Modelling survival and allele complementation in the evolution of genomes with polymorphic loci

We have simulated the evolution of sexually reproducing populations composed of individuals represented by diploid genomes. A series of eight bits formed an allele occupying one of 128 loci of one haploid genome (chromosome). The environment required a specific activity of each locus, this being the sum of the activities of both alleles located at the corresponding loci on two chromosomes. This activity is represented by the number of bits set to zero. In a constant environment the best fitted individuals were homozygous with alleles’ activities corresponding to half of the environment requirement for a locus (in diploid genome two alleles at corresponding loci produced a proper activity). Changing the environment under a relatively low recombination rate promotes generation of more polymorphic alleles. In the heterozygous loci, alleles of different activities complement each other fulfilling the environment requirements. Nevertheless, the genetic pool of populations evolves in the direction of a very restricted number of complementing haplotypes and a fast changing environment kills the population. If simulations start with all loci heterozygous, they stay heterozygous for a long time.

💡 Research Summary

The paper presents a computational study of how diploid sexual populations evolve under constraints imposed by a changing environment. Each individual carries two haploid chromosomes, each composed of 128 loci. At each locus an allele is encoded by an eight‑bit string; the number of zero bits in the string defines the allele’s “activity”. The phenotype for a locus is the sum of the activities of the two alleles occupying that locus on the two chromosomes, and the environment specifies a target activity value for each locus. Fitness is measured by how closely the summed activity matches the environmental requirement.

The simulation proceeds through generations using a standard Wright–Fisher scheme: individuals are selected proportionally to fitness, then undergo recombination (crossover) and mutation to produce the next generation. Two key parameters are varied: the recombination rate (the probability that a crossover occurs between the two parental chromosomes) and the rate of environmental change (either gradual or abrupt shifts in the target activity values).

In a static environment the optimal genotype is homozygous at every locus, with each allele contributing exactly half of the required activity. This configuration yields the highest fitness because the two identical alleles together meet the environmental demand without excess or deficit. When the recombination rate is low and the environment changes slowly, the model favours heterozygous loci. In these cases the two alleles have different activity levels that complement each other, so their sum still satisfies the environmental target. This “complementation” mechanism maintains polymorphic alleles in the population and allows gradual adaptation without needing new mutations.

However, the simulations also reveal a strong tendency toward a limited set of complementary haplotypes. Even when many polymorphic alleles are initially present, selection and limited recombination drive the population toward a small number of highly fit haplotype combinations that repeatedly pair to give the required summed activities. If the environment changes too quickly, the existing complementary pairs cannot be re‑assembled in time; the mismatch between summed activities and the new targets causes a rapid drop in average fitness and leads to population extinction.

An additional experiment starts the population with every locus already heterozygous. Under low recombination and modest environmental drift, the heterozygous state persists for many generations, demonstrating that the initial genetic configuration can lock the system into a complementary regime for a long period.

The authors discuss the biological relevance of these findings. Complementary heterozygosity is analogous to phenomena such as overdominance or balancing selection observed in natural populations, where different alleles at a locus jointly confer an advantage (e.g., pathogen resistance genes). The model suggests that low recombination—common in self‑fertilizing plants, asexual microbes, or regions of low crossover in eukaryotic chromosomes—can preserve such complementary polymorphisms, while high recombination would break them apart.

In conclusion, the study provides a clear mechanistic link between recombination rate, environmental dynamics, and the maintenance of genetic polymorphism through allele complementation. It shows that a modest amount of heterozygosity can be a robust adaptive strategy in slowly changing environments, but that rapid environmental shifts pose a severe extinction risk. The work lays a foundation for future extensions that could incorporate multiple environmental factors, epistatic interactions, or empirical genomic data to test the model’s predictions in real biological systems.