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
$C_v^0$	Plantation host density of cultivar v	0.1 m-2 c
$C_v^{max}$	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 $g\left(\Vert z^{\prime }-z\Vert \right)=\frac{\left(b-2\right)\left(b-1\right)}{2.\pi .a^2}.{\left(1+\frac{\Vert z^{\prime }-z\Vert }{a}\right)}^{-b}$ with ‖z′ − z‖ the Euclidian distance between locations z and z’ in fields i and i’, respectively; the mean dispersal distance is given by: $\frac{2a}{\left(b-3\right)}=20m$.

^e the position of the inflexion point of the sigmoid curve is given by the relation $x_0={\left(\left(\sigma -1\right)/\kappa \sigma \right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sigma $}\right.}\approx 0.5$

^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.