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Tracking past population fluctuations can give insight into current levels of genetic variation present within species. Analysing population dynamics over larger timescales can be aligned to known climatic changes to determine the response of species to varying environments. Here, we applied the Pairwise Sequentially Markovian Coalescent (psmc) model to infer past population dynamics of three widespread grouse species; black grouse, willow grouse and rock ptarmigan. This allowed the tracking of the effective population size (Ne ) of all three species beyond 1 Mya, revealing that (i) early Pleistocene cooling (~2.5 Mya) caused an increase in the willow grouse and rock ptarmigan populations, (ii) the mid-Brunhes event (~430 kya) and following climatic oscillations decreased the Ne of willow grouse and rock ptarmigan, but increased the Ne of black grouse and (iii) all three species reacted differently to the last glacial maximum (LGM) - black grouse increased prior to it, rock ptarmigan experienced a severe bottleneck and willow grouse was maintained at large population size. We postulate that the varying psmc signal throughout the LGM depicts only the local history of the species. Nevertheless, the large population fluctuations in willow grouse and rock ptarmigan indicate that both species are opportunistic breeders while black grouse tracks the climatic changes more slowly and is maintained at lower Ne . Our results highlight the usefulness of the psmc approach in investigating species' reaction to climate change in the deep past, but also that caution should be taken in drawing general conclusions about the recent past.

We study the the following question in Random Graphs. We are given two disjoint sets L,R with |L| = n and |R| = m. We construct a random graph G by allowing each x∈L to choose d random neighbours in R. The question discussed is as to the size μ(G) of the largest matching in G. When considered in the context of Cuckoo Hashing, one key question is as to when is μ(G) = n whp? We answer this question exactly when d is at least three. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.

Genomic-level analyses of DNA from non-invasive sources would facilitate powerful conservation and evolutionary studies in natural populations of endangered and otherwise elusive species. However, the typical low quantity and poor quality of DNA that is extracted from non-invasive samples have generally precluded such work. Here we apply a modified DNA capture protocol that, when used in combination with massively-parallel sequencing technology, facilitates efficient and highly-accurate resequencing of megabases of specified nuclear genomic regions from fecal DNA samples. We validated our approach by comparing genetic variants identified from corresponding fecal and blood DNA samples of six western chimpanzees (Pan troglodytes verus) across more than 1.5 megabases of chromosome 21, chromosome X, and the complete mitochondrial genome. Our results suggest that it is now feasible to conduct genomic studies in natural populations for which constraints on invasive sampling have otherwise long been a barrier. The data we collected also provided an opportunity to examine western chimpanzee genetic diversity at unprecedented scale. Despite high mitochondrial genome diversity (π = 0.585%), western chimpanzees have a low ratio (0.42) of X chromosomal (π = 0.034%) to autosomal (chromosome 21 π = 0.081%) sequence diversity, a pattern that may reflect an unusual demographic history of this subspecies.