A Bayesian method for assessing multi-scale species-habitat relationships

Abstract

Context Scientists face several theoretical and methodological challenges in appropriately describing fundamental wildlife-habitat relationships in models. The spatial scales of habitat relationships are often unknown, and are expected to follow a multi-scale hierarchy. Typical frequentist or information theoretic approaches often suffer under collinearity in multiscale studies, fail to converge when models are complex or represent an intractable computational burden when candidate model sets are large. Objectives Our objective was to implement an automated, Bayesian method for inference on the spatial scales of habitat variables that best predict animal abundance. Methods We introduce Bayesian latent indicator scale selection (BLISS), a Bayesian method to select spatial scales of predictors using latent scale indicator variables that are estimated with reversible-jump Markov chain Monte Carlo sampling. BLISS does not suffer from collinearity, and substantially reduces computation time of studies. We present a simulation study to validate our method and apply our method to a case-study of land cover predictors for ring-necked pheasant (Phasianus colchicus) abundance in Nebraska, USA. Results Our method returns accurate descriptions of the explanatory power of multiple spatial scales, and unbiased and precise parameter estimates under commonly encountered data limitations including spatial scale autocorrelation, effect size, and sample size. BLISS outperforms commonly used model selection methods including stepwise and AIC, and reduces runtime by 90%. Conclusions Given the pervasiveness of scale-dependency in ecology, and the implications of mismatches between the scales of analyses and ecological processes, identifying the spatial scales over which species are integrating habitat information is an important step in understanding species-habitat relationships. BLISS is a widely applicable method for identifying important spatial scales, propagating scale uncertainty, and testing hypotheses of scaling relationships.

How characteristic is the species characteristic selection scale?

“…Decision rules would need to be carefully considered to establish whether a particular environmental characteristic appears scale independent because there is no ecological relationship to detect (e.g., coefficient effect size biologically zero), or because all measured scales are equally important (e.g., coefficient effect size biologically non‐zero). Indeed, uncertainty in spatial scale selection increases as coefficient effect sizes decrease (Stuber et al, ). Nevertheless, our conclusions hold even if we restrict our analysis to PCSS designations with relatively low uncertainty.…”

“…To address whether within species, there is a characteristic scale across multiple environmental predictors, for each species we performed a multi‐scale, multi‐predictor analysis. To incorporate multiple candidate spatial scales we used Bayesian latent indicator scale selection (BLISS; Stuber et al, ) estimated with Markov chain Monte Carlo (MCMC) sampling. BLISS is not sensitive to collinearity and enables complete flexibility in exploring candidate spatial scale model space such that all possible combinations of land cover types at different spatial scales are evaluated.…”

“…BLISS is not sensitive to collinearity and enables complete flexibility in exploring candidate spatial scale model space such that all possible combinations of land cover types at different spatial scales are evaluated. Furthermore, BLISS outperforms other model selection techniques commonly used in multi‐scale investigations and is robust to between‐ and within‐predictor autocorrelation, and sample size variation (Stuber et al, ). Furthermore, BLISS is one of only a few methods that has been validated through simulation studies to identify “true” scales of species–environment relationships across a range of sampling schemes, and environmental characteristics (see Stuber et al, for details).…”

“…Furthermore, BLISS outperforms other model selection techniques commonly used in multi‐scale investigations and is robust to between‐ and within‐predictor autocorrelation, and sample size variation (Stuber et al, ). Furthermore, BLISS is one of only a few methods that has been validated through simulation studies to identify “true” scales of species–environment relationships across a range of sampling schemes, and environmental characteristics (see Stuber et al, for details). Briefly, the nine spatial scales represent candidate spatial scales that enter the base N‐mixture model as latent variables where each land cover predictor can appear in the model at any of the nine potential scales.…”

“…Instead, the majority of investigations continue to make spatial scale selections based on convenience, lack of a priori expectations regarding the specific scale of effect, or unsubstantiated hypothesized relationships (e.g., a relationship between scale and species’ average territory size) between species’ response and scale, without examining whether the examined scale is appropriate. Even for the minority of studies using data‐driven methods of scale selection, most are limited by convenience or convention to identifying a single best, or characteristic, spatial scale to understand all species–environment relationships (see Stuber, Gruber, & Fontaine, for details), despite the awareness that alternative land cover types may provide biologically different ecological resources over unique spatial scales (Bergman et al, ; Hinsley, Bellamy, Newton, & Sparks, ; Naugle, Higgins, Estey, Johnson, & Nusser, ; Sandin & Johnson, ). Particularly, collecting data or making inferences at inappropriate spatial scales is problematic when species–environment relationships are scale‐dependent.…”