Fig 1.
Soil quality and cash yield variations in a rotation sequence and selection of 10 sequences that maximise cash yield.
a) Each time step corresponds to a harvesting season. Dots indicate discrete values for soil quality (blue circles) and cash yield (red squares). Season crop type is indicated by yellow (lighter) for cash crops and purple (darker) for cover crops. b) Ten optimal rotation patterns according to total cash yield Y. Each row is a rotation sequence, ordered from maximum to minimum yield (top to bottom) among the selection.
Fig 2.
Host-pathogen ecological dynamics, within and between seasons.
a) Dynamics between seasons. After each harvest, initial host density (h(0) = 50) is reinitialised and pathogen density is readjusted according to the pathogen retainment (ϵ = 0.5). b) Dynamics within a season, when there is a susceptible cash crop (i = 1). Host density decreases due to the presence of the pathogen, while the pathogen load increases as long as there are enough crops to infect. c) Dynamics within a season, when there is a non-host cover crop (i = 2). The cover crop maintains its output while remaining unaffected by the pathogen. The pathogen dies since it cannot grow on the cover crop. Both b) and c) show how the dynamics would continue without the harvest.
Fig 3.
Only ecological vs. eco-evolutionary dynamics of host-pathogen interaction.
a) Ecological dynamics, without pathogen evolution. Dynamics between seasons are represented, with infection starting at t = 0 (as in Fig 2a). b) The pathogen population is homogeneous, due to the absence of mutation. c) Eco-evolutionary dynamics with pathogen virulence evolution. Dynamics between seasons are represented, with infection starting at t = 0. Due to pathogen evolution (with μ = 0.1), the impact of the infection in the last cash seasons provokes higher host density loss, compared to a). d) Time evolution of pathogen shows that the relative abundance of fitter strains—in darker colours—increases along seasons. In both b) and d), relative abundances of the pathogen strains are plotted.
Table 1.
List of fixed parameters used in the model.
Fig 4.
Best patterns under infection in different conditions.
a) Selection of ten best patterns from 1024 possible sequences when cash yield loss due to infection is computed using the reference values. Each row is a rotation sequence. b) Best rotation sequence in the set of 10 optimal patterns for each of the conditions. The set index corresponds to conditions as indicated in Table 2. c) Intersection array for the sets of optimal sequences under different conditions. Each cell shows the number of sequences found in the intersection between the sets indicated in the vertical and horizontal labels. Highlighted sequences in (a): We allow for the 1024 possible sequences to repeat twice or thrice i.e. two or three generations. Rotation A is the sequence that maximises yield over multiple generations while Rotation B maximises yield only in the first generation but not later on.
Table 2.
Yield and crop ratio for different pathogen and soil conditions.
Sets refer to the selection of 10 sequences which best maximise yield in each condition. Values in bold indicate the change of conditions in the set with respect to the reference set.
Table 3.
Performance of rotation A and B along three generations.
A and B are the highlighted sequences in Fig 4. Rotation A is the sequence that maximises yield over multiple generations. Rotation B maximises yield in the first generation but not in the subsequent. For each rotation and generation there are shown values for total yield, final soil quality and final frequency of the most virulent strain (p5).
Fig 5.
Eco-evolutionary dynamics of rotation A when repeated thrice (30 seasons).
A) Soil quality (blue circles) and cash yield (red squares) variations, in discrete time-steps which correspond to the harvesting seasons. B) Eco-evolutionary dynamics of crop (yellow = cash, purple = cover) and pathogen (grey) within and between seasons. C) Relative abundances of pathogen strains during the rotation.