Ecological Models

Abstract

The exponential and logistic population growth models, which are used in ecology to describe population dynamics, are presented. These models can be applied to census data obtained from studbooks. Data from the European blesbok studbook are used to illustrate fitting these models. The method of fitting and testing the exponential growth model as a linear regression model on logarithmic transformed census counts is described. The fitted model and observed census data of the blesbok are compared, and the regression coefficient, which represents the intrinsic rate of increase (r), is tested. The example shows that a significant fit of the exponential population growth model is not necessarily describing the latest trend. This is demonstrated by fitting the logistic growth model using nonlinear least square regression on the blesbok data. The χ ² goodness of fit test is applied to fitted and observed data in the blesbok example. Interpretation of r in the logistic growth model is discussed. Adaptation of model data to retrieve realistic values for initial population size and start date of the logistic model in R is explored. The advantages and limitations of the “simple” exponential and logistic growth models, and other available methods to analyse time series, are discussed.