Genetic diversity and species richness patterns in Baetidae (Ephemeroptera) in the Montseny Mountain range (North-East Iberian Peninsula)

This study aimed to describe patterns of diversity of Baetidae (Ephemeroptera) at the ommunity and population levels within the Montseny Mountain range (North-East Iberian Peninsula). We studied both the distribution of 4 species of baetids in 20 sites among three catchments along the altitudinal gradient (350-1700 masl); and the genetic diversity of the mtDNA cytochrome c oxidase subunit I (cox1) gene of the two common species Baetis alpinus and Baetis rhodani. We found a gradual replacement of the dominant species along the altitudinal gradient. Baetis alpinus inhabited sites at high-altitudes, and this species was replaced by B. rhodani when the altitude decreased. Baetis melanonyx and Alainites muticus attained low abundance at all river sections, and no clear altitudinal trend appeared. Our hypothesis at the population level was that genetic structuring is associated with geographic distance and limited by drainage boundaries among the three studied catchments because of the short-time dispersion of adults. Unexpectedly, analyses of molecular variance (AMOVA) and isolation-bydistance (IBD) showed genetic diversity was unstructured by distance for both species, which may be explained by the relatively short spatial scale studied and small topographic barriers among the three catchments. The Generalized Mixed Yule-Coalescent (GMYC) model showed that B. rhodani had two differentiated genetic lineages that co-occurred in all sites. Overall, diversity of baetids was structured at the community level along the altitudinal gradient, whereas it was unstructured at the population level within the Montseny Mountain range.

On the structure of cooperative and competitive solutions for a generalized assignment game

We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of ma- trices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.