While multi-species occupancy models (MSOMs) are emerging as a popular method for analyzing biodiversity data, formal checking and validation approaches for this class of models have lagged behind. Concurrent with the rise in application of MSOMs among ecologists, a quiet regime shift is occurring in Bayesian statistics where predictive model comparison approaches are experiencing a resurgence. Unlike single-species occupancy models that use integrated likelihoods, MSOMs are usually couched in a Bayesian framework and contain multiple levels. Standard model checking and selection methods are often unreliable in this setting and there is only limited guidance in the ecological literature for this class of models. We examined several different contemporary Bayesian hierarchical approaches for checking and validating MSOMs and applied these methods to a freshwater aquatic study system in Colorado, USA, to better understand the diversity and distributions of plains fishes. Our findings indicated distinct differences among model selection approaches, with cross-validation techniques performing the best in terms of prediction.
Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many of the statistical methods used to account for autocorrelation can be viewed as regression models that include basis functions.Understanding the concept of basis functions enables ecologists to modify commonly used ecological models to account for autocorrelation, which can improve inference and predictive accuracy. Understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of multicollinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.
The dynamic, multi‐season occupancy model framework has become a popular tool for modeling open populations with occupancies that change over time through local colonizations and extinctions. However, few versions of the model relate these probabilities to the occupancies of neighboring sites or patches. We present a modeling framework that incorporates this information and is capable of describing a wide variety of spatiotemporal colonization and extinction processes. A key feature of the model is that it is based on a simple set of small‐scale rules describing how the process evolves. The result is a dynamic process that can account for complicated large‐scale features. In our model, a site is more likely to be colonized if more of its neighbors were previously occupied and if it provides more appealing environmental characteristics than its neighboring sites. Additionally, a site without occupied neighbors may also become colonized through the inclusion of a long‐distance dispersal process. Although similar model specifications have been developed for epidemiological applications, ours formally accounts for detectability using the well‐known occupancy modeling framework. After demonstrating the viability and potential of this new form of dynamic occupancy model in a simulation study, we use it to obtain inference for the ongoing Common Myna (Acridotheres tristis) invasion in South Africa. Our results suggest that the Common Myna continues to enlarge its distribution and its spread via short distance movement, rather than long‐distance dispersal. Overall, this new modeling framework provides a powerful tool for managers examining the drivers of colonization including short‐ vs. long‐distance dispersal, habitat quality, and distance from source populations.
Statistical population reconstruction offers a robust approach to demographic assessment for harvested populations, but current methods are restricted to big‐game species with multiple age classes. We extended this approach to small game and analyzed 14 years of age‐at‐harvest data for greater sage‐grouse (Centrocercus urophasianus) in Oregon, USA, in conjunction with radiotelemetry data to reconstruct annual abundance levels, recruitment, and natural survival probabilities. Abundance estimates ranged from a low of 26,236 in 1995 to a high of 39,492 in 2004. Annual abundance estimates for adult males were correlated with a spring lek count index (r = 0.849, P < 0.029). We estimated the average annual harvest mortality for the population to be 0.028, ranging from 0.021 to 0.031 across years. We estimated the probability of natural survival of adult females to be 0.818 ( = 0.052), somewhat higher than that of adult males (Ŝ = 0.609, = 0.163). Our precision in reconstructing the population was hampered by low harvest rates and the few birds tagged in the radiotelemetry investigations. Despite these issues, our analysis illustrates how modern statistical reconstruction procedures offer a flexible framework for demographic assessment using commonly collected data. This approach offers a useful alternative to small‐game indices and would be most appropriate for species with 5 or more years of age‐at‐harvest data and moderate‐to‐heavy harvest rates.
Abstract. Determining the range of a species and exploring species-habitat associations are central questions in ecology and can be answered by analyzing presence-absence data. Often, both the sampling of sites and the desired area of inference involve neighboring sites; thus, positive spatial autocorrelation between these sites is expected. Using survey data for the Southern Ground Hornbill (Bucorvus leadbeateri ) from the Southern African Bird Atlas Project, we compared advantages and disadvantages of three increasingly complex models for species occupancy: an occupancy model that accounted for nondetection but assumed all sites were independent, and two spatial occupancy models that accounted for both nondetection and spatial autocorrelation. We modeled the spatial autocorrelation with an intrinsic conditional autoregressive (ICAR) model and with a restricted spatial regression (RSR) model. Both spatial models can readily be applied to any other gridded, presence-absence data set using a newly introduced R package.The RSR model provided the best inference and was able to capture small-scale variation that the other models did not. It showed that ground hornbills are strongly dependent on protected areas in the north of their South African range, but less so further south. The ICAR models did not capture any spatial autocorrelation in the data, and they took an order of magnitude longer than the RSR models to run. Thus, the RSR occupancy model appears to be an attractive choice for modeling occurrences at large spatial domains, while accounting for imperfect detection and spatial autocorrelation.
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