Abstract. Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasiPoisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.

Abstract. Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Thermal regimes are fundamental determinants of aquatic ecosystems, which makes description and prediction of temperatures critical during a period of rapid global change. The advent of inexpensive temperature sensors dramatically increased monitoring in recent decades, and although most monitoring is done by individuals for agency‐specific purposes, collectively these efforts constitute a massive distributed sensing array that generates an untapped wealth of data. Using the framework provided by the National Hydrography Dataset, we organized temperature records from dozens of agencies in the western U.S. to create the NorWeST database that hosts >220,000,000 temperature recordings from >22,700 stream and river sites. Spatial‐stream‐network models were fit to a subset of those data that described mean August water temperatures (AugTw) during 63,641 monitoring site‐years to develop accurate temperature models (r2 = 0.91; RMSPE = 1.10°C; MAPE = 0.72°C), assess covariate effects, and make predictions at 1 km intervals to create summer climate scenarios. AugTw averaged 14.2°C (SD = 4.0°C) during the baseline period of 1993–2011 in 343,000 km of western perennial streams but trend reconstructions also indicated warming had occurred at the rate of 0.17°C/decade (SD = 0.067°C/decade) during the 40 year period of 1976–2015. Future scenarios suggest continued warming, although variation will occur within and among river networks due to differences in local climate forcing and stream responsiveness. NorWeST scenarios and data are available online in user‐friendly digital formats and are widely used to coordinate monitoring efforts among agencies, for new research, and for conservation planning.

The imminent demise of montane species is a recurrent theme in the climate change literature, particularly for aquatic species that are constrained to networks and elevational rather than latitudinal retreat as temperatures increase. Predictions of widespread species losses, however, have yet to be fulfilled despite decades of climate change, suggesting that trends are much weaker than anticipated and may be too subtle for detection given the widespread use of sparse water temperature datasets or imprecise surrogates like elevation and air temperature. Through application of large water-temperature databases evaluated for sensitivity to historical air-temperature variability and computationally interpolated to provide high-resolution thermal habitat information for a 222,000-km network, we estimate a less dire thermal plight for cold-water species within mountains of the northwestern United States. Stream warming rates and climate velocities were both relatively low for 1968-2011 (average warming rate = 0.101°C/ decade; median velocity = 1.07 km/decade) when air temperatures warmed at 0.21°C/decade. Many cold-water vertebrate species occurred in a subset of the network characterized by low climate velocities, and three native species of conservation concern occurred in extremely cold, slow velocity environments (0.33-0.48 km/decade). Examination of aggressive warming scenarios indicated that although network climate velocities could increase, they remain low in headwaters because of strong local temperature gradients associated with topographic controls. Better information about changing hydrology and disturbance regimes is needed to complement these results, but rather than being climatic cul-de-sacs, many mountain streams appear poised to be redoubts for cold-water biodiversity this century.climate refugia | climate velocity | biodiversity | fish | network M ountain landscapes constitute 12% of the Earth's land surface (1) and have long served as sanctuaries for certain species by restricting human incursions and juxtaposing diverse environments (2). Mountains also host a suite of endemic species, many of which are perceived to be condemned to extinction as their habitats contract or disappear as a result of climate change-related temperature increases, environmental stochasticity, and nonnative species invasions (3-5). A substantial literature, to which we have contributed, has developed in previous decades suggesting a similar fate for cold-water fishes and other aquatic taxa in montane environments (6-8), but it rests largely on predictions about temperature increases and untested assumptions about the relationship between air temperature and water temperature. In particular, previous studies have failed to recognize that the highest and coldest streams are relatively insensitive to air temperature fluctuations (9, 10), and that the morphologies of many mountain ranges and their stream networks may mediate climate warming such that shifts in thermal habitat are small (2, 11).Dense stream networks drain moun...