Building Statistical Models to Analyze

Models of the geographic distributions of species have wide application in 12 ecology. But the non-spatial, single-level regression models that ecologists typically employ 13 do not deal with problems of irregular sampling intensity or spatial dependence, and do not 14 adequately quantify uncertainty. We show here how to build statistical models that can 15 handle these features of spatial prediction and provide richer, more powerful inference 16 about species niche relations, distributions, and the effects of human disturbance. We 17 begin with a familiar generalized linear model and build in additional features, including 18 spatial random effects and hierarchical levels. Since these models are fully specified 19 statistical models, we show that it is possible to add complexity without sacrificing 20 interpretability. This step-by-step approach, together with attached code that implements 21 a simple spatially explicit regression model, is structured to facilitate self-teaching. All 22 models are developed in a Bayesian framework. We assess the performance of the models 23 by using them to predict the distributions of two plant species (Proteaceae) from South 24 Africa’s Cape Floristic Region. We demonstrate that making distribution models spatially 25 explicit can be essential for accurately characterizing the environmental response of species, 26 predicting their probability of occurrence, and assessing uncertainty in the model results. 27 Adding hierarchical levels to the models has further advantages in allowing human 28 transformation of the landscape to be taken into account, as well as additional features of 29 the sampling process. 30