Timing of Pathogen Adaptation to a Multicomponent Treatment

The sustainable use of multicomponent treatments such as combination therapies, combination vaccines/chemicals, and plants carrying multigenic resistance requires an understanding of how their population-wide deployment affects the speed of the pathogen adaptation. Here, we develop a stochastic model describing the emergence of a mutant pathogen and its dynamics in a heterogeneous host population split into various types by the management strategy. Based on a multi-type Markov birth and death process, the model can be used to provide a basic understanding of how the life-cycle parameters of the pathogen population, and the controllable parameters of a management strategy affect the speed at which a pathogen adapts to a multicomponent treatment. Our results reveal the importance of coupling stochastic mutation and migration processes, and illustrate how their stochasticity can alter our view of the principles of managing pathogen adaptive dynamics at the population level. In particular, we identify the growth and migration rates that allow pathogens to adapt to a multicomponent treatment even if it is deployed on only small proportions of the host. In contrast to the accepted view, our model suggests that treatment durability should not systematically be identified with mutation cost. We show also that associating a multicomponent treatment with defeated monocomponent treatments can be more durable than associating it with intermediate treatments including only some of the components. We conclude that the explicit modelling of stochastic processes underlying evolutionary dynamics could help to elucidate the principles of the sustainable use of multicomponent treatments in population-wide management strategies intended to impede the evolution of harmful populations.Comment: 3 figure

Sustainable deployment of QTLs conferring quantitative resistance to crops: first lessons from a stochastic model

Quantitative plant disease resistance is believed to be more durable than qualitative resistance, since it exerts less selective pressure on the pathogens. However, the process of progressive pathogen adaptation to quantitative resistance is poorly understood, which makes it difficult to predict its durability or to derive principles for its sustainable deployment. Here, we study the dynamics of pathogen adaptation in response to quantitative plant resistance affecting pathogen reproduction rate and its carrying capacity. We developed a stochastic model for the continuous evolution of a pathogen population within a quantitatively resistant host. We assumed that pathogen can adapt to a host by the progressive restoration of reproduction rate or of carrying capacity, or of both. Our model suggests that a combination of QTLs affecting distinct pathogen traits was more durable if the evolution of repressed traits was antagonistic. Otherwise, quantitative resistance that depressed only pathogen reproduction was more durable. In order to decelerate the progressive pathogen adaptation, QTLs that decrease the pathogen's ability to extend must be combined with QTLs that decrease the spore production per lesion or the infection efficiency or that increase the latent period. Our theoretical framework can help breeders to develop principles for sustainable deployment of quantitative trait loci.

Spreading of virulence regarding spatial distribution resistant cultivars inferred from population modeling coupled with genetics

One of the control strategies of fungal crop diseases is planting highly resistant varieties. However selection pressure on the pathogen, imposed by major resistance genes, leads to the development of new virulent races. In most cases breakdown of resistance has been reported for crop-pathogen systems with a genetically uniform crop distributed over large areas [2]. Des choix stratégiques en matière de construction et de déploiement de génotypes résistants combinant des gènes de résistance se pose aujourd’hui de manière aigüe afin de tendre vers une agriculture à résistance durable. To reach this objective, we start a study that combined population modeling with genetics to (1) identify keys traits of life of the pathogen involved in resistance breakdown (2) simulate virulence spreading regarding spatial host distribution

Exponentiality of first passage times of continuous time Markov chains

Let (X,\p_x) be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $\mu$ is a quasi-stationary distribution relatively to $T$, then this time is exponentially distributed under \p_\mu. However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution $\mu$ for $T$ to be exponentially distributed under \p_\mu. We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of $T$ exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity

Spatially explicit modeling of pathogen adaptation to hosts with multiple resistance genes

One of the control strategies of fungal crop diseases is planting highly resistant varieties. However selection pressure on the pathogen, imposed by major resistance genes, leads to the development of new virulent races. In most cases breakdown of resistance has been reported for crop-pathogen systems with a genetically uniform crop distributed over large areas[2]. To derive strategies leading to durable resistance we focus on studying the role of recombination of pathogen genotypes and their spread in the process of succes-sive breakdowns of resistant hosts carrying different major resistance genes and their pyramids

Pathogen invasion assisted by evolution : a spatially explicit model for a multilocus gene-for-gene system

International audienc

On the Importance of Non-Gaussianity in Chlorophyll Fluorescence Imaging

We propose a mathematical study of the statistics of chlorophyll fluorescence indices. While most of the literature assumes Gaussian distributions for these indices, we demonstrate their fundamental non-Gaussian nature. Indeed, while the noise in the raw fluorescence images can be assumed as Gaussian additive, the deterministic ratio between them produces nonlinear non-Gaussian distributions. We investigate the states in which this non-Gaussianity can affect the statistical estimation when wrongly approached with linear estimators. We provide an expectation–maximization estimator adapted to the non-Gaussian distributions. We illustrate the interest of this estimator with simulations from images of chlorophyll fluorescence indices.. We demonstrate the benefits of our approach by comparison with the standard Gaussian assumption. Our expectation–maximization estimator shows low estimation errors reaching seven percent for a more pronounced deviation from Gaussianity compared to Gaussianity assumptions estimators rising to more than 70 percent estimation error. These results show the importance of considering rigorous mathematical estimation approaches in chlorophyll fluorescence indices. The application of this work could be extended to various vegetation indices also made up of a ratio of Gaussian distributions

Spatial deployment of gene-for-gene resistance governs evolution and spread of pathogen populations

International audienceWe formulate a spatially realistic population-genetic model for ascertaining the synergetic effect between genetic and spatial composition of the host population on the pathogen spread reinforced by evolutionary processes. We show that spatial arrangement of host genotypes is crucial to the efficacy of host genetic diversification. In particular, the reductive effect of multigenic resistance on the pathogen density can be produced by a random patterning of monogenic resistances. Random patterns can reduce both density and genetic diversity of the pathogen population and delay invasion promoted by sexual recombination. By contrast, patchy distributions diversify pathogen population and, hence, reduce the efficacy of resistance genes. The proposed approach provides theoretical support for studying fast emergence and spread of novel pathogen genotypes carrying multiple virulence genes. It has a practical applicability to design innovative strategies for the most appropriate deployment of plant resistance genes