Exponential Growth Model and Stochastic Population Models: A Comparison via Goat Population Data

Abstract

A population dynamic model explains the changes of a population in the near future, given its current status and the environmental conditions that the population is exposed to. In modelling a population dynamic, deterministic model and stochastic models are used to describe and predict the observed population. For modelling population size, deterministic model may provide sufficient biological understanding about the system, but if the population numbers become small, then a stochastic model is necessary with certain conditions. In this study, both types of models such as exponential, discrete-time Markov chain (DTMC), continuous-time Markov chain (CTMC) and stochastic differential equation (SDE) are applied to goat population data of small size. Results from the simulations of stochastic realizations as well as deterministic counterparts are shown and tested by root mean square error (RMSE). The SDE model gives the smallest RMSE value which indicate the best model in fitting the data.