Properties of the asymptotic nA+mB->C reaction-diffusion fronts

We discuss, at the mean-field level, the asymptotic shape of the reaction fronts in the general nA+mB->C reaction-diffusion processes with initially separated reactants, thus generalizing to arbitrary reaction-order kinetics the work done by Galfi and Racz for the case n=m=1. Consequences for the formation of Liesegang patterns are discussed.Comment: EPJ-TeX, 6 pages, 2 figs included. Statement on tails' decay revised. References added and correcte

Phenotypic evolution and hidden speciation in Candidula unifasciata ssp. (Helicellinae, Gastropoda) inferred by 16S variation and quantitative shell traits

In an effort to link quantitative morphometric information with molecular data on the population level, we have analysed 19 populations of the conchologically variable land snail Candidula unifasciata from across the species range for variation in quantitative shell traits and at the mitochondrial 16S ribosomal (r)DNA locus. In genetic analysis, including 21 additional populations, we observed two fundamental haplotype clades with an average pairwise sequence divergence of 0.209 ± 0.009 between clades compared to 0.017 ± 0.012 within clades, suggesting the presence of two different evolutionary lineages. Integrating additional shell material from the Senckenberg Malacological Collection, a highly significant discriminant analysis on the morphological shell traits with fundamental haplotype clades as grouping variable suggested that the less frequent haplotype corresponds to the described subspecies C. u. rugosiuscula, which we propose to regard as a distinct species. Both taxa were highly subdivided genetically (FST = 0.648 and 0.777 P < 0.001). This was contrasted by the partition of morphological variance, where only 29.6% and 21.9% of the variance were distributed among populations, respectively. In C. unifasciata, no significant association between population pairwise FST estimates and corresponding morphological fixation indices could be detected, indicating independent evolution of the two character sets. Partial least square analysis of environmental factors against shell trait variables in C. u. unifasciata revealed significant correlations between environmental factors and certain quantitative shell traits, whose potential adaptational values are discussed