A Bayesian Dirichlet process community occupancy model to estimate community structure and species similarity

Abstract

Community occupancy models estimate species‐specific parameters while sharing information across species by treating parameters as sampled from a common distribution. When communities consist of discrete groups, shrinkage of estimates toward the community mean can mask differences among groups. Infinite‐mixture models using a Dirichlet process (DP) distribution, in which the number of latent groups is estimated from the data, have been proposed as a solution. In addition to community structure, these models estimate species similarity, which allows testing hypotheses about whether traits drive species response to environmental conditions. We develop a community occupancy model (COM) using a DP distribution to model species‐level parameters. Because clustering algorithms are sensitive to dimensionality and distinctiveness of clusters, we conducted a simulation study to explore performance of the DP‐COM with different dimensions (i.e., different numbers of model parameters with species‐level DP random effects) and under varying cluster differences. Because the DP‐COM is computationally expensive, we compared its estimates to a COM with a normal random species effect. We further applied the DP‐COM model to a bird data set from Uganda. Estimates of the number of clusters and species cluster identity improved with increasing difference among clusters and increasing dimensions of the DP; but the number of clusters was always overestimated. Estimates of number of sites occupied and species and community‐level covariate coefficients on occupancy probability were generally unbiased with (near‐) nominal 95% Bayesian Credible Interval coverage. Accuracy of estimates from the normal and the DP‐COM was similar. The DP‐COM clustered 166 bird species into 27 clusters regarding their affiliation with open or woodland habitat and distance to oil wells. Estimates of covariate coefficients were similar between a normal and the DP‐COM. Except sunbirds, species within a family were not more similar in their response to these covariates than the overall community. Given that estimates were consistent between the normal and the DP‐COM, and considering the computational burden for the DP models, we recommend using the DP‐COM only when the analysis focuses on community structure and species similarity, as these quantities can only be obtained under the DP‐COM.

A new statistical approach for identifying rare species under imperfect detection

“…However, we found identifiability issues in some of our simulations due to label‐switching among clusters. (Similar issues were reported by Sollmann et al (2021) when using infinite mixtures for modelling the joint distribution of occupancy parameters, especially when variation among clusters was high). Thus, in this work, we have specified finite mixtures for the state process only because our primary goal is to identify species based on their rarity rather than their elusiveness.…”

“…Unfortunately, selecting appropriate proposal densities is challenging and difficult to implement (Nasserinejad et al, 2017). Recently, Sollmann et al (2021) proposed a truncated stick‐breaking Dirichlet process to describe the community structure in terms of the estimated classes and the similarity in species responses to environmental conditions. However, Sollmann et al (2021) reported an overestimation of the number of classes and poor mixing due to label‐switching issues attributed to high dimensionality and variability among clusters.…”

“…Finally, the species heterogeneity model (Equation (c)) is characterized by the individual species logit‐scaled occupancy and detection probabilities drawn from the same normal prior distribution with hyperparameters describing the overall community response. It is important to notice that logit‐scale Normal distributions can overlap to different degrees depending on the mean and variance of each class, which affects the performance of the model in correctly identifying the members of each latent class (Sollmann et al, 2021). Issues with the model's performance can also arise if the density mass is heavily skewed due to an imbalanced number of observations allocated to certain classes.…”

“…For instance, finite mixtures in Capture‐Recapture models have been used to account for heterogeneity in individual capture probabilities (Norris & Pollock, 1996; Pledger, 2000). Within the context of occupancy models, mixture models have been used to model heterogeneity in detection probabilities (Royle, 2006), to account for false‐positive errors (Royle & Link, 2006), and more recently, to characterize the structure of a community based on latent groups of species that have similar responses to environmental conditions (Sollmann et al, 2021).…”

Flavivirus Persistence in Wildlife Populations

“…Moreover, additional information, such as population temporal trend data, taxonomy, conservation status, and habitat usage, are essential, all of which can be obtained from the International Union for Conservation of Nature (IUCN) [ 267 ]. Additional parameters to include in the model algorithm comprise metabolic rate, body temperature and body mass, and foraging characteristics (e.g., such as diet, foraging strata, and foraging time), which may be downloaded from databases BirdLife International and IUCN12 [ 267 , 268 , 269 ]. Global distribution data sets are also collected, which indicate the bearing of other factors, such as bioclimatic variables, mammalian and avian biodiversity, and anthropogenic variables, all of which are obtained from multiple sources [ 270 , 271 , 272 ].…”