Regulation of Population Density Due to Individual Differences and Patchy Environment

Abstract

A theoretical model of population regulation is presented and discussed, based on the variation in individual resource intake within a single species population. There are several sources of this variation, which can be hereditary as well as non-hereditary, the latter being due to individual age, stochastic events occurring during the life of individual, or social structure within the population. A general model of population growth and regulation of a differentiated population in discrete time units is given and analytical solutions for two extreme cases are presented. Stability is impossible in a population with equal resource partitioning among individuals, while unequal resource partitioning allows very stable populations. A further consequence of unequal resource partitioning and heterogeneous environment is the regulation of population density by emigration, which brings about lower population density, higher food density and even higher stability than without emigration. A simple model of the evolution of reproductive rates in heterogeneous environment shows that the reproductive rates are linearly proportional to random mortality in local habitats. The occurrence of regulation of population density by emigration implies a new approach to the relation between ecosystem stability and species diversity.