Wendi Wang

Adaptation of prey and predators between patches

Mathematical models are proposed to simulate migrations of prey and predators between patches. In the absence of predators, it is shown that the adaptation of prey leads to an ideal spatial distribution in the sense that the maximal capacity of each patch is achieved. With the introduction of co-adaptation of predators, it is proved that both prey and predators achieve ideal spatial distributions when the adaptations are weak. Further, it is shown that the adaptation of prey and predators increases the survival probability of predators from the extinction in both patches to the persistence in one patch. It is also demonstrated that there exists a pattern that prey and predators cooperate well through adaptations such that predators are permanent in every patch in the case that predators become extinct in each patch in the absence of adaptations. For strong adaptations, it is proved that the model admits periodic cycles and multiple stability transitions.

On evolution under symmetric and asymmetric competitions

This paper considers the coevolution of phenotypic traits in a community comprising two competitive species subject to strong Allee effects. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy under symmetric competition. Secondly, we find that evolutionary suicide is impossible when the two species undergo symmetric competition, however, evolutionary suicide can occur in an asymmetric competition model with strong Allee effects. Thirdly, it is found that evolutionary bistability is a likely outcome of the process under both symmetric and asymmetric competitions, which depends on the properties of symmetric and asymmetric competitions. Fourthly, under asymmetric competition, we find that evolutionary cycle is a likely outcome of the process, which depends on the properties of both intraspecific and interspecific competition. When interspecific and intraspecific asymmetries vary continuously, we also find that the evolutionary dynamics may admit a stable equilibrium and two limit cycles or two stable equilibria separated by an unstable limit cycle or a stable equilibrium and a stable limit cycle.

Effect of parental care and aggregation on population dynamics

Behavioral changes of animal species can influence the consequence of population dynamics. One of the most remarkable behaviors of animal species is the aggregation by which species can reduce predation risk as a consequence of dilution or the other effects by forming a group. Empirical studies have demonstrated that an incompatibility exists in aggregation since resource competition might become severe at the cost of reducing predation pressure from predatory species. Parental care by supplying the food consumed by adults to their juveniles would reduce the mortality of juvenile due to starvation, but it would reduce the reproduction rate at the same time. In this paper, we study a class of stage-structured resource-consumer models to investigate the effect of behavioral changes on population dynamics. It is shown that under the presence of trade-off in parental care, moderate degrees of parental care will be favored as maximizing the equilibrium density of consumers. For consumer species having a long maturation period, consumer species might get benefit from dilution effects as a result of aggregation despite the elevated resource competition. Aggregation gives rise to two different outcomes in consumer extinction. Resource exhaustion as a consequence of over-exploitation can induce extinction of consumers due to Allee effects if aggregation strongly mediates juvenile survival.

Dynamical adaptation of parental care.

Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases.