A geostatistical state‐space model of animal densities for stream networks

Daniel J. Hocking, James T. Thorson, Kyle O'Neil, Benjamin H. Letcher

Population dynamics are often correlated in space and time due to correlations in environmental drivers as well as synchrony induced by individual dispersal. Many statistical analyses of populations ignore potential autocorrelations and assume that survey methods (distance and time between samples) eliminate these correlations, allowing samples to be treated independently. If these assumptions are incorrect, results and therefore inference may be biased and uncertainty under-estimated. We developed a novel statistical method to account for spatio-temporal correlations within dendritic stream networks, while accounting for imperfect detection in the surveys. Through simulations, we found this model decreased predictive error relative to standard statistical methods when data were spatially correlated based on stream distance and performed similarly when data were not correlated. We found that increasing the number of years surveyed substantially improved the model accuracy when estimating spatial and temporal correlation coefficients, especially from 10 to 15 years. Increasing the number of survey sites within the network improved the performance of the non-spatial model but only marginally improved the density estimates in the spatio-temporal model. We applied this model to Brook Trout data from the West Susquehanna Watershed in Pennsylvania collected over 34 years from 1981 - 2014. We found the model including temporal and spatio-temporal autocorrelation best described young-of-the-year (YOY) and adult density patterns. YOY densities were positively related to forest cover and negatively related to spring temperatures with low temporal autocorrelation and moderately-high spatio-temporal correlation. Adult densities were less strongly affected by climatic conditions and less temporally variable than YOY but with similar spatio-temporal correlation and higher temporal autocorrelation. This article is protected by copyright. All rights reserved.