cchar, v. 1.6: Count characters in sequence data.
cpg, v. 0.7: Compute the CpG content of DNA sequences.
cutSeq, v. 0.11: Cut regions from molecular sequences.
generateQuerySbjct, v. 0.4: Generate pairs of homologous DNA sequences.
gd, v. 0.12: Calculate genetic diversity (pi, S, and Tajima's D) from aligned DNA sequences with or without sliding window.
getSeq, v. 0.4: Get specific sequences from a FASTA file containing multiple entries.
ms2dna, v. 1.16: Generate samples of homologous DNA sequences evolved under defined evolutionary scenarios by converting the output of Richard Hudson's coalescent simulation program ms. As of version 1.11, it can also deal with output generated by Gary Chen's fast coalescent simulator MaCS using the pipeline macs [options] | msformatter | ms2dna -a.
randomizeSeq, v. 0.8: Randomize sequences.
sequencer, v. 1.14: Simulate shotgun sequencing with paired (as of version 1.11) or unpaired reads and a user-defined error rate.
simK, v. 0.4: Simulate pair of sequences with given number of substitutions/site (K).
The rpanel package has two aims. The first is to provide tools which make the construction of gui control panels for R applications as easy as possible. The package is aimed at those who know R but are not familiar with the technicalities of the various gui construction systems which are available. The rpanel package is built on rtcltk and manages the process of communication so that controls can be constructed directly by R simple function calls.
Selection is one of the factors that most influence the shape of genealogical trees. Here we report results of simulations of the infinite-sites version of Moran's model of population genetics aiming at quantifying how the presence of selection affects the branching pattern (topology) of binary genealogical trees. In particular, we consider a scenario of purifying or negative selection in which all mutations are deleterious and each new mutation reduces the fitness of the individual by the same fraction. Analysis of five statistical measures of tree balance or symmetry borrowed from taxonomy indicates that the genealogical trees of samples of populations in which selection is actuating are in the average more asymmetric than neutral trees and that this effect is enhanced by increasing the sample size. However, a quantitative evaluation of the power of these balance measures to detect a tree topology significantly distinct from the neutral one indicates that they are not useful as tests of neutrality of mutations.
C. Mueller, и R. Sowers. Stochastic analysis (Ithaca, NY, 1993), том 57 из Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, Finally, T. Shiga has pointed out that there is a dual process for (1.4),
which is a system of branching Brownian motions, in which particles
coalesce at a Poisson rate, measured according to the local time beween
pairs of particles. We do not give a more precise description..(1995)
J. Fleischman. Trans. Amer. Math. Soc., (1978)Branching Brownian motion, the subject of this article, is a continuous time Galton-Watson process in which particles also have positions. On splitting, each particle is replaced by its daughter particles and they then follow independent Brownian motions until they split. The branching process is assumed to be critical. Let $N_A(t)$ be the number of particles in the bounded set $A$, of Lebesgue measure $m(A)$, at the time $t$.
It is shown that if there is only one particle initially and the movement of the particles occurs in the plane then $c_2(tlogt)PN_A(t)>c_1m(A)łambdate^-łambda$ for $łambda>0$ as $t\rightarrowınfty$, where $c_1$ and $c_2$ are specified constants. The method of proof is to obtain good estimates of $EN_A(t)^k$ for all $k$ and hence of the moment generating function of $N_A(t)/(m(A)t)$; from this the result is derived. If the set of initial particles forms a homogeneous Poisson process of unit rate in the plane (in fact, a slightly weaker assumption, as made by the author, is sufficient), then $c_3logtPN_A(t)>c_1m(A)łambdate^-łambda$ for $łambda>0$ as $t\rightarrowınfty$, where $c_1$ and $c_3$ are specified constants..
L. Rogers, и J. Pitman. Ann. Probab., 9 (4):
573--582(1981)Let $(G,G)$ and $(H,H)$ be two measurable spaces, and $f$ be a measurable function of $G$ into $H$. If $\X(t)\$ is a homogeneous Markov process with initial distribution $łambda$ and state space $G$, under what conditions is the process $f(X(t))$ Markov? Conditions are well known for $f(X)$ to be Markov for all the initial distributions $łambda$, or invariant $łambda$. This article provides conditions for $f(X)$ to be Markov when there may be no invariant $łambda$, or for some though not all initial $łambda$. The main result is then applied to present a simple proof of Williams' result: For a linear Brownian motion $B(t)$ starting from 0 and with drift $\mu$, the process $Y(t)=2M(t)-B(t)$ (where $M(t)=B(s)\ 0st$) is a diffusion following the same law as the radial part of a three-dimensional Brownian motion starting from the origin and with drift $|\mu|$..
A. Kolmogorov. Mathematics and its Applications (Soviet Series) Kluwer Academic Publishers Group, Dordrecht, (1991)Mathematics and mechanics, With commentaries by V. I. Arnol\cprimed, V. A. Skvortsov, P. L. Ul\cprimeyanov et al, Translated from the Russian original by V. M. Volosov, Edited and with a preface, foreword and brief biography by V. M. Tikhomirov.
D. Kendall. Biometrika, (1948)The author discusses a ``birth-and-death process'' for which the Kolmogorov differential equations assume the form $$ P_n'(t)=-n(a+b)+cP_n(t)+(n-1)a+cP_n-1(t)\\ +(n+1)bP_n+1(t), $$ where $P_n(t)$ is the probability of a population size $n$. The case $c0$ corresponds to mortality and fertility proportional to the actual population size. The $c$-term accounts for an increase by immigration. The generating function of $P_n(t)$ is obtained and it is shown that for small $c$ one obtains approximations to R. A. Fisher's ``logarithmic series distribution'' which has found several applications in biology..
D. Blackwell, и D. Kendall. J. Appl. Probability, (1964)Consider an ``urn scheme'' in which balls of $k$ colors are present in a single urn (initially one of each color) and successive random drawings made. After each drawing, the selected ball is replaced together with another of the same color. The authors add to the existing supply of examples by determining the Martin boundary of this process, which turns out to be homeomorphic to the set of $k$-vectors with non-negative components summing to 1. Applications to a moment problem and a stochastic birth process are discussed. Reviewer's remark: In case $k=2$, the boundary is the unit interval, as in T. Watanabe's coin-tossing example J. Math. Soc. Japan 12 (1960), 192--206; MR0120683 (22 #11432). In fact, the Pólya process is an $h$-process for coin-tossing, so that this agreement is no coincidence..