New measures for assessing model equilibrium and prediction mismatch in species distribution models

Models based on species distributions are widely used and serve important purposes in ecology, biogeography and conservation. Their continuous predictions of environmental suitability are commonly converted into a binary classification of predicted (or potential) presences and absences, whose accuracy is then evaluated through a number of measures that have been the subject of recent reviews. We propose four additional measures that analyse observation-prediction mismatch from a different angle – namely, from the perspective of the predicted rather than the observed area – and add to the existing toolset of model evaluation methods. We explain how these measures can complete the view provided by the existing measures, allowing further insights into distribution model predictions. We also describe how they can be particularly useful when using models to forecast the spread of diseases or of invasive species and to predict modifications in species’ distributions under climate and land-use change

Transferability of environmental favourability models in geographic space: The case of the Iberian desman (Galemys pyrenaicus) in Portugal and Spain

Transferring distribution models between different geographical areas may be problematic, as the performance of models outside their original scope is hard to predict. A modelling procedure is needed that gets the gist of the environmental descriptors of a distribution area, without either overfitting to the training data or overestimating the species’ distribution potential.We tested the transferability power of the favourability function, a generalized linear model, on the distribution of the Iberian desman (Galemys pyrenaicus) in the Iberian territories of Portugal and Spain.We also tested the effects of two of the main potential constraints on model transferability: the analysed ranges of the predictor variables, and the completeness of the species distribution data. We modelled 10 km×10km presence/absence data from Portugal and Spain separately, extrapolated each model to the other country, and compared predictions with observations. The Spanish model, despite arguably containing more false absences, showed good predictive ability in Portugal. The Portuguese model, whose predictors ranged between only a subset of the values observed in Spain, overestimated desman distribution when transferred.We discuss possible reasons for this differential model behaviour, and highlight the importance of this kind of models for prediction and conservation applications

Obtaining environmental favourability functions from logistic regression

Logistic regression is a statistical tool widely used for predicting species’ potential distributions starting from presence/absence data and a set of independent variables. However, logistic regression equations compute probability values based not only on the values of the predictor variables but also on the relative proportion of presences and absences in the dataset, which does not adequately describe the environmental favourability for or against species presence. A few strategies have been used to circumvent this, but they usually imply an alteration of the original data or the discarding of potentially valuable information. We propose a way to obtain from logistic regression an environmental favourability function whose results are not affected by an uneven proportion of presences and absences. We tested the method on the distribution of virtual species in an imaginary territory. The favourability models yielded similar values regardless of the variation in the presence/absence ratio. We also illustrate with the example of the Pyrenean desman’s (Galemys pyrenaicus) distribution in Spain. The favourability model yielded more realistic potential distribution maps than the logistic regression model. Favourability values can be regarded as the degree of membership of the fuzzy set of sites whose environmental conditions are favourable to the species, which enables applying the rules of fuzzy logic to distribution modelling. They also allow for direct comparisons between models for species with different presence/absence ratios in the study area. This makes themmore useful to estimate the conservation value of areas, to design ecological corridors, or to select appropriate areas for species reintroductions.

Otter (Lutra lutra) distribution modeling at two resolution scales suited to conservation planning in the Iberian Peninsula

We used the results of the Spanish Otter Survey of 1994–1996, a Geographic Information System and stepwise multiple logistic regression to model otter presence/absence data in the continental Spanish UTM 10 10-km squares. Geographic situation, indicators of human activity such as highways and major urban centers, and environmental variables related with productivity, water availability, altitude, and environmental energy were included in a logistic model that correctly classified about 73% of otter presences and absences. We extrapolated the model to the adjacent territory of Portugal, and increased the model’s spatial resolution by extrapolating it to 1 1-km squares in the whole Iberian Peninsula. The model turned out to be rather flexible, predicting, for instance, the species to be very restricted to the courses of rivers in some areas, and more widespread in others. This allowed us to determine areas where otter populations may be more vulnerable to habitat changes or harmful human interventions. # 2003 Elsevier Ltd. All rights reserved.

Factors affecting southern water vole (Arvicola sapidus) detection and occupancy probabilities in Mediterranean farmland

Failure to detect a species at sites where it is present (i.e. imperfect detection) is known to occur frequently, but this is often disregarded in monitoring programs and metapopulation studies. Here we modelled for the first time the probability of patch occupancy by a threatened small mammal, the southern water vole (Arvicola sapidus, while accounting for the probability of detection given occupancy. Based on replicated presence sign surveys conducted in autumn (November–December 2013) and winter (February–March 2014) in a farmland landscape, we used occupancy detection modelling to test the effects of vegetation, sampling effort, observer experience, and rainfall on detection probability. We then assessed whether occupancy was related to patch size, isolation, vegetation, or presence of water, after correcting for imperfect detection. The mean detection probabilities of water vole signs in autumn (0.71) and winter (0.81) indicated that false absences may be generated in about 20–30% of occupied patches surveyed by a single observer on a single occasion. There was no statistical support for the effects of covariates on detectability. After controlling for imperfect detection, the mean probabilities of occupancy in autumn (0.31) and winter (0.29) were positively related to patch size and presence of water, and negatively so, albeit weakly, to patch isolation. Overall, our study underlined the importance of accounting for imperfect detection in sign surveys of small mammals such as water voles, pointing out the need to use occupancy detection modelling together with replicate surveys for accurately estimating occupancy and the factors affecting it.