Co‐evolutionary Dynamics of a Social Parasite–host Interaction Model: Obligate Versus Facultative Social Parasitism

Abstract

Abstract. Host-parasite co-evolution can have profound impacts on a wide range of ecological and evolutionary processes, including population dynamics, the maintenance of genetic diversity, and the evolution of recombination. To examine the co-evolution of quantitative traits in hosts and parasites, we present and study a co-evolutionary model of a social parasite-host system that incorporates (i) ecological dynamics that feed back into their co-evolutionary outcomes; (ii) variation in whether the social parasite is obligate or facultative; and (iii) Holling Type II functional responses between host and social parasite, which are particularly suitable for social parasites that face time costs for host location and its social manipulation. We perform local and global analyses for the co-evolutionary model and the corresponding ecological model. In the absence of evolution, our ecological model analyses imply that an extremely small value of the death rate for facultative social parasites can drive a host extinct globally under certain conditions, while an extremely large value of the death rate can drive the parasite extinct globally. The facultative parasite system can have one, two, or three coexistence equilibria, while the obligate parasite system can have either one or three coexistence equilibria. Multiple coexistence equilibria result in rich dynamics with multiple attractors. The ecological system, in particular, can exhibit bi-stability between the facultative parasite-only equilibrium and the coexistence equilibrium when it has two coexistence equilibria. Our analysis on the co-evolutionary model provides important insights on how co-evolution can change the ecological and evolutionary outcomes of host-parasite interactions. Our findings suggest that: (i) The host and parasite can select different strategies that may result in local extinction of host or parasite. These strategies can have convergence stability (CS), but may not be evolutionary stable strategies (ESS); (ii) The host and its facultative (or obligate) parasite can have ESS that drive the host (or the obligate parasite) extinct locally; (iii) The dependence of vital rates on the phenotypic trait plays an important role in the CS of both exclusion and coexistence equilibria, as well as their ESS; and (iv) A small variance in the trait difference that measures parasitism efficiency can destabilize the co-evolutionary system, and

Spatiotemporal dynamics of a diffusive predator-prey model with generalist predator

“…where u and v represent the population densities of prey and predator at time t, respectively, r i , K i (i = 1, 2), a, e, h, d are positive constants with specific ecological interpretations : r 1 and r 2 denote the intrinsic growth rate of species u and v, respectively, in the absence of other species; K 1 and K 2 are the carrying capacities of species u and v individuals, respectively; d stands for the dead rate of predator individuals due to hunting or attacking all potential prey resources; a is the capturing efficiency of a predator and h is the predator handling time. In [18], the ecological dynamics for model (1), including the boundedness, permanence, stability of boundary and interior equilibria, and extinction of one species, were performed.…”

“…The work of Kang et.al. [18,19] indicates that models with generalist predator could exhibit more complicate dynamics and more likely to have "top down" regulation by comparing to the similar models with specialist predator. We also refer to [14,13,31,9,24,29,6] for some references on the study of predator-prey models with generalist predators.…”

“…(2) has a trivial constant steady state E 00 = (0, 0), and at most three positive constant steady states E * = (u * , v * )(see [18]). The interior equilibrium E * (u * , v * ) of system (1) satisfies the following two equations…”

“…Introduction. Recently, Kang and Fewell [18] studied a host-parasite coevolutionary model, in which the relationship between host(prey) and parasite(predator) is described by the following ecological model with Holling Type II functional response  …”

“…Non-persistence. It is known from [18] that system (2) has two semi-trivial constant steady states E 10 = (K 1 , 0) and…”