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A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

Fig 3

A gradual decrease in predator density remodels the fitness landscape, triggering transient cycling.

(A) A closeup of the dynamics for a typical entry into cycling. A high predator density y (magenta) slowly decays while the prey density x (turquoise) remains nearly constant. Once the predator density becomes small enough, the prey density abruptly increases, causing a decrease in the mean trait value (black) that provokes cycling. The right vertical axis ticks (x*, c*, etc.) correspond to analytical predictions for critical points, as described in the next section. (B) The fitness function r (from Eq (9)) computed for the values of (x, y, ) at the timepoints shown in (A), plotted with c as the vertical axis. Local minima (white) and maxima (black) in c are overlaid for the portion of the dynamics shown in (A). The color gradient is centered with white at 0 and the positive (red) and negative(blue) fitness values scaled by the log transform modulus. (C) The fitness function as a function of c at two representative timepoints (indicated by white dashed lines in (B)). All parameters as given in Fig 2B.

doi: https://doi.org/10.1371/journal.pcbi.1005644.g003