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- Richard Durrett
- SIAM Review
- 1992

contribution is concerned with dynamic game theoryma good example of the wide range of applications for Riccati equations. I think that this book can be a good starting point for work on Riccati equations. It does not seem suitable as a text for a graduate class (no exercises and very few examples are given). Workers in the field will not find many new… (More)

Let W 1 ... . , W N be N nonnegative random variables and let 9J~ be the class of all probability measures on [0, m). Define a transformation T on 9J~ by letting T# be the distribution of W a X 1 + . . . + WNXN, where the X i are independent random variables with distribution /~, which are independent of W1, ..., W N as well. In earlier work, first Kahane… (More)

- S. Kruglyak, Richard Durrett, Malcolm D. Schug, Charles F. Aquadro
- Proceedings of the National Academy of Sciences…
- 1998

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation… (More)

- Richard Durrett, Jason Schweinsberg
- Theoretical population biology
- 2004

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… (More)

- Feinan Wu, Nancy T. Eannetta, +4 authors Steven D. Tanksley
- Theoretical and Applied Genetics
- 2009

We report herein the development of a pepper genetic linkage map which comprises 299 orthologous markers between the pepper and tomato genomes (including 263 conserved ortholog set II or COSII markers). The expected position of additional 288 COSII markers was inferred in the pepper map via pepper–tomato synteny, bringing the total orthologous markers in… (More)

- Todd J. Vision, Daniel G. Brown, David B. Shmoys, Richard Durrett, Steven D. Tanksley
- Genetics
- 2000

Historically, linkage mapping populations have consisted of large, randomly selected samples of progeny from a given pedigree or cell lines from a panel of radiation hybrids. We demonstrate that, to construct a map with high genome-wide marker density, it is neither necessary nor desirable to genotype all markers in every individual of a large mapping… (More)

When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample n individuals at the end of a selective sweep. If we focus on a site on the chromosome that is close to the location of the beneficial mutation, then many of the lineages will likely be… (More)

- Richard Durrett, Stephen Moseley
- Theoretical population biology
- 2010

Inspired by previous work of Iwasa et al. (2006) and Haeno et al. (2007), we consider an exponentially growing population of cancerous cells that will evolve resistance to treatment after one mutation or display a disease phenotype after two or more mutations. We prove results about the distribution of the first time when k mutations have accumulated in… (More)

- Richard Durrett, Simon A. Levin
- Theoretical population biology
- 1998

Using several variants of a stochastic spatial model introduced by Silvertown et al., we investigate the effect of spatial distribution of individuals on the outcome of competition. First, we prove rigorously that if one species has a competitive advantage over each of the others, then eventually it takes over all the sites in the system. Second, we examine… (More)

- Richard Durrett
- 2005

We consider a system that models the shape of a growing polymer. Our basic problem concerns the asymptotic behavior of Xt, the location of the end of the polymer at time t. We obtain bounds on Xt in the (physically uninteresting) case that d = 1 and the interaction function f (x ) > O. If, in addition, f (x ) behaves for large x like Cx -p with fi < 1 we… (More)