Generalizing Fisher's “reproductive value”: “Incipient” and “penultimate” reproductive-value functions when environment limits growth; linear approximants for nonlinear Mendelian mating models - Samuelson, Paul A. (1978)
In the usual Darwinian case in which struggle for existence leads to density limitations on the environment's carrying capacity, R. A. Fisher's reproductive-value concept reduces to zero for every initial age group. To salvage some meaning for Fisher's notion, two variant reproductive-value concepts are defined here: an “incipient reproductive-value function,” applicable to a system's early dilute stage when density effects are still ignorable; and a “second-order penultimate reproductive-value function,” linking to a system's initial conditions near equilibrium its much later small deviations from carrying-capacity equilibrium. Also, slowly changing age-structured mortality and fertility parameters of Lotka and Mendelian mating systems are shown to suggest linear reproductive-value surrogates that provide approximations for truly nonlinear diploid and haploid models.