Population and land management relies on understanding population regulation and growth, which may be impacted by variation in population growth parameters within and among populations. We explored the interactions between variation in carrying capacity (K), intrinsic population growth rate (r), and strength of density dependence (β) within and among elk (Cervus elaphus) herds in a small part of the geographic range of the species. We also estimated stochastic fluctuations in abundance around K for each herd. We fit linear Ricker growth models using Bayesian statistics to seven time series of elk population survey data. Our results indicate that K and β varied among herds, and that r and β varied temporally within herds. We also found that herds with smaller K had less stochastic fluctuation in abundances around K, but higher temporal variation in β within herds. Population regulation and the rate of return to the equilibrium abundance is often understood in terms of β, but ecological populations are dynamic systems, and temporal variation in population growth parameters may also influence regulation. Population models which accommodate variation both within and among herds in population growth parameters are necessary, even in mild climates, to fully understand population dynamics and manage populations.
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.
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