Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Contact with green space in the environment has been associated with mental health benefits, but the mechanism underpinning this association is not clear. This study extends an earlier exploratory study showing that more green space in deprived urban neighbourhoods in Scotland is linked to lower levels of perceived stress and improved physiological stress as measured by diurnal patterns of cortisol secretion. Salivary cortisol concentrations were measured at 3, 6 and 9 h post awakening over two consecutive weekdays, together with measures of perceived stress. Participants (n = 106) were men and women not in work aged between 35–55 years, resident in socially disadvantaged districts from the same Scottish, UK, urban context as the earlier study. Results from linear regression analyses showed a significant and negative relationship between higher green space levels and stress levels, indicating living in areas with a higher percentage of green space is associated with lower stress, confirming the earlier study findings. This study further extends the findings by showing significant gender differences in stress patterns by levels of green space, with women in lower green space areas showing higher levels of stress. A significant interaction effect between gender and percentage green space on mean cortisol concentrations showed a positive effect of higher green space in relation to cortisol measures in women, but not in men. Higher levels of neighbourhood green space were associated with healthier mean cortisol levels in women whilst also attenuating higher cortisol levels in men. We conclude that higher levels of green space in residential neighbourhoods, for this deprived urban population of middle-aged men and women not in work, are linked with lower perceived stress and a steeper (healthier) diurnal cortisol decline. However, overall patterns and levels of cortisol secretion in men and women were differentially related to neighbourhood green space and warrant further investigation.

Adaptive radiation is facilitated by a rugged adaptive landscape, where fitness peaks correspond to trait values that enhance the use of distinct resources. Different species are thought to occupy the different peaks, with hybrids falling into low-fitness valleys between them. We hypothesize that human activities can smooth adaptive landscapes, increase hybrid fitness and hamper evolutionary diversification. We investigated this possibility by analysing beak size data for 1755 Geospiza fortis measured between 1964 and 2005 on the island of Santa Cruz, Galápagos. Some populations of this species can display a resourcebased bimodality in beak size, which mirrors the greater beak size differences among species. We first show that an historically bimodal population at one site, Academy Bay, has lost this property in concert with a marked increase in local human population density. We next show that a nearby site with lower human impacts, El Garrapatero, currently manifests strong bimodality. This comparison suggests that bimodality can persist when human densities are low (Academy Bay in the past, El Garrapatero in the present), but not when they are high (Academy Bay in the present). Human activities may negatively impact diversification in 'young' adaptive radiations, perhaps by altering adaptive landscapes.

Summary Model selection is difficult. Even in the apparently straightforward case of choosing between standard linear regression models, there does not yet appear to be consensus in the statistical ecology literature as to the right approach. We review recent works on model selection in ecology and subsequently focus on one aspect in particular: the use of the Akaike Information Criterion (AIC) or its small‐sample equivalent, AICC. We create a novel framework for simulation studies and use this to study model selection from simulated data sets with a range of properties, which differ in terms of degree of unobserved heterogeneity. We use the results of the simulation study to suggest an approach for model selection based on ideas from information criteria but requiring simulation. We find that the relative predictive performance of model selection by different information criteria is heavily dependent on the degree of unobserved heterogeneity between data sets. When heterogeneity is small, AIC or AICC are likely to perform well, but if heterogeneity is large, the Bayesian Information Criterion (BIC) will often perform better, due to the stronger penalty afforded. Our conclusion is that the choice of information criterion (or more broadly, the strength of likelihood penalty) should ideally be based upon hypothesized (or estimated from previous data) properties of the population of data sets from which a given data set could have arisen. Relying on a single form of information criterion is unlikely to be universally successful.

[1] Currently, there is minimal information relating to temporal variability of water source contributions in alpine glacierized basins or the influence of glacier meltwater in a basin-wide context. This study adopts an end-member mixing approach to understand basin-scale water source dynamics in a French Pyrenean, alpine glacierized river system (Taillon-Gabiétous). Major ion and Si data were collected for snow, groundwater tributaries, and four mainstream sites during the 2002/2003 melt seasons. Three conceptual water sources were identified: ''quick flow'' (dilute, rapidly routed meltwater), ''distributed'' (SO 4 2À enriched, slow routed subglacial waters), and ''groundwater'' (Si-enriched groundwater). Water source contributions at nested spatial and temporal scales were determined using end-member mixing and uncertainty analysis. Changes in stream hydrochemistry indicated marked meltwater-groundwater mixing. Quick flow contributions typically decreased over the melt season; groundwater contributions were highest at the beginning of the melt seasons following recharge by snowmelt but also later in the 2002 melt season following prolonged precipitation. Overall, the results suggest an alternative alpine basin melt season hydrological progression compared with previous models (i.e., simple snowmelt to glacier melt to groundwater domination) and emphasize the need to understand water source dynamics to inform related water resource availability, water quality, and stream ecology studies within alpine basins.