Genetically-controlled plant resistance can reduce the damage caused by pathogens. However, pathogens have the ability to evolve and overcome such resistance. This often occurs quickly after resistance is deployed, resulting in significant crop losses and a continuing need to develop new resistant cultivars. To tackle this issue, several strategies have been proposed to constrain the evolution of pathogen populations and thus increase genetic resistance durability. These strategies mainly rely on varying different combinations of resistance sources across time (crop rotations) and space. The spatial scale of deployment can vary from multiple resistance sources occurring in a single cultivar (pyramiding), in different cultivars within the same field (cultivar mixtures) or in different fields (mosaics). However, experimental comparison of the efficiency (i. e. ability to reduce disease impact) and durability (i. e. ability to limit pathogen evolution and delay resistance breakdown) of landscape-scale deployment strategies presents major logistical challenges. Therefore, we developed a spatially explicit stochastic model able to assess the epidemiological and evolutionary outcomes of the four major deployment options described above, including both qualitative resistance (i. e. major genes) and quantitative resistance traits against several components of pathogen aggressiveness: infection rate, latent period duration, propagule production rate, and infectious period duration. This model, implemented in the R package landsepi, provides a new and useful tool to assess the performance of a wide range of deployment options, and helps investigate the effect of landscape, epidemiological and evolutionary parameters. This article describes the model and its parameterisation for rust diseases of cereal crops, caused by fungi of the genus Puccinia. To illustrate the model, we use it to assess the epidemiological and evolutionary potential of the combination of a major gene and different traits of quantitative resistance. The comparison of the four major deployment strategies described above will be the objective of future studies.
The deployment of resistant cultivars in agricultural landscapes aims to reduce the ability of plant pathogens to cause disease on crops. However, the durability of plant resistance has often been limited by evolutionary changes in pathogen populations [1]. Typically, there are two main types of resistance. Although exceptions exist, qualitative (or ‘major gene’) resistance is usually monogenic and complete, i. e. conferring full immunity [2–4]. In contrast, quantitative resistance is mostly polygenic and partial, i. e. infection is still possible but pathogen development is reduced to a greater or lesser extent. Consequently, quantitative resistance is often described as affecting one or more components of pathogen aggressiveness (defined as the quantitative ability to colonise and cause damage to the host): lower rate of infection, longer latent period, reduced propagule production, shorter infectious period or lower toxin production [5–8]. Regardless of the source of resistance, pathogens have the potential to evolve infectivity (defined as the qualitative ability to infect the host) and aggressiveness in response to the selection posed by plant resistance [4,9]. This adaptation of pathogens at the population level is generally driven by mutations from non-adapted pathogen genotypes, changes in frequencies of pre-existing adapted genotypes, or introductions via migration from distant areas [9–11]. Emergence of novel pathotypes can result in the breakdown of qualitative resistance or the erosion of quantitative resistance, and consequently restoration of the infectivity or aggressiveness of pathogen population. The economic costs induced by pathogen adaptation may be huge, due firstly to the yield losses directly associated with an epidemic, and secondly because of the significant research and breeding efforts required to identify new resistance sources and develop new resistant cultivars [12]. Several deployment strategies have been proposed to improve the cost-effectiveness of plant resistance and prevent the frequently documented breakdown of major genes after their uniform deployment over large areas [3,4, 9,13,14]. These strategies rely on the use of quantitative resistance, which is thought to be more durable because it poses smaller selection pressure on pathogen populations [1], or on the management of host genetic diversity [15–17]. This diversity can be introduced in time through crop rotations (e. g. recurring succession of different crops in the same field [18]). In space, different crops can be combined in the same field in cultivar mixtures [19,20] or in different fields of the landscape as mosaics [3,17]. Finally, several resistance sources can be stacked in the same cultivar through pyramiding [21,22]. Few empirical studies have directly compared the performance of these different strategies, probably owing to the difficulty of implementing landscape scale experiments in practice (but see [23] for a comparison of all these strategies, except mosaics, using plastic tunnels). Models are not constrained by this difficulty, but surprisingly there are currently no published models enabling a global comparison. Indeed, most models focus on a single strategy (e. g. crop rotation [24,25]; mixtures [26–28]; pyramiding [29,30]; mosaics [31–42]) or a combination of strategies (e. g. mixture and pyramiding: [43]; mosaic and pyramiding: [44,45]). Only a few studies explicitly compare two types of strategies [46–50] and only two studies evaluated more than two strategies [51,52]. As a result, a comprehensive evaluation of different deployment schemes is complicated, and currently only feasible via pairwise comparisons [53,54]. The situation for quantitative resistance is similar, since often only one [28,34,41,42,55], two [36,37,56], or a combination [26,44,49] of pathogen aggressiveness components are targeted, although quantitative resistance can affect several life-history traits of the pathogen. As articulated above, this current gap in our ability to predict which strategy will maximise our ability to control disease epidemics as well as pathogen evolutionary potential (or indeed whether these goals are compatible) emphasises the need for models that can compare different deployment schemes within the same framework, using standardised assumptions. Comparison of different resistance deployment strategies requires the use of relevant evaluation criteria, which may vary depending on stakeholder objectives, and thus have an impact on the optimal strategy [39,45]. Most published models focused only on one criterion, like resistance durability (i. e. the duration from initial deployment to the time when resistance is considered to have been overcome) (e. g. [30,37,47,51,52]), or epidemiological protection (i. e. reduction in pathogen population size and consequently in the proportion of diseased plants) (e. g. [26,28,32,34–36,43,49,50]). However, no correlation seems to exist between durability and epidemiological protection [45,57], and those objectives can even be incompatible in severe epidemic contexts [33]. It is therefore essential to develop methods to assess deployment strategies against multiple evolutionary and epidemiological criteria [3,17,58]. The present study describes a demo-genetic model (i. e. it includes pathogen population demographic dynamics and its genetic evolution) which simulates the spread of a pathogen in a spatially explicit agricultural landscape. The model is flexible and can simulate mosaics, mixtures, rotation, and pyramiding of different major genes and up to four traits for quantitative resistance, acting on different components of pathogen aggressiveness (infection rate, latent period, infectious period, reproduction rate). Performance of resistance deployment is evaluated using several criteria from evolutionary (e. g. durability) or epidemiological (e. g. disease severity) perspectives. Thus, the model enables direct comparison of a range of spatio-temporal deployment strategies, but also enables investigation of the effects of landscape, epidemiological and evolutionary parameters on the ability of a given strategy to control disease. Although the main purpose of this paper is to provide a comprehensive description of the simulation model, we take advantage of the generality of the model and address three specific questions of interest to the scientific community. These questions aim to assess the potential of the combination of qualitative and quantitative resistance, given that the former prevents disease spread but is prone to breakdown, whereas the latter allows some disease development but to a lesser extent: The model can be parameterised to simulate various pathogen life histories. Here, we investigate the above questions in the context of rust diseases of cereal crops, caused by fungi of the genus Puccinia which can dramatically affect crop yields worldwide [59,60]. Over the past decades, breeders have been engaged in an arms race against these pathogens, which exhibit high evolutionary potential in terms of their ability to overcome resistant crop cultivars following deployment [45,60–63].
The model is stochastic, spatially explicit (the basic spatial unit is an individual field), based on a SEIR (‘susceptible-exposed-infectious-removed’) structure with a discrete time step. It simulates the spread (through clonal reproduction and dispersal) and evolution (via mutation) of a pathogen in an agricultural landscape, across cropping seasons split by host harvests which represent potential bottlenecks to the pathogen. The model is based on the model described in previous articles [40,45], but has been considerably modified and extended to enable simulation of a wide array of deployment strategies: mosaics, mixtures, rotations and pyramiding of multiple major resistance genes which affect pathogen infectivity, and up to four quantitative resistance traits. These traits target different aggressiveness components of the pathogen, i. e. the infection rate, the duration of the latent period and the infectious period, and the propagule production rate. Initially, the pathogen is not adapted to any source of resistance and is only present on susceptible hosts. However, through mutation, it can evolve and may acquire infectivity genes (which leads to breakdown of major resistance genes) or increase aggressiveness (which leads to the erosion of the relevant quantitative resistance traits). Evolution of a pathogen toward infectivity or increased aggressiveness on a resistant host is often penalised by a fitness cost on susceptible hosts [2,64–66]. Consequently, in the present model, pathogens carrying infectivity genes may have lower infection rates (cost of infectivity) on susceptible hosts relative to pathogens that do not carry these genes. Similarly, a gain in pathogen aggressiveness on quantitatively resistant hosts is penalised by decreased aggressiveness on susceptible hosts, leading to a trade-off. The evolutionary outcome of a deployment strategy is assessed by measuring the time until the pathogen achieves the three steps to adapt to plant resistance: (d1) first appearance of adapted mutants, (d2) initial migration to resistant hosts and infection (also referred as ‘arrival’ or ‘introduction’ in invasion biology), and (d3) broader establishment in the resistant host population (i. e. the point at which extinction becomes unlikely). Epidemiological outcomes are evaluated using the Green Leaf Area (GLA) as a proxy for yield, and the area under the disease progress curve (AUDPC) to measure disease severity. In this study, a cropping landscape is represented by both its physical structure (defined as the spatial arrangement of field boundaries) and its genetic composition (defined by the allocation of crop cultivars within and among individual fields). All model parameters and values used in the simulations are listed in Table 1 (see S1 Text for details on model parameterisation to rust pathogens). The demo-genetic dynamics of the host-pathogen interaction are based on a SEIR structure. However, to avoid any confusion with the ‘susceptible’ cultivar, we have labelled this structure HLIR for ‘healthy-latent-infectious-removed’. Thus, in the following, Hi, v, t, Li, v, p, t, Ii, v, p, t, Ri, v, p, t, and Pri, p, t respectively denote the number of healthy, latent, infectious and removed individuals (in this model, an ‘individual’ is a given amount of plant tissue, and is referred to as a ‘host’ hereafter for simplicity), and pathogen propagules, in field i (i = 1, …, J), for cultivar v (v = 1, …, V), pathogen genotype p (p = 1, …, P) at time step t (t = 1, …, TxY). T is the number of time steps in a cropping season and Y the number of simulated years (i. e. cropping seasons). Since the host is cultivated, we assume there is no host reproduction, dispersal or natural mortality (leaf senescence near the end of the cropping season is considered as part of host harvest). Fig 3 gives a schematic representation of the model structure. The epidemiological impact of pathogen spread is evaluated by two different measures. Firstly, we use a measure termed Green Leaf Area (GLA), based on the Healthy Area Duration initially developed by Waggoner et al. [73]. The GLA represents the average number of productive hosts per time step and per surface unit, and is considered as a proxy for crop yield [74]. Secondly, we use the area under the disease progress curve (AUDPC), which is the average proportion of diseased hosts relative to the carrying capacity and represents disease severity [74]. We assume only heathy hosts (state H) contribute to crop production (Fig 3). Thus, for cultivar v during year y: GLAv, y=∑t=t0 (y) tf (y) ∑i=1JHi, v, tT×∑i=1JAi (21) AUDPCv, y=∑t=t0 (y) tf (y) ∑i=1J∑p=1P{Ii, v, p, t+Ri, v, p, t}∑t=t0 (y) tf (y) ∑i=1JKi, v (22) In this section, ten scenarios are simulated using the model to assess the evolutionary and epidemiological outcomes of deploying different pyramided combinations of qualitative and quantitative resistances. In this context, the model was parameterised to approximate biotrophic foliar fungal diseases as typified by rusts of cereal crops, caused by fungi of the genus Puccinia.
To assess the durability of a single major gene, the time period from the beginning of the simulation to appearance of mutants able to overcome the major gene (d1), first infection of the resistant cultivar (d2), and broader establishment on the resistant cultivar (d3) were used. Under the simulated conditions, mutants always appeared, dispersed across the landscape and established on a resistant cultivar carrying one major gene in less than one year (Fig 5A, ‘MG1’). When the resistant cultivar carried a second major gene (i. e. as a pyramid with two major genes), the first infection of a resistant host was delayed to 8. 3 years (90% central range, CR90: 0. 4–23. 4) on average, and the pathogen population was not established before, on average, 20. 7 years (CR90: 0. 9–50. 0) (Fig 5A, ‘MG2’). In contrast, when a major gene was combined with a quantitative resistance with a 50% efficiency, the breakdown of the major gene was nearly as quick as if the major gene was alone, regardless of the pathogen life-history trait targeted by the quantitative resistance (Fig 5A, column 3 to 6, and inset). This conclusion is consistent with the results of an experimental study on pepper resistance against root-knot nematode [121], but differs from those of other studies carried out on different pathosystems, showing that a quantitative resistant background can significantly increase the durability of a cultivar carrying a major gene for resistance [122–124]. In order to test if this difference could be due to our assumption that quantitative resistance has a 50% efficiency, we replicated the numerical experiment with higher efficiencies (ρw = 60%, 70%, 80%, 90%). The results of these new simulations indicated that when quantitative resistance efficiency is higher than 80%, durability of the major gene is improved in combination with quantitative resistance, especially if latent period is targeted (time to establishment delayed to 5. 2 years, CR90: 1. 7–10. 8, see S3A Fig). Furthermore, above 90% efficiency, quantitative resistance can increase the durability of the major gene compared to pyramiding of two major genes (average time to establishment between 11. 0 and 30. 9 years depending on the targeted trait, Fig 5B). When deployed alone, quantitative resistance was on average eroded by 26. 4% (CR90: 20–40), 20. 8% (CR90: 0–40), 22. 0% (CR90: 0–40), and 19. 2% (CR90: 0–40) by the end of the simulation, for resistances targeting respectively infection rate, duration of the latent period, sporulation rate and duration of the sporulation period (Fig 6). The associated average speeds of erosion were 2. 16,0. 78,1. 44 and 1. 02% per year, respectively. The targeted pathogen life-history trait appeared to have a significant effect on the final level (Kruskal Wallis χ2 tests with 3 degrees of freedom, p = 8. 10−9) and speed (p = 6. 10−5) of resistance erosion. The combination with a major gene significantly affected the final level (Kruskal Wallis χ2 test with 1 df, p = 8. 10−3), but not the speed (p = 0. 85) of erosion. It is important to remember that the speed of erosion was computed from the time point when quantitative resistance started to erode (hence, following breakdown of the major gene) and not from the beginning of simulations. Assessing the average speed of erosion from the beginning of the simulations would greatly impact the results if the major gene was durable for several years. As previously described, this is not the case with a 50% efficiency of quantitative resistance. However, with a 90% efficiency, the average speed of erosion of quantitative resistance from the beginning of the simulation was 2. 5 to 3. 0% per year when deployed alone, and only 0. 7 to 1. 7% per year when combined with a major gene. In this context, the combination of quantitative resistance with a major gene significantly delayed the start of quantitative resistance erosion (Kruskal Wallis χ2 test with 1 df, p<10−15). The AUDPC of the susceptible cultivar (AUDPCSC), the resistant cultivar (AUDPCRC) and across the entire cropping landscape (AUDPCTOT) averaged across the whole simulation period were used as indicators of the severity of epidemics in the simulated scenarios (see S4 Fig for examples). As expected, regardless of the cultivar or the deployment scenario, disease severity in a landscape where a resistant cultivar is deployed was lower than in a fully susceptible landscape (dashed line in Fig 7). When only a single resistance source was incorporated into the resistant cultivar, the most effective source was quantitative resistance against duration of the latent period (AUDPCRC = 0. 25), followed by quantitative resistance against infection rate, sporulation rate and duration of the sporulation period (AUDPCRC = 0. 32,0. 33 and 0. 34, respectively), and finally major gene resistance (AUDPCRC = 0. 37). When a major gene was combined with one of these resistance sources, the combination of two major genes became the most efficient strategy (AUDPCRC = 0. 22) but also the most variable (CR90: 0. 00–0. 37). Below this, were combinations including quantitative resistance traits in the same order as above and with similar efficiencies (AUDPCRC = 0. 24,0. 31,0. 32, and 0. 33 against latent period, infection rate, sporulation rate and sporulation duration, respectively). For the susceptible cultivar, disease severity was less variable between scenarios than for the resistant cultivar. The average AUDPCSC was 0. 33,0. 37,0. 37,0. 36 and 0. 36, respectively when a major gene or a quantitative resistance trait against infection rate, latent period, sporulation rate or duration of the sporulation period was deployed alone. However, when a major gene was combined with these sources, AUDPCSC was smaller (0. 28,0. 30,0. 29,0. 29 and 0. 30, respectively). Globally, across the whole landscape, disease severity (AUDPCTOT), was very similar to levels of disease severity seen in the resistant cultivar (AUDPCRC), since this cultivar constituted a high proportion of the area being cropped (80%, see Fig 1D for an example). The global severity of disease could also be assessed using the GLA (focusing on healthy hosts) instead of the AUDPC (focusing on diseased hosts). In our context, GLATOT was highly negatively correlated with AUDPCTOT (Pearson correlation coefficient of -0. 92, p<10−15).
Three main properties distinguish models simulating the deployment of resistance and the interpretation of their results: whether they are demographic or demo-genetic, whether they are deterministic or stochastic, and whether they are spatial or not. In contrast with purely demographic models, our model includes the genetic evolution of the pathogen in addition to pathogen population dynamics and host growth during a cropping season. This enables the explicit simulation of the appearance of new genotypes through mutation [29,30,46,48], which represents the first step towards resistance breakdown or erosion (i. e. prior to migration to and broader establishment onto resistant hosts). The time required for the achievement of this first step can be the main determinant of the durability of some deployment strategies, like pyramiding [51]. This step is thus essential to comprehensively assess the relative performance of different deployment strategies. We further note that the present model is stochastic, i. e. it relies on probabilistic computations of simulated biological processes. It is consequently well able to account for biologically realistic random events [127]. As illustrated by Lo Iacono et al. [35], who used a stochastic version of the model developed by van den Bosch et al. [39], the likelihood of extinction events in pathogen populations can considerably impact the performance of a deployment strategy. Finally, because our model is able to simulate explicit landscapes, it accounts for spatial heterogeneity, which affects landscape connectivity and consequently the ability of the pathogen to disperse. Pathogen dispersal, in addition to being one of the unavoidable steps of adaptation to plant resistance, strongly shapes pathogen evolutionary dynamics [12,41,128]. Moreover, the spatial nature of this model enables a wide range of deployment options to be considered at different spatial scales, particularly given the possibility to vary deployment parameters like the proportion of the landscape across which resistant cultivars are planted [32,51], as well as the level of spatial aggregation [28,45,48,49,129,130]. Resistance durability (i. e. the period of time from initial deployment of a resistant cultivar to when resistance is considered to have been overcome) is a typical evolutionary target of resistance deployment strategies, but its computation in a model is not obvious. Proposed methods include targeting the point in time when the first adapted pathogens appear [29,30,39], when their prevalence [37,48,55,131] or frequency in pathogen population [39,51,52] exceeds a threshold, or when productivity of the resistant cultivar drops below an arbitrary threshold [45]. Since different measures give different information, the present model includes several measures of durability: the time until first appearance of mutants, the time until first infection of a resistant host by such mutant, and the time until the prevalence of these mutants exceeds a threshold. The first measure assesses the ability of deployment strategies to reduce the probability of appearance of mutants by reducing pathogen population size. The difference between the first and the second measure provides information on the potential to hinder pathogen migration to resistant hosts, and the difference between the second and the last measure is related to the rate of establishment on resistant cultivars as a result of the balance between selection and genetic drift (occurring between seasons in this model). With respect to the establishment process, it is interesting to note that different stages of invasion can be targeted by changing the value of the threshold. Importantly, we considered that time to establishment was best computed using a prevalence threshold (i. e. total number of resistant hosts infected by adapted pathogens) as opposed to using a frequency-dependent threshold in the pathogen population (i. e. the proportion of adapted pathogens in the global pathogen population). This is because the frequency of adapted pathogens may never (or always) exceed a threshold simply as a result of a very low (or very high) proportion of resistant hosts in the landscape relative to susceptible hosts. As pointed out in the introduction, evolutionary and epidemiological outcomes are not necessarily correlated. In this context, several epidemiological outputs are used in this study to characterise the level of protection provided by a deployment strategy against the potential damage caused by an epidemic. Some previous studies focused on the final state of the simulations or on the point at which a stable evolutionary equilibrium is reached, thus proposing criteria related to the final proportion of healthy [43,44] or infected [26,49,129] hosts. However, in addition to long-term measures related to stable equilibria, short-term and transitory periods measures are important because severe epidemics responsible for heavy losses may occur during these stages [125,132]. These periods can be accounted for by averaging the number of healthy hosts over the whole simulation run using an analogy of our Green Leaf Area [35–37,40,42,133] or the number of infected hosts using the area under disease progress curve (AUDPC) [28,32,33,48,50]. Interestingly, these measures offer the possibility to concentrate on different evolutionary phases, for example the short-term period following resistance deployment until resistance breakdown, and the long-term period once resistance is overcome [45]. In the present study, the proposed outputs are based on both GLA and AUDPC, computed not only for the whole simulation run to have a global snapshot of the epidemiological outcome, but also for different time periods: from initial resistance deployment until the first resistance is overcome, from the time when all resistances are overcome until the end of the simulation as well as during the transitory period. The performance of various deployment strategies can differ during these three periods, since they are associated with different epidemiological contexts. Thus, it is important to consider these different measures together. Moreover, the objectives of different stakeholders define whether such criteria should be computed from the AUDPC or from the GLA. Indeed, if the objective is to limit the amount of disease, the use of AUDPC-based variables may be more appropriate, since they target infected hosts. In contrast, GLA-based variables represent the amount of healthy hosts which generally represent the largest contribution to crop yield. Thus, this variable can be useful when considering the impact of a given deployment strategy on productivity, especially when resistance costs, different planting densities, or different host species are involved. It is interesting to note that here, only healthy hosts were assumed to participate in host growth and contribute to final yield, considering that the infection by a pathogen consumes host resources. For rust pathogens of cereal crops, this assumption seems reasonable since it has been shown that manual defoliation of wheat leaves decreases yield less than infection by Puccinia striiformis [73]. Nevertheless, this assumption can easily be changed by including hosts at different sanitary stages (e. g. latently infected but not yet diseased) in the logistic equation of host growth and in computation of the GLA. In this study, we present an initial exploration of the model where we evaluate the potential of combining qualitative and quantitative resistance to control rust of cereal crops. We note that in this exploration some parameters (in particular mutation probabilities, see S1 Text) were arbitrarily fixed to study a simple and theoretical situation where a resistant cultivar carrying a single major gene would be rapidly overcome following deployment. This is because our intent in this case was to compare different resistance combinations rather than provide an absolute prediction of the durability and efficiency of a particular strategy. Regardless, altering the mutation probabilities, as long as they are the same for all infectivity genes and aggressiveness components, changes our results quantitatively but not qualitatively (see S1 Text and the results of simulation performed with smaller mutation probabilities in S5 Fig). In a recent review dealing with the combination of qualitative and quantitative resistances, Pilet-Nayel et al. [143] wrote “There is still a need to adequately choose resistance QTLs to create optimal combinations and limit QTL erosion”. The present work highlights that longer latent periods may be one promising target. Nevertheless, the general features of the model could be used to test if our conclusions hold in different contexts. Our simulations showed that the efficiency of quantitative resistance (ρw) has a strong impact on the durability and epidemiological control of plant resistance. Therefore, in future studies we plan to assess the influence of the efficiency of qualitative resistance by including partially effective major genes (ρg<1, [3]). We also envisage varying the mutation probabilities (τg and τw), cost of infectivity (θg), cost of aggressiveness (θw), and number of steps to erode a trait for quantitative resistance (Qw), to simulate various possible choices of major genes and traits for quantitative resistance. It would also be of interest to simulate and investigate the potential for combinations of several sources of quantitative resistance, whose performance on disease severity has been experimentally demonstrated [144]. Finally, we will also explore different spatiotemporal strategies to deploy plant resistance to pathogens. In particular, we plan to compare mosaics, mixtures, rotations and pyramids of genetic resistances with respect to their epidemiological and evolutionary outcomes. The challenge is to identify strategies for a given host-pathogen interaction that are not only durable and efficient, but also feasible and likely to be adopted. In this context, promising strategies identified with the simulation model could be experimentally tested in the field. In addition, broader consideration of the economic context will also help maximise the chances that identified strategies are considered for real deployment.
There are many recent examples which demonstrate the evolutionary potential of plant pathogens to overcome the resistances deployed in agricultural landscapes to protect our crops. Increasingly, it is recognised that how resistance is deployed spatially and temporally can impact on rates of pathogen evolution and resistance breakdown. Such deployment strategies are mainly based on the combination of several sources of resistance at different spatiotemporal scales. However, comparison of these strategies in a predictive sense is not an easy task, owing to the logistical difficulties associated with experiments involving the spread of a pathogen at large spatio-temporal scales. Moreover, both the durability of a strategy and the epidemiological protection it provides to crops must be assessed since these evaluation criteria are not necessarily correlated. Surprisingly, no current simulation model allows a thorough comparison of the different options. Here we describe a spatio-temporal model able to simulate a wide range of deployment strategies and resistance sources. This model, implemented in the R package landsepi, facilitates assessment of both epidemiological and evolutionary outcomes across simulated scenarios. In this work, the model is used to investigate the combination of different sources of resistance against fungal diseases such as rusts of cereal crops.
medicine and health sciences
pathology and laboratory medicine
infectious disease epidemiology
pathogens
plant science
fungal evolution
crops
plant pathology
infectious diseases
mycology
crop science
epidemiology
pathogenesis
evolutionary genetics
agriculture
host-pathogen interactions
plant pathogens
biology and life sciences
evolutionary biology
Assessing the durability and efficiency of landscape-based strategies to deploy plant resistance to pathogens