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.

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

Favourable areas for expansion and reintroduction of Iberian lynx accounting for distribution trends and genetic diversity of the European rabbit

Although on a local scale Iberian lynx distribution is determined by the availability of prey rabbits, recent modelling analyses have uncovered broad-scale disagreements between these two species’ distribution trends. These analyses showed also that the lynx had become restricted to only a fraction of the rabbit’s genetic diversity, and that this could be jeopardising its survival in the face of environmental hazards and uncertainty. In the present paper, a follow-up was carried out through the building of lynx and rabbit distribution models based on the most recent Spanish mammal atlas. Environmental favourability values for lynx and rabbit were positively correlated within the lynx’s current distribution area, but they were negatively correlated within the total Spanish area where lynx used to occur in the 1980’s. Environmental favourability for rabbits was significantly higher where lynx maintains reproductive populations than where it recently disappeared, indicating that rabbit favourability plays an important role and can be a good predictor of lynx persistence. The lynx and rabbit models were extrapolated to predict favourable areas for both species in Spain as well as in Portugal, on the original scale of the distribution data (10x10 km) and on a 100 times finer spatial resolution (1x1 km). The lynx and rabbit models were also combined through fuzzy logic to forecast the potential for lynx occurrence incorporating information on favourable areas for its main prey. Several areas are proposed as favourable for lynx expansion or re-introduction,

Relative effect of food supplementation and natural resources on female red deer distribution in a Mediterranean ecosystem

Supplementary feeding is a widespread game management practice in several red deer (Cervus elaphus) populations, with important potential consequences on the biology of this species. InMediterranean ecosystems food supplementation occurs in the rutting period, when it may change mating system characteristics. We studied the role of food supplementation relative to natural resources in the spatial distribution, aggregation, and mean harem size of females in Iberian red deer (Cervus elaphus hispanicus) during the rut. We studied 30 red deer populations of southwestern Spain, 63% of which experienced supplementary feeding. Using multivariate spatial analyses we found that food supplementation affected distribution of females in 95% of the populations in which it occurred. Green meadows present during the mating season acted as an important natural resource influencing female distribution. Additionally, the level of female aggregation and mean harem size were significantly higher in those populations in which food supplementation determined female distribution than in populations in which female distribution did not depend on supplementary feeding. Because female aggregation and mean harem size are key elements in sexual selection, supplementary feeding may constitute an important anthropogenic element with potential evolutionary implications for populations of Iberian red deer.

Distribution modelling of wild rabbit hunting yields in its original area (S Iberian Peninsula)

In this work we used the information of the Annual Hunting Reports (AHRs) to obtain a high-resolution model of the potential favourableness for wild rabbit harvesting in Andalusia (southern Spain), using environmental and land-use variables as predictors. We analysed 32,134 AHRs from the period 1993/2001 reported by 6049 game estates to estimate the average hunting yields of wild rabbit in each Andalusian municipality (n5771). We modelled the favourableness for obtaining good hunting yields using stepwise logistic regression on a set of climatic, orographical, land use, and vegetation variables. The favourability equation was used to create a downscaled image representing the favourableness of obtaining good hunting yields for the wild rabbit in 161 km squares in Andalusia, using the Idrisi Image Calculator. The variables that affected hunting yields of wild rabbit were altitude, dry wood crops (mainly olive groves, almond groves, and vineyards), temperature, pasture, slope, and annual number of frost days. The 161 km squares with high favourableness values are scattered throughout the territory, which seems to be caused mainly by the effect of vegetation. Finally, we obtained quality categories for the territory by combining the probability values given by logistic regression with those of the environmental favourability function.