Limit theorems for multi-type general branching processes with population dependence
Abstract
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population density as a measure-valued process and obtain its asymptotics, as the population grows with the environmental carrying capacity. "Density" in this paper generally refers to the population size as compared to the carrying capacity. Thus, a deterministic approximation is given, in the form of a Law of Large Numbers, as well as a Central Limit Theorem. Migration can also be incorporated. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.
Cite
@article{arxiv.1903.04747,
title = {Limit theorems for multi-type general branching processes with population dependence},
author = {Jie Yen Fan and Kais Hamza and Peter Jagers and Fima C. Klebaner},
journal= {arXiv preprint arXiv:1903.04747},
year = {2019}
}