Individual variation in reproductive success is a key feature of evolution, but also has important implications for predicting population responses to variable environments. Although such individual variation in reproductive outcomes has been reported in numerous studies, most analyses to date have not considered whether these realized differences were due to latent individual heterogeneity in reproduction or merely random chance causing different outcomes among like individuals. Furthermore, latent heterogeneity in fitness components might be expressed differently in contrasted environmental conditions, an issue that has only rarely been investigated. Here, we assessed (i) the potential existence of latent individual heterogeneity and (ii) the nature of its expression (fixed vs. variable) in a population of female Weddell seals (Leptonychotes weddellii), using a hierarchical modeling approach on a 30-year mark-recapture data set consisting of 954 individual encounter histories. We found strong support for the existence of latent individual heterogeneity in the population, with "robust" individuals expected to produce twice as many pups as "frail" individuals. Moreover, the expression of individual heterogeneity appeared consistent, with only mild evidence that it might be amplified when environmental conditions are severe. Finally, the explicit modeling of individual heterogeneity allowed us to detect a substantial cost of reproduction that was not evidenced when the heterogeneity was ignored.

Model choice is usually an inevitable source of uncertainty in model-based statistical analyses. While the focus of model choice was traditionally on methods for choosing a single model, methods to formally account for multiple models within a single analysis are now accessible to many researchers. The specific technique of model averaging was developed to improve predictive ability by combining predictions from a set of models. However, it is now often used to average regression coefficients across multiple models with the ultimate goal of capturing a variable's overall effect. This use of model averaging implicitly assumes the same parameter exists across models so that averaging is sensible. While this assumption may initially seem tenable, regression coefficients associated with particular explanatory variables may not hold equivalent interpretations across all of the models in which they appear, making explanatory inference about covariates challenging. Accessibility to easily implementable software, concerns about being criticized for ignoring model uncertainty, and the chance to avoid having to justify choice of a final model have all led to the increasing popularity of model averaging in practice. We see a gap between the theoretical development of model averaging and its current use in practice, potentially leaving well-intentioned researchers with unclear inferences or difficulties justifying reasons for using (or not using) model averaging. We attempt to narrow this gap by revisiting some relevant foundations of regression modeling, suggesting more explicit notation and graphical tools, and discussing how individual model results are combined to obtain a model averaged result. Our goal is to help researchers make informed decisions about model averaging and to encourage question-focused modeling over method-focused modeling.

26Fishways designed for salmonids often restrict passage by non-salmonids and effective tools are 27 needed both to identify passage problems for non-target species and to inform remediation 28 planning. In this case study, we used migration histories from 2170 radio-tagged adult Pacific 29 lamprey (Entosphenus tridentatus) to identify locations of poor passage ("bottlenecks") at a 30 large, multi-fishway dam. Over ten years, 49% of tagged lamprey that entered fishways failed to 31 pass the dam. Models accounting for repeated attempts by individual lamprey indicated 32 successful passage strongly depended on attempted passage route. Success also varied with time 33 of fishway entry, water temperature, and lamprey body size. Most failed passage attempts 34 terminated in lower fishway segments, but extensive seasonal shifts in bottleneck locations were 35 detected. Ranking metrics helped prioritize bottlenecks and identified sites where structural or 36 operational modifications should improve lamprey passage. Our integration of spatially-37 intensive monitoring with novel analytical techniques was critical to understanding the complex 38 relationships between fishway features, environmental variation, and lamprey behavior. The 39 prioritization framework can be applied to a wide range of fish passage assessments. 40 41 42

We propose a model for a point-referenced spatially correlated ordered categorical response and methodology for estimation of model parameters. Models and methods for spatially correlated continuous response data are widespread, but models for spatially correlated categorical data, and especially ordered multicategory data, are less developed. Bayesian models and methodology have been proposed for the analysis of independent and clustered ordered categorical data, and also for binary and count point-referenced spatial data. We combine and extend these methods to describe a Bayesian model for point-referenced (as opposed to lattice) spatially correlated ordered categorical data. We include extensive simulation results and show that our model offers superior predictive performance as compared to a non-spatial cumulative probit model and a more standard generalized linear model with spatial random effects. We demonstrate the usefulness of our model using a real-world example to predict ordered categories describing stream health within the state of Maryland.

The investigation of individual heterogeneity in vital rates has recently received growing attention among population ecologists. Individual heterogeneity in wild animal populations has been accounted for and quantified by including individually varying effects in models for mark–recapture data, but the real need for underlying individual effects to account for observed levels of individual variation has recently been questioned by the work of Tuljapurkar et al. (Ecology Letters, 12, 93, 2009) on dynamic heterogeneity. Model-selection approaches based on information criteria or Bayes factors have been used to address this question. Here, we suggest that, in addition to model-selection, model-checking methods can provide additional important insights to tackle this issue, as they allow one to evaluate a model's misfit in terms of ecologically meaningful measures. Specifically, we propose the use of posterior predictive checks to explicitly assess discrepancies between a model and the data, and we explain how to incorporate model checking into the inferential process used to assess the practical implications of ignoring individual heterogeneity. Posterior predictive checking is a straightforward and flexible approach for performing model checks in a Bayesian framework that is based on comparisons of observed data to model-generated replications of the data, where parameter uncertainty is incorporated through use of the posterior distribution. If discrepancy measures are chosen carefully and are relevant to the scientific context, posterior predictive checks can provide important information allowing for more efficient model refinement. We illustrate this approach using analyses of vital rates with long-term mark–recapture data for Weddell seals and emphasize its utility for identifying shortfalls or successes of a model at representing a biological process or pattern of interest.We show how posterior predictive checks can be used to strengthen inferences in ecological studies. We demonstrate the application of this method on analyses dealing with the question of individual reproductive heterogeneity in a population of Antarctic pinnipeds.

Occupancy models are widely applied to estimate species distributions, but few methods exist for model checking. Thorough model assessments can uncover inadequacies and allow for deeper ecological insight by exploring structure in the observed data not accounted for by a model. We introduce occupancy model residual definitions that utilize the posterior distribution of the partially latent occupancy states. Residual‐based assessments are valuable because they can target specific assumptions and identify ways to improve a model, such as adding spatial correlation or meaningful covariates. Our approach defines separate residuals for occupancy and detection, and we use simulation to examine whether missing structure for modeling detection probabilities can be distinguished from that for occupancy probabilities. In many scenarios, our residual diagnostics were able to separate inadequacies at the different model levels successfully, but we describe other situations when this may not be the case. Applying Moran's I residual diagnostics to assess models for silver‐haired (Lasionycteris noctivagans) and little brown (Myotis lucifugus) bats only provided evidence of residual spatial correlation among detections. Targeting specific model assumptions using carefully chosen residual diagnostics is valuable for any analysis, and we remove previous barriers for occupancy analyses—lack of examples and practical advice.

Aim Use of local‐scale non‐native plant species (NNS) distribution models has the potential to decrease survey effort and improve population prioritization for management. We developed and evaluated data collection methods and minimum sampling requirements to inform local‐scale models of NNS distribution. We also evaluated overall model predictive performance for 16 species at two sites and determined how classes of variables contributed to model performance and suggest invasion drivers. Location Wyoming and Idaho, USA Methods A simulation study was used to test the efficiency of different sampling methods to predict imposed species distributions. Empirical distribution models of species occurrence data from two environmentally disparate sites were cross‐validated at increasing sample sizes, and the asymptotic maximum predictive performance and relative contribution of classes of variables were determined for 16 NNS. Results Transect sampling was the most efficient method for maximizing model performance after accounting for logistics. Minimum sample sizes to reach model maximum predictive performance were similar for the simulation (< 0.5% of study area) and empirical studies (mean of 0.13% using transects). Maximum predictive performance tended to be greater at the site with steeper environmental gradients, and topo‐climatic/biotic variables were most important to model improvement. Main conclusions Local‐scale SDMs can be useful to NNS managers. Using transect methodology, enough data can be collected (ca. 0.13% of the management area) to fit models within logistical/budgetary constraints. These models are most predictive for well‐established species as opposed to new invaders and in areas with steeper environmental gradients. Finally, topo‐climatic/biotic predictors are the most important variables for predicting more established species, but disturbance and dispersal limitation should be considered and quantified to ensure variables associated with dominant processes are included in the SDM.

It is increasingly common for studies of animal ecology to use model-based predictions of environmental variables as explanatory or predictor variables, even though model prediction uncertainty is typically unknown. To demonstrate the potential for misleading inferences when model predictions with error are used in place of direct measurements, we compared snow water equivalent (SWE) and snow depth as predicted by the Snow Data Assimilation System (SNODAS) to field measurements of SWE and snow depth. We examined locations on elk (Cervus canadensis) winter ranges in western Wyoming, because modeled data such as SNODAS output are often used for inferences on elk ecology. Overall, SNODAS predictions tended to overestimate field measurements, prediction uncertainty was high, and the difference between SNODAS predictions and field measurements was greater in snow shadows for both snow variables compared to non-snow shadow areas. We used a simple simulation of snow effects on the probability of an elk being killed by a predator to show that, if SNODAS prediction uncertainty was ignored, we might have mistakenly concluded that SWE was not an important factor in where elk were killed in predatory attacks during the winter. In this simulation, we were interested in the effects of snow at finer scales (< 1 km2) than the resolution of SNODAS. If bias were to decrease when SNODAS predictions are averaged over coarser scales, SNODAS would be applicable to population-level ecology studies. In our study, however, averaging predictions over moderate to broad spatial scales (9-2200 km2) did not reduce the differences between SNODAS predictions and field measurements. This study highlights the need to carefully evaluate two issues when using model output as an explanatory variable in subsequent analysis: (1) the model's resolution relative to the scale of the ecological question of interest and (2) the implications of prediction uncertainty on inferences when using model predictions as explanatory or predictor variables.