Measure-valued solutions to size-structured population model of prey controlled by optimally foraging predator harvester

Abstract

Radon-measure-valued solutions to a size structured population model of the McKendrick–von Foerster-type are analytically studied under general assumptions on individuals’ growth, birth and mortality rates. The model is used to describe changes in size structure of zooplankton when prey size-dependent mortality rate is a consequence of a planktivorous fish foraging in low prey-density environment (commonly found in predator-controlled populations). The model of foraging is based on the optimization of the rate of net energy intake as a function of predator speed. Mortality is defined as an operator on a metric space of nonnegative Radon measures equipped with the bounded Lipschitz distance. The solutions to the size structured model of zooplankton population are studied analytically and numerically. Numerical solutions (derived using the Escalator Boxcar Train (EBT)-like schema), in particular those starting from Dirac deltas corresponding to distinct cohorts, exhibit regularization in time and convergence to the same stationary state.