Connected networks of sea lice populations: dynamics and implications for control

Abstract

In studies of the population dynamics of parasitic sea lice and the implications of outbreaksfor salmon farms, several types of mathematical models have been implemented. Delaydifferential equation models describe the temporal dynamics of average adult lice densities overmany farm sites. In contrast, larval transport models consider the relative densities of lice at farmsites by modelling larval movements between them but do not account for temporal dynamics orfeedbacks created by reproduction. Finally, several recent studies have investigated spatiotemporalvariation in site lice abundances using statistical models and distance-based proxies for connectivity.We developed a model which integrates connectivity estimates from larval transportmodels into the delay differential equation framework. This allows representation of sea licedevelopmental stages, dispersal between sites, and the impact of management actions. Even withidentical external infection rates, lice abundances differ dramatically between farms over a productioncycle (dependent on oceanographic conditions and resulting between-farm connectivity).Once infected, lice dynamics are dominated by site reproduction and subsequent dispersal. Licecontrol decreases actual lice abundances and also reduces variation in abundance between sites(within each simulation) and between simulation runs. Control at sites with the highest magnitudeof incoming connections, computed directly from connectivity modelling, had the greatest impacton lice abundances across all sites. Connectivity metrics may therefore be a reasonable approximationof the effectiveness of management practices at particular sites. However, the model alsoprovides new opportunities for investigation and prediction of lice abundances in interconnectedsystems with spatially varying infection and management.