Stochastic, spatially-explicit, demo-genetic model simulating the spread and evolution of a pathogen in a heterogeneous landscape.
model_landsepi(timeP, landscape, dispersal, inits, val_seed, hostP, pathoP,
evolP)list of simulation parameters (number of years, number of time-steps per year)
landscape generated through AgriLand
list of dispersal parameters (vectorised dispersal matrix of the pathogen, vectorised dispersal matrix of the host)
list initial conditions (initial probability of infection by the pathogen)
seed (for random number generation)
list of host parameters (number of cultivars, initial planting density, maximal carrying capacity, growth rate, reproduction rate, death rate, resistance formula, parameters of the sigmoid invasion function: kappa, sigma and s)
list of pathogen parameters (probability to survive the off-season, probability to reproduce via sex rather than via cloning, infection rate, reproduction rate, average latent period duration, variance of the latent period, average infectious period duration , variance of the infectious period duration, parameters of the sigmoid contamination function: kappa, sigma, s)
list of evolution parameters (cost of infectivity, cost of aggressiveness, mutation rate, efficiency of major resistance genes, efficiency of quantitative resistance, trade-off strength, number of increments of quantitative resistance erosion, average time to expression of quantitative resistance, Variance of the time to expression of quantitative resistance, adaptation formula)
A set of binary files is generated for every year of simulation and every compartment:
H: healthy hosts,
Hjuv: juvenile healthy hosts,
L: latently infected hosts,
I: infectious hosts,
R: removed hosts,
S: propagules.
Each file indicates for every time-step the number of individuals in each field, and when appropriate for each cultivar and pathotype)
The model is stochastic, spatially explicit (the basic spatial unit is an individual field), based on a SEIR (<U+2018>susceptible-exposed-infectious-removed<U+2019>) structure with a discrete time step. It simulates the spread and evolution of a pathogen in an agricultural landscape, across cropping seasons split by host harvests which impose potential bottlenecks to the pathogen.
A wide array of deployment strategies can be simulated: 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. Quantitative resistance may be expressed from the time of planting, or later in the cropping season (Adult Plant Resistance or Mature Plant Resistance).
The genotype of cultivated plant cultivars is specified using the "resistance formulas", i.e. a vector of size 8. the four first elements indicate whether the cultivar carries major resistance genes #1, #2, #3 and #4, respectively. The following four elements indicate whether the cultivar carried a quantitative resistance trait against the infection rate, the latent period duration, the sporulation rate, or the sporulation duration of the pathogen, respectively. For example, the formula c(1,0,0,0,0,1,0,0) indicates the presence of major gene #1 and a quantitative resistance which increases the duration of the latent period of the pathogen.
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). These genes may also be reassorted via sexual reproduction.
Evolution of a pathogen toward infectivity or increased aggressiveness on a resistant host is often penalised by a fitness cost on susceptible hosts. Consequently, in the present model, pathogens carrying infectivity genes may have reduced infection rate (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 a decreased aggressiveness on susceptible hosts, leading to a trade-off.
Rimbaud L., Papa<U+00EF>x J., Rey J.-F., Barrett L. G. and Thrall P. H. (2018). Assessing the durability and efficiency of landscape-based strategies to deploy plant resistance to pathogens. PLoS Computational Biology 14(4):e1006067.