Weakest link epistasis and the geometry of genetic load

Because natural selection must optimise multiple traits at once, previous work has suggested that phenotypic dimensionality can substantially worsen the equilibrium fitness defect of a population relative to the phenotypic optimum. However, it remains unclear how conclusions drawn from classical theoretical phenotype-fitness maps extend to models grounded in explicit biological mechanisms. Here we introduce weakest-link epistasis (WLE), a framework in which fitness is determined by the least-fit phenotypic component, an extreme form of diminishing returns epistasis. We show that in this framework, increasing dimensionality amplifies the load in a manner comparable to, but surprisingly not more than, Fisher's geometric model (FGM). Building on this similarity, we demonstrate why genetic load is often invariant across different rules for combining trait-specific fitness components into an overall organismal fitness. We explore these ideas by considering the family of models where the organismal fitness is determined based on the ${\ell }^p$ -norm of the vector of trait-specific fitness defects, a framework that includes both FGM and WLE, but also captures a continuum of genetic architectures, ranging from generalist to specialist regimes. Altogether, our approach proposes a new perspective on the geometry of adaptive landscapes, and may help provide quantitative insight into the cost of complexity.