Population genomics of speciation and admixture

The application of population genomics to the understanding of speciation has led to the emerging field of speciation genomics. This has brought new insight into how divergence builds up within the genome during speciation and is also revealing the extent to which species can continue to exchange genetic material despite reproductive barriers. It is also providing powerful new approaches for linking genotype to phenotype in admixed populations. In this chapter, we give an overview of some of the methods that have been used and some of the novel insights gained. We also outline some of the pitfalls of the most commonly used methods and possible problems with interpretation of the results

A precise bare simulation approach to the minimization of some distances. Foundations

In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface)