The Complexity of Genetic Diversity: Sex with Two Chromosomes is Advantageous but Unpredictable

Understanding the limits of predictability of biological evolution is a question of both practi-cal and theoretical interest. A key inquiry along these lines is whether genetic diversity persists or not as a result of evolutionary pressures. We explore this question in the case of diploid species, i.e., organisms with two chromosomes per gene, which includes humans and the vast majority of all living organisms. Informally, genetic diversity is shown to be sustainable (even likely) in diploid species, but hard to predict even if we restrict ourselves to species with a single gene. This reveals a stark dichotomy when compared to the case of haploid species where diversity dies out [30], hinting at a strong evolutionary advantage that could help explain the near universal adoption of diploidy in living systems. Technically, our results revolve around bounding the likelihood of the existence of stable mixed (i.e., genetically diverse) equilibria given randomly chosen system parameters as well as characterizing the complexity of the corresponding decision problem. Critically, our results are structurally robust along several dimensions (e.g., choice of parameter distribution, choice of stability concept, restriction to typical subclasses of system instances). This is a strong indica-tion that they are not an artifact of problem formulation, but instead reflect actual properties of biological systems. ar X i