The proportion of resistant hosts in mixtures should be biased towards the resistance with the lowest breaking cost.

Current agricultural practices facilitate emergence and spread of plant diseases through the wide use of monocultures. Host mixtures are a promising alternative for sustainable plant disease control. Their effectiveness can be partly explained by priming-induced cross-protection among plants. Priming occurs when plants are challenged with non-infective pathogen genotypes, resulting in increased resistance to subsequent infections by infective pathogen genotypes. We developed an epidemiological model to explore how mixing two distinct resistant varieties can reduce disease prevalence. We considered a pathogen population composed of three genotypes infecting either one or both varieties. We found that host mixtures should not contain an equal proportion of resistant plants, but a biased ratio (e.g. 80 : 20) to minimize disease prevalence. Counter-intuitively, the optimal ratio of resistant varieties should contain a lower proportion of the costliest resistance for the pathogen to break. This benefit is amplified by priming. This strategy also prevents the invasion of pathogens breaking all resistances.

Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen lesions.

Within-host spread of pathogens is an important process for the study of plant-pathogen interactions. However, the development of plant-pathogen lesions remains practically difficult to characterize beyond the common traits such as lesion area. Here, we address this question by combining image-based phenotyping with mathematical modelling. We consider the spread of Peyronellaea pinodes on pea stipules that were monitored daily with visible imaging. We assume that pathogen propagation on host-tissues can be described by the Fisher-KPP model where lesion spread depends on both a logistic growth and an homogeneous diffusion. Model parameters are estimated using a variational data assimilation approach on sets of registered images. This modelling framework is used to compare the spread of an aggressive isolate on two pea cultivars with contrasted levels of partial resistance. We show that the expected slower spread on the most resistant cultivar is actually due to a significantly lower diffusion coefficient. This study shows that combining imaging with spatial mechanistic models can offer a mean to disentangle some processes involved in host-pathogen interactions and further development may allow a better identification of quantitative traits thereafter used in genetics and ecological studies.

Improving sustainable crop protection using population genetics concepts.

Growing genetically resistant plants allows pathogen populations to be controlled and reduces the use of pesticides. However, pathogens can quickly overcome such resistance. In this context, how can we achieve sustainable crop protection? This crucial question has remained largely unanswered despite decades of intense debate and research effort. In this study, we used a bibliographic analysis to show that the research field of resistance durability has evolved into three subfields: (1) "plant breeding" (generating new genetic material), (2) "molecular interactions" (exploring the molecular dialogue governing plant-pathogen interactions) and (3) "epidemiology and evolution" (explaining and forecasting of pathogen population dynamics resulting from selection pressure[s] exerted by resistant plants). We argue that this triple split of the field impedes integrated research progress and ultimately compromises the sustainable management of genetic resistance. After identifying a gap among the three subfields, we argue that the theoretical framework of population genetics could bridge this gap. Indeed, population genetics formally explains the evolution of all heritable traits, and allows genetic changes to be tracked along with variation in population dynamics. This provides an integrated view of pathogen adaptation, in particular via evolutionary-epidemiological feedbacks. In this Opinion Note, we detail examples illustrating how such a framework can better inform best practices for developing and managing genetically resistant cultivars.

How growers make decisions impacts plant disease control.

While the spread of plant disease depends strongly on biological factors driving transmission, it also has a human dimension. Disease control depends on decisions made by individual growers, who are in turn influenced by a broad range of factors. Despite this, human behaviour has rarely been included in plant epidemic models. Considering Cassava Brown Streak Disease, we model how the perceived increase in profit due to disease management influences participation in clean seed systems (CSS). Our models are rooted in game theory, with growers making strategic decisions based on the expected profitability of different control strategies. We find that both the information used by growers to assess profitability and the perception of economic and epidemiological parameters influence long-term participation in the CSS. Over-estimation of infection risk leads to lower participation in the CSS, as growers perceive that paying for the CSS will be futile. Additionally, even though good disease management can be achieved through the implementation of CSS, and a scenario where all controllers use the CSS is achievable when growers base their decision on the average of their entire strategy, CBSD is rarely eliminated from the system. These results are robust to stochastic and spatial effects. Our work highlights the importance of including human behaviour in plant disease models, but also the significance of how that behaviour is included.

Spatial spread of infectious diseases with conditional vector preferences.

We explore the spatial spread of vector-borne infections with conditional vector preferences, meaning that vectors do not visit hosts at random. Vectors may be differentially attracted toward infected and uninfected hosts depending on whether they carry the pathogen or not. The model is expressed as a system of partial differential equations with vector diffusion. We first study the non-spatial model. We show that conditional vector preferences alone (in the absence of any epidemiological feedback on their population dynamics) may result in bistability between the disease-free equilibrium and an endemic equilibrium. A backward bifurcation may allow the disease to persist even though its basic reproductive number is less than one. Bistability can occur only if both infected and uninfected vectors prefer uninfected hosts. Back to the model with diffusion, we show that bistability in the local dynamics may generate travelling waves with either positive or negative spreading speeds, meaning that the disease either invades or retreats into space. In the monostable case, we show that the disease spreading speed depends on the preference of uninfected vectors for infected hosts, but also on the preference of infected vectors for uninfected hosts under some circumstances (when the spreading speed is not linearly determined). We discuss the implications of our results for vector-borne plant diseases, which are the main source of evidence for conditional vector preferences so far.

Coinfections by noninteracting pathogens are not independent and require new tests of interaction.

If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of coinfected hosts is expected to be higher than multiplication would suggest. By modelling the dynamics of multiple noninteracting pathogens causing chronic infections, we develop a pair of novel tests of interaction that properly account for nonindependence between pathogens causing lifelong infection. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates how methods to identify interactions between pathogens can be updated using simple epidemic models.

Epidemiological and ecological consequences of virus manipulation of host and vector in plant virus transmission.

Many plant viruses are transmitted by insect vectors. Transmission can be described as persistent or non-persistent depending on rates of acquisition, retention, and inoculation of virus. Much experimental evidence has accumulated indicating vectors can prefer to settle and/or feed on infected versus noninfected host plants. For persistent transmission, vector preference can also be conditional, depending on the vector's own infection status. Since viruses can alter host plant quality as a resource for feeding, infection potentially also affects vector population dynamics. Here we use mathematical modelling to develop a theoretical framework addressing the effects of vector preferences for landing, settling and feeding-as well as potential effects of infection on vector population density-on plant virus epidemics. We explore the consequences of preferences that depend on the host (infected or healthy) and vector (viruliferous or nonviruliferous) phenotypes, and how this is affected by the form of transmission, persistent or non-persistent. We show how different components of vector preference have characteristic effects on both the basic reproduction number and the final incidence of disease. We also show how vector preference can induce bistability, in which the virus is able to persist even when it cannot invade from very low densities. Feedbacks between plant infection status, vector population dynamics and virus transmission potentially lead to very complex dynamics, including sustained oscillations. Our work is supported by an interactive interface https://plantdiseasevectorpreference.herokuapp.com/. Our model reiterates the importance of coupling virus infection to vector behaviour, life history and population dynamics to fully understand plant virus epidemics.

Taking Advantage of Pathogen Diversity and Immune Priming to Minimize Disease Prevalence in Host Mixtures: A Model.

Host mixtures are a promising method for agroecological plant disease control. Plant immunity is key to the success of host mixtures against polymorphic pathogen populations. This immunity results from priming-induced cross-protection, whereby plants able to resist infection by specific pathogen genotypes become more resistant to other pathogen genotypes. Strikingly, this phenomenon was absent from mathematical models aiming at designing host mixtures. We developed a model to specifically explore how priming affects the coexistence of two pathogen genotypes in host mixtures composed of two host genotypes and how it affects disease prevalence. The main effect of priming is to reduce the coexistence region in the parameter space (due to the cross-protection) and to generate a singular mixture of resistant and susceptible hosts corresponding to the maximal reduction disease prevalence (in absence of priming, a resistant pure stand is optimal). The epidemiological advantage of host mixtures over a resistant pure stand thus appears as a direct consequence of immune priming. We also showed that there is indirect cross-protection between host genotypes in a mixture. Moreover, the optimal mix prevents the emergence of a resistance-breaking pathogen genotype. Our results highlight the importance of considering immune priming to design optimal and sustainable host mixtures.

Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions.

Assessing life-history traits of parasites on resistant hosts is crucial in evolutionary ecology. In the particular case of sporulating pathogens with growing lesions, phenotyping is difficult because one needs to disentangle properly pathogen spread from sporulation. By considering Phytophthora infestans on potato, we use mathematical modelling to tackle this issue and refine the assessment of pathogen response to quantitative host resistance. We elaborate a parsimonious leaf-scale model by convolving a lesion growth model and a sporulation function, after a latency period. This model is fitted to data obtained on two isolates inoculated on three cultivars with contrasted resistance level. Our results confirm a significant host-pathogen interaction on the various estimated traits, and a reduction of both pathogen spread and spore production, induced by host resistance. Most interestingly, we highlight that quantitative resistance also changes the sporulation function, the mode of which is significantly time-lagged. This alteration of the infectious period distribution on resistant hosts may have strong impacts on the dynamics of parasite populations, and should be considered when assessing the durability of disease control tactics based on plant resistance management. This inter-disciplinary work also supports the relevance of mechanistic models for analysing phenotypic data of plant-pathogen interactions.

Mate Limitation in Fungal Plant Parasites Can Lead to Cyclic Epidemics in Perennial Host Populations.

Fungal plant parasites represent a growing concern for biodiversity and food security. Most ascomycete species are capable of producing different types of infectious spores both asexually and sexually. Yet the contributions of both types of spores to epidemiological dynamics have still to been fully researched. Here we studied the effect of mate limitation in parasites which perform both sexual and asexual reproduction in the same host. Since mate limitation implies positive density dependence at low population density, we modeled the dynamics of such species with both density-dependent (sexual) and density-independent (asexual) transmission rates. A first simple SIR model incorporating these two types of transmission from the infected compartment, suggested that combining sexual and asexual spore production can generate persistently cyclic epidemics in a significant part of the parameter space. It was then confirmed that cyclic persistence could occur in realistic situations by parameterizing a more detailed model fitting the biology of the Black Sigatoka disease of banana, for which literature data are available. We discuss the implications of these results for research on and management of Sigatoka diseases of banana.

Modeling Virus Coinfection to Inform Management of Maize Lethal Necrosis in Kenya.

Maize lethal necrosis (MLN) has emerged as a serious threat to food security in sub-Saharan Africa. MLN is caused by coinfection with two viruses, Maize chlorotic mottle virus and a potyvirus, often Sugarcane mosaic virus. To better understand the dynamics of MLN and to provide insight into disease management, we modeled the spread of the viruses causing MLN within and between growing seasons. The model allows for transmission via vectors, soil, and seed, as well as exogenous sources of infection. Following model parameterization, we predict how management affects disease prevalence and crop performance over multiple seasons. Resource-rich farmers with large holdings can achieve good control by combining clean seed and insect control. However, crop rotation is often required to effect full control. Resource-poor farmers with smaller holdings must rely on rotation and roguing, and achieve more limited control. For both types of farmer, unless management is synchronized over large areas, exogenous sources of infection can thwart control. As well as providing practical guidance, our modeling framework is potentially informative for other cropping systems in which coinfection has devastating effects. Our work also emphasizes how mathematical modeling can inform management of an emerging disease even when epidemiological information remains scanty. [Formula: see text] Copyright © 2017 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

The evolution of plant virus transmission pathways.

The evolution of plant virus transmission pathways is studied through transmission via seed, pollen, or a vector. We address the questions: under what circumstances does vector transmission make pollen transmission redundant? Can evolution lead to the coexistence of multiple virus transmission pathways? We restrict the analysis to an annual plant population in which reproduction through seed is obligatory. A semi-discrete model with pollen, seed, and vector transmission is formulated to investigate these questions. We assume vector and pollen transmission rates are frequency-dependent and density-dependent, respectively. An ecological stability analysis is performed for the semi-discrete model and used to inform an evolutionary study of trade-offs between pollen and seed versus vector transmission. Evolutionary dynamics critically depend on the shape of the trade-off functions. Assuming a trade-off between pollen and vector transmission, evolution either leads to an evolutionarily stable mix of pollen and vector transmission (concave trade-off) or there is evolutionary bi-stability (convex trade-off); the presence of pollen transmission may prevent evolution of vector transmission. Considering a trade-off between seed and vector transmission, evolutionary branching and the subsequent coexistence of pollen-borne and vector-borne strains is possible. This study contributes to the theory behind the diversity of plant-virus transmission patterns observed in nature.

Mate Finding, Sexual Spore Production, and the Spread of Fungal Plant Parasites.

Sexual reproduction and dispersal are often coupled in organisms mixing sexual and asexual reproduction, such as fungi. The aim of this study is to evaluate the impact of mate limitation on the spreading speed of fungal plant parasites. Starting from a simple model with two coupled partial differential equations, we take advantage of the fact that we are interested in the dynamics over large spatial and temporal scales to reduce the model to a single equation. We obtain a simple expression for speed of spread, accounting for both sexual and asexual reproduction. Taking Black Sigatoka disease of banana plants as a case study, the model prediction is in close agreement with the actual spreading speed (100 km per year), whereas a similar model without mate limitation predicts a wave speed one order of magnitude greater. We discuss the implications of these results to control parasites in which sexual reproduction and dispersal are intrinsically coupled.

The functional response predicts the effect of resource distribution on the optimal movement rate of consumers.

Understanding how often individuals should move when foraging over patchy habitats is a central question in ecology. By combining optimality and functional response theories, we show analytically how the optimal movement rate varies with the average resource level (enrichment) and resource distribution (patch heterogeneity). We find that the type of functional response predicts the effect of enrichment in homogeneous habitats: enrichment should decrease movement for decelerating functional responses, but increase movement for accelerating responses. An intermediate resource level thus maximises movement for type-III responses. Counterintuitively, greater movement costs favour an increase in movement. In heterogeneous habitats predictions further depend on how enrichment alters the variance of resource distribution. Greater patch variance always increases the optimal rate of movement, except for type-IV functional responses. While the functional response is well established as a fundamental determinant of consumer-resource dynamics, our results indicate its importance extends to the understanding of individual movement strategies.

Allee effects and the evolution of polymorphism in cyclic parthenogens.

Cyclic parthenogens alternate asexual reproduction with periodic episodes of sexual reproduction. Sexually produced free-living forms are often their only way to survive unfavorable periods. When sexual reproduction requires the mating of two self-incompatible individuals, mating limitation may generate an Allee effect, which makes small populations particularly vulnerable to extinction; parthenogenetic reproduction can attenuate this effect. However, asexual reproduction likely trades off with sexual reproduction. To explore the evolutionary implications of such a trade-off, we included recurrent mating events associated with seasonal interruptions in a simple population dynamics model. Following an adaptive dynamics approach, we showed that positive density dependence associated with Allee effects in cyclic parthenogens promotes evolutionary divergence in the level of investment in asexual reproduction. Although polymorphism may be transient, morphs mostly investing into sexual reproduction may eventually exclude those predominantly reproducing in an asexual manner. Asexual morphs can be seen as making cooperative investments into the common pool of mates, while sexual morphs defect, survive better, and may eventually fix in the population. Our findings provide a novel hypothesis for the frequent coexistence of sexual and asexual lineages, notably in plant parasitic fungi.

Simple signaling games of sexual selection (Grafen's revisited).

We investigate several versions of a simple game of sexual selection, to explore the role of secondary sexual characters (the "handicap paradox") with the tools of signaling theory. Our models admit closed form solutions. They are very much inspired by Grafen's (J Theor Biol 144:517-546, 1990a; J Theor Biol 144:473-516, 1990b) seminal companion papers. By merging and simplifying his two approaches, we identify a not so minor artifact in the seminal study. We propose an alternative model to start with Grafen's sexual selection theory, with several similarities with Getty (Anim Behav 56:127-130, 1998).

Host mixtures for plant disease control: Benefits from pathogen selection and immune priming.

Multiline and cultivar mixtures are highly effective methods for agroecological plant disease control. Priming-induced cross protection, occurring when plants are challenged by avirulent pathogen genotypes and resulting in increased resistance to subsequent infection by virulent ones, is one critical key to their lasting performance against polymorphic pathogen populations. Strikingly, this mechanism was until recently absent from mathematical models aiming at designing optimal host mixtures. We developed an epidemiological model to explore the effect of host mixtures composed of variable numbers of single-resistance cultivars on the equilibrium prevalence of the disease caused by pathogen populations polymorphic for virulence complexity. This model shows that a relatively large amount of resistance genes must be deployed to achieve low disease prevalence, as pathogen competition in mixtures tends to select for intermediate virulence complexity. By contrast, priming significantly reduces the number of plant genotypes needed to drop disease prevalence below an acceptable threshold. Given the limited availability of resistance genes in cultivars, this mechanism of plant immunity should be assessed when designing host mixtures.

Seasonality and the evolutionary divergence of plant parasites.

The coexistence of closely related plant parasites is widespread. Yet, understanding the ecological determinants of evolutionary divergence in plant parasites remains an issue. Niche differentiation through resource specialization has been widely researched, but it hardly explains the coexistence of parasites exploiting the same host plant. Time-partitioning has so far received less attention, although in temperate climates, parasites may specialize on either the early or the late season. Accordingly, we investigated whether seasonality can also promote phenotypic divergence. For plant parasites, seasonality generally engenders periodic host absence. To account for abrupt seasonal events, we made use of an epidemic model that combines continuous and discrete dynamics. Based on the assumption of a trade-off between in-season transmission and inter-season survival, we found through an "evolutionary invasion analysis" that evolutionary divergence of the parasite phenotype can occur. Since such a trade-off has been reported, this study provides further ecological bases for the coexistence of closely related plant parasites. Moreover, this study provides original insights into the coexistence of sibling plant pathogens which perform either a single or several infection cycles within a season (mono- and polycyclic diseases, or uni- and multivoltine life cycles).

Fitness costs associated with unnecessary virulence factors and life history traits: evolutionary insights from the potato late blight pathogen Phytophthora infestans.

BACKGROUND: In gene-for-gene models of plant-pathogen interactions, the existence of fitness costs associated with unnecessary virulence factors still represents an issue, both in evolutionary biology and agricultural sciences. Measuring such costs experimentally has proven difficult, especially in pathogens not readily amenable to genetic transformation, since the creation of isogenic lines differing only by the presence or absence of avirulence genes cannot be achieved in many organisms. Here, we circumvented this difficulty by comparing fitness traits in groups of Phytophthora infestans isolates sharing the same multilocus fingerprint, but differing by their virulence/avirulence spectrum. RESULTS: Fitness was assessed from calculations derived from the basic reproduction number, combining several life history traits (latent period, spore density and lesion growth rate) evaluated on leaflets of the potato cultivar Bintje, which is free of resistance genes. A statistically significant fitness cost was found in isolates virulent to the R10 resistance gene. That cost was due to a lower spore production in virulent isolates; however, the latent period was shorter in virulent isolates. Similar trends, although not statistically significant, were observed for the other genes tested. CONCLUSION: The data likely reflect the adaptive response of the pathogen to the cost associated with virulence. They suggest strong trade-offs between life history traits related to pathogenicity and adaptive biology of pathogens.

A differential game theoretical analysis of mechanistic models for territoriality.

In this paper, elements of differential game theory are used to analyze a spatially explicit home range model for interacting wolf packs when movement behavior is uncertain. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of individuals within each pack and whose steady-state solutions describe the patterns of space-use associated to each pack. By controlling the behavioral parameters in a spatially-dynamic fashion, packs adjust their patterns of movement so as to find a Nash-optimal balance between spreading their territory and avoiding conflict with hostile neighbors. On the mathematical side, we show that solving a nonzero-sum differential game corresponds to finding a non-invasible function-valued trait. From the ecological standpoint, when movement behavior is uncertain, the resulting evolutionarily stable equilibrium gives rise to a buffer-zone, or a no-wolf's land where deer are known to find refuge.