Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Phylogeographical relationships of Sicilian brown trout and the effects of genetic introgression on morphospace occupation

Genetic introgression of aquaculture stocks in local forms is well documented in many fish species but their evolutionary consequences for the local populations have not been thoroughly explored. Due to its wide geographical range, the existence of many locally adapted forms and the frequent occurrence of introgression of aquaculture stocks in local forms, brown trout represents the ideal system to study the effects of such introgressions. Here, we focus on a group of rivers and streams in Sicily (Italy), and, by using molecular tools, we show that autochthonous populations are probably derived from the Southern Atlantic clade, which is present in the Iberian peninsula and North Africa. Three out of the four studied rivers reveal signs of genetic introgression of domestic stocks. Finally, by using advanced geometric morphometric analyses, we show that genetic introgression produces a higher degree of morphological variability relative to that observed in non-introgressed populations.