Survival of the weakest?

Evolution doesn’t unfold in a stable, predictable world—genes compete, environments fluctuate, and sometimes a few individuals produce most of the next generation. These combined forces can dramatically influence whether a weak allele survives or disappears. Maite Wilke Berenguer analysed two-type Wright–Fisher models that include both selection in a random environment and skewed offspring distributions. They developed a practical criterion to compare how different forms of selection shape the fate of the weaker allele. Their key tool is a duality between allele frequency dynamics and genealogy, which they show holds in both quenched and, in some cases, annealed random environments, and for finite as well as large populations. This dual framework provides new insights into branching–coalescing processes in random settings and clarifies their long-term evolutionary behaviour. Find out more in the Annals of Applied Probability Article!

Abstract

We analyse a family of two-types Wright–Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allele, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the population’s allele frequencies and genealogy, both in the case of finite population size and in the scaling limit for large size. Duality also yields new insight on properties of branching-coalescing processes in random environment, such as their long-term behaviour.