Spatio-temporal transferability of environmentally-dependent population models: Insights from the intrinsic predictabilities of Adélie penguin abundance time series

Ecological predictions are necessary for testing whether processes hypothesized to regulate species population dynamics are generalizable across time and space. In order to demonstrate generalizability, model predictions should be transferable in one or more dimensions, where transferability is the successful prediction of responses outside of the model data bounds. While much is known as to what makes spatially-oriented models transferable, there is no general consensus as to the spatio-temporal transferability of ecological time series models. Here, we examine whether the intrinsic predictability of a time series, as measured by its complexity, could limit such transferability using an exceptional long-term dataset of Adelie penguin breeding abundance time series collected at 24 colonies around Antarctica. For each colony, we select a suite of environmental variables from the Community Earth System Model, version 2 to predict population growth rates, before assessing how well these environmentally-dependent population models transfer temporally and how reliably temporal signals replicate through space. We show that weighted permutation entropy (WPE), a model-free measure of intrinsic predictability recently introduced to ecology, varies spatially across Adelie penguin populations, perhaps in response to stochastic environmental events. We demonstrate that WPE can strongly limit temporal predictive performance, although this relationship could be weakened if intrinsic predictability is not constant over time. Lastly, we show that WPE can also limit spatial forecast horizon, which we define as the decay in spatial predictive performance with respect to the physical distance between focal colony and predicted colony. Irrespective of intrinsic predictability, spatial forecast horizons for all Adelie penguin breeding colonies included in this study are surprisingly short and our population models often have similar temporal and spatial predictive performance compared to null models based on long-term average growth rates. For cases where time series are complex, as measured by WPE, and the transferability of biologically-motivated mechanistic models are poor, we advise that null models should instead be used for prediction. These models are likely better at capturing more generalizable relationships between average growth rates and long-term environmental conditions. Lastly, we recommend that WPE can provide valuable insights when evaluating model performance, designing sampling or monitoring programs, or assessing the appropriateness of preexisting datasets for making conservation management decisions in response to environmental change.