Harvesting and predation of a sex- and age-structured population

Abstract

We study a discrete-time system of equations for a structured ungulate population exploited by human harvesting or a dynamic predator. The population is divided into juveniles, and female and male adults. Harvesting is concentrated on adults (trophy hunting of males or population control measures on females), whereas predation occurs in juveniles. Though the model consists of four nonlinear equations, we find explicit expressions for the steady states. We use these explicit expressions to investigate harvesting rates that allow population persistence, rates that ensure population control, and optimal harvesting efforts. Several reductions of complexity allow for a detailed analysis of the dynamics of the model. Most notably, we find that even compensatory density dependence can lead to a period doubling bifurcation, that the model does not support consumer-resource cycles, and that an Allee effect can emerge from the interplay of stage-specific predation and density-dependent prey reproduction.

Extinction, periodicity and multistability in a Ricker model of stage-structured populations

“…For the system (1)- (2) we generally assume that for all n ≥ 0: α n , β n , σ i,n , c i,n ≥ 0, i = 1, 2 (4) β n , σ 1,n > 0 for inifinitely many n…”

“…Planar systems of type x n+1 = σ 1,n y n + σ 2,n x n (1) y n+1 = β n x n e αn−c 1,n xn−c 2,n yn (2) where α n , β n , σ i,n , c i,n are non-negative numbers for i = 1, 2 and n ≥ 0 have been used to model single-species, two-stage populations (e.g. juvenile and adult); see [2]- [4], [6] and [11]. The exponential function that defines the time and density dependent fertility rate classifies the above system as a Ricker model.…”

Effects of size‐ and sex‐selective harvesting: An integral projection model approach

“…For several harvested species, for example, of crustaceans, bovids, and cervids, there are size‐ and sex‐selective harvest regulations, and they are often male‐biased (Clark & Tait, ). In general, both empirical and theoretical studies have found that a male‐biased harvest reduces mean male age and size, and that the number of sexually active males in the population decreases (Carver, Wolcott, Wolcott, & Hines, ; Fenberg & Roy, ; Giordano & Lutscher, ; McLoughlin, Taylor, & Messier, ; Mysterud et al, ; Sørdalen et al, ). A shift toward younger, smaller, and fewer males can have a negative impact on female fertility and population growth through sperm limitation, reduced birthweights, and delayed parturition dates (e.g.…”

Component Allee Effects and Stage‐specific Predation: A Brief Insight Into Conservation and Biological Control Issues

“…Queen conch Strombus gigas suffers Allee effects in reproduction and exploitation on different adult stages (Gascoigne and Lipcius []). Allee effects in reproduction also affect some ungulate populations, the juveniles of which suffer predation and harvest acts upon the adults (Giordano and Lutscher []).…”