A partly stage-structured model for the abundance of salmon lice in salmonid farms.

The parasitic salmon louse constrains growth in the Norwegian salmon farming industry through density dependent host-parasite interaction. Hence, there is a need for insight into how increases in salmon production, varying spatial organisation of the production and pest control strategies affect salmon louse population dynamics. Here we present a new salmon louse model for exploring effects of varying salmon farming conditions on spatio-temporal abundances of the parasite. The salmon louse model is partly stage-structured, comprising of (i) adult female lice and (ii) other mobile stages of lice. The abundance of adult females depend on survival of females from previous weeks and recruitment from the other mobile group of lice. The other mobiles also depend on survival of other mobiles from previous weeks, as well as recruitment from the previous generation of reproducing adult females from the same farm or from farms in the neighbourhood. In addition, expected abundances of the two stage-groups are modelled as functions of biological and physical covariates. The model is fitted to weekly salmon farm data covering all marine farms producing salmonids along the Norwegian cost over the years 2012-2016. Among novel results from fitting the model are estimates of the time-lag structure representing recruitment of other mobile lice from the previous generation adult females for different temperatures. Furthermore, the model estimates how various factors affect the susceptibility of fish on farms to louse infection and effects of treatments to control infection. Finally, the model estimates density dependent effects of increasing the number of fish in farms and of increasing the numbers of farms, on the rate of recruitment of other mobile lice. Analytically, the parameters representing density dependencies suggest that few farms with many fish and large between farm distances is effective in terms of minimising the overall output of salmon lice infection.