A generalized model of mutation-selection balance with applications to aging

A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The model accommodates epistatic as well as additive selective costs. Closed form characterizations are obtained for solutions in finite time, along with proofs of convergence to stationary distributions and a proof of the uniqueness of solutions in a restricted case. Examples are given of applications to the biodemography of aging, including instabilities in current formulations of mutation accumulation.Comment: 20 pages Updated to include more historical comment and references to the literature, as well as to make clear how our non-linear, non-Markovian model differs from previous linear, Markovian particle system and measure-valued diffusion models. Further updated to take into account referee's comment

Biodemography comes of Age

Biodemography has emerged and grown over the last fifteen years, with loyal and farsighted support from its patrons. As it enters what might be called its adolescence as a field, it faces challenges along with abounding opportunities. One challenge is to continue to generate knowledge that contributes to human health and well-being. A second is to insist on high standards of quality control within its cross-disciplinary environment. Opportunities appear in a variety of directions, including mathematical modeling, genomic analyses, and field studies of aging in the wild.aging in the wild, biodemography, evolutionary demography, longevity

The Age-Specific Force of Natural Selection and Walls of Death

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow Walls of Death at ages before the end of reproduction. Haldane's Principle for genetic load has an exact but unfamiliar generalization.Comment: 27 page

Concentration inequalities for mean field particle models

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentration properties, with respect to the time parameter, are also derived. The concentration inequalities presented here generalize the classical Hoeffding, Bernstein and Bennett inequalities for independent random sequences to interacting particle systems, yielding very new results for this class of models. We illustrate these results in the context of McKean-Vlasov-type diffusion models, McKean collision-type models of gases and of a class of Feynman-Kac distribution flows arising in stochastic engineering sciences and in molecular chemistry.Comment: Published in at http://dx.doi.org/10.1214/10-AAP716 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Negative Selection on BRCA1 Susceptibility Alleles Sheds Light on the Population Genetics of Late-Onset Diseases and Aging Theory

The magnitude of negative selection on alleles involved in age-specific mortality decreases with age. This is the foundation of the evolutionary theory of senescence. Because of this decrease in negative selection with age, and because of the absence of reproduction after menopause, alleles involved in women's late-onset diseases are generally considered evolutionarily neutral. Recently, genetic and epidemiological data on alleles involved in late onset-diseases have become available. It is therefore timely to estimate selection on these alleles. Here, we estimate selection on BRCA1 alleles leading to susceptibility to late-onset breast and ovarian cancer. For this, we integrate estimates of the risk of developing a cancer for BRCA1-carriers into population genetics frameworks, and calculate selection coefficients on BRCA1 alleles for different demographic scenarios varying across the extent of human demography. We then explore the magnitude of negative selection on alleles leading to a diverse range of risk patterns, to capture a variety of late-onset diseases. We show that BRCA1 alleles may have been under significant negative selection during human history. Although the mean age of onset of the disease is long after menopause, variance in age of onset means that there are always enough cases occurring before the end of reproductive life to compromise the selective value of women carrying a susceptibility allele in BRCA1. This seems to be the case for an extended range of risk of onset functions varying both in mean and variance. This finding may explain the distribution of BRCA1 alleles' frequency, and also why alleles for many late-onset diseases, like certain familial forms of cancer, coronary artery diseases and Alzheimer dementia, are typically recent and rare. Finally, we discuss why the two most popular evolutionary theories of aging, mutation accumulation and antagonistic pleiotropy, may underestimate the effect of selection on survival at old ages

Vital Rates from the Action of Mutation Accumulation

New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the biodemography of longevity, including proposed explanations of Gompertz hazards and mortality plateaus