Evolution of drift robustness in small populations

Abstract

Most mutations are deleterious and cause a reduction in population fitness known as the mutational load. In small populations, weakened selection against slightly-deleterious mutations results in an additional fitness reduction. Many studies have established that populations can evolve a reduced mutational load by evolving mutational robustness, but it is uncertain whether small populations can evolve a reduced susceptibility to drift-related fitness declines. Here, using mathematical modeling and digital experimental evolution, we show that small populations do evolve a reduced vulnerability to drift, or 'drift robustness'. We find that, compared to genotypes from large populations, genotypes from small populations have a decreased likelihood of small-effect deleterious mutations, thus causing small-population genotypes to be drift-robust. We further show that drift robustness is not adaptive, but instead arises because small populations can only maintain fitness on drift-robust fitness peaks. These results have implications for genome evolution in organisms with small effective population sizes.

Fig. 1

Conceptual diagram of drift robustness. a A single-peak fitness landscape. In this landscape, the large population (red circles) can climb to the top of the fitness peak, while the small population (black circles) can only maintain fitness on an intermediate part of the peak. b A multi-peak fitness landscape. The large population evolves to the same fitness peak as in a. The small population evolves to the steeper, drift-robust peak. While this peak is still lower than the drift-fragile peak, the small population attains greater fitness than it would have on the drift-fragile peak in the single-peak fitness landscape

Fig. 2

The fitness landscapes for the Markov model to test for the evolution of drift robustness. Each circle represents one genotype and is labeled with its fitness. Each arrow represents the transition between one genotype to another (including the identical genotype) and is labeled with the transition probability. a The fitness landscape for the minimal model. s represents the selection coefficient of the drift-fragile peak and $ϵ$ represents the small fitness difference between the drift-fragile peak and the drift-robust peak. u _ij and π _ij represent the mutation rate between genotypes and probability of fixation from one genotype to another, respectively. b The fitness landscape for the extended model. Variables as in a. Transition probabilities omitted for clarity

Fig. 3

Critical population size for shift between robust and fragile peaks. a Results for various n values with κ = 0.01. b Results for various κ values with n = 2

Fig. 4

Differences in mutational effects between small-population genotypes and large-population genotypes. Black and red represent small-population and large-population genotypes, respectively. a The combined distribution of fitness effects (DFE) across all 100 small-population genotypes and 100 large-population genotypes. b Same data as in panel a, but grouped into different classes of mutations, where a small-effect deleterious mutation is defined as having an effect less than 5%. Here, and throughout, deleterious mutation refers to viable deleterious mutations, while lethal mutation refers to non-viable deleterious mutations. c The likelihood of a small-effect deleterious mutation for small-population and large-population genotypes. Red lines are medians, edges of the box are first and third quartile, whiskers are at most 1.5 times the interquartile range, and the plus signs are outliers. d The mean relative fitness of every possible point mutation (1250 mutations) for each genotype

Fig. 5

Small-population genotypes are drift-robust due to a decreased likelihood of small-effect deleterious mutations. Black and red data points represent small-population genotypes and large-population genotypes, respectively. a Relative fitness of the most-abundant genotype from every population during the drift robustness test. Each circle represents the relative fitness of one genotype from one replicate. b Relationship between relative fitness in the drift robustness test (a) and the likelihood of small-effect deleterious mutations (Fig. 4c)

Fig. 6

Fraction of small-effect deleterious mutations for genotypes from small populations and large populations with equal fitness. Each area separated by a dashed line shows genotypes with equal fitness (w). S and L represent small-population and large-population genotypes, respectively. Differences for each fitness value are significant. (Mann-Whitney U-test; Bonferroni-corrected p < 3 × 10⁻³). Box plots as described for Fig. 4c

Fig. 7

Evidence of small-population adaptation to drift-robust fitness peaks. a Distribution of maintained beneficial mutational effects for (effects for mutations whose fitness gain was at-least partially maintained during subsequent evolution) small-population genotypes (black) and large-population genotypes (red). b Spearman correlation coefficients between fitness and the likelihood of a deleterious mutation for each maintained beneficial mutation from each population c The likelihood of (viable) deleterious and lethal mutations, shown in magenta and green, respectively, in a representative small population’s lineage. The strong decrease in the likelihood of a (viable) deleterious mutation early in the population’s history is evidence of epistatic mutations resulting in drift robustness. d Number of populations that fixed a maintained beneficial mutation that decreased the likelihood of a (viable) deleterious mutation by at least a specified amount. Colors as in a

Fig. 8

The evolution of drift robustness in small populations with or without deleterious mutations in the initial adaptation experiments. Black and blue data points represent small-population genotypes adapted with deleterious mutations and small-population genotypes adapted without deleterious mutations, respectively. a Relative fitness to the ancestral genotype after 10⁵ generations of adaptation. Box plots as described for Fig. 4c. b Likelihood of small-effect deleterious mutations. c Relative fitness of the most-abundant genotype from every population during the drift robustness test. Each circle represents the relative fitness of one genotype from one replicate. d Relationship between relative fitness in the drift robustness test (b) and the likelihood of small-effect deleterious mutations (c)