Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern United States

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Abstract
Many critical ecological issues require the analysis of large spatial point data sets – for example, modelling species distributions, abundance and spread from survey data. But modelling spatial relationships, especially in large point data sets, presents major computational challenges. We use a novel Bayesian hierarchical statistical approach, ‘spatial predictive process’ modelling, to predict the distribution of a major invasive plant species,Celastrus orbiculatus, in the northeastern USA. The model runs orders of magnitude faster than traditional geostatistical models on a large data set ofc. 4000 points, and performs better than generalized linear models, generalized additive models and geographically weighted regression in cross‐validation. We also use this approach to model simultaneously the distributions of a set of four major invasive species in a spatially explicit multivariate model. This multispecies analysis demonstrates that some pairs of species exhibit negative residual spatial covariation, suggesting potential competitive interaction or divergent responses to unmeasured factors.

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