## DÉBARRE Florence

*CIRB UMR 7241, CNRS, Paris, France*- Evolutionary Dynamics, Evolutionary Ecology, Evolutionary Epidemiology, Evolutionary Theory
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*06 May 2019*

### When sinks become sources: adaptive colonization in asexuals

#### Fisher to the rescue

*Recommended by*

**François Blanquart**and**Florence Débarre**based on reviews by 3 anonymous reviewersThe ability of a population to adapt to a new niche is an important phenomenon in evolutionary biology. The colonisation of a new volcanic island by plant species; the colonisation of a host treated by antibiotics by a-resistant strain; the Ebola virus transmitting from bats to humans and spreading epidemically in Western Africa, are all examples of a population invading a new niche, adapting and eventually establishing in this new environment.

Adaptation to a new niche can be studied using source-sink models. In the original environment —the “source”—, the population enjoys a positive growth-rate and is self-sustaining, while in the new environment —the “sink”— the population has a negative growth rate and is able to sustain only by the continuous influx of migrants from the source. Understanding the dynamics of adaptation to the sink environment is challenging from a theoretical standpoint, because it requires modelling the demography of the sink as well as the transient dynamics of adaptation. Moreover, local selection in the sink and immigration from the source create distributions of genotypes that complicate the use of many common mathematical approaches.

In their paper, Lavigne et al. [1], develop a new deterministic model of adaptation to a harsh sink environment in an asexual species. The fitness of an individual is maximal when a number of phenotypes are tuned to an optimal value, and declines monotonously as phenotypes are further away from this optimum. This model —called Fisher’s Geometric Model— generates a GxE interaction for fitness because the phenotypic optimum in the sink environment is distinct from that in the source environment [2]. The authors circumvent mathematical difficulties by developing an original approach based on tracking the deterministic dynamics of the cumulant generating function of the fitness distribution in the sink. They derive a number of important results on the dynamics of adaptation to the sink:

From the point where immigration from the source to the sink starts, four phases of adaptation are observed. After a short transient phase (phase 1), a migration-selection balance is reached in the sink (phase 2). After a while, thanks to the immigration of rare adapted migrants and mutation in the sink, a small fraction of the sink population exhibits a close-to-optimal phenotype. This small adapted fraction grows in frequency and mean fitness rapidly increases in the sink (phase 3). Finally, the population settles around the sink optimum (phase 4) and, hurray, the sink is now a source!

Interestingly, in this model the evolutionary dynamics do not depend on the immigration rate. In other words, adaptation will proceed at the same rate regardless of how many immigrants invade the sink. This is because the impact of immigration on adaptation depends on the rate of immigration relative to the sink density. This ratio is actually independent of immigration in a model where the sink is initially empty, migration from the sink back to the source is negligible and without density-dependence in the sink.

In this model, mutation is a double-edged sword. Adapted phenotypes emerge from new mutations, and under this effect alone a higher mutation rate would translate into a shorter time to establishment in the sink. However, mutations may also have deleterious effects by displacing the phenotype away from the optimum. This mutation load will be greater when individuals need to simultaneously tune a large number of phenotypes. As a consequence of these two effects of mutations, time to establishment is minimal for an intermediate mutation rate. This result emerges from Fisher’s Geometric Model, but may hold more generally for biologically plausible fitness landscapes where mutations generates both beneficial (allowing adaptation to the sink) and deleterious genotypes.

Lastly, in Fisher’s Geometric Model, the time to establishment increases superlinearly with harshness of the sink when the sink is too harsh, and establishment may occur only after a very long time. In these harsh sinks, the adapted genotypes are very few and increase very slowly in frequency, making the second phase of adaptation much longer. Thus, and as a direct consequence of Fisher’s Geometric Model, adding a “stepping stone” intermediate environment would allow faster adaptation to the extreme environment.

In conclusion, this theoretical work presents a method based on Fisher’s Geometric Model and the use of cumulant generating functions to resolve some aspects of adaptation to a sink environment. It generates a number of theoretical predictions for the adaptive colonisation of a sink by an asexual species with some standing genetic variation. It will be a fascinating task to examine whether these predictions hold in experimental evolution systems: will we observe the four phases of the dynamics of mean fitness in the sink environment? Will the rate of adaptation indeed be independent of the immigration rate? Is there an optimal rate of mutation for adaptation to the sink? Such critical tests of the theory will greatly improve our understanding of adaptation to novel environments.

**References**

[1] Lavigne, F., Martin, G., Anciaux, Y., Papaïx, J., and Roques, L. (2019). When sinks become sources: adaptive colonization in asexuals. bioRxiv, 433235, ver. 5 peer-reviewed and recommended by PCI Evolutionary Biology. doi: 10.1101/433235

[2] Martin, G., and Lenormand, T. (2006). A general multivariate extension of Fisher's geometrical model and the distribution of mutation fitness effects across species. Evolution, 60, 893-907. doi: 10.1111/j.0014-3820.2006.tb01169.x