ABSTRACT
Considered is a mathematical model for dynamics of an isolated population with non-overlapping generations. The individuals' birth process (emergence of new-generation individuals) is assumed to have a discrete nature (there exist some fixed time moments at which the new generations emerge), while the death process is assumed to be continuous. In addition, the birth rate is assumed to be a function of the number of individuals survived till the moment of reproduction, the function being non-monotone: there exists an optimal value of the population size at which the birth rate reaches its maximum (Alley principle). Analysis of the discrete-continuous models has revealed that each of the new models has a rich set of dynamical regimes. New models are compared with a number of well-known discrete ones (like Skellam, Moran-Ricker, Hassell, Maynard Smith-Slatkin models, and others) when approximating an empirical time series on fluctuations of a green oak moth population (Korzukhin, Semevsky, 1992). Neither of the models can provide for a satisfactory description of the green oak moth dynamics. It is also shown that usage of the discrete-continuous models for approximation of real datasets enables one to find several important population parameters, which can hardly (or cannot) be found by means of traditional discrete models.
