Genetic drift in range expansions is very sensitive to density feedback in dispersal and growth

Birzu, Gabriel; Matin, Sakib; Hallatschek, Oskar; Korolev, Kirill S.

doi:10.1101/565986

Cited by 7 publications

(14 citation statements)

References 80 publications

(83 reference statements)

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“…Although pulled and pushed waves are typically distinguished based on the growth dynamics, a similar distinction can be drawn based on how the dispersal rate depends on the population density (18).…”

Section: Introductionmentioning

confidence: 99%

Cooperation mitigates diversity loss in a spatially expanding microbial population

Gandhi

Korolev

Gore

2019

Preprint

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The evolution and potentially even the survival of a spatially expanding population depends on its genetic diversity, which can decrease rapidly due to a serial founder effect. The strength of the founder effect is predicted to depend strongly on the details of the growth dynamics. Here, we probe this dependence experimentally using a single microbial species, Saccharomyces cerevisiae, expanding in multiple environments that induce varying levels of cooperativity during growth. We observe a drastic reduction in diversity during expansions when yeast grows noncooperatively on simple sugars, but almost no loss of diversity when cooperation is required to digest complex metabolites. These results are consistent with theoretical expectations. When cells grow independently from each other, the expansion proceeds as a pulled wave driven by the growth at the low-density tip of the expansion front. Such populations lose diversity rapidly because of the strong genetic drift at the expansion edge. In contrast, diversity loss is substantially reduced in pushed waves that arise due to cooperative growth. In such expansions, the lowdensity tip of the front grows much more slowly and is often reseeded from the genetically diverse population core. Additionally, in both pulled and pushed expansions, we observe a few instances of abrupt changes in allele fractions due to rare fluctuations of the expansion front and show how to distinguish such rapid genetic drift from selective sweeps. KeywordsRange expansions | Cooperative growth | Serial founder effect | Genetic drift| Allee effect 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Significance statementSpatially expanding populations lose genetic diversity rapidly because of the repeated bottlenecks formed at the front as a result of the serial founder effect.However, the rate of diversity loss depends on the specifics of the expanding population, such as its growth and dispersal dynamics. We have previously demonstrated that changing the amount of within-species cooperation leads to a qualitative transition in the nature of expansion from pulled (driven by migration at the low density tip) to pushed (driven by migration from the high density region at the front, but behind the tip). Here we demonstrate experimentally that pushed waves, which emerge in the presence of sufficiently strong cooperation, result in strongly reduced genetic drift during range expansions, thus preserving genetic diversity in the newly colonized region.

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Section: Introductionmentioning

confidence: 99%

Cooperation mitigates diversity loss in a spatially expanding microbial population

Gandhi

Korolev

Gore

2019

Preprint

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“…Noting that at early times in a mutant’s life and at small population sizes stochastic effects dominate, we have spatio-temporal dynamics for the wild-type ( b ) and mutant ( b m ): where η ( x, t ) and η m ( x, t ) are Itô white noises satisfying 〈 η ( x 1 , t 1 ) η ( x 2 , t 2 )〉 = δ ( t 1 − t 2 ) δ ( x 1 − x 2 ), and γ b ( b ) and describe the magnitude of fluctuations for the wild-type and mutant waves respectively. It can be shown that γ b ( b ) and are determined by the sum of variance of birth and non-birth events divided by their co-variance for the wild-type and mutant populations respectively 23–27 . In other words, the strength of these fluctuations varies indirectly with population size, N , thus adding stochastic genetic drift effects to the deterministic Fisher equation.…”

Section: Resultsmentioning

confidence: 99%

Range expansion shifts clonal interference patterns in evolving populations

Krishnan

Fusco

Scott

2019

Preprint

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The movement of a population through space can have profound impacts on its evolution, as observed theoretically, experimentally, and clinically. Furthermore, it has been observed that mutants emerging at the spreading front develop higher frequencies in the population than their counterparts further from the front. Here we use fundamental arguments from population genetics regarding expected time scales of beneficial mutant establishment and fixation in a population undergoing range expansion to characterize the degree of clonal interference expected in various regions while the population is migrating. By quantifying the degree of clonal interference along the wave front of a population undergoing range expansion using a measure we term the 'Clonal Interference Index', we show that evolution is increasingly mutation-limited toward the wave tip. In addition, we predict that the degree of clonal interference varies non-monotonically with respect to position along the wave front. The work presented here extends a powerful framework in population genetics to a canonical physical model of range expansion, which we hope allows for continued development of these models in both fields.It has been observed in a variety of clinical and experimental contexts that cell populations in a spatially complex 2 environment can rapidly adapt to selective pressures, including the presence of antibiotics 1-5 . Theoretical work has 3 revealed how the spatial dynamics of population movement actively modulate evolutionary dynamics. Indeed, in 4 many circumstances, movement of a population to a new environment, or range expansion, drives population allele 5 frequencies from steady state 6 . 6For example, it has been demonstrated that mutants arising closer to the front of the moving population during 7 range expansion carry a higher likelihood of fixing throughout the migrating population than in a well-mixed 8 population 7-9 . Further, range expansion can facilitate fixation of mutants that would otherwise not occur in a static 9 population 6, 10, 11 . This can be observed in a canonical reaction-diffusion model of range-expansion (Box 1), which 10 models population movement in a wave-like manner. In this model, individuals at the front of the wave proliferate 11 faster than those that do not due to access to empty space 12 . In addition, as the population continues to move, 12 the offspring of individuals at the wave front remain there and continue to exploit the empty space ahead of the 13 front. In this way, mutants arising at the wave front have enhanced proliferative capacity. Theoretical work on this 14 phenomenon, called mutation surfing, often in the context of an analogous stochastic model 13 , has shown that this 15 phenomenon occurs for deleterious, neutral, and beneficial mutations alike, underscoring the non-trivial impact of 16 range expansion on evolutionary dynamics 8, 14-16 . 17 We hypothesize that the observation that mutation surfing is less likely for a mutant arising from the wave bulk 18 than a mutant from the...

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“…From the above calculation, we conclude that equation 2has at most two different types of travelling waves. Travelling waves that connect the trivial null equilibrium with a non-trivial equilibrium of the form (6). Travelling waves connecting two equilibria of the form (6) for different values of k 0 .…”

Section: Analysis Of the Deterministic Limitmentioning

confidence: 99%

“…Travelling waves that connect the trivial null equilibrium with a non-trivial equilibrium of the form (6). Travelling waves connecting two equilibria of the form (6) for different values of k 0 . The former travelling wave corresponds to the expansion of a population in an empty available habitat.…”

Section: Analysis Of the Deterministic Limitmentioning

confidence: 99%

The spatial Muller’s ratchet: surfing of deleterious mutations during range expansion

Foutel-Rodier

Etheridge

2019

Preprint

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During a range expansion, deleterious mutations can "surf" on the colonisation front. The resultant decrease in fitness is known as expansion load. An Allee effect is known to reduce the loss of genetic diversity of expanding populations, by changing the nature of the expansion from "pulled" to "pushed". We study the impact of an Allee effect on the formation of an expansion load with a new model, in which individuals have the genetic structure of a Muller's ratchet. A key feature of Muller's ratchet is that the population fatally accumulates deleterious mutations due to the stochastic loss of the fittest individuals, an event called a click of the ratchet. We observe fast clicks of the ratchet at the colonization front owing to small population size, followed by a slow fitness recovery due to migration of fit individuals from the bulk of the population, leading to a transient expansion load. For large population size, we are able to derive quantitative features of the expansion wave, such as the wave speed and the frequency of individuals carrying a given number of mutations. Using simulations, we show that the presence of an Allee effect reduces the rate at which clicks occur at the front, and thus reduces the expansion load. Impact of an Allee effect.A population exhibits an Allee effect if its maximal per-capita growth rate is achieved at intermediate population density rather than at low population density. Allee effects arise in many biological contexts, including for example the presence of cooperation, or the difficulty in finding mates for reproduction [33,45]. In the context of range expansion, an Allee effect shifts the location of the individuals with the highest per-capita growth rate towards the bulk of the population, see Figure 2 panel (a). In the absence of an Allee effect, individuals far in the front, where the population density is the lowest, have the highest growth rate. The wave is pulled by these individuals in the front. Conversely, if the Allee effect is strong enough, individuals with the highest growth rate are located midway between the front and the bulk of the population. The wave is then pushed by the bulk of the population. The distinction between pushed and pulled waves is a well-established paradigm of the reaction-diffusion literature, see [46,48].

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Genetic drift in range expansions is very sensitive to density feedback in dispersal and growth

Cited by 7 publications

References 80 publications

Cooperation mitigates diversity loss in a spatially expanding microbial population

Cooperation mitigates diversity loss in a spatially expanding microbial population

Range expansion shifts clonal interference patterns in evolving populations

The spatial Muller’s ratchet: surfing of deleterious mutations during range expansion

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