Better inferences from population-dynamics experiments using Monte Carlo state-space likelihood methods

In experimental population ecology, there is often a gap between realistic models used to hypothesize about population dynamics and statistical models used to analyze data. Ecologists routinely conduct experiments where the data from each replicate are short time series of estimated population abundances structured by stage, species, and/or other information, and the conventional test for treatment effects uses a general linear model (GLM) such as analysis of variance (ANOVA). However, GLMs do not incorporate demographic relationships between abundances through time. An alternative is to use population-dynamics models as frameworks for statistical hypothesis testing. This approach requires general methods for-fitting structured population models that can incorporate both process noise (stochastic dynamics) and observation error (inaccurate data). This paper presents such methods and compares them to GLMs for testing population-dynamics hypotheses from experiments. The methods are Monte Carlo state-space likelihood methods, including a basic Monte Carlo integration method and a recently developed Monte Carlo kernel likelihood method. Three simulated examples of population-dynamics experiments were used to compare analysis with a population model to ANOVA, analysis of covariance (ANCOVA), and, repeated-measures ANOVA. The examples considered manipulations of host-plant growth conditions, causing decreased survival and increased fecundity; predator addition to investigate a behaviorally mediated change in prey demography; and changed host-plant growth conditions with a more complex model for herbivore dynamics than the one used for analysis. For the first example, a population model gave much, higher statistical power than any of the ANOVA methods and provides greater biological insight. For the second example, ANOVA models are not suited to test for the behavioral effect, but a population model detected it with high statistical power. The third example suggests that even incorrect biological structure can provide better inferences than omitting all biological structure. The likelihood methods presented here make analysis with structured population models feasible for a wide range of models incorporating process noise and observation error, thus offering higher statistical power and greater biological insight for population-dynamics experiments.