Genetic complementation promotes evolvability in a two-sequence, two-locus, two-allele model. We started our simulations with the simplest possible case, a two-locus, two-allele system with groups of two sequences, which yields four possible individual sequences (0–0, 1 − 0, 0–1 and 1–1) and 10 different sequence pairs. This will be later generalized to multiple loci and larger groups. To investigate how evolutionary optimization takes place in the presence of deleterious intermediates, we assigned each of the four sequences the following fitness values: f11 = 1, f00 = 0.2 and f10 = f01 = 0 (Fig. 2A). The population initially consisted exclusively of 0–0 sequences, and we explored whether the 1–1 sequence was reached by a stochastic mutation-selection process. In the absence of interactions between different sequences, this could only occur via a double mutation transforming directly 0–0 into 1–1, since each mutation alone was lethal. To introduce complementation, we formed random pairs of individuals and allowed them to mutually compensate for their genetic defects (trans-complementation; Fig. 1B-C). We first assumed that the fitness of a pair was determined by the best allele present in each gene (full trans-complementation; Fig. 2B). For instance, pairs of 0–1 and 1 − 0 sequences would rescue both, allowing each of them to reach a fitness value equal to f11. As intuitively expected, we found that this form of cooperation accelerated evolutionary optimization in this simple model (Fig. 2C-D).
Genetic parasites undermine complementation but can be avoided in highly structured populations. We then allowed for genetic parasites, which function as social cheaters. Similar to defective interfering particles in viruses, these were defined as sequences that contained large deletions and hence contributed only partially to complementation (defective), but in addition took a greater share of group-associated fitness to the detriment of helper sequences (interfering). Simulations were started from 0–0 sequences capable of complementing but, in each generation, helper sequences had a certain probability of mutating to parasites. We found that parasites took over the population, and that this had a negative impact on mean population fitness at endpoint (Fig. 3A-C). Initially, trans-complementation fostered evolvability, but this effect was lost after the emergence of parasites. To try to avoid parasite invasion, we restricted interactions to progeny derived from a common parental pair of sequences. We will refer to this type of structure as “kin groups”, as opposed to the randomly formed groups explored above. This describes the way viruses are transmitted using extracellular vesicles or occlusion bodies, as well as direct cell-to-cell viral spread using specialized structures such as viral synapses or plasmodesmata [34]. In all these types of collective spread, group members are viral particles derived from the same producer cell. Unless cells are coinfected with multiple such groups or free viral particles, the resulting virus-virus interactions are necessarily restricted to progeny derived from a common parental group. We found that this type of structure increased genetic relatedness enough to prevent parasite invasion, yet allowed trans-complementation to promote evolvability (Fig. 3D-F). Complementation was revealed by an increase in intra-group genetic diversity, which was concomitant to an increase in population fitness. This diversity peak was nevertheless transient, since intra-group diversity regained low values after this episode, leaving fewer opportunities for parasites to take over the population.
Partial trans-complementation can also promote evolvability. In the above simulations, we assumed that genetic defects were fully compensated in trans. Here, we assumed a different situation (average trans-complementation), in which the fitness assigned to a given group (here, a pair) was equal to the average fitness of all allele combinations in the group. For instance, in interactions involving 0–1 and 1 − 0 sequences, the resulting fitness was equal to the average of fitness values for 0–1, 1 − 0, 0–0, and 1–1 sequences whereas, in the full trans-complementation model, the resulting fitness was determined solely by the fittest possible combination 1–1. We found that evolvability was substantially reduced compared to the full trans-complementation case, but that partial complementation still had a positive effect on evolvability (Figure Supplementary S1 online).
Cis-complementation can also foster evolvability. Next, we explored a different type of interaction that could be relevant in the context of conformational epistasis. This form of epistasis takes place when one or more sites in the sequence of a protein affect the stability of other sites [13]. Since this concerns variants of a given locus, effects in trans are excluded. Thus, the main difference between this situation and the previous complementation model is that, here, the fitness of the group was a function of the individual performance of each existing sequence, rather than being determined by all combinations of alleles present in different sequences. As above, we allowed for genetic parasites but assumed that populations were structured in kin groups. We first considered a situation in which the fitness value associated with a group was equal to the fitness of the best sequence present in the group (full cis-complementation), and found that under these conditions, evolvability was promoted (Fig. 4).
We then considered a different model in which the fitness value assigned to a group was equal to the average of the fitness values of each group member (average cis-complementation). Similar to what we found with trans-complementation, the positive effects on evolvability were reduced, but still observed (Supplementary Figure S2 online).
Effects of genetic complementation in a multi-locus epistatic model. To generalize our analysis, we used random NK models [31] to create arbitrary fitness landscapes from N genes and K gene-gene interactions. We also considered groups of m > 2 individuals, using the same complementation rules as above. In these simulations, genetic parasites were also allowed but populations were structured in kin groups. We changed K (which determines the ruggedness of the fitness landscape) keeping gene number constant (N = 5). As expected, increasing K generally hampered evolutionary optimization. With minimal epistasis (K = 1), full trans-complementation was slightly detrimental for evolvability (Fig. 5A-B). In contrast, in landscapes with abundant epistasis (K = 4), full trans-complementation strongly favored evolvability despite the presence of parasites (Fig. 5C-D). This effect became more pronounced as group size increased, since mutual compensation of genetic defects was more likely in larger groups. However, this positive effect on evolvability was reversed when trans-complementation was only partial (average trans-complementation; Supplementary Figure S3 online).
We also applied the NK model to the cis-complementation case. As above, we allowed for parasites but restricted interactions to progeny derived from the same parental group. We found that evolvability was also fostered by this type of complementation, but that this effect strongly depended on whether group-associated fitness was determined by the fittest sequence (full cis-complementation; Figure S4 online) or by the average fitness value of all group members (average cis-complementation; Supplementary Figure S5 online). Since these results are qualitatively similar to those obtained with the trans-complementation model, we conclude that the main benefit of sequence interactions did not lie in the ability to explore novel allele combinations. Instead, we suggest that complementation fostered evolvability by allowing low-fitness sequences to be maintained in the population, thereby promoting the ability of the population to traverse rugged fitness landscapes.
Trans-complementation fosters exploration of rugged fitness landscapes. To better understand how complementation promoted evolvability, we inspected evolutionary trajectories in the rugged fitness landscape (N = 5, K = 4). As above, in these simulations we allowed for parasites, but populations were structured in kin groups. We plotted mean population fitness among the 150-generation simulation as a function of the Hamming distance to the highest-fitness sequence (global optimum), starting each simulation from a different position in the landscape. In the absence of interactions (m = 1), populations were systematically trapped in local sub-optimal peaks (Fig. 6). In contrast, when full trans-complementation was allowed, populations reached maximal fitness. This positive effect was accentuated as group size, m, increased. However, the Hamming distance to the optimum was not always zero, since adaptation was achievable by a set of sequences that mutually compensated for their genetic defects. This indicates that trans-complementation allowed exploration of complex fitness landscapes by buffering the deleterious effects of mutations. Hence, the downside of this enhanced evolvability was a higher abundance of conditionally deleterious mutations at equilibrium. Systematic analysis of all possible single mutations at endpoint confirmed that, in populations displaying trans-complementation, mutations had much lower fitness effects than in populations of non-interacting sequences, as expected in a relaxed selection scenario.