Comparing the Ricker and θ-logistic models for estimating elk population growth

Abstract

Conflicting evidence exists supporting linear and nonlinear density-dependent population growth when species have slow life histories. The Ricker (linear) and θ-logistic (nonlinear) models are commonly used to analyze survey data for these species, but no evaluation has examined whether these hypotheses can be differentiated with field data. We conducted a simulation exploring effects from shape of density dependence and variation in vital rates on the fit of these models. When vital rates had moderate to high variation, the models had similar fit. The θ-logistic model differed from the Ricker model and was biologically realistic (θ > 1) when variation in vital rates was low and the growth response was nonlinear. Furthermore, the θ-logistic model has issues with model convergence when using vague priors and when variation in vital rates as high. These results indicate that the Ricker model is appropriate for population survey data of species with slow life histories. Recommendations for Resource Managers The shape of the growth response (i.e., the relationship between abundance and population growth rate) depends on the shape of the relationships between abundance and vital rates (survival and pregnancy). The variation in the environmental setting of a population over time, as well as the species life history traits, can influence whether linear or nonlinear models fit time series of population survey data. Random changes over time in the growth rate of a population can mask the shape of the relationship between abundance and growth rate. When modeling population dynamics of species with slow life histories, the Ricker model is often more appropriate than the θ-logistic model, especially when environmental variation over time is high or when using vague priors when fitting the models.