Estimating a population model for stage-structured cohort data with individual heterogeneity in development

Background/Question/Methods

Individual variation in demographic traits has considerable consequences for population dynamics in many systems. Variation in development can be observed most clearly in stage-structured cohorts, in which a group of individuals, born at the same time, ages through distinct life stages. Most models assume that local developmental processes occur identically across individuals, ignoring any genetic or phenotypic variation in the duration of time spent in each stage. Several sets of approaches have tackled this limitation by including time-delays, variation in time to entry to cohort, or allowing individual stage duration to follow some probability distribution. However, we still lack a flexible framework in which we can analyze and fit a full population model with an assumption of variable development. In this study we extend an existing general model of mortality and variable development for a stage-structured cohort by including reproduction. Our problem is further complicated by the non-independence of the cohort data which follows the same groups of individuals through time, instead of sampling from a larger population. We employ a sequential Monte Carlo algorithm (particle filter) in an approximate Bayesian computation (ABC) framework to fit the stochastic development model to simulated data.

Results/Conclusions

We show that ABC algorithms are useful tools for complex population modelling in ecology. Our methods provide a flexible, though computationally intense, framework that is robust to different assumptions of the population dynamics. Sequential Monte Carlo methods greatly increase efficiency. We illustrate these methods with simulated data of spider mite (Tetranychus pacificus) cohorts. Parameter estimates of mortality, fecundity, and stage durations are given and compared to values from previous studies. Our flexible approach could be extended to include covariates or random effects on any of the demographic parameters, correlations between distributions of stage durations, or imperfect detection of individuals. We provide a general method to explore many questions about stage-structured populations in any ecosystem.