Superspreaders increase deleterious mutant burden and can accelerate the evolution of complex traits in pathogens

Degree heterogeneity in contact networks is known to accelerate the spread of infectious diseases through the presence of superspreaders, but its evolutionary consequences remain less understood. Here we study how network heterogeneity shapes the fate of competing pathogen strains in a stochastic susceptible-infected-susceptible framework. We show that heterogeneous networks act as strong suppressors of selection: both advantageous and disadvantageous mutants exhibit fixation probabilities close to neutral expectations, in stark contrast to well-mixed populations. We derive an analytical theory that captures this effect through a single suppression factor determined by network structure and infection dynamics, and validate it against simulations on synthetic and empirical contact networks. Mechanistically, suppression arises because most transmission events are effectively neutral, while selection acts only in rare configurations. As a consequence, heterogeneous networks substantially increase the persistence of deleterious mutants and elevate mutation-selection balance, but they can either accelerate or decelerate multi-step evolutionary processes such as fitness valley crossing. Our results reveal a fundamental trade-off induced by superspreaders: while they enhance epidemic spread, they weaken selective pressures and thereby promote evolutionary diversification.