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Authier, M., Saraux, C., & Péron, C. (2017). Variable selection and accurate predictions in habitat modelling: a shrinkage approach. Ecography, 40(4), 549–560.
Résumé: Habitat modelling is increasingly relevant in biodiversity and conservation studies. A typical application is to predict potential zones of specific conservation interest. With many environmental covariates, a large number of models can he investigated but multi-model inference may become impractical. Shrinkage regression overcomes this issue by dealing with the identification and accurate estimation of effect size for prediction. In a Bayesian framework we investigated the use of a shrinkage prior, the Horseshoe, for variable selection in spatial generalized linear models (GLM). As study cases, we considered 5 datasets on small pelagic fish abundance in the Gulf of Lion (Mediterranean Sea, France) and 9 environmental inputs. We compared the predictive performances of a simple kriging model, a full spatial GLM model with independent normal priors for regression coefficients, a full spatial GLM model with a Horseshoe prior for regression coefficients and 2 zero-inflated models (spatial and non-spatial) with a Horseshoe prior. Predictive performances were evaluated by cross validation on a hold-out subset of the data: models with a Horseshoe prior performed best, and the full model with independent normal priors worst. With an increasing number of inputs, extrapolation quickly became pervasive as we tried to predict from novel combinations of covariate values. By shrinking regression coefficients with a Horseshoe prior, only one model needed to be fitted to the data in order to obtain reasonable and accurate predictions, including extrapolations.
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Triantis, K. A., Economo, E. P., Guilhaumon, F., & Ricklefs, R. E. (2015). Diversity regulation at macro-scales: species richness on oceanic archipelagos. Global Ecology and Biogeography, 24(5), 594–605.
Résumé: Aim Understanding the mechanisms that generate diversity patterns requires analyses at spatial and temporal scales that are appropriate to the dispersal capacities and ecological requirements of organisms. Oceanic archipelagos provide a range of island sizes and configurations which should predictably influence colonization, diversification and extinction. To explore the influence of these factors on archipelagic diversity, we relate the numbers of native and endemic species of vascular plants, birds, land snails and spiders – taxa having different dispersal capabilities and population densities – to the number and sizes of islands in the major oceanic archipelagos of the globe. Location Fourteen major oceanic archipelagos of the globe. Methods Species richness was collated for native and endemic species in each archipelago. We used linear mixed effect models to quantify the influence on diversity of total area, number of islands, isolation and latitude. We then applied process-based modelling in a Bayesian framework to evaluate how speciation, colonization and extinction are influenced by characteristics of archipelagos associated with species richness, i.e. area, isolation and number of islands. Results We found parallel scaling of species richness among taxa with respect to total area and number of islands across groups. The process-based model supported effects of isolation on colonization and of area and number of islands on extinction rates, with the scaling exponents mostly similar across taxa. Data are consistent with a range of scaling exponents for speciation rate, implying that those relationships are difficult to infer from the data used. Conclusions We demonstrate an unexpected parallel scaling of species richness of four taxa with area and number of islands for the major oceanic archipelagos of the globe. We infer that this scaling arises through similar effects of the physical characteristics of archipelagos on extinction, colonization and speciation rates across these disparate taxa, indicating that similar mechanisms have created variation in diversity.
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