Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian P values are relatively easy to compute, but are well known to be conservative, producing P values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross‐validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness‐of‐fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N‐mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive P values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross‐validation and pivot discrepancy measures (including the “sampled predictive P value”) appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

Abstract. Checking that models adequately represent data is an essential component

Low genetic heterozygosity is associated with loss of fitness in many natural populations. However, it remains unclear whether the mechanism is related to general (i.e. inbreeding) or local effects, in particular from a subset of loci lying close to genes under balancing selection. Here we analyse involving heterozygosity-fitness correlations on neonatal survival of California sea lions and on susceptibility to hookworm (Uncinaria spp.) infection, the single most important cause of pup mortality. We show that regardless of differences in hookworm burden, homozygosity is a key predictor of hookworm-related lesions, with no single locus contributing disproportionately. Conversely, the subsequent occurrence of anaemia due to blood loss in infected pups is overwhelmingly associated with homozygosity at one particular locus, all other loci showing no pattern. Our results suggest contrasting genetic mechanisms underlying two pathologies related to the same pathogen. First, relatively inbred pups are less able to expel hookworms and prevent their attachment to the intestinal mucosa, possibly due to a weakened immune response. In contrast, infected pups that are homozygous for a gene near to microsatellite Hg4.2 are strongly predisposed to anaemia. As yet, this gene is unknown, but could plausibly be involved in the blood-coagulation cascade. Taken together, these results suggest that pathogenic burden alone may not be the main factor regulating pathogen-related mortality in natural populations. Our study could have important implications for the conservation of small, isolated or threatened populations, particularly when they are at a risk of facing pathogenic challenges.

We compared the nonbreeding-season foraging behavior of lactating California sea lions ( Zalophus californianus californianus (Lesson, 1828)) at San Miguel Island, California, during El Niño conditions in 1993 and non-El Niño conditions in 1996. Lactating females were instrumented with satellite-linked time–depth recorders between January and March in 1993 (n = 6) and 1996 (n = 10) and data were collected through May in each year. Females foraged northwest of the colony, up to 367 km from it and 230 km from the California coast. Mean dive depths ranged from 19.5 to 279.3 m, but most females achieved dives deeper than 400 m. Most females fed exclusively in the offshore habitat, traveled farther from the colony, spent more time traveling, made deeper and longer dives, and terminated lactation earlier during the 1993 El Niño. The results suggest that prey were concentrated in the offshore habitat and located farther from the colony and deeper in the water column during El Niño. Females did not change their foraging direction, foraging-trip duration, foraging effort, or prey species consumed.