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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.
1. The health of managed and wild honeybee colonies appears to have declined substantially in Europe and the United States over the last decade. Sustainability of honeybee colonies is important not only for honey production, but also for pollination of crops and wild plants alongside other insect pollinators. A combination of causal factors, including parasites, pathogens, land use changes and pesticide usage, are cited as responsible for the increased colony mortality. 2. However, despite detailed knowledge of the behaviour of honeybees and their colonies, there are no suitable tools to explore the resilience mechanisms of this complex system under stress. Empirically testing all combinations of stressors in a systematic fashion is not feasible. We therefore suggest a cross-level systems approach, based on mechanistic modelling, to investigate the impacts of (and interactions between) colony and land management. 3. We review existing honeybee models that are relevant to examining the effects of different stressors on colony growth and survival. Most of these models describe honeybee colony dynamics, foraging behaviour or honeybee - varroa mite - virus interactions. 4. We found that many, but not all, processes within honeybee colonies, epidemiology and foraging are well understood and described in the models, but there is no model that couples in-hive dynamics and pathology with foraging dynamics in realistic landscapes. 5. Synthesis and applications. We describe how a new integrated model could be built to simulate multifactorial impacts on the honeybee colony system, using building blocks from the reviewed models. The development of such a tool would not only highlight empirical research priorities but also provide an important forecasting tool for policy makers and beekeepers, and we list examples of relevant applications to bee disease and landscape management decisions.
BEEHAVE offers a valuable tool for researchers to design and focus field experiments, for regulators to explore the relative importance of stressors to devise management and policy advice and for beekeepers to understand and predict varroa dynamics and effects of management interventions. We expect that scientists and stakeholders will find a variety of applications for BEEHAVE, stimulating further model development and the possible inclusion of other stressors of potential importance to honeybee colony dynamics.
The causes underlying the increased mortality of honeybee Apis mellifera colonies observed over the past decade remain unclear. Since so far the evidence for monocausal explanations is equivocal, involvement of multiple stressors is generally assumed. We here focus on various aspects of forage availability, which have received less attention than other stressors because it is virtually impossible to explore them empirically. We applied the colony model BEEHAVE, which links within-hive dynamics and foraging, to stylized landscape settings to explore how foraging distance, forage supply, and “forage gaps”, i.e. periods in which honeybees cannot find any nectar and pollen, affect colony resilience and the mechanisms behind. We found that colony extinction was mainly driven by foraging distance, but the timing of forage gaps had strongest effects on time to extinction. Sensitivity to forage gaps of 15 days was highest in June or July even if otherwise forage availability was sufficient to survive. Forage availability affected colonies via cascading effects on queen's egg-laying rate, reduction of new-emerging brood stages developing into adult workers, pollen debt, lack of workforce for nursing, and reduced foraging activity. Forage gaps in July led to reduction in egg-laying and increased mortality of brood stages at a time when the queen's seasonal egg-laying rate is at its maximum, leading to colony failure over time. Our results demonstrate that badly timed forage gaps interacting with poor overall forage supply reduce honeybee colony resilience. Existing regulation mechanisms which in principle enable colonies to cope with varying forage supply in a given landscape and year, such as a reduction in egg-laying, have only a certain capacity. Our results are hypothetical, as they are obtained from simplified landscape settings, but they are consistent with existing empirical knowledge. They offer ample opportunities for testing the predicted effects of forage stress in controlled experiments.
Forage availability has been suggested as one driver of the observed decline in honey bees. However, little is known about the effects of its spatiotemporal variation on colony success. We present a modeling framework for assessing honey bee colony viability in cropping systems. Based on two real farmland structures, we developed a landscape generator to design cropping systems varying in crop species identity, diversity, and relative abundance. The landscape scenarios generated were evaluated using the existing honey bee colony model BEEHAVE, which links foraging to in-hive dynamics. We thereby explored how different cropping systems determine spatiotemporal forage availability and, in turn, honey bee colony viability (e.g., time to extinction, TTE) and resilience (indicated by, e.g., brood mortality). To assess overall colony viability, we developed metrics,P(H)andP(P,)which quantified how much nectar and pollen provided by a cropping system per year was converted into a colony's adult worker population. Both crop species identity and diversity determined the temporal continuity in nectar and pollen supply and thus colony viability. Overall farmland structure and relative crop abundance were less important, but details mattered. For monocultures and for four-crop species systems composed of cereals, oilseed rape, maize, and sunflower,P(H)andP(P)were below the viability threshold. Such cropping systems showed frequent, badly timed, and prolonged forage gaps leading to detrimental cascading effects on life stages and in-hive work force, which critically reduced colony resilience. Four-crop systems composed of rye-grass-dandelion pasture, trefoil-grass pasture, sunflower, and phacelia ensured continuous nectar and pollen supply resulting in TTE > 5 yr, andP(H)(269.5 kg) andP(P)(108 kg) being above viability thresholds for 5 yr. Overall, trefoil-grass pasture, oilseed rape, buckwheat, and phacelia improved the temporal continuity in forage supply and colony's viability. Our results are hypothetical as they are obtained from simplified landscape settings, but they nevertheless match empirical observations, in particular the viability threshold. Our framework can be used to assess the effects of cropping systems on honey bee viability and to develop land-use strategies that help maintain pollination services by avoiding prolonged and badly timed forage gaps.
Forage availability has been suggested as one driver of the observed decline in honey bees. However, little is known about the effects of its spatiotemporal variation on colony success. We present a modeling framework for assessing honey bee colony viability in cropping systems. Based on two real farmland structures, we developed a landscape generator to design cropping systems varying in crop species identity, diversity, and relative abundance. The landscape scenarios generated were evaluated using the existing honey bee colony model BEEHAVE, which links foraging to in-hive dynamics. We thereby explored how different cropping systems determine spatiotemporal forage availability and, in turn, honey bee colony viability (e.g., time to extinction, TTE) and resilience (indicated by, e.g., brood mortality). To assess overall colony viability, we developed metrics,P(H)andP(P,)which quantified how much nectar and pollen provided by a cropping system per year was converted into a colony's adult worker population. Both crop species identity and diversity determined the temporal continuity in nectar and pollen supply and thus colony viability. Overall farmland structure and relative crop abundance were less important, but details mattered. For monocultures and for four-crop species systems composed of cereals, oilseed rape, maize, and sunflower,P(H)andP(P)were below the viability threshold. Such cropping systems showed frequent, badly timed, and prolonged forage gaps leading to detrimental cascading effects on life stages and in-hive work force, which critically reduced colony resilience. Four-crop systems composed of rye-grass-dandelion pasture, trefoil-grass pasture, sunflower, and phacelia ensured continuous nectar and pollen supply resulting in TTE > 5 yr, andP(H)(269.5 kg) andP(P)(108 kg) being above viability thresholds for 5 yr. Overall, trefoil-grass pasture, oilseed rape, buckwheat, and phacelia improved the temporal continuity in forage supply and colony's viability. Our results are hypothetical as they are obtained from simplified landscape settings, but they nevertheless match empirical observations, in particular the viability threshold. Our framework can be used to assess the effects of cropping systems on honey bee viability and to develop land-use strategies that help maintain pollination services by avoiding prolonged and badly timed forage gaps.