Predicting patterns of long-term adaptation and extinction with population genetics

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. To make these concepts concrete, 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 8 different environmental conditions. In this dataset, 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.

Mutation bias can shape adaptation in large asexual populations experiencing clonal interference

The extended evolutionary synthesis invokes a role for development in shaping adaptive evolution, which in population genetics terms corresponds to mutation-biased adaptation. Critics have claimed that clonal interference makes mutation-biased adaptation rare. We consider the behaviour of two simultaneously adapting traits, one with larger mutation rate U, the other with larger selection coefficient s, using asexual travelling wave models. We find that adaptation is dominated by whichever trait has the faster rate of adaptation v in isolation, with the other trait subject to evolutionary stalling. Reviewing empirical claims for mutation-biased adaptation, we find that not all occur in the 'origin-fixation' regime of population genetics where v is only twice as sensitive to s as to U. In some cases, differences in U are at least ten to twelve times larger than differences in s, as needed to cause mutation-biased adaptation even in the 'multiple mutations' regime. Surprisingly, when U > s in the 'diffusive-mutation' regime, the required sensitivity ratio is also only two, despite pervasive clonal interference. Given two traits with identical v, the benefit of having higher s is surprisingly small, occurring largely when one trait is at the boundary between the origin-fixation and multiple mutations regimes.

Evolutionary Rescue Through Partly Heritable Phenotypic Variability

Environmental variation is commonplace, but unpredictable. Populations that encounter a deleterious environment can sometimes avoid extinction by rapid evolutionary adaptation. Phenotypic variability, whereby a single genotype can express multiple different phenotypes, might play an important role in rescuing such populations from extinction. This type of evolutionary bet-hedging need not confer a direct benefit to a single individual, but it may increase the chance of long-term survival of a lineage. Here, we develop a population genetic model to explore how partly heritable phenotypic variability influences the probability of evolutionary rescue and the mean duration of population persistence in changing environments. We find that the probability of population persistence depends nonmonotonically on the degree of phenotypic heritability between generations: some heritability can help avert extinction, but too much heritability removes any benefit of phenotypic variability. Partly heritable phenotypic variation is particularly advantageous when it extends the persistence time of a declining population and thereby increases the chance of rescue via beneficial mutations at linked loci. We discuss the implications of these results in the context of therapies designed to eradicate populations of pathogens or aberrant cellular lineages.

An evolutionary tipping point in a changing environment

Populations can persist in directionally changing environments by evolving. Quantitative genetic theory aims to predict critical rates of environmental change beyond which populations go extinct. Here, we point out that all current predictions effectively assume the same specific fitness function. This function causes selection on the standing genetic variance of quantitative traits to become increasingly strong as mean trait values depart from their optima. Hence, there is no bound on the rate of evolution and persistence is determined by the critical rate of environmental change at which populations cease to grow. We then show that biologically reasonable changes to the underlying fitness function can impose a qualitatively different extinction threshold. In particular, inflection points caused by weakening selection create local extrema in the strength of selection and thus in the rate of evolution. These extrema can produce evolutionary tipping points, where long-run population growth rates drop from positive to negative values without ever crossing zero. Generic early-warning signs of tipping points are found to have little power to detect imminent extinction, and require hard-to-gather data. Furthermore, we show how evolutionary tipping points produce evolutionary hysteresis, creating extinction debts.