphid, Aphis gossypii, to host-plant resistance : evidence for high adaptive potential despite low genetic variability[END_REF]). In addition, M. persicae contains considerable genetic variation for host plant adaptation [START_REF] Weber | Genetic variability in host plant adaptation of the green peach aphid, Myzus persicae[END_REF][START_REF] Nikolakakis | Performance of Myzus persicae (Hemiptera: Aphididae) clones on different host-plants and their host preference[END_REF] and insecticide resistance has evolved in the populations from which aphids used in the present work were sampled (Guillemaud et al. 2003b). On the other hand, the selection pressure exerted by Rm2 remained very low for more than 30 years, a situation that should not favour the evolution of virulence. In orchards, Rubira is planted as rootstock and thus does not interact with aphid populations. In nursery, it is cultivated as seedling but under strong insecticidal pressure that prevents aphid colonization.

Finally, the important and intriguing finding of this study was the identification of significant quantitative variation in the aphid plant-leaving tendency within the range of avirulent genotypes tested. The conclusion that can be drawn from this result is that virulence in the Rubira-M. persicae interaction may not be qualitative and may also evolve according to the chemical coevolution hypothesis. This assertion seems inconsistent with the interpretation of the first series of experimentations, but it adds weight to the idea that plant-aphid interactions involving genes of the R type may exhibit features consistent with both models of coevolution. There are now at least two cases the gene Vat from melon, Cucumis melo L., are the only two genes of resistance to insects (namely aphids) that have been cloned so far [START_REF] Rossi | The nematode resistance gene Mi of tomato confers resistance against the potato aphid[END_REF][START_REF] Dogimont | Gene resistant to Aphis gossypii[END_REF]). Both belong to the socalled NBS-LRR family of R resistance genes. [START_REF] Hebert | Quantitative differences in aphid virulence and foliar symptom development on tomato plants carrying the Mi resistance gene[END_REF] found that Mi-1.2 differentially affected the population growth of distinct isolates of the potato aphid, Macrosiphum euphorbiae (Thomas) (Hemiptera: Aphididae), all of which were classified as avirulent. In melon, Vat confers both resistance to the melon aphid, Aphis gossypii Glover (Hemiptera: Aphididae), and resistance to non-persistent viruses transmission by this same aphid species. [START_REF] Lombaert | Response of the melon aphid, Aphis gossypii, to host-plant resistance : evidence for high adaptive potential despite low genetic variability[END_REF] detected in aphid populations a continuum of performance response to Vat from complete avirulence to strong virulence, but no variability and no overcoming of Vat resistance were observed for the trait 'virus transmission'. This suggests that A. gossypii is effectively recognized by Vat melon plants, even if the trait 'plant resistance' is overcome.

Large scale analysis of M. persicae populations collected from peach genotypes carrying Rm2 in experimental orchards is now required to get more information about the formal genetics of the interaction. A detailed characterization of the biochemical interactions that occur in Rubira upon aphid attack is also needed to give evidence for a gene-for-gene interaction. This characterization could also benefit to breeding for durable resistance. Genetic variation in induction of plant metabolites has been reported in several systems [START_REF] Zangerl | Furanocoumarin induction in wild parsnip -Genetics and[END_REF][START_REF] Agrawal | Ecological genetics of an induced plant defense against herbivores: additive genetic variance and costs of phenotypic plasticity[END_REF][START_REF] Stevens | Induced resistance in the indeterminate growth of aspen (Populus tremuloides)[END_REF]. If similar variation exists in plant material derived from Rubira, breeders could select for peach genotypes harbouring the highest concentrations in induced defensive compounds, which might improve the efficiency and durability of resistance.

Comment

  Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript threshold density of inducing aphids required to elicit induced resistance, and is the level of induced resistance related to the number of inducing aphids (experiment a)? What is the minimum duration after the beginning of feeding by inducing aphids required to detect induced resistance (experiment b)? Is duration of aphid feeding the same, or can shorter feeding durations trigger induced resistance as well (experiment c)? Finally, what is the time course of induced resistance in the absence of additional aphid feeding (experiment d)?

  Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript completing the final moult. We evaluated the 30 field clones and the reference clone Mp03. We performed two replicates for each clone.

  by examining the null hypothesis H 0 β = 0 by a likelihood ratio statistics. Covariates in the experiments on host resistance were successively the density and duration of infestation. The baseline hazard was set to the control. Right-censored data were used to take into account aphids remaining on plants after the period of observation had expired, i.e. 48 h. The covariate in the experiment on herbivore virulence was the aphid genotype. The baseline hazard at the mean of all covariates in the Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript model was set to the genotype Got 1. Plant replicates were specified as strata in the model. Strata in a

  χ 2 = 5.1, d.f. = 2, P = 0.079). Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Induced resistance persisted for at least 48 hours after the end of a 48 hour preinfestation (Table

  citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Discussion Data from the first part of this study are not sufficient to prove that the interaction between the gene Rm2 from Rubira and M. persicae follows a gene-for-gene model, but the results are a first step towards accepting such a model. The phenotypic expression of resistance as characterized by the aphid plant-leaving tendency matches the enemy perception and defense induction processes involved in R

  Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript feeding duration is required for producing the defense signal. Then, a short time lag between infestation and defense activation ensures rapid and efficient protection against the aphid, compared to other M. persicae-inducible peach genotypes lacking major resistance gene (Sauge et al. 2006). After peak induction at 48 hours, induced resistance decayed over time in the absence of additional infestation. Determining the possible costs and benefits associated with the activation of defensive traits and maintenance of the induction status for prolonged periods of time deserves investigations, because they may influence the evolution of resistance.

  Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript supporting this hypothesis. The gene Mi-1.2 from tomato, Lycopersicon peruvianum (L.) P. Mill., and

  citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript populational variation. Ecology 7: 1933-1940 Zehnder CB, Hunter MD (2007) Interspecific variation within the genus Asclepias in response to herbivory by a phloem-feeding insect herbivore. J Chem Ecol 33: 2044-20. doi:10.1007/s10886-007-9364-4 Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript

  compared to the baseline hazard (uninfested control) for the coefficients at P < 0.05, 0.01 and 0.001 respectively. + indicates an increasing effect of the covariate on the plant-leaving tendency. The more remote the hazard ratio to zero, the stronger the plant-leaving tendency Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript

  χ 2 correspond to a likelihood ratio test. *, **, ***, levels of significance as compared to the baseline hazard (clone Got 1) for the coefficients at P < 0.05, 0.01 Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8 Version préliminaire du manuscrit/ Preliminary version of the manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript Manuscrit d'auteur / Author manuscript and 0.001 respectively. + indicates an increasing effect; -indicates a decreasing effect of the covariate on the plant-leaving tendency

  in the aphid response to host resistance among natural populations of M. persicae and tested

		Version préliminaire du manuscrit/ Preliminary version of the manuscript
	Manuscrit d'auteur / Author manuscript
	Manuscrit d'auteur / Author manuscript	. In addition, there
		are currently no aphid genotypes known to exibit virulence towards Rm2, probably because no
	Manuscrit d'auteur / Author manuscript	resistant commercial variety bearing this gene has been released so far. Since intensive screening for virulence has never been performed to date, we do not know if there are variants with preadaptive advantages among natural populations. Thereupon, our specific objectives were twofold. We first wanted to determine if the induced phenotype of resistance, as measured by the tendency of aphids to leave plants, matches the enemy perception and defense induction processes involved in R gene-mediated resistance. For that, we investigated aphid density and time-dependent aspects of induction. Second, we looked for genetic Comment citer ce document :
		Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (2011).
		Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer)
		and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4),
		369-377. , DOI : 10.1007/s11829-011-9141-8

variation

Table 1

 1 Geographical origin and number (n) of Myzus persicae genotypes collected from peach orchards in southern France. The distance between the sampled orchards is given in Guillemaud et Version préliminaire du manuscrit/ Preliminary version of the manuscript

	al. (2003a)
	Location	Date	n	Longitude	Latitude	Genotype label
	Gotheron	25 February 2002	8	4°57´E	44°58´N	Got 1-8
	Carros	27-28 March 2002	16	7°11´E	43°47´N	Car 1-16
	Avignon	2 April 2002	6	4°48´E	43°56´N	Avi 1-6

Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (

2011

). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8

Table 2

 2 Experimental design used to characterize the expression of plant resistance in response to varying densities (experiment a) and timing of aphid preinfestation (experiments b, c and d). Each experiment included control plants that were not preinfested Version préliminaire du manuscrit/ Preliminary version of the manuscript

	Experiment	Number of	Total time from beginning of feeding by inducing aphids to
		inducing	testing for induced resistance (h) [1]+[2]
		aphids
			Duration of	Time between the end of	[1]+[2]
			feeding [1]	feeding and testing for
				induced resistance [2]
	a (n = 10)	1	48	0	48
		5	48	0	48
		10	48	0	48
		20	48	0	48
	b (n = 6)	20	6	0	6
		20	12	0	12
		20	24	0	24
		20	48	0	48
	c (n = 9 to 10)	20	3	45	48
		20	6	42	48
		20	9	39	48
	d (n = 10)	20	48	0	0
		20	48	24	72
		20	48	48	96
	n represents the number of plant replicates, with 10 aphids per plant

Comment citer ce document : Sauge, M.-H. (Auteur de correspondance), Poëssel, J.-L., Guillemaud, T., Lapchin, L. (

2011

). Resistance induction and herbivore virulence in the interaction between Myzus persicae (Sulzer) and a major aphid resistance gene (Rm2) from peach. Arthropod Plant Interactions, 5 (4), 369-377. , DOI : 10.1007/s11829-011-9141-8

Table 3

 3 Effect of aphid density (experiment a) and timing of preinfestation (experiments b, c and d) on the plant-leaving tendency of Myzus persicae

	Experiment Covariates	β	SE (β)	exp (β)	n	χ 2 (d.f.) P	Effect on
								leaving
								tendency
	a	Treatment effect				500	135 (4)	<0.0001
		-1 aphid	1.84	0.210	6.31***			+
		-5 aphids	1.71	0.206	5.53***			+
		-10 aphids	1.78	0.208	5.95***			+
		-20 aphids	1.57	0.206	4.80***			+
	b	Treatment effect				300	37.2 (4)	<0.0001
		-6 h	0.339	0.218	0.71			no effect
		-12 h	0.322	0.211	1.38			no effect
		-24 h	0.267	0.215	1.31			no effect
		-48 h	0.911	0.207	2.45***			+
	c	Treatment effect				390	24.3 (3)	<0.0001
		-3 h + 45h	0.432	0.164	1.54**			+
		-6 h + 42h	0.610	0.164	1.84***			+
		-9 h + 39 h	0.726	0.162	2.07***			+
	d	Treatment effect				400	71.9 (3)	<0.0001
		-48 h	1.427	0.201	4.17***			+
		-48 h + 24 h	1.228	0.205	3.41***			+
		-48 h + 48 h	0.494	0.209	1.64*			+
	Estimated regression coefficients (β), standard errors (SE) and hazard ratios [exp (β)] for the covariates of a
	Cox proportional hazards model. χ 2 correspond to a likelihood ratio test. *, **, ***, levels of significance as

Table 4

 4 Effect of the genotype of Myzus persicae on the plant-leaving tendency as estimated by a Cox proportional hazards model (n = 1550, χ 2 = 167, d.f. = 30, P < 0.0001)

	Covariates	β	SE (β)	exp (β)	Effect on
					leaving
					tendency
	-Mp03	-0.692	0.205	0.500 ***	-
	-Car 16	-0.094	0.202	0.909	no effect
	-Car 8	-0.086	0.203	0.917	no effect
	-Car 14	-0.077	0.200	0.926	no effect
	-Car 6	-0.053	0.202	0.948	no effect
	-Avi 5	-0.028	0.200	0.972	no effect
	-Car 11	-0.003	0.201	0.996	no effect
	-Car 3	0.008	0.201	1.009	no effect
	-Car 15	0.043	0.204	1.044	no effect
	-Car 2	0.047	0.201	1.048	no effect
	-Got 7	0.122	0.201	1.131	no effect
	-Car 4	0.149	0.200	1.161	no effect
	-Avi 3	0.189	0.201	1.208	no effect
	-Avi 2	0.197	0.200	1.218	no effect
	-Avi 6	0.208	0.201	1.232	no effect
	-Got 4	0.228	0.209	1.257	no effect
	-Got 5	0.242	0.201	1.275	no effect
	-Got 2	0.288	0.200	1.334	no effect
	-Car 10	0.288	0.200	1.334	no effect
	-Got 8	0.296	0.200	1.345	no effect
	-Avi 1	0.307	0.201	1.360	no effect
	-Car 5	0.365	0.200	1.442	no effect
	-Got 3	0.375	0.201	1.456	no effect
	-Got 6	0.388	0.201	1.475	no effect
	-Car 9	0.419	0.201	1.521 *	+
	-Car 12	0.509	0.201	1.664 *	+
	-Car 7	0.639	0.201	1.895 **	+
	-Car 13	0.750	0.201	2.119 ***	+
	-Avi 4	0.942	0.202	2.567 ***	+
	-Car 1	1.302	0.202	3.679 ***	+
	Estimated regression coefficients (β), standard errors (SE) and hazard
	ratios [exp (β)] for the covariates of the model.

Acknowledgements We acknowledge J.P. Lacroze for technical assistance, S. Simon for aphid sampling and C. Favret for english correction of an earlier draft. Part of this work received financial supports from the Institut Français de la Biodiversité and Département Santé des Plantes et Environnement, Institut National de la Recherche Agronomique.