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

Abstract

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 underestimated. We developed a novel statistical method to account for spatiotemporal 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 yr. Increasing the number of survey sites within the network improved the performance of the nonspatial model but only marginally improved the density estimates in the spatiotemporal model. We applied this model to brook trout data from the West Susquehanna Watershed in Pennsylvania collected over 34 yr from 1981 to 2014. We found the model including temporal and spatiotemporal 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 spatiotemporal correlation. Adult densities were less strongly affected by climatic conditions and less temporally variable than YOY but with similar spatiotemporal correlation and higher temporal autocorrelation.

Uncovering the complete biodiversity structure in spatial networks: the example of riverine systems

“…This must be done in a spatially explicit perspective, which is non-trivial in dendritic riverine networks. To account for the unique structure of river networks, new statistical frameworks have arisen to either account for spatial autocorrelation, so that estimates of the relationships determining biodiversity or ecosystem function are unbiased, or to explicitly measure the contribution of spatial relationships in determining these responses (Ver Hoef et al 2014, Hocking et al 2018) . Methods such as spatial stream network models (SSNM's) incorporate spatial covariance structures that make sense for riverine networks, and allow the incorporation of both Euclidean and network distance matrices, as well as flow directionality, which can be seen as an analogous approach to phylogenetic comparative methods, analyzing phylogenetic trees and incorporating their inherent structure in the analysis (Felsenstein 1985).…”

“…Finally, they can be used to partition the variance in metrics such as biodiversity and ecosystem functions into those attributable to predictor variables (typically environmental variables, or perhaps biodiversity) or to other spatial aspects. Use of such statistical techniques has already led to important insights about controls on water chemistry (Brennan et al 2016), bacterial contamination (Holcomb et al 2018), the relationship between abiotic conditions and species habitat (Isaak et al 2009), and species abundances through networks (Hocking et al 2018). These approaches also provide a way to match highly-resolved environmental data with biotic responses for which only local data is available, combining them to make catchment-and reach-scale predictions (Isaak et al 2014).…”

Improving estimates of species distribution change by incorporating local trends

“…In addition to being used for estimating population density or spatial distributions, output from these modeling approaches has been used to generate model‐based summaries to track change in species distributions, including the COG or area occupied, with more robust estimation than that provided by design‐based estimates (Thorson et al 2016a). As tools to implement these methods have become accessible in open source software, such as INLA (Rue et al 2009), VAST (Thorson 2019b) or sdmTMB (Anderson et al 2019, 2020), these approaches have seen broad application to populations in diverse ecosystems around the world, including terrestrial plants (Banerjee et al 2008, Finley et al 2009, Latimer et al 2009) and animals (Thorson et al 2016b), freshwater (Hocking et al 2018) and marine communities (Shelton et al 2014, Thorson et al 2015, 2016a, Thorson and Barnett 2017, Anderson and Ward 2019).…”

Effects of Topographic Resolution and Geologic Setting on Spatial Statistical River Temperature Models

“…These models are based on Tobler's first law of geography “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970). They have proven to be powerful tools in river temperature studies in high relief, montane regions (Jackson et al, 2018; Steel et al, 2017), and preliminary efforts to model aquatic biota populations are encouraging (Hocking et al, 2018; Isaak et al, 2017). In this study, we found mixed success and sometimes poor outcomes for the SSN models, and the reason appears to be a function of geology.…”