Symbiont survival and host-symbiont disequilibria under differential vertical transmission

Interspecific genetic interactions in host-symbiont systems raise intriguing coevolutionary questions and may influence the effectiveness of public health and management policies. Here we present an analytical and numerical investigation of the effects of host genetic heterogeneity in the rate of vertical transmission of a symbiont. We consider the baseline case with a monomorphic symbiont and a single diallelic locus in its diploid host, where vertical transmission is the sole force. Our analysis introduces interspecific disequilibria to quantify nonrandom associations between host genotypes and alleles and symbiont presence/absence. The transient and equilibrium behavior is examined in simulations with randomly generated initial conditions and transmission parameters. Compared to the case where vertical transmission rates are uniform across host genotypes, differential transmission (i) increases average symbiont survival from 50% to almost 60%, (ii) dramatically reduces the minimum average transmission rate for symbiont survival from 0.5 to 0.008, and (iii) readily creates permanent host-symbiont disequilibria de novo, whereas uniform transmission can neither create nor maintain such associations. On average, heterozygotes are slightly more likely to carry and maintain the symbiont in the population and are more randomly associated with the symbiont. Results show that simple evolutionary forces can create substantial nonrandom associations between two species.