Temporal and spatial equivalence in demographic responses of emperor penguins (<i>Aptenodytes forsteri</i>) to environmental change

Population ecology and biogeography applications often necessitate the transfer of models across spatial and/or temporal dimensions to make predictions outside the bounds of the data used for model fitting. However, ecological data are often spatiotemporally unbalanced such that the spatial or the temporal dimension tends to contain more data than the other. This unbalance frequently leads model transfers to become substitutions, which are predictions to a different dimension than the predictive model was built on. Despite the prevalence of substitutions in ecology, studies validating their performance and their underlying assumptions are scarce. Here, we present a case study demonstrating both space-for-time and time-for-space substitutions (TFSS) using emperor penguins (Aptenodytes forsteri) as the focal species. Using an abundance-based species distribution model (aSDM) of adult emperor penguins in attendance during spring across 50 colonies, we predict long-term annual fluctuations in fledgling abundance and breeding success at a single colony, Pointe Géologie. Subsequently, we construct statistical models from time series of extended counts on Pointe Géologie to predict average colony abundance distribution across 50 colonies. Our analysis reveals that the distance to nearest open water (NOW) exhibits the strongest association with both temporal and spatial data. Space-for-time substitution performance of the aSDM, as measured by the Pearson correlation coefficient, was 0.63 and 0.56 when predicting breeding success and fledgling abundance time series, respectively. Linear regression of fledgling abundance on NOW yields similar TFSS performance when predicting the abundance distribution of emperor penguin colonies with a correlation coefficient of 0.58. We posit that such space-time equivalence arises because: (1) emperor penguin colonies conform to their existing fundamental niche; (2) there is not yet any environmental novelty when comparing the spatial versus temporal variation of distance to the nearest open water; and (3) models of more specific components of life histories, such as fledgling abundance, rather than total population abundance, are more transferable. Identifying these conditions empirically can enhance the qualitative validation of substitutions in cases where direct validation data are lacking.