A diffusion-taking value in probability-measures on a graph with vertex set V, ∑i∈Vxiδi is studied. The masses on each vertex satisfy the stochastic differential equation of the form ...dxi=∑j∈N(i)xixjdBij on the simplex, where {Bij} are independent standard Brownian motions with skew symmetry, and N(i) is the neighbour of the vertex i. A dual Markov chain on integer partitions to the Markov semigroup associated with the diffusion is used to show that the support of an extremal stationary state of the adjoint semigroup is an independent set of the graph. We also investigate the diffusion with a linear drift, which gives a killing of the dual Markov chain on a finite integer lattice. The Markov chain is used to study the unique stationary state of the diffusion, which generalizes the Dirichlet distribution. Two applications of the diffusions are discussed: analysis of an algorithm to find an independent set of a graph, and a Bayesian graph selection based on computation of probability of a sample by using coupling from the past.
Recent studies of microbial biogeography have revealed the global distribution of cosmopolitans and dispersal of regional endemics, but little is known about how these processes are affected by ...microbial evolution. Here, we compared DNA sequences from snow/glacier algae found in an 8000-year-old ice from a glacier in central Asia with those from modern snow samples collected at 34 snow samples from globally distributed sites at the poles and mid-latitudes, to determine the evolutionary relationship between cosmopolitan and endemic phylotypes of snow algae. We further applied a coalescent theory-based demographic model to the DNA sequences. We found that the genus Raphidonema (Trebouxiophyceae) was distributed over both poles and mid-latitude regions and was detected in different ice core layers, corresponding to distinct time periods. Our results indicate that the modern cosmopolitan phylotypes belonging to Raphidonema were persistently present long before the last glacial period. Furthermore, endemic phylotypes originated from ancestral cosmopolitan phylotypes, suggesting that modern regional diversity of snow algae in the cryosphere is a product of microevolution. These findings suggest that the cosmopolitans dispersed across the world and then derived new localized endemics, which thus improves our understanding of microbial community formation by microevolution in natural environments.
Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics ...from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many researchers have attempted to develop techniques to choose informative summary statistics. The present study evaluated the utility of a kernel-based ABC method Fukumizu, K., L. Song and A. Gretton (2010): “Kernel Bayes’ rule: Bayesian inference with positive definite kernels,” arXiv, 1009.5736 and Fukumizu, K., L. Song and A. Gretton (2011): “Kernel Bayes’ rule. Advances in Neural Information Processing Systems 24.” In: J. Shawe-Taylor and R. S. Zemel and P. Bartlett and F. Pereira and K. Q. Weinberger, (Eds.), pp. 1549–1557., NIPS 24: 1549–1557 for complex problems that demand many summary statistics. Specifically, kernel ABC was applied to population genetic inference. We demonstrate that, in contrast to conventional ABCs, kernel ABC can incorporate a large number of summary statistics while maintaining high performance of the inference.
The Japanese Archipelago stretches over 4000 km from north to south, and is the homeland of the three human populations; the Ainu, the Mainland Japanese and the Ryukyuan. The archeological evidence ...of human residence on this Archipelago goes back to >30 000 years, and various migration routes and root populations have been proposed. Here, we determined close to one million single-nucleotide polymorphisms (SNPs) for the Ainu and the Ryukyuan, and compared these with existing data sets. This is the first report of these genome-wide SNP data. Major findings are: (1) Recent admixture with the Mainland Japanese was observed for more than one third of the Ainu individuals from principal component analysis and frappe analyses; (2) The Ainu population seems to have experienced admixture with another population, and a combination of two types of admixtures is the unique characteristics of this population; (3) The Ainu and the Ryukyuan are tightly clustered with 100% bootstrap probability followed by the Mainland Japanese in the phylogenetic trees of East Eurasian populations. These results clearly support the dual structure model on the Japanese Archipelago populations, though the origins of the Jomon and the Yayoi people still remain to be solved.
The first detection of a gravitational wave (GW) has been achieved by two detectors of the advanced LIGO. Routine detections of GW events from various GW sources are expected in the coming decades. ...Although the first signal was statistically significant, we expect to see numerous low signal-to-noise ratio (SNR) events with which we may be able to learn various aspects of the Universe that have yet to be unveiled. On the other hand, instrumental glitches due to nonstationarity and/or a non-Gaussian tail of detector noise distribution prevent us from confidently identifying true but low SNR GW signals out of instrumental noise. Thus, to make the best use of data from GW detectors, it is important to establish a method to safely distinguish true GW signals from false signals due to instrumental noises. For this purpose, we urgently need to understand characteristics of detector noises, since the nonstationarity and non-Gaussianity inherent in detector outputs are known to increase false detections of signals. Focusing on identifying the non-Gaussian noise components, this paper introduces a new measure for characterizing the non-Gaussian noise components using the parameter nu which characterizes the weight of tail in a Student-t distribution. A confidence interval is reported on the extent to which detector noise deviates from Gaussianity. Our method revealed stationary and transient deterioration of Gaussianity in LIGO S5 data.
The Asian black bear Ursus thibetanus is widely distributed in Asia and is adapted to broad-leaved deciduous forests, playing an important ecological role in the natural environment. Several ...subspecies of U. thibetanus have been recognized, one of which, the Japanese black bear, is distributed in the Japanese archipelago. Recent molecular phylogeographic studies clarified that this subspecies is genetically distantly related to continental subspecies, suggesting an earlier origin. However, the evolutionary relationship between the Japanese and continental subspecies remained unclear. To understand the evolution of the Asian black bear in relation to geological events such as climatic and transgression-regression cycles, a reliable time estimation is also essential. To address these issues, we determined and analyzed the mt-genome of the Japanese subspecies. This indicates that the Japanese subspecies initially diverged from other Asian black bears in around 1.46Ma. The Northern continental population (northeast China, Russia, Korean peninsula) subsequently evolved, relatively recently, from the Southern continental population (southern China and Southeast Asia). While the Japanese black bear has an early origin, the tMRCAs and the dynamics of population sizes suggest that it dispersed relatively recently in the main Japanese islands: during the late Middle and Late Pleistocene, probably during or soon after the extinction of the brown bear in Honshu in the same period. Our estimation that the population size of the Japanese subspecies increased rapidly during the Late Pleistocene is the first evidential signal of a niche exchange between brown bears and black bears in the Japanese main islands. This interpretation seems plausible but was not corroborated by paleontological evidence that fossil record of the Japanese subspecies limited after the Late Pleistocene. We also report here a new fossil record of the oldest Japanese black bear from the Middle Pleistocene, and it supports our new evolutionary hypothesis of the Japanese black bear.
The Ryukyu Islands are located to the southwest of the Japanese archipelago. Archaeological evidence has revealed the existence of prehistoric cultural differentiation between the northern Ryukyu ...islands of Amami and Okinawa, and the southern Ryukyu islands of Miyako and Yaeyama. To examine a genetic subdivision in the Ryukyu Islands, we conducted genome-wide single nucleotide polymorphism typing of inhabitants from the Okinawa Islands, the Miyako Islands, and the Yaeyama Islands. Principal component and cluster analyses revealed genetic differentiation among the island groups, especially between Okinawa and Miyako. No genetic affinity was observed between aboriginal Taiwanese and any of the Ryukyu populations. The genetic differentiation observed between the inhabitants of the Okinawa Islands and the Miyako Islands is likely to have arisen due to genetic drift rather than admixture with people from neighboring regions. Based on the observed genetic differences, the divergence time between the inhabitants of Okinawa and Miyako islands was dated to the Holocene. These findings suggest that the Pleistocene inhabitants, whose bones have been found on the southern Ryukyu Islands, did not make a major genetic contribution, if any, to the present-day inhabitants of the southern Ryukyu Islands.
Goats (Capra hircus) are one of the oldest domesticated species, and they are kept all over the world as an essential resource for meat, milk, and fiber. Although recent archeological and molecular ...biological studies suggested that they originated in West Asia, their domestication processes such as the timing of population expansion and the dynamics of their selection pressures are little known. With the aim of addressing these issues, the nearly complete mitochondrial protein-encoding genes were determined from East, Southeast, and South Asian populations. Our coalescent time estimations suggest that the timing of their major population expansions was in the Late Pleistocene and significantly predates the beginning of their domestication in the Neolithic era (≈10,000 years ago). The ω (ratio of non-synonymous rate/synonymous substitution rate) for each lineage was also estimated. We found that the ω of the globally distributed haplogroup A which is inherited by more than 90% of goats examined, turned out to be extremely low, suggesting that they are under severe selection pressure probably due to their large population size. Conversely, the ω of the Asian-specific haplogroup B inherited by about 5% of goats was relatively high. Although recent molecular studies suggest that domestication of animals may tend to relax selective constraints, the opposite pattern observed in our goat mitochondrial genome data indicates the process of domestication is more complex than may be presently appreciated and cannot be explained only by a simple relaxation model.
Noise hunting is a critical requirement for realizing design sensitivity of a detector, and consequently, noise origins and its features have been revealed partially. Among the noise sources to be ...hunted, sources of nonlinearly correlated noise, such up-conversion noise, are hard to find and can limit the sensitivity of gravitational wave searches with advanced detectors. We propose using a correlation analysis method called maximal information coefficient (MIC) to find both nonlinear and linear correlations. We apply MIC to the scattered light noise correlated between the seismic activity and the strain signal, which limited the sensitivity of the Virgo detector during the first science run. The results show that MIC can find nonlinearly correlated noise more efficiently than the Pearson correlation method. When the data is linearly correlated, the efficiency of the Pearson method and MIC is comparable. On the other hand, when the data is known to be nonlinearly correlated, MIC finds the correlation while the Pearson method fails completely.
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