In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model‐averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information‐theoretical to cross‐validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model‐averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non‐parametric methods such as cross‐validation for a reliable uncertainty quantification of model‐averaged predictions.

Species distribution models (SDMs) are widely used in ecology and related fields. They are frequently adopted to predict the expected occurrence (presence/absence) or abundance over large spatial scales, that is, to produce a species distribution map. Two issues that almost universally affect these models are measurement errors (especially imperfect detection) and residual spatial autocorrelation. We explored the effects of imperfect detection and autocorrelation in abundance models by simulating datasets which did or did not contain these two effects and analysing them with four different models that did or did not accommodate them. Specifically, we used a Poisson GLM as a baseline, an N‐mixture model accounting only for imperfect detection and two N‐mixture models that accounted for imperfect detection, but differed in their specification of spatial autocorrelation (CAR random effects vs. two‐dimensional splines). In a case study, we then applied these models to Common Redstart Phoenicurus phoenicurus data from the second Swiss Breeding Bird Atlas (1993–1996) and validated them using an independent monitoring dataset. We found that both imperfect detection and autocorrelation strongly affected the quality and the uncertainty of abundance maps, especially when they occurred together. Spatial N‐mixture models were well able to estimate the true abundance maps. Explicit modelling of measurement error and spatial autocorrelation can thus greatly improve the quality of SDMs and should not be ignored when producing large‐scale abundance or occurrence maps.

Summary1. Spatial capture-recapture models make use of auxiliary data on capture location to provide density estimates for animal populations. Previously, models have been developed primarily for fixed trap arrays which define the observable locations of individuals by a set of discrete points. 2. Here, we develop a class of models for 'search-encounter' data, i.e. for detections of recognizable individuals in continuous space, not restricted to trap locations. In our hierarchical model, detection probability is related to the average distance between individual location and the survey path. The locations are allowed to change over time owing to movements of individuals, and individual locations are related formally by a model describing individual activity or home range centre which is itself regarded as a latent variable in the model. We provide a Bayesian analysis of the model in Win-BUGS, and develop a custom MCMC algorithm in the R language. 3. The model is applied to simulated data and to territory mapping data for the Willow Tit from the Swiss Breeding Bird Survey MHB. While the observed density was 15 territories per nominal 1 km 2 plot of unknown effective sample area, the model produced a density estimate of 21AE12 territories per square km (95% posterior interval: 17-26). 4. Spatial capture-recapture models are relevant to virtually all animal population studies that seek to estimate population size or density, yet existing models have been proposed mainly for conventional sampling using arrays of traps. Our model for search-encounter data, where the spatial pattern of searching can be arbitrary and may change over occasions, greatly expands the scope and utility of spatial capture-recapture models.

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Ring re‐encounter data, in particular ring recoveries, have made a large contribution to our understanding of bird movements. However, almost every study based on ring re‐encounter data has struggled with the bias caused by unequal observer distribution. Re‐encounter probabilities are strongly heterogeneous in space and over time. If this heterogeneity can be measured or at least controlled for, the enormous number of ring re‐encounter data collected can be used effectively to answer many questions. Here, we review four different approaches to account for heterogeneity in observer distribution in spatial analyses of ring re‐encounter data. The first approach is to measure re‐encounter probability directly. We suggest that variation in ring re‐encounter probability could be estimated by combining data whose re‐encounter probabilities are close to one (radio or satellite telemetry) with data whose re‐encounter probabilities are low (ring re‐encounter data). The second approach is to measure the spatial variation in re‐encounter probabilities using environmental covariates. It should be possible to identify powerful predictors for ring re‐encounter probabilities. A third approach consists of the comparison of the actual observations with all possible observations using randomization techniques. We encourage combining such randomisations with ring re‐encounter models that we discuss as a fourth approach. Ring re‐encounter models are based on the comparison of groups with equal re‐encounter probabilities. Together these four approaches could improve our understanding of bird movements considerably. We discuss their advantages and limitations and give directions for future research.