Unveiling the factors shaping the distribution of widely distributed alpine vertebrates, using multi-scale ecological niche modelling of the bat Plecotus macrobullaris

Several alpine vertebrates share a distribution pattern that extends across the South-western Palearctic but is limited to the main mountain massifs. Although they are usually regarded as cold-adapted species, the range of many alpine vertebrates also includes relatively warm areas, suggesting that factors beyond climatic conditions may be driving their distribution. In this work we first recognize the species belonging to the mentioned biogeographic group and, based on the environmental niche analysis of Plecotus macrobullaris, we identify and characterize the environmental factors constraining their ranges. Distribution overlap analysis of 504 European vertebrates was done using the Sorensen Similarity Index, and we identified four birds and one mammal that share the distribution with P. macrobullaris. We generated 135 environmental niche models including different variable combinations and regularization values for P. macrobullaris at two different scales and resolutions. After selecting the best models, we observed that topographic variables outperformed climatic predictors, and the abruptness of the landscape showed better predictive ability than elevation. The best explanatory climatic variable was mean summer temperature, which showed that P. macrobullaris is able to cope with mean temperature ranges spanning up to 16 degrees C. The models showed that the distribution of P. macrobullaris is mainly shaped by topographic factors that provide rock-abundant and open-space habitats rather than climatic determinants, and that the species is not a cold-adapted, but rather a cold-tolerant eurithermic organism. P. macrobullaris shares its distribution pattern as well as several ecological features with five other alpine vertebrates, suggesting that the conclusions obtained from this study might be extensible to them. We concluded that rock-dwelling and open-space foraging vertebrates with broad temperature tolerance are the best candidates to show wide alpine distribution in the Western Palearctic.

Distribution of Healthcare resources II.Study and Comparison of a Linear Programming Problem and its Dual. Resolution and Evaluation of a Practical Case and its Programming using Excel and Win QSB.

[EN]This research had as primary objective to model different types of problems using linear programming and apply different methods so as to find an adequate solution to them. To achieve this objective, a linear programming problem and its dual were studied and compared. For that, linear programming techniques were provided and an introduction of the duality theory was given, analyzing the dual problem and the duality theorems. Then, a general economic interpretation was given and different optimal dual variables like shadow prices were studied through the next practical case: An aesthetic surgery hospital wanted to organize its monthly waiting list of four types of surgeries to maximize its daily income. To solve this practical case, we modelled the linear programming problem following the relationships between the primal problem and its dual. Additionally, we solved the dual problem graphically, and then we found the optimal solution of the practical case posed through its dual, following the different theorems of the duality theory. Moreover, how Complementary Slackness can help to solve linear programming problems was studied. To facilitate the solution Solver application of Excel and Win QSB programme were used.