Determinants of distribution and prevalence of avian malaria in blue tit populations across Europe : separating host and parasite effects

Although avian malarial parasites are globally distributed, the factors that affect the geographical distribution and local prevalence of different parasite lineages across host populations or species are still poorly understood. Based on the intense screening of avian malarial parasites in nine European blue tit populations, we studied whether distribution ranges as well as local adaptation, host specialization and phylogenetic relationships can determine the observed prevalences within populations. We found that prevalence differed consistently between parasite lineages and host populations, indicating that the transmission success of parasites is lineage specific but is partly shaped by locality-specific effects. We also found that the lineage-specific estimate of prevalence was related to the distribution range of parasites: lineages found in more host populations were generally more prevalent within these populations. Additionally, parasites with high prevalence that were also widely distributed among blue tit populations were also found to infect more host species. These findings suggest that parasites reaching high local prevalence can also realize wide distribution at a global scale that can have further consequences for host specialization. Although phylogenetic relationships among parasites did not predict prevalence, we detected a close match between a tree based on the geographic distance of the host populations and the parasite phylogenetic tree, implying that neighbouring host populations shared a related parasite fauna

A Girsanov Result through Birkhoff Integral

A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by substitution, in order to fix the measure-theoretic tools needed for the main result, Theorem 6, where a martingale equivalent to the underlying vector probability has been obtained in order to represent the modified process as a martingale with the same marginals as the original one

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces