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. 2011 Jan 7;278(1702):144-51.
doi: 10.1098/rspb.2010.0992. Epub 2010 Jul 21.

Evolutionary Demography and Quantitative Genetics: Age-Specific Survival as a Threshold Trait

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Evolutionary Demography and Quantitative Genetics: Age-Specific Survival as a Threshold Trait

Jacob A Moorad et al. Proc Biol Sci. .
Free PMC article

Abstract

Researchers must understand how mutations affect survival at various ages to understand how ageing evolves. Many models linking mutation to age-specific survival have been proposed but there is little evidence to indicate which model is most appropriate. This is a serious problem because the predicted evolutionary endpoints of ageing depend upon the details of the specific model. We apply an explicitly quantitative genetic perspective to the problem. To determine the inheritance of dichotomous traits (such as survival), quantitative genetics has long employed a threshold model. Beginning from first principles, we show how this is the most defensible mutational model for age-specific survival and how this, relative to the standard model, predicts delayed senescence and mortality deceleration at late age. These are commonly observed patterns of ageing that heretofore have required more complicated survival models. We also show how this model can be developed further to unify quantitative genetics and evolutionary demography into a more complete conceptual framework for understanding the evolution of ageing.

Figures

Figure 1.
Figure 1.
Selection on liability is negative frequency dependent. Selection is the difference between the phenotypic mean of a population (unweighted by fitness) and the mean weighted by fitness. (a) Illustrates this difference for the case where incidence is 50% (half the population has the character state associated with positive liability) and fitness is solely determined by the character state. The two phenotypic means are indicated by the broken vertical lines. Selection is the difference between these two lines. Figure 2 shows the case where incidence is 90%. These two cases demonstrate how selection becomes weaker as the more fit character state becomes more common.
Figure 2.
Figure 2.
Effect of mean liability on selection for liability. The normal distribution hazard function T on the scale of liability. Increasing liability decreases mortality. If mutations act linearly on the liability scale, then the figure also illustrates the relative strength of selection against the build-up of mutational load (liability z decreases with increased load). Selection is clearly directional against deleterious mutations (it is positive) and negative frequency dependent (it decreases with increasing z).
Figure 3.
Figure 3.
Effect of mortality on selection gradients under the threshold model. The strength of selection on survival alleles is the product of the normal distribution hazard function T and Hamilton's sensitivity (dotted line). This function is illustrated here on the ln(mortality) scale. Compared with Hamilton's model, the threshold model predicts weaker selection against the build-up of deleterious mutations when mutational load is low but stronger selection when load is high.
Figure 4.
Figure 4.
Example of how the threshold model predicts different changes in selection intensity with increased age. Using United States life-history tables [44,45] and the ‘demogR’ package in R 2.9.1 [46,47], we plotted mortality rates to age 40 in (a). Using the same software and data, we calculated sensitivities of fitness on age-specific survival. These are divided by survival rates to find Hamilton's indicators (following Baudisch [6]) and standardized by the value at the first age to show the proportional decline in the strength of selection with age as predicted by Hamilton and applied to the human data (illustrated by the dashed curve in (b)). Using equation (2.7), we calculated the strength of selection on liability if mutation acts additively on this scale. This is also standardized by the first value and illustrated in (b) (solid line).
Figure 5.
Figure 5.
Illustration of a quantitative genetic perspective on demographic heterogeneity. Bottom and right univariate probability density functions illustrate a population's liability distributions for survival at ages 1 and 2. These distributions are drawn to represent the latent distributions before survival is determined. Only those individuals with liability z1 > 0 survive to age 2. Only those individuals with liability z1, z2 > 0 survive to age 3. The plot in the centre illustrates some arbitrary confidence contour for the bivariate distribution of age-specific liability. In this case, liability values are highly correlated and the variance along the principle component axis (thick grey line) defines the frailty variance. The minor axis (thin grey line) defines variation for a trade-off.

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