Table 1. Summary of the parameters used in the model and values for rust pathogens.
Notation | Parameter | Value(s) for rust pathogens used in the simulations a |
---|---|---|
Simulation parameters | ||
Y | Number of simulated years | 50 years |
T | Number of time steps in a cropping season | 120 days.year-1 |
J | Number of fields in the landscape | {155; 154; 152; 153; 156} b |
V | Number of host cultivars | 2 |
Initial conditions and seasonality | ||
Plantation host density of cultivar v | 0.1 m-2 c | |
Maximal host density of cultivar v | 2 m-2 c | |
δv | Host growth rate of cultivar v | 0.1 day-1 c |
ϕ | Initial probability of infection | 5.10−4 |
λ | Off-season survival probability | 10−4 |
Pathogen aggressiveness components | ||
emax | Maximal expected infection rate | 0.40 spore-1 |
γmin | Minimal expected latent period duration | 10 days |
γvar | Variance of the latent period duration | 9 days |
Υmax | Maximal expected infectious period duration | 24 days |
Υvar | Variance of the infectious period duration | 105 days |
rmax | Maximal expected propagule production rate | 3.125 spores.day-1 |
Pathogen dispersal | ||
g(.) | Dispersal kernel | Power-law function d |
a | Scale parameter | 40 |
b | Width of the tail | 7 |
π(.) | Contamination function | Sigmoid curve |
κ | Related to position of the inflexion point | 5.33 e |
σ | Related to position of the inflexion point | 3 e |
Host-pathogen genetic interaction | ||
G | Total number of major genes | {1; 2} |
τg | Mutation probability for infectivity gene g f | 10−4 g |
τw | Mutation probability for aggressiveness component w f | 10−4 g |
Qw | Number of pathotypes relative to aggressiveness component w | 6 g |
ρg | Efficiency of major gene g | 1.0 g |
ρw | Efficiency of quantitative trait w | 0.5 g |
θg | Cost of infectivity of infective gene g | 0.5 g |
θw | Cost of aggressiveness for component w | 0.5 g |
βw | Trade-off strength for aggressiveness component w | 1.0 g |
a model parameterisation is detailed in S1 Text.
b values for the five landscape structures.
c same value for all cultivars (no cost of resistance).
d with ‖z′ − z‖ the Euclidian distance between locations z and z’ in fields i and i’, respectively; the mean dispersal distance is given by: .
e the position of the inflexion point of the sigmoid curve is given by the relation
f probability for a propagule to change its infectivity or its aggressiveness on a resistant cultivar carrying major gene g or quantitative resistance trait w.
g same value for all major genes, quantitative resistance traits, infectivity genes and aggressiveness components.