Biomedical subjects

Richard Durrett

Publications and source records attributed to Richard Durrett.

5 recordsLinked to original sources

PubMed2004

Subfunctionalization: How often does it occur? How long does it take?

The mechanisms responsible for the preservation of duplicate genes have been debated for more than 70 years. Recently, Lynch and Force have proposed a new explanation: subfunctionalization--after duplication the two gene copies specialize to perform complementary functions. We investigate the probability that subfunctionalization occurs, the amount of time after duplication that it takes for the outcome to be resolved, and the relationship of these quantities to the population size and mutation rates.

Gene Duplication↗

PubMed2004

Approximating selective sweeps.

The fixation of advantageous mutations in a population has the effect of reducing variation in the DNA sequence near that mutation. Kaplan et al. (1989) used a three-phase simulation model to study the effect of selective sweeps on genealogies. However, most subsequent work has simplified their approach by assuming that the number of individuals with the advantageous allele follows the logistic differential equation. We show that the impact of a selective sweep can be accurately approximated by a random partition created by a stick-breaking process. Our simulation results show that ignoring the randomness when the number of individuals with the advantageous allele is small can lead to substantial errors.

Alleles↗

PubMed2004

Bayesian estimation of genomic distance.

We present a Bayesian approach to the problem of inferring the number of inversions and translocations separating two species. The main reason for developing this method is that it will allow us to test hypotheses about the underlying mechanisms, such as the distribution of inversion track lengths or rate constancy among lineages. Here, we apply these methods to comparative maps of eggplant and tomato, human and cat, and human and cattle with 170, 269, and 422 markers, respectively. In the first case the most likely number of events is larger than the parsimony value. In the last two cases the parsimony solutions have very small probability.

Animals↗

PubMed2002

Competition and species packing in patchy environments.

In models of competition in which space is treated as a continuum, and population size as continuous, there are no limits to the number of species that can coexist. For a finite number of sites, N, the results are different. The answer will, of course, depend on the model used to ask the question. In the Tilman-May-Nowak ordinary differential equation model, the number of species is asymptotically C log N with most species packed in at the upper end of the competitive hierarchy. In contrast, for metapopulation models with discrete individuals and stochastic spatial systems with various competition neighborhoods, we find a traditional species area relationship CN(a), with no species clumping along the phenotypic gradient. The exponent a is larger by a factor of 2 for spatially explicit models. In words, a spatial distribution of competitors allows for greater diversity than a metapopulation model due to the effects of recruitment limitation in their competition.

Competitive Behavior↗

PubMed2002

Bayesian estimation of the number of inversions in the history of two chromosomes.

We present a Bayesian approach to the problem of inferring the history of inversions separating homologous chromosomes from two different species. The method is based on Markov Chain Monte Carlo (MCMC) and takes full advantage of all the information from marker order. We apply the method both to simulated data and to two real data sets. For the simulated data, we show that the MCMC method provides accurate estimates of the true posterior distributions and in the analysis of the real data we show that the most likely number of inversions in some cases is considerably larger than estimates obtained based on the parsimony inferred number of inversions. Indeed, in the case of the Drosophila repleta-D. melanogaster comparison, the lower boundary of a 95% highest posterior density credible interval for the number of inversions is considerably larger than the most parsimonious number of inversions.

Animals↗