Fitness-valley crossing with generalized parent-offspring transmission

Simple and ubiquitous gene interactions create rugged fitness landscapes composed of coadapted gene complexes separated by "valleys" of low fitness. Crossing such fitness valleys allows a population to escape suboptimal local fitness peaks to become better adapted. This is the premise of Sewall Wright's shifting balance process. Here we generalize the theory of fitness-valley crossing in the two-locus, biallelic case by allowing bias in parent-offspring transmission. This generalization extends the existing mathematical framework to genetic systems with segregation distortion and uniparental inheritance. Our results are also flexible enough to provide insight into shifts between alternate stable states in cultural systems with "transmission valleys". Using a semi-deterministic analysis and a stochastic diffusion approximation, we focus on the limiting step in valley crossing: the first appearance of the genotype on the new fitness peak whose lineage will eventually fix. We then apply our results to specific cases of segregation distortion, uniparental inheritance, and cultural transmission. Segregation distortion favouring mutant alleles facilitates crossing most when recombination and mutation are rare, i.e., scenarios where crossing is otherwise unlikely. Interactions with more mutable genes (e.g., uniparental inherited cytoplasmic elements) substantially reduce crossing times. Despite component traits being passed on poorly in the previous cultural background, small advantages in the transmission of a new combination of cultural traits can greatly facilitate a cultural transition. While peak shifts are unlikely under many of the common assumptions of population genetic theory, relaxing some of these assumptions can promote fitness-valley crossing.