Evolutionary dynamics of exploited populations selected by density dependent competitive interactions

Abstract

Life-history models have traditionally dealt with short-term evolution where evolutionary equilibria arise from genotypic and phenotypic covariance that have evolved by natural selection. For the case of body mass evolution in mobile organisms with non-overlapping generations, I analyse an alternative model of long-term evolution by the ecological constraint of density dependence in the number of intraspecific competitive interactions per individual. The model is based on the principle that phenotypic constraints that may explain the evolution of life-histories shall not be assumed unless the constraints reflect laws that lie outside the domain of evolutionary biology. It is argued that the model may explain population dynamic cycles either by selection acting directly on genotypic variation or by long-term selection for inheritable phenotypic responses that react to the density dependent changes in the ecology. The model has an evolutionary equilibrium that is a continuously stable strategy (CSS) when, at equilibrium abundance, the second derivative of the density regulation function with respect to the intra-population variation in ln body mass is smaller than the density regulation function or the first derivative of that function. On the time-scale of population dynamics the model shows inertial dynamics with damped, stable, or repelling cycles in population abundance and life-history traits like the body mass and the intrinsic population dynamic growth rate. For harvested populations that are allowed sufficient time to equilibrate at the CSS, the equilibrium abundance is constant and independent of the harvest while the intrinsic growth rate is positively related to the harvest. This implies no upper limit to the long-term sustainable harvest of individuals, although there is an upper limit to the sustainable harvest of biomass. It is also shown that the evolutionary maximal harvest does not generally coincide with the maximal sustainable yield. And that harvest functions that increase more than proportional with the abundance will stabilise the cyclic population dynamics, while harvest functions that increase less than proportional will destabilise the dynamics.