Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I

Abstract

Approaches to modeling population dynamics using discrete-time models are described in this two-part review. The development of the scientific ideas of discrete time models, from the Malthus model to modern population models that take into account many factors affecting the structure and dynamics, is presented. The most important and interesting results of recurrent equation application to biological system analysis obtained by the authors are given. In the first part of this review, the population dynamic effects that result from density-dependent regulation of population, the age and sex structures, and the influence of external factors are considered.

Embedded Estimation Sequential Bayes Parameter Inference for the Ricker Dynamical System

“…Ricker's model is often used to explain the dynamics of two populations that are linked through migrations [50][51][52][53][54][55][56][57][58]. As a result, nothing is known about how Ricker communities evolved.…”

“…Assume that after the ðk − 1Þ-th time step MCMC procedure, M samples (i.e., particles) [48][49][50][51][52][53][54][55][56][57][58][59][60]. This results in the estimated density p Mix ðΩ, m k−1 jy 1:k−1 Þ based on GMMs.…”

“…This results in the estimated density p Mix ðΩ, m k−1 jy 1:k−1 Þ based on GMMs. The methodology developed and implemented in [48][49][50][51][52][53][54][55][56][57][58][59][60] ensures that the fitted GMM is close to the true posterior density pðΩ,…”

Harvesting Strategies in the Migratory Prey-Predator Model with a Crowley-Martin Type Response Function and Constant Efforts

“…The dynamics of populations were not only affected by their growth rate and interaction but also by some other factors like the death rate, competition, predation response, harvesting, and migration, see [7]. The dynamical population analysis not only studies and predicts sustainability but also considers social and economic aspects, see [8].…”