Population structure can reduce clonal interference when sexual reproduction and dispersal are synchronized

In populations with limited recombination, clonal interference among beneficial mutations limits the maximum rate of adaptation. Spatial structure slows the spread of beneficial alleles; in purely asexual populations, this increases the amount of clonal interference. Beyond this extreme case, however, it is unclear how spatial structure and recombination interact to determine the amount of clonal interference. This interaction is particularly interesting because dispersal and recombination are often at least partially synchronized in natural populations, both at the individual and population level, as when plants switch from vegetative growth to sexual reproduction or stress responses increase both motility and recombination in microbes. We simulate island models of populations evolving on a smooth fitness landscape and find that synchronized dispersal and sexual reproduction allow them to adapt faster than matched well-mixed populations. This is because the spatial structure preserves genetic diversity, while the synchronization increases the chance that recombination events occur between diverged individuals from different demes, i.e., the pairings where negative linkage disequilibrium can most effectively be reduced.


INTRODUCTION
On smooth fitness landscapes, adaptation is driven by the fixation of beneficial mutations. When beneficial 21 mutations are rare, they can fix independently from each other in sequential selective sweeps. But if the 22 beneficial mutation supply is large, multiple beneficial mutations will be simultaneously polymorphic in 23 the population, and may compete with each other for fixation. This "clonal interference" effectively puts 24 an upper limit on the rate of adaptation, particularly when recombination is limited [Muller, 1932, Gerrish  . Schematic illustration of how population structure and synchronization can combine to accelerate adaptation. Darker red represents higher fitness, i.e., more mutations. (A) In a well-mixed population, mutations can rapidly spread to the whole population but drive all other diversity extinct in the process, with few opportunities for recombination between competing genotypes. (B) In a structured population, sweeps are slower but this preserves other beneficial mutations, which then can be brought together by synchronized dispersal and sexual reproduction, leading to faster long-term adaptation. interrupted by occasional generations of sexual reproduction and/or mixing among demes. 118 We use a form of Wright-Fisher reproduction, in which the entire population is replaced every 119 generation. To produce an individual in deme d in generation t + 1, we first determine whether it is a 120 resident (with probability 1 − m(t)) or a migrant (with probability m(t)). We then determine if it is the 121 offspring of uniparental or biparental reproduction. In the absence of individual-level synchronization,  The key outcome variable is the rate of adaptation v, defined as the rate of increase of mean log fitness.

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This is proportional to the probability of fixation of beneficial mutations, P fix : v = NDUP fix ln(1 + s) ≈ 133 NDUP fix s. In the absence of clonal interference, P fix = 2s independent of the spatial structure [Maruyama, adaptation is equal to the (genetic) variance in fitness. In our simulations, the standard deviation of log 139 fitness is always ≤ 0.15, which means that the variance in fitness is close to the variance in log fitness 140 (see Text S1). In linkage equilibrium, this is simply s 2 ∑ i p i (1 − p i ), proportional to the heterozygosity.

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The extent to which v/s 2 lags behind the heterozygosity therefore provides a measure of total multilocus 142 negative linkage disequilibrium. To track the dynamics of the nose of the fitness distribution, we follow 143 the frequency of "best genotypes", which we define as those within s of the maximum current log fitness  generations, the first and last data points are the beginning of two consecutive bursty cycles, i.e., t gap + 1 158 generations are shown.

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Population structure can very slightly speed adaptation even without synchronization 161 In asexual populations, clonal interference is stronger in spatially structured populations than it is in  reproduction is even larger (Fig. S2A). Thus, spatial structure reduces clonal interference in this instance.

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The population with synchronized sexual reproduction and dispersal achieves its higher adaptation 194 speed via bursts of adaptation every t gap generations. These bursts move both the nose and the mean of the 195 fitness distribution. But the nose (Fig. 3B) shifts in genotype space by far more than the distribution moves 196 toward the optimal genotype (Fig. 3C). This indicates that the leading genotype is replaced by a distantly  population-level synchronization so that either only migrants or only residents can reproduce sexually. 214 We do not increase the rate of sexual reproduction among the group where it is allowed, so this lowers the 215 overall rate of sexual reproduction-drastically so when sexual reproduction is limited to migrants, who 216 are typically a minority of the population. For example, at the value t gap = 100 where synchronization 217 provides the greatest benefit, 25% of individuals are migrants in the high-dispersal generations. But we 218 see that limiting sexual reproduction to these migrants hardly slows down adaptation, while limiting 219 it to the 75% of individuals who are residents reduces the rate of adaptation by more than a factor of 220 two (Fig. 4B). We therefore see that sexual reproduction among migrants is essential to the advantage 221 of synchronization, suggesting that the limited benefits of individual-level synchronization are simply 222 because population-level synchronization already creates a strong association between the two processes. so that fit recombinants can quickly be redistributed across demes in the next dispersal event. This is 247 because the demes vary in fitness (Fig. 5C), so dispersal will tend to move very fit recombinants into 248 less-fit demes, where they will compete with each other less. For these very long offsets, the absolute 249 adaptation speed (5.23 ± 0.11 × 10 −3 for offset = 99) is similar to that for populations with synchronized 250 dispersal but unsynchronized sexual reproduction (5.68 ± 0.15 × 10 −3 , Fig. S2C) or no synchronization 251 (5.19 ± 0.12 × 10 −3 , Fig. S2B).

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In this paper, we demonstrate that population structure, by creating the possibility for synchronized Adaptation speed as a function of the delay between high-dispersal generations and high-sexual reproduction generations. Dispersal occurs at times 0 and 100 on the horizontal axis, so an offsets of 0 or 100 are identical. Increasing the delay before sexual reproduction lowers the rate of adaptation, as the increased within-deme genetic diversity introduced by dispersal is lost. Surprisingly, there is a slight uptick in the rate of adaptation for very long delays such that dispersal follows shortly after sexual reproduction. (B) Increase in the fitness of the fittest individual in a deme over the t gap = 100 generations between dispersal events, for different values of the delay before sexual reproduction. This local maximum fitness jumps in the sexual reproduction generation, but by less as the delay increases and the genetic diversity introduced by dispersal decays. It appears to reach a steady state at ≈ 80 generations, partially explaining the uptick in panel A. (C) Standard deviation of local maximum fitness across demes shows the same qualitative pattern as overall adaptation speed (A), initially decreasing as the delay increases and then rebounding for very long delays. Facultatively sexual reproduction is often a response to stressful conditions [Otto, 2009]. To the extent 291 that these stressful conditions affect multiple individuals, this provides one mechanism for synchronization.

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As dispersal is also often a response to stress (e.g., is static. Presumably the primary reason that sexual reproduction and dispersal can be triggered by stress 296 is that it is a signal that the organism is poorly adapted to its present habitat, and that it should try to 297 improve the match by producing offspring with different haplotypes or moving to a new environment. In 298 other words, the response most likely evolved as a way to track the fluctuating components of the fitness 299 landscape. Our work shows that a side effect can be more rapid adaptation to the fixed components of the 300 landscape as well.