Optimal somatic growth and reproduction in a limited, constant environment: Organisms with determinate growth

Abstract

A partial differential equation model of natural selection in a limited environment concerns a mass structured population whose residents must divide available energy between somatic growth and reproduction. This model gives rise to an optimal phenotype criterion that identifies the energy allocation pattern most favored by natural selection. This criterion in turn produces an equation for optimal adult body mass in terms of the original demographic rate functions. Its examination confirms the long accepted intuitively based claim of the theory of r- and K-selection that increased mortality favors earlier reproduction and hence smaller adult body size. This mechanistic analysis provides both justification, for this problem, of the intuitively based optimization procedures of classical life history theory and also further information that may help facilitate this theory's application to natural populations.