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

Steinsaltz, David; Evans, Steven N.; Wachter, Kenneth W.

doi:10.1016/j.aam.2004.09.003

Cited by 43 publications

(67 citation statements)

References 40 publications

(70 reference statements)

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“…The process Y t can be stopped randomly at time T. The conditional distribution of T given trajectories of Y u , 0 ≤u≤t is completely characterized by the conditional hazard μ(t, Y t ), which is assumed to be: (2) Here μ 0 (t) is the background hazard characterizing the mortality rate which would remain if a vector of covariates Y t follows the optimal trajectory coinciding with f(t). An asterisk in (2) and in formulas below denotes the transposition of respective vectors or matrices.…”

Section: General Descriptionmentioning

confidence: 99%

“…An asterisk in (2) and in formulas below denotes the transposition of respective vectors or matrices. Matrix Q (t) is a non-negative-definite symmetric matrix of respective dimension (k × k).…”

Section: General Descriptionmentioning

confidence: 99%

“…Thus, appropriate restrictions on parameters of respective functions defining the dynamics of Y t are necessary in the estimation procedure. In addition to this, restrictions are necessary for functions in the mortality risk (2). These restrictions should reasonably impose constraints on parameters of: a) an initial distribution Y 0 (to ensure a negligible probability of negative values); b) functions f 1 (t) and f(t) (to ensure non-negative values for each age); c) matrix a(t) (to ensure that the feedback coefficient in (1) does not become too small and the trajectories of Y t tend to f 1 (t)); d) the background hazard μ 0 (t) (to ensure non-negative values for each age and a nondecreasing age pattern); and e) matrix Q(t) (to ensure that the matrix is non-negative definite for each age).…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…A substantial part of this research is going on within an analytical framework aiming to derive observed features of mortality curves using respective theoretical concepts. These studies include evolutionary biology theory of senescence [1], mutation-selection balance [2], reliability theory [3,4], and economic theory [5], among others. Such abstract analyses became possible because of remarkable regularities revealed in the shape of the mortality curve: the decline in the childhood, the exponential increase in the adult ages and the tendency to deceleration and leveling off at the oldest old ages.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stochastic model for analysis of longitudinal data on aging and mortality

Yashin

Arbeev

Akushevich

et al. 2007

Mathematical Biosciences

133

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Aging-related changes in a human organism follow dynamic regularities, which contribute to the observed age patterns of incidence and mortality curves. An organism's "optimal" (normal) physiological state changes with age, affecting the values of risks of disease and death. The resistance to stresses, as well as adaptive capacity, declines with age. An exposure to improper environment results in persisting deviation of individuals' physiological (and biological) indices from their normal state (due to allostatic adaptation), which, in turn, increases chances of disease and death. Despite numerous studies investigating these effects, there is no conceptual framework, which would allow for putting all these findings together, and analyze longitudinal data taking all these dynamic connections into account. In this paper we suggest such a framework, using a new version of stochastic process model of aging and mortality. Using this model, we elaborated a statistical method for analyses of longitudinal data on aging, health and longevity and tested it using different simulated data sets. The results show that the model may characterize complicated interplay among different components of aging-related changes in humans and that the model parameters are identifiable from the data.

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Section: General Descriptionmentioning

confidence: 99%

Section: General Descriptionmentioning

confidence: 99%

Section: Estimation Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic model for analysis of longitudinal data on aging and mortality

Yashin

Arbeev

Akushevich

et al. 2007

Mathematical Biosciences

133

View full text Add to dashboard Cite

show abstract

“…An alternative nonlinear model without recombination is presented in ref. 20. In that model, distributions for allele counts are not Poisson, the counterpart of the force of natural selection is a complicated object depending on a whole suite of probabilities, and absence of mixing allows the persistence of subpopulations untouched by mutation, bypassing Theorems 1, 2, and 3.…”

mentioning

confidence: 99%

The age-specific force of natural selection and biodemographic walls of death

Wachter

Evans

Steinsaltz

2013

Proc. Natl. Acad. Sci. U.S.A.

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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 nonlinear demographic model for mutation accumulation recently developed by Evans, Steinsaltz, and Wachter, we find surprising differences. Nonlinear 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.biodemography | hazard functions | senescence T he best-known formula at the intersection of genetics and demography is doubtless W. D. Hamilton's "age-specific force of natural selection," the starting point for the models in ref. 1 applied in this paper. Hamilton (2, 3) differentiated a measure of fitness, Lotka's intrinsic rate of natural increase, with respect to an increment to age-specific mortality at an age a. Thus, he obtained a linear approximation for loss in fitness due to any deleterious mutations that raised mortality at an age a. The greater the loss in fitness, the faster should mutant alleles be selected out of a population, and the fewer should be found at equilibrium as recurring mutations balance natural selection.By this route, Sir Peter Medawar's concept of mutation accumulation as an evolutionary reason for senescence takes on mathematical form. As in refs. 4-6, richly developed in ref. 7, the idea involves genetic load produced by large numbers of mildly deleterious mutations occurring at widely separated loci, each with some small age-specific effect on vital schedules.Hamilton's work has been assessed and extended by Baudisch (8). Sophisticated genetic models of mutation-selection balance are available (9). Demographers mainly put up with less sophisticated models of the genome in return for more refined treatments of agespecific structure, as we do here. Age-specific predictions for vital schedules may be robust to details of genetic specification, in line with a principle of Haldane (10), which equates the population loss in fitness from genetic load to the total mutation rate, independent of the form of action of mutations.Current interest has been stimulated by the expansion of biodemography, reviewed in refs. 11-14, and by the appreciation of two widely occurring cross-species commonalities in graphs of mortality rates as functions of age: exponential increase at adult ages (the "Gompertz-Makeham" mortality pattern) and plateaulike shapes at older ages. Working with an appealingly simple specification, Brian Charlesworth (15) gave an elegant demonstration that Gompertz-Makeham mortality could be predicted exactly by the Hamilton-based linear approximate model. He also proposed an optional fix that would lead to plateaus at extreme ages. In Charlesworth's setting, a "wall of death" with infinite mortality rates and zero survivorship ...

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Why organisms age: Evolution of senescence under positive pleiotropy?

2015

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Two classic theories maintain that aging evolves either because of alleles whose deleterious effects are confined to late life or because of alleles with broad pleiotropic effects that increase early-life fitness at the expense of late-life fitness.However, empirical studies often reveal positive pleiotropy for fitness across age classes, and recent evidence suggests that selection on early-life fitness can decelerate aging and increase lifespan, thereby casting doubt on the current consensus. Here, we briefly review these data and promote the simple argument that aging can evolve under positive pleiotropy between early-and late-life fitness when the deleterious effect of mutations increases with age. We argue that this hypothesis makes testable predictions and is supported by existing evidence.

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

Cited by 43 publications

References 40 publications

Stochastic model for analysis of longitudinal data on aging and mortality

Stochastic model for analysis of longitudinal data on aging and mortality

The age-specific force of natural selection and biodemographic walls of death

Why organisms age: Evolution of senescence under positive pleiotropy?

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