Genetic differentiation of European grayling (Thymallus thymallus) populations in Serbia, based on mitochondrial and nuclear DNA analyses

<p>Abstract</p> <p>Background</p> <p>The structure and diversity of grayling (<it>Thymallus thymallus</it>) populations have been well studied in most of its native habitat; however the southernmost populations of the Balkan Peninsula remain largely unexplored. The purpose of this study was to assess the genetic diversity of Serbian grayling populations, detect the impact of stocking and provide guidelines for conservation and management.</p> <p>Methods</p> <p>Eighty grayling individuals were collected from four rivers (Ibar, Lim, Drina and Rzav). The mitochondrial DNA control region (CR; 595 bp of the 3'end and 74 bp of flanking tRNA) and the ATP6 gene (630 bp fragment) were sequenced for 20 individuals (five from each locality). In addition, all individuals were genotyped with 12 microsatellite loci. The diversity and structure of the populations as well as the recent and ancient population declines were studied using specialized software.</p> <p>Results</p> <p>We detected three new haplotypes in the mtDNA CR and four haplotypes in the ATP6 gene of which three had not been described before. Previously, one CR haplotype and two ATP6 gene haplotypes had been identified as allochthonous, originating from Slovenia. Reconstruction of phylogenetic relations placed the remaining two CR haplotypes from the River Danube drainage of Serbia into a new clade, which is related to the previously described sister Slovenian clade. These two clades form a new Balkan clade. Microsatellite marker analysis showed that all four populations are genetically distinct from each other without any sign of intra-population structure, although stocking of the most diverse population (Drina River) was confirmed by mtDNA analysis. Recent and historical population declines of Serbian grayling do not differ from those of other European populations.</p> <p>Conclusions</p> <p>Our study shows that (1) the Ibar, Lim and Drina Rivers grayling populations are genetically distinct from populations outside of Serbia and thus should be managed as native populations in spite of some introgression in the Drina River population and (2) the Rzav River population is not appropriate for further stocking activities since it originates from stocked Slovenian grayling. However, the Rzav River population does not represent an immediate danger to other populations because it is physically isolated from these.</p

Finite spectra and quasinilpotent equivalence in Banach algebras

summary:This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally, in the second part, we show that two elements possessing finite spectra are quasinilpotent equivalent if and only if they share the same set of Riesz projections. This is then used to obtain further characterizations in a number of general, as well as more specific situations. Thirdly, we show that the ideas in the preceding sections turn out to be useful in the case of $C^*$-algebras, but now for elements with infinite spectra; we give two results which may indicate a direction for further research