12. Genetic Evolutionary Demography

From the early days, biodemographers benefitted from the authoritative 1990 volume Longevity, Senescence, and the Genome by Caleb Finch, joined in 2000 by a comprehensive mathematical treatment by Reinhard Buerger, The Mathematical Theory of Selection, Recombination, and Mutation. They also built on the extensive works of Brian Charlesworth, (e.g. 1994), leading up to his influential paper (2001). In 1997, under the auspices of the Committee on Population (CPOP) of the U.S. National Research Council, Between Zeus and the Salmon (Wachter and Finch, 1997) crystallized biodemography as a field.

Among demographers, the NRR is the most popular measure of population growth from generation to generation. It is also called the Generational Replacement Ratio. Properties are described e.g. in Essential Demographic Methods (Wachter, 2014, pp. 79 ff.). The NRR is preferred to the other popular measure, Lotka’s intrinsic rate of natural increase, for reasons explained by Charlesworth (2000, p. 930) and by Wachter, Evans and Steinsaltz (Wachter et al. 2013, p. 10146).

Nurture as well as procreation affects the successful formation of each next generation. The NRR can be easily modified to incorporate effects of parental survival on the survival of their offspring. With more effort, selective costs can be defined to take account of grandparental nurturing of grandchildren — individuals who can carry their grandparents’ alleles.

It may be reasonable to suppose that, over evolutionary time, homeostatic regulation responding to population density and resource availability maintained near-zero long-term population growth. In applications, the level of recruitment is often reset to be consistent with long-term zero growth.

It is essential to bear in mind that each new mutation occurs in the genome of an individual. Early humans lived in bands, but a new mutation does not occur simultaneously in the genomes of all members of a band. It occurs in an individual. On average, about half of the individual’s children and a quarter of the grandchildren carry the new mutant allele, a little more if beneficial, a little fewer if deleterious, but a small portion of the band.

Beneficial alleles differ from deleterious alleles in their age-specific demographic relevance. Beneficial mutations are much less common than deleterious ones. Striking at random, it is easier to break than to improve. Low numbers mean there is less chance for small beneficial effects to cumulate into noticeable total impacts. Those who study beneficial mutations mainly focus, not on mildly beneficial ones, but on strongly beneficial ones. Strongly beneficial alleles spread quickly toward fixation and leave their mark as what are called selective sweeps. It is true that a mildly beneficial allele at any site runs a risk of extinction before fixation, and the risk does depend on the age-specific action profile. But recurrent mutations at the site blur this dependence. Beneficial alleles now fixed in the genome may derive from mutations so far back in time as to allow for multiple tries before success at fixation. Thus, Medawar’s story connecting deleterious mutations to demographic schedules does not have a clear counterpart for beneficial mutations.

Among deleterious mutations, the model of Evans, Steinsaltz and Wachter treats those that mainly matter to the demography: those with effects that are mild, that is, not too strong and not too nearly neutral. Strongly deleterious mutant alleles head toward extinction possibly faster than recombination can thoroughly shuffle them, and possibly faster than the model predicts. Very nearly neutral mutant alleles have very small effects on demographic schedules. For them, the finite sizes over time of real populations matter. Genetic drift, not included in the model, gives extra help in removing the alleles or very occasionally lets them edge upward in frequency toward fixation.

According to the model, a randomly sampled individual carries a randomly sampled, Poisson-distributed load of alleles. The alleles are drawn randomly from each team, teams being labelled by their shared action profile. In fact, the alleles in each team are located at sites in the genome, and individuals can only carry zero, one or two copies at any site. The model envisions the count for a team being summed up over draws from many sites at which the deleterious alleles have low population frequencies. If some sites display high frequencies, differences between Binomial and Poisson sampling could introduce distortions. At each site, intrinsic randomness in family size and survival from generation to generation mean that a new mutant allele may quickly become extinct or may wander randomly upward in frequency for a while. The overall load from a team averages out over these random outcomes, site by site, and takes a smooth path through time predicted by the model.

This compensation mechanism does not adjust away any age-specific structure in the mutation rates themselves. Those rates are generally taken to be relatively unstructured, but that remains a hypothesis.

Misleading impressions about the salience of collapse arose when proofs of collapse under contrived conditions were offered in mathematical papers (e.g. Wachter et al., 2013). The proofs were offered for the purpose of dispelling any notion that the new nonlinear models were just fancy ways to obtain the same qualitative predictions as the linear models of Charlesworth that inspired them. The proofs remain of theoretical interest but should not draw attention away from realistic cases. Collapse is easily avoided, and the ease with which it is avoided is itself illuminating.

Any deleterious allele acting over the long term necessarily has some age-specific profile of action, either uniform or structured. It stands to reason that some genetic imperfections manifest themselves earlier in life than others. It is readily imagined that it may be easier for physiological adjustments to postpone rather than eliminate ill effects. Something like ages of onset may show up often in action profiles. As mentioned already, however, the kinds of effects at issue are too small to be observed directly, allele by allele.

Small imperfections are another matter. Genetic programs for basic biochemical and cellular processes, for systems of resource deployment and for systems for repair have roots far back in evolutionary time. Variants that induce slightly less efficient or resilient versions of these processes could have been affecting health and viability over many generations and still be doing so today.

The Polyphen approach supplements information on conserved sequences with knowledge about the effects of DNA mutations on amino acids and functional properties of proteins. The upshot is an alternative score with a mix of advantages and limitations.

These approaches give demographers analysing genomic data a basis for marking and counting up numbers of mildly deleterious alleles carried by each individual. Different criteria yield different indices. All indices are subject to wide margins of uncertainty, but geneticists are continually developing new and improved strategies.

Counterbalancing these limitations is a piece of technical good luck which can stand demographers in good stead. The outputs produced by the consortia carrying out studies with combined samples typically report coefficients and standard errors for constructs called polygenic scores. As long as these coefficients have been computed in their original simple form, without various complicating refinements, the reported outputs are sufficient for demographers independently to compute regressions and other analyses relating their indices of genetic load to the measured traits.

This work was supported by the Centre for the Economics and Demography of Ageing at UC Berkeley under Grant 5P30AG012839 from the National Institute on Ageing. Thanks to David Steinsaltz, Steve Evans, Iain Mathieson and Amal Harrati for many ideas presented here, and to Ronald Lee and anonymous reviewers for helpful critiques.