Dynamical behaviour of a two-predator model with prey refuge

Two predators, one prey model that integrates the effect of supplementary food resources due to one predator's kleptoparasitism under the possibility of retribution by the other predator

In ecology, foraging requires animals to expend energy in order to obtain resources. The cost of foraging can be reduced through kleptoparasitism, the theft of a resource that another individual has expended effort to acquire. Thus, kleptoparasitism is one of the most significant feeding techniques in ecology. The phenomenon of kleptoparasitism has garnered significant attention from scholars due to its substantial impact on the food chain. However, the proportionate amount of mathematical modelling to facilitate the analysis has made limited progress in the literature. This circumstance motivated us to develop mathematical models that could explain the population dynamics of the prey-predator food chain. This study explores a scenario with two predators and one prey, where one predator is a kleptoparasite and the other is a host. The energy depletion caused by the predator's counterattack subsequent to kleptoparasitism, notwithstanding the nonlethal nature of this antagonism, is an additional component incorporated into this model. It has been suggested that biologically viable equilibria must meet certain parametric conditions in order to exist and to be stable both locally and globally. This article delves deeply into the occurrences of various one-parametric bifurcations, such as saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, as well as two-parametric bifurcations, such as Bautin bifurcation. A subcritical Hopf bifurcation happens when the growth rate of the first predator is relatively low, while a supercritical Hopf bifurcation occurs when the growth rate of the first predator is quite large, allowing for the coexistence of all three species. Numerical simulations have been conducted to validate our theoretical findings.

DYNAMIC BEHAVIOR OF A STOCHASTIC NON-AUTONOMOUS PREDATOR–PREY MODEL WITH CROWLEY–MARTIN FUNCTIONAL RESPONSE AND IMPULSES

A stochastic non-autonomous one-prey two-predator model with Crowley–Martin functional response and impulses is proposed in this paper. First, by constructing the equivalent system without impulses, we investigate the existence and uniqueness of the global positive solution of the system. Second, by using Itô formula, strong law of large numbers and Chebyshev’s inequality, some sufficient conditions are established to ensure the extinction, non-persistence in the mean, persistence in the mean and stochastic permanence of the system. Third, we prove the system is globally attractive under some conditions. Finally, we choose different white noise intensities and impulsive parameters to illustrate the analytical results by numerical simulations.

Exponential Time Differencing Method for Studying Prey-Predator Dynamic during Mating Period

This paper addresses a first numerical simulation to the nonlinear dynamic system of equations that describes the prey-predator model at the predator mating period. Some male species accompany the females during the mating period. In this case, both male and female feed on the same prey. The presented work shows the numerical solution for this specific case of the prey-predator mathematical model via an exponential time differencing method. In addition, the paper provides the biological implication of the solution.

Prey preferences of notonectids towards larval mosquitoes across prey ontogeny and search area

BACKGROUND

Predatory biological control agents can be effective natural means of managing pests, vectors and invasive species. However, the strength of predator-prey interactions can be regulated through context-dependencies that often remain unquantified. In particular, refuge effects can influence the efficacy of biological agents towards target species, and such effects are often driven by prey size and search area differences. In this study, we quantify the prey preferences of two predaceous notonectids, Anisops breddini and Anisops sardeus, towards four different aquatic larval instar stages of the medically important mosquito Culex quinquefasciatus across variations in surface area and water depth.

RESULTS

Consumption rates differed significantly among the four larval sizes but not between the notonectids. Search area variations also elicited differences in consumption rates. Both predators tended to prefer second-instar mosquito prey among surface area and water depth variations, while generally avoiding the largest (fourth instar) and smallest (first instar) prey instar stages. For both predators, differential selectivity traits were emergent across surface area variations and water depth, with refuge effects for small prey generally greatest at intermediate-large depths with high surface areas. We thus demonstrate that predatory impacts of notonectids towards mosquito larvae differ significantly according to prey size, and likely peak at intermediate size classes.

CONCLUSION

Different mosquito size classes often coexist and compete, selectivity has important implications for adult mosquito proliferations. Further, in ephemeral aquatic habitats where surface areas and water depths are highly variable spatiotemporally, the efficacy of notonectids in controlling mosquito prey may differ substantially. © 2019 Society of Chemical Industry.

Effects of size refuge specificity on a predator-prey model

Predation is a major cause of early-stage mortality for prey individuals, which are often forced to use refuges in order to reduce the risk of being consumed. The ability of certain genotypes in a prey population to reach a size refuge from predation may contribute significantly to the preservation of community diversity. We investigate how the specificity of this behavior affects the evolution of a given population by using a modified Lotka-Volterra model, in which the proportion of each genotype available for predation consists of two components: an intrinsic part and a combination from all genotypes present in the population. The trade-off of these components is characterized by a specificity parameter. From the viewpoint of population dynamics, we observe that the ability of the mutant to invade the resident population strongly depends on the values of this parameter. Finally, we describe the possible evolutionary outcomes, analytically and numerically.