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

1. 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. 2. 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. 3. We initially included all factors found to affect vital rates, which included inbreeding, post-release effects, 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. 4. The essential factors for replicating the population's dynamics were density-dependence in juvenile survival and post-release effects, 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. 5. 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. 13-Aug-2021 --We surveyed the island 121 times over 26 years (April 1992 to January 2018) to obtain data on survival, abundance and habitat availability, and monitored most breeding pairs over the first 20 years to obtain data on reproductive success. We always conducted surveys in September (start of breeding season) and January (toward end of breeding season), and conducted additional surveys when needed to quantify factors likely to affect survival. The analysis presented here uses 76 surveys, including surveys conducted to quantify post-release effects, bykill caused by the poison drop, removal of birds during harvests, and changes in juvenile survival with age. Surveying involved walking through all areas of closed-canopy forest playing territorial calls to attract toutouwai and recording their colour combinations. We also counted any unbanded toutouwai detected in September surveys so that these individuals were included in the abundance estimates made at the start of each breeding season (unbanded individuals were easily distinguished because the birds are rigidly territorial at that time and most of the population was always colour banded). We mapped any extensions to the forest cover each September to measure changes in habitat area. Breeding monitoring involved checking all breeding pairs throughout the breeding season to determine numbers of offspring fledged (see Armstrong & Ewen 2002 for details). We colour-banded most of these offspring in the nest 9–14 days after hatching, but otherwise caught them ca. 4 weeks post-fledging when they could be lured under hand nets to eat mealworms. These birds were considered to enter the population as juveniles at the January survey and transition to adults at the September survey (Fig. 2). Offspring from unmonitored pairs were captured as independent juveniles or adults using a mealworm-baited clap trap, and entered the population as adults at the September survey if detected. We discontinued this intensive breeding monitoring in 2013 but continued to band a sample of nestlings and independent birds found. This monitoring resulted in 559 observations of reproductive success (number of offspring fledged by a female over a breeding season) and encounter histories for 1458 colour-banded birds, including the 58 birds released, 1234 birds banded as nestlings or fledglings, and 166 birds banded as independents