Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Landscape genomics and biased FST approaches reveal single nucleotide polymorphisms under selection in goat breeds of North-East Mediterranean

<p>Abstract</p> <p>Background</p> <p>In this study we compare outlier loci detected using a <it>F<smcaps>ST </smcaps></it>based method with those identified by a recently described method based on spatial analysis (SAM). We tested a panel of single nucleotide polymorphisms (SNPs) previously genotyped in individuals of goat breeds of southern areas of the Mediterranean basin (Italy, Greece and Albania). We evaluate how the SAM method performs with SNPs, which are increasingly employed due to their high number, low cost and easy of scoring.</p> <p>Results</p> <p>The combined use of the two outlier detection approaches, never tested before using SNP polymorphisms, resulted in the identification of the same three loci involved in milk and meat quality data by using the two methods, while the <it>F<smcaps>ST </smcaps></it>based method identified 3 more loci as under selection sweep in the breeds examined.</p> <p>Conclusion</p> <p>Data appear congruent by using the two methods for <it>F<smcaps>ST </smcaps></it>values exceeding the 99% confidence limits. The methods of <it>F<smcaps>ST </smcaps></it>and SAM can independently detect signatures of selection and therefore can reduce the probability of finding false positives if employed together. The outlier loci identified in this study could indicate adaptive variation in the analysed species, characterized by a large range of climatic conditions in the rearing areas and by a history of intense trade, that implies plasticity in adapting to new environments.</p