Evolutionary Rescue Play

Evolutionary rescue through partly heritable phenotypic variability

Preprint: https://www.biorxiv.org/content/early/2017/09/28/092718

Abstract: Environmental variation is commonplace, but unpredictable. Populations that encounter a deleterious environment can sometimes avoid extinction by rapid evolutionary adaptation. Phenotypic plasticity, 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 non-monotonically on the degree of phenotypic heritability between generations: some heritability can help avert extinction, but too much heritability removes any benefit of phenotypic plasticity. We discuss the implications of these results in the context of therapies designed to eradicate populations of pathogens or aberrant cellular lineages.

We use a continuous-time Moran-type model to describe changes in allele numbers in a finite population of changing size N, with carrying capacity K. Each individual's genotype is defined by a single biallelic locus A/a, which controls its phenotype. The A allele encodes a fixed phenotypic value, whereas individuals with the a allele may express a wider range of phenotypes, drawn from a fixed distribution.

Play: population extinction of a genetically monomorphic population

What happens to a population fixed for the wild-type allele A? Default parameters are chosen such that, after an abrupt environmental change, the population fixed on A is bound to go extinct (i.e. death rates exceed birth rates). This would lead to a demographic decline, such as the ones experienced by bacterial populations at the start of drug treatment.

Click anywhere on the population to start or stop the simulation. Use the form to change the carrying capacity or the birth rate of A. It's important to stop the simulation (by clicking on it) before changing parameters (I still have to fix a bug :( ).

Play: evolutionary rescue with phenotypic plasticity

What happens if, when the antibiotic is introduced, the population has access to phenotypic plasticity?

In the paper, we ask what is the probability of evolutionary rescue if, at time t=0, a new mutant phenotypically-plastic allele appears in the population? The phenotype of this one initial mutant is assumed to be sampled randomly from the phenotypic distribution available to a. This phenotypic distribution is chosen such that both alleles A and a have the same expected fitness, so that the only difference between them is the possibility of (partly heritable) phenotypic variability. We analyze the probability of rescue as a function of the phenotypic variance and the phenotypic memory associated with the a allele.

Here, for speed and convenience, we start with equal numbers of the two alleles. The size of the circles is proportional to the birth rate / fitness of the allele (observe the differences in size for the green allele individuals).

Click anywhere on the population to start or stop the simulation.

The chance of evolutionary rescue crucially depends on the strength of phenotypic memory.

When the plastic allele is introduced with a beneficial phenotype, the probability of rescue monotonically increases with the phenotypic memory available to the plastic allele. This result makes intuitive sense: high-fitness variants of the plastic allele are preferentially transmitted to the next generation, and greater phenotypic memory increases their propensity to maintain the high-fitness phenotype and become established in the population.

When the plastic allele is introduced with a deleterious phenotype, whose birth rate is smaller than its death rate, there is still the possibility of evolutionary rescue, because the phenotype of type-a individuals may change between generations. In this case, the probability of evolutionary rescue depends non-monotonically on the strength of phenotypic memory. There is simple intuition for this result as well, and it is informed by our mathematical analysis. Intuitively, the probability of rescue is contingent on a plastic individual producing an offspring with the beneficial phenotype, before the a-lineage is lost.

Play with the phenotypic memory parameter below. Observe how, for large phenotypic memory (let's say 0.9) the population is more likely to persist and not go extinct compared to when phenotypic memory is small (let's say 0.1).

Population persistence in periodically changing environments

Phenotypic variability and phenotypic memory also influence population persistence in periodically changing environments, in addition to the case of a single environmental change that has been the subject of most work on evolutionary rescue. With a periodically changing environment, the question of persistence is conveniently framed in terms of the mean time before population extinction. Even in this more complicated setting we once again observe a non-monotonic effect of phenotypic memory on population persistence: populations go extinct quickly for either small or large memory, whereas intermediate amounts of phenotypic memory can promote persistence for long periods of time. More in the paper... :)

Simulations adapted from cool visualization work by Dirk Brockmann: http://rocs.hu-berlin.de/interactive/index.html .