Using Microsatellites to Assess Genetic Variation in a Selective Breeding Program of Chinese Bay Scallop (Argopecten irradians irradians)

This study aimed to improve our understanding of the genetics of the Chinese bay scallop (Argopecten irradians irradians), one of the most important maricultured shellfish in China. Ten polymorphic microsatellite loci were examined to assess the allelic diversity, heterozygosity, and genetic variation between two domesticated populations selected for fast growth in breeding programs, and their base population. Forty-one alleles were found throughout the loci and the mean number of alleles per locus ranged 3.30-3.50. The average heterozygosity ranged 0.38-0.45, whereas the polyamorphic information content ranged 0.1504-0.7518. Genetic differences between the three populations were detected based on the number of alleles per locus, effective number of alleles, Shannon index, inbreeding coefficient (Fis), p values, genetic distance, and pairwise Fst values. There was no significant loss of genetic variability in the breeding program but changes in gene frequencies were detectable over the populations, implying that thea loci were saffected by the pressures of selective culture

Nearly optimal minimax estimator for high-dimensional sparse linear regression

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic factor of the optimal for any design matrix. Then by utilizing a semi-definite programming relaxation technique developed in [SIAM J. Comput. 36 (2007) 1764-1776], we obtain an approximation algorithm for computing the minimax risk for any such estimation task and also a polynomial time nearly optimal estimator for the important case of $\ell_1$ sparsity constraint. Such results were only known before for special cases, despite decades of studies on this problem. We also extend the method to the adaptive case when the parameter radius is unknown.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1141 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org