Capturing the dynamics of small populations: A retrospective assessment using long-term data for an island...

The art of population modelling is to incorporate factors essential for capturing a population's dynamics while otherwise keeping the model as simple as possible. However, it is unclear how optimal model complexity should be assessed, and whether this optimal complexity has been affected by recent advances in modelling methodology. This issue is particularly relevant to small populations because they are subject to complex dynamics but inferences about those dynamics are often constrained by small sample sizes. We fitted Bayesian hierarchical models to long-term data on vital rates (survival and reproduction) for the toutouwai Petroica longipes population reintroduced to Tiritiri Matangi, a 220-ha New Zealand island, and quantified the performance of those models in terms of their likelihood of replicating the observed population dynamics. These dynamics consisted of overall growth from 33 (±0.3) to 160 (±6) birds from 1992-2018, including recoveries following five harvest events for further reintroductions to other sites. We initially included all factors found to affect vital rates, which included inbreeding, post-release effects (PRE), density-dependence, sex, age and random annual variation, then progressively removed these factors. We also compared performance of models where data analysis and simulations were done simultaneously to those produced with the traditional two-step approach, where vital rates are estimated first then fed into a separate simulation model. Parametric uncertainty and demographic stochasticity were incorporated in all projections. The essential factors for replicating the population's dynamics were density-dependence in juvenile survival and PRE, i.e. initial depression of survival and reproduction in translocated birds. Inclusion of other factors reduced the precision of projections, and therefore the likelihood of matching observed dynamics. However, this reduction was modest when the modelling was done in an integrated framework. In contrast, projections were much less precise when done with a two-step modelling approach, and the cost of additional parameters was much higher under the two-step approach. These results suggest that minimization of complexity may be less important than accounting for covariances in parameter estimates, which is facilitated by integrating data analysis and population projections using Bayesian methods.