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

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.

Using long-term data for a reintroduced population to empirically estimate future consequences of inbreeding.

Inbreeding depression is an important long-term threat to reintroduced populations. However, the strength of inbreeding depression is difficult to estimate in wild populations because pedigree data are inevitably incomplete and because good data are needed on survival and reproduction. Predicting future population consequences is especially difficult because this also requires projecting future inbreeding levels and their impacts on long-term population dynamics, which are subject to many uncertainties. We illustrate how such projections can be derived through Bayesian state-space modeling methods based on a 26-year data set for North Island Robins (Petroica longipes) reintroduced to Tiritiri Matangi Island in 1992. We used pedigree data to model increases in the average inbreeding level (F) over time based on kinship of possible breeding pairs and to estimate empirically Ne /N (effective/census population size). We used multiple imputation to model the unknown components of inbreeding coefficients, which allowed us to estimate effects of inbreeding on survival for all 1458 birds in the data set while modeling density dependence and environmental stochasticity. This modeling indicated that inbreeding reduced juvenile survival (1.83 lethal equivalents [SE 0.81]) and may have reduced subsequent adult survival (0.44 lethal equivalents [0.81]) but had no apparent effect on numbers of fledglings produced. Average inbreeding level increased to 0.10 (SE 0.001) as the population grew from 33 (0.3) to 160 (6) individuals over the 25 years, giving a Ne/N ratio of 0.56 (0.01). Based on a model that also incorporated habitat regeneration, the population was projected to reach a maximum of 331-1144 birds (median 726) in 2130, then to begin a slow decline. Without inbreeding, the population would be expected stabilize at 887-1465 birds (median 1131). Such analysis, therefore, makes it possible to empirically derive the information needed for rational decisions about inbreeding management while accounting for multiple sources of uncertainty.

Uso de Datos a Largo Plazo de una Población Reintroducida para Estimar Empíricamente las Consecuencias Futuras de la Endogamia Resumen La depresión endogámica es una amenaza importante a largo plazo para las poblaciones reintroducidas. Sin embargo, es complicado estimar la fuerza de la depresión endogámica en las poblaciones silvestres porque los datos sobre el linaje sin duda estarán incompletos y porque se necesitan datos sólidos sobre la supervivencia y la reproducción. Es especialmente difícil predecir las consecuencias poblacionales a futuro pues esto requiere proyectar a futuro los niveles de endogamia y sus impactos sobre las dinámicas poblacionales a largo plazo, las cuales están sujetas a muchas incertidumbres. Ilustramos cómo dichas proyecciones pueden derivarse mediante métodos de modelado bayesiano de estado-espacio basados en un conjunto de datos obtenidos durante 26 años para los tordos de la Isla del Norte (Petroica longipes) reintroducidos a la isla Tiritiri Matangi en 1992. Usamos datos de linaje para modelar los incrementos en el nivel promedio de endogamia ( F̲ ) a lo largo del tiempo con base en el parentesco de las posibles parejas reproductoras y para estimar empíricamente Ne/N (tamaño poblacional efectivo/por censo). Usamos una imputación múltiple para modelar los componentes desconocidos de los coeficientes de endogamia, lo que nos permitió estimar los efectos de la endogamia sobre la supervivencia para todas las aves (1458) incluidas en el conjunto de datos a la vez que modelamos la dependencia de la densidad y la estocasticidad ambiental. Este modelado indicó que la endogamia redujo la supervivencia juvenil (1.83 equivalentes letales [SE 0.81]) y podría haber reducido la subsecuente supervivencia adulta (0.44 equivalentes letales [0.81]) pero no tuvo un efecto aparente sobre los números de polluelos producidos. El nivel promedio de endogamia incrementó a 0.10 (SE 0.001) conforme la población creció de 33 (0.3) a 160 (6) individuos a lo largo de los 25 años, lo que resultó en una proporción Ne/N de 0.56 (0.01). Con base en un modelo que también incorporó la regeneración del hábitat, se proyectó que la población alcanzaría un máximo de 331-1144 aves (mediana: 726) para 2130 y después comenzaría una lenta disminución. Sin la endogamia, se esperaría que la población se estabilizaría con 887-1465 (mediana: 1131) aves. Por lo tanto, dicho análisis hace posible la derivación empírica de la información necesaria para las decisiones racionales sobre el manejo de la endogamia a la vez que considera a varias fuentes de incertidumbre.

Adaptive harvesting of source populations for translocation: a case study with New Zealand Robins.

Reintroductions are conducted frequently throughout the world, and some source populations are harvested repeatedly to provide animals for translocation. The responses of these source populations to harvest should be monitored, and the resulting data used to refine population models will guide management. After North Island Robins ( Petroica longipes) were reintroduced to Tiritiri Matangi, New Zealand, in 1992, the population became a source for robins for additional reintroductions in the region. We constructed an initial model for the population on the basis of the data collected from 1992 to 1998 and used it to predict the population's response to the first translocation of robins from the island in the autumn (March) of 1999. We then analyzed postharvest data on survival (with mark-recapture analysis) and fecundity (with generalized linear-mixed modeling) to reassess and update the model. In the initial model, juvenile survival was assumed to be limited by the island's fixed carrying capacity, with excess juveniles dying over winter; hence, the autumn harvest was expected to cause an immediate increase in juvenile survival. In postharvest analysis, however, most juvenile mortality occurred before autumn, and the best predictor of juvenile survival was the number of breeding pairs present the previous spring (start of the breeding season). Consequently, the updated population model predicted sustainable harvest levels about half those given by the initial model, and this model has been used to guide the number of individuals removed for two subsequent translocations. The ongoing development of the model has been invaluable for assuring conservation authorities that the population is not being unsustainably harvested, which has allowed surplus animals to be used to establish new populations. Our case study illustrates the value of an adaptive approach to harvesting source populations for reintroduction and illustrates the value of such studies for understanding the density-dependent mechanisms regulating populations.