Substitution load (cost of selection)
Haldane observed in 1957 that for a beneficial allele to sweep, individuals with alternative alleles must die (or forgo fertility), and that this imposes a speed limit to adaptation. We are working to clarify a complex set of concepts around this idea of "selective deaths" (see panel A in figure below), including the need to account for finite reproductive excess (panel C) (Matheson et al. 2023). Standard relative fitness models of population genetics, e.g. the Wright-Fisher model, implicitly assume infinite reproductive excess, but we have developed models that explicitly treat its finite nature (Bertram & Masel 2019). The "lag load" is the difference between population mean fitness and some theoretical optimal fitness that is never obtained; inappropriate use of the lag load is one contributor to confusion (panel B). The more appropriate load is the difference between the population mean fitness and the highest fitness individual actually found in a population - this quantity was rediscovered and named the "lead" (Desai & Fisher 2007).
In the title of a 1995 paper, Alexey Kondrashov posed the puzzle "Why have we not died 100 times over?". We still don't have an answer. It should take one selective death to purge one new deleterious mutation, but the mean number of new deleterious mutations per human seems to be more than 2, exceeding the number of selective deaths available. Most work on mutation load periodically renormalizes relative fitness to deal with the fact that fitness keeps declining no matter what, or else treats only a subset of the genome. Either way, this is dodging the problem, not tackling its fundamentals, which are not specific to human mutation rates or to small population sizes. One historical solution to the mutation load paradox was synergistic epistasis, often modeled in extreme forms such as truncation selection. Since then, data has come out showing that the mean effects of two deleterious mutations are extraordinarily close to multiplicative. We are exploring models by which very weak epistasis (compatible with data) might be sufficient and/or a "ratchet" occurs in which many small-effect deleterious fixations are counterbalanced by a much smaller number of large-effect beneficial fixations.
Matheson JD, Bertram J, Masel J. Population deterioration from a realistically high genome-wide deleterious mutation rate can be countered by rare beneficial mutations of asymmetric effect, manuscript in preparation.
Matheson JD, Masel J. (2023) Background selection from unlinked sites causes non-independent evolution of deleterious mutations, BioRxiv
Matheson JD, Exposito-Alonso M, Masel J (2023). The cost of selection in selective deaths paid out of reproductive excess, BioRxiv.
Bertram J., & Masel J. (2019) Density-dependent selection and the limits of relative fitness, Theoretical Population Biology 129:81–92.