Fig 1.
Stock-and-flow icons are used to graphically build systems of difference (lavender-pink square in cell capsule) and differential (lime-green square in agent capsule) equations that Nova encapsulates as chips with input output pins (pale blue squares) at higher levels of representation, through drag and drop construction.
Agent and cell capsules respectively dropped onto the clover and purple colored components of an aggregator that creates an array of agents able to move over either a rectangular or hexagonal cellular array, of specifiable dimensions with toroidal or non-toroidal topologies.
Fig 2.
Left hand panel: individual level processes controlling the replenishment of resource patches and the growth (biomass) of individuals, through extraction of resources from these patches, are depicted using graphical Nova elements. Central panel: ecological level process managed by a Nova simworld aggregator are graphically depicted, with consumers either foraging within patches or moving from patch-to-patch during each tick of the intragenerational clock. The progeny of the fittest individuals (i.e., greatest biomass at t = n) inherit perturbed (mutational process) parameter values from one (clonal reproduction) or two (sexual reproduction) parents at the end of each generation. Right panel: the evolutionary level process, represented by changes to the parameter values of individuals (i.e., genotypes and corresponding phenotypes), is monitored by the epochal clock that runs the evolutionary algorithm for G generations. (See S1 Text for discussion of Nova platform).
Table 1.
Terms and definitions used in genetic algorithms (GAs).
Table 2.
Baseline Parameter Values.
Table 3.
Results for two agents.
Fig 3.
Evolved values of parameters (introduced in the Moore neighborhood movement section above).
The left and right panels are the result from two different 10-agent runs using the same baseline data (Table 2). Parameter values for each of the ten agents in the final generation (T = 200) are plotted as a function of their fitnesses (ranging from 30 to 33). The evolved neighbor-discount parameter α (green triangles), competition-tradeoff parameter δ (red squares), and movement-threshold parameter ρ (blue diamonds), across the 10 agents differ, in the two runs; but yield similar fitness distributions, although the left panel shows a little more chance variance than the right.
Fig 4.
Evolved values of the movement-threshold parameter ρ.
The four panels provide snapshots of the final values of ρ (T = 200), which range between just under 0.3 and just over 0.70 for the two 50-agent (two upper panels) and two 100-agent (two lower panels) runs, using the same baseline parameter values listed in Table 2.
Fig 5.
Evolution of the movement-threshold value ρ.
The five scatter graphs (top two rows) represents snapshots over a particular 200-generation (T), 100-agent run of the parameter values ρ at times T = 1,50,100,150 and 200. The lower panel depicts the mean plus/minus the standard deviation of the values of ρ for the 100 agents over the interval 0 ≤ T ≤ 200.
Fig 6.
Evolved parameter values of different movement types in the 150-agent case.
The final values (T = 200) of the three parameters ρ (blue diamonds), α (green triangles) and δ (red squares) are plotted for 150 individuals agents in the simulation, which we see have self-organized into eight different movement types (movement polymorphism), identified by the eight variously colored arrows: same colored arrows identify three parameter values that define each of the eight movement types.
Fig 7.
Time course of average fitness.
(i.e., final biomass Ba(n) among NA agents). The average fitness is plotted over T = 1,…,200 generations for illustrative runs with the following number of clonal reproducing individuals, except for one sexually reproducing group, as indicated: 2 (blue), 10 (red), 50 (green), 100 (purple), 100 with sexual reproduction (turquoise), 150 (orange) and 200 (grey) agents.
Fig 8.
Evolving biomass production efficiency of guilds.
Total biomass produced per generation (solid lines are averages over n runs, dotted lines are plus and minus one standard deviation) under clonal reproduction (red) and random mating (blue), by evolving guilds over 250 generations of, respectively from left to right, 60 (n = 50), 100 (n = 50), and 140 agent (n = 50) guilds of foragers. For a reference to these data see S4 Text.
Table 4.
Foraging guild biomass extraction efficiency: total produced over the two labeled 125-generation periods.
Fig 9.
Evolved values of parameters under random mating.
Parameter phenotype values for each of the 140 agents in the final generation (T = 250) of the first two of 50 simulations are plotted as a function of their fitnesses (ranging from 0 to 12). The evolved neighbor-discount parameter α (green triangles), competition-tradeoff parameter δ (red squares), and movement-threshold parameter ρ (blue diamonds), across the 140 agents differ in the two runs and show different degrees of dispersion, but reflect both heterogeneous and homogeneous phenotypes: viz. in Run 1 we see six α phenotypes that arise from the emergence of three alleles, as discussed in Table 5.
Table 5.
Foraging guild phenotypes at the end of 140 agent exemplar runs.