Accounting for preferential sampling in species distribution models

Abstract

Species distribution models (SDMs) are now being widely used in ecology for management and conservation purposes across terrestrial, freshwater, and marine realms. The increasing interest in SDMs has drawn the attention of ecologists to spatial models and, in particular, to geostatistical models, which are used to associate observations of species occurrence or abundance with environmental covariates in a finite number of locations in order to predict where (and how much of) a species is likely to be present in unsampled locations. Standard geostatistical methodology assumes that the choice of sampling locations is independent of the values of the variable of interest. However, in natural environments, due to practical limitations related to time and financial constraints, this theoretical assumption is often violated. In fact, data commonly derive from opportunistic sampling (e.g., whale or bird watching), in which observers tend to look for a specific species in areas where they expect to find it. These are examples of what is referred to as preferential sampling, which can lead to biased predictions of the distribution of the species. The aim of this study is to discuss a SDM that addresses this problem and that it is more computationally efficient than existing MCMC methods. From a statistical point of view, we interpret the data as a marked point pattern, where the sampling locations form a point pattern and the measurements taken in those locations (i.e., species abundance or occurrence) are the associated marks. Inference and prediction of species distribution is performed using a Bayesian approach, and integrated nested Laplace approximation (INLA) methodology and software are used for model fitting to minimize the computational burden. We show that abundance is highly overestimated at low abundance locations when preferential sampling effects not accounted for, in both a simulated example and a practical application using fishery data. This highlights that ecologists should be aware of the potential bias resulting from preferential sampling and account for it in a model when a survey is based on non-randomized and/or non-systematic sampling.

Keywords: Bayesian modelling; integrated nested Laplace approximation; point processes; species distribution models; stochastic partial differential equation.

Figure 1

Representation of one of the one hundred Gaussian field simulated and the respective preferentially sampling locations generated

Figure 2

Study area and sampling locations (hauls) of blue and red shrimp (Aristeus antennatus). The size of the dots represents the amount caught in each of the locations

Figure 3

Improvement of the preferential model against a conventional model in model fit scores (DIC, LCPO, and MAE). Comparison is based on 100 preferentially and randomly sampled datasets. Note that positive values represent an improvement on model fit and vice versa

Figure 4

Simulated abundance against predicted abundance in the non‐preferential model (left) and in the model with the preferential correction (right) for one of the one hundred simulations performed. The non‐preferential model predicts worse than the preferential model at low‐abundance areas

Figure 5

Posterior predictive mean maps of one of the one hundred simulated abundance processes without (left) and with (right) the preferential sampling correction

Figure 6

Sensitivity analysis of the pc.prior distributions for the range and variance of a simulated spatial field. Dashed lines represent prior distributions, solid lines posterior distributions and vertical lines the real values of each of the hyperparameters of the spatial field: range in the left panel and variance in the right panel. Range priors were set so that the probability of having a range smaller than 10%, 20%, 30%, 40% and 50% of the maximum distance of the study area was 0.25. Similarly, priors over the variance of the spatial field were set so that the probability of having a variance higher than 2, 3, 4, 5 and 6 was 0.1

Figure 7

Maps of the mean of the posterior distribution of the spatial effect in the model without (left) and with (right) preferential sampling. Black dots represent sampling locations

Figure 8

Posterior predictive mean maps of the blue and red shrimp (Aristeus antennatus) species, without and with the preferential sampling correction. Black dots represent sampling locations