Comparative interpretation of count, presence-absence and point methods for species distribution models

1. The need to understand the processes shaping population distributions has resulted in a vast increase in the diversity of spatial wildlife data, leading to the development of many novel analytical techniques that are fit-for-purpose. One may aggregate location data into spatial units (e.g. grid cells) and model the resulting counts or presenceabsences as a function of environmental covariates. Alternatively, the point data may be modelled directly, by combining the individual observations with a set of random or regular points reflecting habitat availability, a method known as a use-availability design (or, alternatively a presence pseudo-absence or casecontrol design). 2. Although these spatial point, count and presence-absence methods are widely used, the ecological literature is not explicit about their connections and how their parameter estimates and predictions should be interpreted. The objective of this study is to recapitulate some recent statistical results and illustrate that under certain assumptions, each method can be motivated by the same underlying spatial inhomogeneous Poisson point process (IPP) model in which the intensity function is modelled as a log-linear function of covariates. 3. The Poisson likelihood used for count data is a discrete approximation of the IPP likelihood. Similarly, the presence-absence design will approximate the IPP likelihood, but only when spatial units (i.e. pixels) are extremely small (Electric Journal of Statistics, 2010, 4, 1151-1201). For larger pixel sizes, presence-absence designs do not differentiate between one or multiple observations within each pixel, hence leading to information loss. 4. Logistic regression is often used to estimate the parameters of the IPP model using point data. Although the response variable is defined as 0 for the availability points, these zeros do not serve as true absences as is often assumed; rather, their role is to approximate the integral of the denominator in the IPP likelihood (The Annals of Applied Statistics, 2010, 4, 1383-1402). Because of this common misconception, the estimated exponential function of the linear predictor (i.e. the resource selection function) is often assumed to be proportional to occupancy. Like IPP and count models, this function is proportional to the expected density of observations. 5. Understanding these (dis-)similarities between different species distribution modelling techniques should improve biological interpretation of spatial models and therefore advance ecological and methodological cross-fertilization.