Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete-Time Prey-Predator Model

Prey-predator models with refuge effect have great importance in the context of ecology. Constant refuge and refuge proportional to prey are the most popular concepts of refuge in the existing literature. Now, there are new different types of refuge concepts attracting researchers. This study considers a refuge concept proportional to the predator due to the fear induced by predators. When predators increase, fears also increase and that is why prey refuges also increase. Here, we examine the influence of prey refuge proportional to predator effect in a discrete prey-predator interaction with the Holling type II functional response model. Is this refuge stabilizing or destabilizing the system? That is the central question of this study. The existence and stability of fixed points, Period-Doubling Bifurcation, Neimark–Sacker Bifurcation, the influence of prey refuge, and chaos are analyzed. This work provides the bifurcation diagrams and Lyapunov exponents to analyze the refuge parameter of the model. The proposed discrete model indicates rich dynamics as the effect of prey refuge through numerical simulations.

Modelling three-dimensional space to design prey refuges using video game software

© 2021 The Authors. Refuges can be ecologically important, allowing access only to some species or individuals and providing prey protection from predators. Creation of refuges can be used to protect threatened species from introduced predators, which can have large negative impacts that are difficult to attenuate via other means. To design refuges for conservation purposes, refuge accessibility to different species must be understood. Traditional techniques are not adequate to measure or describe complex three-dimensional spaces which are often important refuges. We designed a novel predictive method for modeling three-dimensional refuge space using video game software that simulates real-world physics (Unity, PhysX). We use the study system of endemic New Zealand skinks (Oligosoma spp.), their introduced predators, house mice (Mus musculus), and the habitat of interstitial spaces within rock piles to demonstrate how this modeling technique can be used to inform design of habitat enhancement for conservation. We used video game software to model realistic rock piles and measure their interstitial spaces, and found that the spaces we predicted matched those we measured in real rock piles using computed tomography (CT) scanning. We used information about the sizes of gaps accessible to skinks and mice and the results of our modeling to determine the optimal size of rocks to create refuges which would protect skinks from mice. We determined the ideal rock size to be those with graded diameters of 20–40 mm. The approach we developed could be used to describe interstitial spaces in habitats as they naturally occur, or it could be applied to design habitats to benefit particular species.

Modelling three-dimensional space to design prey refuges using video game software

© 2021 The Authors. Refuges can be ecologically important, allowing access only to some species or individuals and providing prey protection from predators. Creation of refuges can be used to protect threatened species from introduced predators, which can have large negative impacts that are difficult to attenuate via other means. To design refuges for conservation purposes, refuge accessibility to different species must be understood. Traditional techniques are not adequate to measure or describe complex three-dimensional spaces which are often important refuges. We designed a novel predictive method for modeling three-dimensional refuge space using video game software that simulates real-world physics (Unity, PhysX). We use the study system of endemic New Zealand skinks (Oligosoma spp.), their introduced predators, house mice (Mus musculus), and the habitat of interstitial spaces within rock piles to demonstrate how this modeling technique can be used to inform design of habitat enhancement for conservation. We used video game software to model realistic rock piles and measure their interstitial spaces, and found that the spaces we predicted matched those we measured in real rock piles using computed tomography (CT) scanning. We used information about the sizes of gaps accessible to skinks and mice and the results of our modeling to determine the optimal size of rocks to create refuges which would protect skinks from mice. We determined the ideal rock size to be those with graded diameters of 20–40 mm. The approach we developed could be used to describe interstitial spaces in habitats as they naturally occur, or it could be applied to design habitats to benefit particular species.