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Collinearity a review of methods to deal with it and a simulation study evaluating their performance
(2013)
Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the folk lore'-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.
Developments of future scenarios of Antarctic ecosystems are still in their infancy, whilst predictions of the physical environment are recognized as being of global relevance and corresponding models are under continuous development. However, in the context of environmental change simulations of the future of the Antarctic biosphere are increasingly demanded by decision makers and the public, and are of fundamental scientific interest. This paper briefly reviews existing predictive models applied to Antarctic ecosystems before providing a conceptual framework for the further development of spatially and temporally explicit ecosystem models. The concept suggests how to improve approaches to relating species' habitat description to the physical environment, for which a case study on sea urchins is presented. In addition, the concept integrates existing and new ideas to consider dynamic components, particularly information on the natural history of key species, from physiological experiments and biomolecular analyses. Thereby, we identify and critically discuss gaps in knowledge and methodological limitations. These refer to process understanding of biological complexity, the need for high spatial resolution oceanographic data from the entire water column, and the use of data from biomolecular analyses in support of such ecological approaches. Our goal is to motivate the research community to contribute data and knowledge to a holistic, Antarctic-specific, macroecological framework. Such a framework will facilitate the integration of theoretical and empirical work in Antarctica, improving our mechanistic understanding of this globally influential ecoregion, and supporting actions to secure this biodiversity hotspot and its ecosystem services.
Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with P-occ, while N, and for most regions K, was generally positively correlated with P-occ. Thus, in temperate forest trees the regions of highest occurrence probability are those with high densities but slow intrinsic population growth rates. The uncertain relationships between demography and occurrence probability suggests caution when linking species distribution and demographic models.
Home range size and resource use of breeding and non-breeding white storks along a land use gradient
(2018)
Biotelemetry is increasingly used to study animal movement at high spatial and temporal resolution and guide conservation and resource management. Yet, limited sample sizes and variation in space and habitat use across regions and life stages may compromise robustness of behavioral analyses and subsequent conservation plans. Here, we assessed variation in (i) home range sizes, (ii) home range selection, and (iii) fine-scale resource selection of white storks across breeding status and regions and test model transferability. Three study areas were chosen within the Central German breeding grounds ranging from agricultural to fluvial and marshland. We monitored GPS-locations of 62 adult white storks equipped with solar-charged GPS/3D-acceleration (ACC) transmitters in 2013-2014. Home range sizes were estimated using minimum convex polygons. Generalized linear mixed models were used to assess home range selection and fine-scale resource selection by relating the home ranges and foraging sites to Corine habitat variables and normalized difference vegetation index in a presence/pseudo-absence design. We found strong variation in home range sizes across breeding stages with significantly larger home ranges in non-breeding compared to breeding white storks, but no variation between regions. Home range selection models had high explanatory power and well predicted overall density of Central German white stork breeding pairs. Also, they showed good transferability across regions and breeding status although variable importance varied considerably. Fine-scale resource selection models showed low explanatory power. Resource preferences differed both across breeding status and across regions, and model transferability was poor. Our results indicate that habitat selection of wild animals may vary considerably within and between populations, and is highly scale dependent. Thereby, home range scale analyses show higher robustness whereas fine-scale resource selection is not easily predictable and not transferable across life stages and regions. Such variation may compromise management decisions when based on data of limited sample size or limited regional coverage. We thus recommend home range scale analyses and sampling designs that cover diverse regional landscapes and ensure robust estimates of habitat suitability to conserve wild animal populations.
Improving our understanding of biodiversity and ecosystem functioning and our capacity to inform ecosystem management requires an integrated framework for functional biodiversity research (FBR). However, adequate integration among empirical approaches (monitoring and experimental) and modelling has rarely been achieved in FBR. We offer an appraisal of the issues involved and chart a course towards enhanced integration. A major element of this path is the joint orientation towards the continuous refinement of a theoretical framework for FBR that links theory testing and generalization with applied research oriented towards the conservation of biodiversity and ecosystem functioning. We further emphasize existing decision-making frameworks as suitable instruments to practically merge these different aims of FBR and bring them into application. This integrated framework requires joint research planning, and should improve communication and stimulate collaboration between modellers and empiricists, thereby overcoming existing reservations and prejudices. The implementation of this integrative research agenda for FBR requires an adaptation in most national and international funding schemes in order to accommodate such joint teams and their more complex structures and data needs.
Density regulation influences population dynamics through its effects on demographic rates and consequently constitutes a key mechanism explaining the response of organisms to environmental changes. Yet, it is difficult to establish the exact form of density dependence from empirical data. Here, we developed an individual-based model to explore how resource limitation and behavioural processes determine the spatial structure of white stork Ciconia ciconia populations and regulate reproductive rates. We found that the form of density dependence differed considerably between landscapes with the same overall resource availability and between home range selection strategies, highlighting the importance of fine-scale resource distribution in interaction with behaviour. In accordance with theories of density dependence, breeding output generally decreased with density but this effect was highly variable and strongly affected by optimal foraging strategy, resource detection probability and colonial behaviour. Moreover, our results uncovered an overlooked consequence of density dependence by showing that high early nestling mortality in storks, assumed to be the outcome of harsh weather, may actually result from density dependent effects on food provision. Our findings emphasize that accounting for interactive effects of individual behaviour and local environmental factors is crucial for understanding density-dependent processes within spatially structured populations. Enhanced understanding of the ways animal populations are regulated in general, and how habitat conditions and behaviour may dictate spatial population structure and demographic rates is critically needed for predicting the dynamics of populations, communities and ecosystems under changing environmental conditions.
Species respond to environmental change by dynamically adjusting their geographical ranges. Robust predictions of these changes are prerequisites to inform dynamic and sustainable conservation strategies. Correlative species distribution models (SDMs) relate species’ occurrence records to prevailing environmental factors to describe the environmental niche. They have been widely applied in global change context as they have comparably low data requirements and allow for rapid assessments of potential future species’ distributions. However, due to their static nature, transient responses to environmental change are essentially ignored in SDMs. Furthermore, neither dispersal nor demographic processes and biotic interactions are explicitly incorporated. Therefore, it has often been suggested to link statistical and mechanistic modelling approaches in order to make more realistic predictions of species’ distributions for scenarios of environmental change. In this thesis, I present two different ways of such linkage. (i) Mechanistic modelling can act as virtual playground for testing statistical models and allows extensive exploration of specific questions. I promote this ‘virtual ecologist’ approach as a powerful evaluation framework for testing sampling protocols, analyses and modelling tools. Also, I employ such an approach to systematically assess the effects of transient dynamics and ecological properties and processes on the prediction accuracy of SDMs for climate change projections. That way, relevant mechanisms are identified that shape the species’ response to altered environmental conditions and which should hence be considered when trying to project species’ distribution through time. (ii) I supplement SDM projections of potential future habitat for black grouse in Switzerland with an individual-based population model. By explicitly considering complex interactions between habitat availability and demographic processes, this allows for a more direct assessment of expected population response to environmental change and associated extinction risks. However, predictions were highly variable across simulations emphasising the need for principal evaluation tools like sensitivity analysis to assess uncertainty and robustness in dynamic range predictions. Furthermore, I identify data coverage of the environmental niche as a likely cause for contrasted range predictions between SDM algorithms. SDMs may fail to make reliable predictions for truncated and edge niches, meaning that portions of the niche are not represented in the data or niche edges coincide with data limits. Overall, my thesis contributes to an improved understanding of uncertainty factors in predictions of range dynamics and presents ways how to deal with these. Finally I provide preliminary guidelines for predictive modelling of dynamic species’ response to environmental change, identify key challenges for future research and discuss emerging developments.
Movement of organisms is one of the key mechanisms shaping biodiversity, e.g. the distribution of genes, individuals and species in space and time. Recent technological and conceptual advances have improved our ability to assess the causes and consequences of individual movement, and led to the emergence of the new field of ‘movement ecology’. Here, we outline how movement ecology can contribute to the broad field of biodiversity research, i.e. the study of processes and patterns of life among and across different scales, from genes to ecosystems, and we propose a conceptual framework linking these hitherto largely separated fields of research. Our framework builds on the concept of movement ecology for individuals, and demonstrates its importance for linking individual organismal movement with biodiversity. First, organismal movements can provide ‘mobile links’ between habitats or ecosystems, thereby connecting resources, genes, and processes among otherwise separate locations. Understanding these mobile links and their impact on biodiversity will be facilitated by movement ecology, because mobile links can be created by different modes of movement (i.e., foraging, dispersal, migration) that relate to different spatiotemporal scales and have differential effects on biodiversity. Second, organismal movements can also mediate coexistence in communities, through ‘equalizing’ and ‘stabilizing’ mechanisms. This novel integrated framework provides a conceptual starting point for a better understanding of biodiversity dynamics in light of individual movement and space-use behavior across spatiotemporal scales. By illustrating this framework with examples, we argue that the integration of movement ecology and biodiversity research will also enhance our ability to conserve diversity at the genetic, species, and ecosystem levels.