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An Analysis of the Distribution of Genotypes for a Recent Model in Population Genetics


Recent genetic studies suggest that many age-related diseases may be attributed not to a single or small number of mutations, but rather to a large number of mutations, each of which is individually slightly deleterious. Following in the tradition of Kimura and Maruyama, we consider mutation accumulation in an infinite population with a large number of mutation types. We compare the distribution of genotypes under two extreme assumptions regarding genetic recombination: no recombination versus ``free" recombination, in which recombination acts more rapidly than mutation and selection. Under a range of assumptions, including realistic mutation rates and demographic fitness measures, we find unexpected similarities in the predictions from the different models. While recombination predictably affects the level of mutant alleles present in the population, the overall shape of the genotype distribution under the two models is quite similar, as are the general behavior of demographic outcomes such as lifespan and hazard rates. Furthermore, the distribution of genotypes under the assumption of no recombination may be well approximated by a Poisson random measure. The qualitative similarities in genotype distributions and demographic characters under these extreme models of genetic recombination suggest that attempts to model recombination in a more realistic manner may not add much to our understanding when viewed from a demographic perspective.

The two models analyzed here, developed by Steinsaltz, Evans, and Wachter, are general enough to connect age-specific effects on demographic characters, such as mortality, to mechanisms of genetic change. While the 2005 model without recombination has a series solution, it cannot be directly evaluated except in the simplest of cases. Sampling from the distribution of genotypes in cases with a large number of mutation types is challenging. In this work we utilize a multiple-try Metropolis algorithm to sample from the distribution of genotypes for spaces containing up to 1000 different mutation types. We consider a variety of test cases, finding scenarios in which typical genotypes contain 100, 350 or even 850 mutations. Our success at accurately estimating genotype distributions and demographic outcomes under assumptions that produce such a large average number of mutations suggests that this model could be utilized under more realistic scenarios, such as mutations associated with age-related disease.

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