Evolutionary Suicide of Prey: Matsuda and Abrams’ Model Revisited

The impact of harvesting on the evolutionary dynamics of prey species in a prey-predator systems

Matsuda and Abrams (Theor Popul Biol 45(1):76-91, 1994) initiated the exploration of self-extinction in species through evolution, focusing on the advantageous position of mutants near the extinction boundary in a prey-predator system with evolving foraging traits. Previous models lacked theoretical investigation into the long-term effects of harvesting. In our model, we introduce constant-effort prey and predator harvesting, along with individual logistic growth of predators. The model reveals two distinct evolutionary outcomes: (i) Evolutionary suicide, marked by a saddle-node bifurcation, where prey extinction results from the invasion of a lower forager mutant; and (ii) Evolutionary reversal, characterized by a subcritical Hopf bifurcation, leading to cyclic prey evolution. Employing an innovative approach based on Gröbner basis computation, we identify various bifurcation manifolds, including fold, transcritical, cusp, Hopf, and Bogdanov-Takens bifurcations. These contrasting scenarios emerge from variations in harvesting parameters while keeping other factors constant, rendering the model an intriguing subject of study.

Ecological and evolutionary consequences of predator-prey role reversal: Allee effect and catastrophic predator extinction

In many terrestrial, marine, and freshwater predator-prey communities, young predators can be vulnerable to attacks by large prey. Frequent prey counter-attacks may hinder the persistence of predators. Despite the commonness of such role reversals in nature, they have rarely been addressed in evolutionary modelling. To understand how role reversals affect ecological and evolutionary dynamics of a predator-prey community, we derived an ecological model from individual-level processes using ordinary differential equations. The model reveals complex ecological dynamics, with possible bistability between alternative coexistence states and an Allee effect for the predators. We find that when prey counter-attacks are frequent, cannibalism is necessary for predator persistence. Using numerical analysis, we also find that a sudden ecological shift from coexistence to predator extinction can occur through several catastrophic bifurcations, including 'saddle-node', 'homoclinic', and 'subcritical Hopf'. The analysis of single-species evolution reveals that predator selection towards increasing or decreasing cannibalism triggers a catastrophic shift towards an extinction state of the predators. Such an evolutionary extinction of the predators may also be caused by prey selection towards increasing foraging activity because it facilitates encounters with vulnerable, young predators. The analysis of predator-prey coevolution further demonstrates that predator's catastrophic extinction becomes an even more likely outcome than in single-species evolution. Our results suggest that when young predators are vulnerable to prey attacks, a sudden extinction of the predators may be more common than currently understood.