Effects of spatial autocorrelation and imperfect detection on species distribution models

Abstract

Species distribution models (SDMs) are widely used in ecology and related fields. They are frequently adopted to predict the expected occurrence (presence/absence) or abundance over large spatial scales, that is, to produce a species distribution map. Two issues that almost universally affect these models are measurement errors (especially imperfect detection) and residual spatial autocorrelation. We explored the effects of imperfect detection and autocorrelation in abundance models by simulating datasets which did or did not contain these two effects and analysing them with four different models that did or did not accommodate them. Specifically, we used a Poisson GLM as a baseline, an N‐mixture model accounting only for imperfect detection and two N‐mixture models that accounted for imperfect detection, but differed in their specification of spatial autocorrelation (CAR random effects vs. two‐dimensional splines). In a case study, we then applied these models to Common Redstart Phoenicurus phoenicurus data from the second Swiss Breeding Bird Atlas (1993–1996) and validated them using an independent monitoring dataset. We found that both imperfect detection and autocorrelation strongly affected the quality and the uncertainty of abundance maps, especially when they occurred together. Spatial N‐mixture models were well able to estimate the true abundance maps. Explicit modelling of measurement error and spatial autocorrelation can thus greatly improve the quality of SDMs and should not be ignored when producing large‐scale abundance or occurrence maps.

Effects of simulated observation errors on the performance of species distribution models

“…We can think of the creation of false negatives (in “EqualPrev”) the same way as one uses pseudo‐absences (i.e., when real absences are not available), setting the weights of those pseudo‐absences to 0.5 (therefore ensuring equal prevalence). As the addition of errors to presences/absences decreased model performance in both cases, it is important to account for imperfect detection in models (see Guélat & Kéry, ; Lahoz‐Monfort et al, for recommendations).…”

Estimating spatially and temporally complex range dynamics when detection is imperfect

“…Accounting for complex spatial structure in SDMs is an active area of research (Reich et al 2006) and other methods exist for handling spatial structure in occupancy models, particularly through the use of conditional autoregressive (CAR) modeling (e.g., Bled et al 2011, Johnson et al 2013, Guélat and Kéry 2018). Both CAR and GAM approaches have been shown to reduce bias in SDM models (Guélat and Kéry 2018), though the GAM approach is generally more computationally efficient, produces more precise parameter estimates, and can be fit using most popular Bayesian software programs, including JAGS, WinBUGS (Lunn et al 2000), NIMBLE (Valpine et al 2017), and STAN (Carpenter et al 2017). These two approaches are not mutually exclusive though and future work integrating GAM and CAR models in occupancy-based SDMs is likely to improve inferences about past and future range dynamics.…”

“…First, SDMs must include sufficient flexibility to quantify highly non-linear spatial patterns in occurrence probability. Although spatial variation in occurrence can in some cases be modeled using environmental covariates, residual spatial variation (which is likely common in most applications of SDMs at large spatial scales) can bias estimates of occurrence probability (Johnson et al 2013, Guélat and Kéry 2018). Second, because occurrence probability at a given point in time is not independent of occurrence probability at earlier points in time, SDMs must explicitly account for temporal auto-correlation in occurrence probability (MacKenzie et al 2003).…”

“…Like GLMs, GAMs use link functions to accommodate response variables with normal or non-normal error distributions (e.g., binomial, Poisson), making it conceptually simple to extend occupancy models to estimate highly nonlinear effects of covariates (Kéry and Royle 2015). Although GAMs have been used to estimate species distributions in a number of contexts (e.g., Bled et al 2013, Guélat and Kéry 2018), this approach has not been widely used in occupancy-based SDMs that account for both temporal dynamics and imperfect detection.…”

A generalized observation confirmation model to account for false positive error in species detection-nondetection data

“…Covariates for expected abundance are noted in Table S1 and were extracted from a circular buffer of 1 or 5 km radius surrounding the camera locations. Spatial smoothing was implemented via a 2-dimensional cubic spline (Guélat and Kéry 2018) across latitude and longitude with 20 knots placed across the state. The detection probability of an individual animal at different sites was modeled as varying in relation to whether the camera was placed on a maintained trail or not and as a quadratic function of the distance between the camera and the location the camera was targeting (as reported by volunteers), and false positive error probability was modeled as a logistic function of the proportion of cropland within a circular buffer with 5 km radius to account for what we expected to be increased prevalence of species confused with gray foxes (red fox, coyote) relative to foxes themselves.…”