Substitution load revisited: a high proportion of deaths can be selective

Haldane’s Dilemma refers to the concern that the need for many “selective deaths” to complete a substitution (i.e. selective sweep) creates a speed limit to adaptation. However, discussion of this concern has been marked by confusion, especially with respect to the term “substitution load”. Here we distinguish different historical lines of reasoning, and identify one, focused on finite reproductive excess and the proportion of deaths that are “selective” (i.e. causally contribute to adaptive allele frequency changes), that has not yet been fully addressed. We develop this into a more general theoretical model that can apply to populations with any life history, even those for which a generation or even an individual are not well defined. The actual speed of adaptive evolution is coupled to the proportion of deaths that are selective. The degree to which reproductive excess enables a high proportion of selective deaths depends on the details of when selection takes place relative to density regulation, and there is therefore no general expression for a speed limit. As proof of principle, we estimate both reproductive excess, and the proportion of deaths that are selective, from a dataset measuring survival of 517 different genotypes of Arabidopsis thaliana grown in eight different environmental conditions. These data suggest that a much higher proportion of deaths contribute to adaptation, in all environmental conditions, than the 10% cap that was anticipated as substantially restricting adaptation during historical discussions of speed limits. LAY SUMMARY Neutral theory was predicated on theoretical arguments that adaptation is subject to a speed limit. We resolve confusions regarding historical speed limit arguments, which depend on differences in fitness, not variance (differences in fitness squared). We generalize the underlying concepts of selective deaths and reproductive excess to populations with any life cycle, even those for which an “individual” and hence generation and fitness, are poorly defined. We apply the revised theory to Arabidopsis data, demonstrating the potential for future related experiments. ### Competing Interest Statement The authors have declared no competing interest. * Absolute fitness of an adult : expected number of individual offspring surviving to adulthood (defined here for hermaphrodite species — half this value, if reproducing sexually with males). Absolute fitness of a juvenile : expected number of individual offspring (or half this value, if reproducing sexually with males). Failure to survive to adulthood (reproductive maturity) implies zero offspring. Adult : Reproductively mature individual. More than one adult life history stage may be defined. Cost of selection : The number of selective deaths that must occur over time to accomplish defined evolutionary change, e.g. to complete a single selective sweep. Generation : A set of life history transitions that ends the first time it returns, with new individuals, to the same life history stage (e.g. adult or juvenile) where it began. Individual : An organism that meets a loosely-defined set of criteria ([Wilson and Barker 2021][1]), including a shared genome, and the degree of integration of parts. Whether e.g. a group of microbes is a closely connected ecological community vs. an individual organism may be a matter of biological judgment. Juvenile : Individuals that are not yet reproductively mature. More than one juvenile life history stage may be defined, e.g. before vs. after dispersal. Lag load : The difference in fitness between a theoretical best genotype that might not be present in the population and the average genotype present. Lead : The difference in fitness between the best genotype present in the population and the average genotype present. Life history transition : Survival (i.e. persistence of an individual), reproduction (i.e. generation of new individuals) and/or organismal growth from one life history stage to the next Load : A difference in fitness between an actual genotype or population and a reference. See “lag load” and “lead” as concrete examples. Relative fitness : expected relative genetic contribution to the next generation Reproductive excess : The degree to which a hypothetical population of the optimal genotype would conclude a life history transition with a larger population than the minimum required to complete a life history cycle without the population shrinking in size. Selective deaths : The subset of deaths (or foregone fertility) that contributes to selective changes in allele frequency. This can be quantified as how many deaths each genotype experiences that would not have been experienced if that genotype were replaced by the best genotype. [1]: #ref-47