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Evolutionary demographic models reveal the strength of purifying selection on susceptibility alleles to late-onset diseases


Assessing the role played by purifying selection on a susceptibility allele to late-onset disease (SALOD) is crucial to understanding the puzzling allelic spectrum of a disease, because most alleles are recent and rare. This fact is surprising because it suggests that alleles are under purifying selection while those that are involved in post-menopause mortality are often considered neutral in the genetic literature. The aim of this article is to use an evolutionary demography model to assess the magnitude of selection on SALODs while accounting for epidemiological and sociocultural factors. We develop an age-structured population model allowing for the calculation of SALOD selection coefficients (1) for a large and realistic parameter space for disease onset, (2) in a two-sex model in which men can reproduce in old age and (3) for situations in which child survival depends on maternal, paternal and grandmaternal care. The results show that SALODs are under purifying selection for most known age-at-onset distributions of late-onset genetic diseases. Estimates regarding various genes involved in susceptibility to cancer or Huntington’s disease demonstrate that negative selection largely overcomes the effects of drift in most human populations. This is also probably true for neurodegenerative or polycystic kidney diseases, although sociocultural factors modulate the effect of selection in these cases. We conclude that neutrality is probably the exception among alleles that have a deleterious effect in old age and that accounting for sociocultural factors is required to understand the full extent of the force of selection shaping senescence in humans.

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Fig. 1: Factors that might explain the persistence of purifying selection on SALODs.
Fig. 2: Estimated coefficient of selection (s).

Data availability

No new data were generated for this study.

Code availability

The code in R language that supports the findings of this study is available on GitHub’s ‘SPavard/Code-for-SALOD’ repository with the identifier


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This study is supported by a grant from the Agence Nationale de la Recherche (no. ANR-18-CE02-0011, MathKinD).

Author information




S.P. designed the study and wrote the manuscript. S.P. and C.F.D.C. developed the model together.

Corresponding author

Correspondence to Samuel Pavard.

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Extended data

Extended Data Fig. 1

Selection coefficients for a large parameter space of onset. ac, Cumulative incidence of disease onset with age according to change in Mean Age at disease Onset (MAO) and First Age at disease Onset (FAO, with FAO from age 20 to MAO − 5 yrs). If disease onset is confounded with morbidity or full incapacitation, cumulative risk is 1-Ld(x), where Ld(x) is the disease-specific survival at age x. Dashed red lines indicate the median age at disease onset. Age at onset distribution if fitted with a two parameters logistic function (see Supplementary Information 2.2). FAO is defined as the age at which 1% of SALOD carrier have develop the disease (1-Ld(x) = 0.01 and setting 1-Ld(x < FAO) = 0). d, Coefficient of selection s as a function of MAO and FAO. Levels of grey indicate relation of selection to drift. Above s = 2.5e-02 (darker grey) selection is expected in all human populations (all of them having Ne > 100). Below s = 2.5e-04, alleles are neutral in most human populations (for which Ne < 10,000). In between selection levels of selection will vary of ‘small’ (dark grey) or large ‘Ne’ (light grey). Allele is rare, autosomal, dominant, disease in both sexes and penetrance is complete.

Extended Data Fig. 2

Selection coefficients with respect to disease cumulative risk. Selection coefficients as a function of Mean Age at disease Onset (MAO), First Age at Onset (FAO) being 20 years earlier, in the case of an autosomal allele leading to disease’s cumulative risk at age 100 [a measure of the genotype penetrance] of 100% (circles), 50% (triangles), 10% (squares) and 1% (stars). In this case, FAO is defined as the age at which of the cumulative distribution respectively reaches 1, 0.5, 0.1 and 0.01; the risk of disease onset being zero before this age. Horizontal lines indicate the level of selection for which alleles become neutral (4.Ne.s < 1) for populations of Ne equal to 102, 103 and 104, that is, the minimum Ne for which effect of selection overcome that of genetic drift, holding that 104 is the Ne estimated at our species level. Mortality is that of a mean hunter-gatherer population and fertility that of Fig. 1b. Selection coefficient is a linear function of penetrance (estimated here by the cumulative risk at age 100). This makes a genotype penetrance a fundamental parameter for estimating magnitudes of selection, even for SALOD leading to a MAO after age 45 (by contrast with a model without variance in disease onset and cultural factors where alleles are neutral after age 45 years, even if penetrance is 100%). Roughly, an allele with MAO at 40 but 1% of penetrance is selected against as an allele of MAO at 70 but penetrance at 100%.

Extended Data Fig. 3

Selection coefficients for sex-specific diseases and genetic compartments. Selection coefficients as a function of Mean Age at Onset (MAO), First Age at Onset (FAO) being 20 years earlier, when maternal, grandmaternal and paternal care are incorporated, as well as both females and males reproduction; in the case of: (circles) a dominant autosomal allele (equation [7]); (pluses) a recessive autosomal allele (the probability for the mother of a female homozygous carrier of being herself homozygous is considered as negligible and the female’s mother is considered as non-carrier in equation [7]); (diamonds) an autosomal allele leading to disease in females only (WC of male carriers is equated to WNC in equation [7]); (triangles) an autosomal allele leading to disease in males only (WC of female carriers equated to WNC in equation [7]); (stars) an allele carried by the mitochondrial chromosome (canceling the male element of equation [7]); and (crosses) an allele carried by the Y-Chrom (canceling the female element of equation [7]). Horizontal lines indicate the level of selection for which alleles become neutral (4.Ne.s < 1) for populations of Ne equal to 102, 103 and 104, that is, the minimum Ne for which effect of selection overcome that of genetic drift, holding that 104 is the Ne estimated at our species level. Mortality is that of a mean hunter-gatherer population and fertility that of Fig. 1b. When variance in disease onset and all socio-cultural factors are accounted for, there are no large difference in magnitude of selection on these alleles for population of medium or large Ne: they all cross the Nemin = 1000 line for 75 < MAO < 85. A differential of selection may however be expected for population of small Ne (between 100 and 1000) between alleles in the Y-Chromosome or leading to disease in males only (more prone to purification when there is large differences in reproductive schedules between men and women) and alleles in the Mt-Chromosome or leading to disease in females only (less prone to purification). This is because coefficient of selection s is less impacted by (grand)maternal care than by male reproduction. No large difference is expected between recessive alleles, autosomal dominant alleles, or allele leading to disease in male only, which all exhibit intermediary level of selection. A decrease in cumulative risk of disease onset at age 100 (here equaled to 100%) would proportionally scale down all these selection coefficients (see Extended Data 2).

Extended Data Fig. 4

Selection coefficients for various demographic regimen. Right panel - Selection coefficients as a function of Mean Age at disease Onset (MAO), First Age at Onset (FAO) being 20 years earlier, in the case of different adult survival shown in the left panel: average Hunter-gatherer (squares) from 39, estimates of females of Sweden 1751 (crosses), 1800 (diamonds), 1850 (triangles) and 1900 (stars) from 40. Horizontal lines indicate the level of selection for which alleles become neutral (4.Ne.s < 1) for populations of Ne equal to 102, 103 and 104, that is, the minimum Ne for which effect of selection overcome that of genetic drift, holding that 104 is the Ne estimated at our species level. Mortality is that of a mean hunter-gatherer population and fertility that of Fig. 1b. Large increase of adult survival has little effect on the decrease in magnitudes of selection coefficients with MAO. This is because selection is always proportional on population mean and increased mortality of carriers compared to that of non-carriers within a population is not that dependent on the age-specific survival in a model where carriers may develop the disease over a large range of ages.

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Pavard, S., Coste, C.F.D. Evolutionary demographic models reveal the strength of purifying selection on susceptibility alleles to late-onset diseases. Nat Ecol Evol 5, 392–400 (2021).

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