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.

Aim:To examine how the distributions of fishes in three rivers changed over four decades of rising air temperatures.Location: Colorado, USA. Methods:We used fish sampling over more than four decades in three rivers in Colorado, USA, to examine changes in the upper and lower distribution limits of fishes. Results:There was a divergent pattern of range shifts among species. One coldwater fish species showed the expected pattern of retraction at its lower limit and expansion at its upper limit. However, warmwater fishes, on average, did not shift their upper distribution limit.Main conclusions: All three rivers displayed a strong habitat transition from upstream, high-gradient reaches to downstream, low-gradient reaches, suggesting that habitat conditions associated with high channel slope may limit the ability of some fish species to track warming water temperatures. In addition, potential anthropogenic barriers to fish movement occurred near species distribution limits, and these may prevent or delay range shifts in river fishes. The overall pattern of range shifts was consistent across the three rivers, suggesting a coherent influence of species' traits, physiological tolerances and habitat requirements on fish species distributions. K E Y W O R D Sclimate change, freshwater fish, plains fish, range limits, range shift, species' distribution, stream isotherm

Summary1. Hill numbers unify biodiversity metrics by combining several into one expression. For example, species richness, Shannon's diversity index and the Gini-Simpson index are a few of the most used diversity measures, and they can be expressed as Hill numbers. Traditionally, Hill numbers have been calculated from relative abundance data, but the expression has been modified to use incidence data as well. We demonstrate an approach for estimating Hill numbers using an occupancy modelling framework that accounts for imperfect detection. 2. We alter the Hill numbers formula to use occupancy probabilities as opposed to the incidence probabilities that have been used previously and to calculate its summations from the modelled species richness. After introducing the occupancy-based Hill numbers, we demonstrate the differences between them and the incidence-based Hill numbers previously used through a simulation study and two applications. 3. In the simulation study and the two examples using real data, the occupancy-based Hill numbers were larger than the incidence-based Hill numbers, although species richness was estimated similarly using both methods. 4. The occupancy-based Hill number estimators are always at their asymptotic values (i.e. as if an infinite number of samples have been taken for the study region), therefore making it easy to compare biodiversity between different assemblages. In addition, the Hill numbers are computed as derived quantities within a Bayesian hierarchical model, allowing for straightforward inference.

The relationship between the strontium content of the outer layers of otoliths (an indication of recent marine, estuarine or riverine habitat use) and the strontium content of roe in ripe female brown trout Salmo trutta was examined in fish collected from the Pomahaka River and the lower reaches of the Clutha River, South Island, New Zealand. A close relationship was found between the strontium content of roe and the outer layers of otoliths. This finding suggests that spawned eggs collected from redds could potentially be used to track the extent of upstream spawning migrations by anadromous brown trout.