Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fr\'{e}chet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension $1$ and hence measure $0$) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky).Comment: Published in at http://dx.doi.org/10.1214/12-AAP899 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Does habitat stability structure intraspecific genetic diversity? It’s complicated...

Regional phylogeographic studies have long been conducted in the southeastern United States for a variety of species. With some exceptions, many of these studies focus on single species or single clades of organisms, and those considering multiple species tend to focus on deep historical breaks causing differentiation. However, in many species more recent factors may be influencing genetic diversity. To understand the roles of historic and contemporary processes in structuring genetic diversity, we reanalyzed existing genetic data from Southeast of North America using approaches gleaned from phylogeographic and landscape genetic literature that were implemented across species including AMOVAs, PCoAs, Species Distribution Modelling, and tests of isolation by distance, environment, and habitat instability. Genetic variance was significantly partitioned by ecoregions, watersheds, and across phylogeographic breaks in the majority of species. Similarly, genetic variation was significantly associated with some combination of geographic or environmental distance or habitat instability in most species. Patterns of genetic variation were largely idiosyncratic across species. While habitat instability over time is significantly correlated with genetic diversity in some species, it appears generally less important than isolation by geographic or environmental distance. Our results suggest that many factors, both historical and contemporary, impact genetic diversity within a species, and more so, that these patterns aren’t always similar in closely related species. This supports the importance of species- specific factors and cautions against assumptions that closely related species will respond to historical and contemporary forces in similar ways

Categorization Reduces the Effect of Context On Hedonic Preference

When moderately hedonically positive test stimuli are presented following better-liked context stimuli, preferences between the test stimuli are reduced. This reduction in preference, hedonic condensation, occurs in settings that also produce negative hedonic contrast-the phenomenon in which moderately hedonically positive test stimuli seem less positive when they follow better-liked context stimuli. Subjects who were instructed that the context and test stimuli were from different categories exhibited less hedonic condensation. Those categories have smaller hedonic ranges than does the full stimulus set. The increase in preference magnitude with reduction in size of the hedonic range is predicted by Parducci\u27s (1995) range-frequency model