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.

“A long-term mortality analysis of subsidized firms in rural areas: an empirical study in the Portuguese Alentejo region”

Studies have demonstrated that public policies to support private firms’ investment have the ability to promote entrepreneurship, but the sustainability of subsidized firms has not often been analysed. This paper aims to examine this dimension specifically through evaluating the mortality of subsidized firms in the long-term. The analysis focuses on a case study of the LEADER+ Programme in the Alentejo region of Portugal. With this purpose, the paper examines the activity status (active or not active) of 154 private, rural, for-profit firms in Alentejo that had received a subsidy to support investment between 2002 and 2008 under the LEADER+ Programme. The methodology is based on binary choice models in order to study the probability of these firms still being active. The explanatory variables used are the following: (1) the characteristics of entrepreneurs and managers’ strategic decisions, (2) firm profile and characteristics, (3) regional economic environment. Data assessment showed that the cumulative mortality rate of firms on 31st December 2013 is over 20 %. Interpretation of the regression model revealed that he probability of firms’ survival increases with higher investment, firm age and regional business concentration, whereas the number of applications made by firms has a negative impact on their survival. So it seems that for subsidized firms the amount of investment is as important as its frequency.