Table 1.

Types of models and their application to the salmon sea louse pathosystem. Key references are included.

model form	characteristics	applications and examples
difference equations	—discrete-time dynamics —spatially homogeneous —deterministic —can include delays	population growth models, e.g. Ricker stock–recruitment relationship [14]; often used within other models —effects of lea louse infection and predation on salmon productivity [15]
ordinary differential equations	—continuous-time dynamics —spatially homogeneous —deterministic —can include delays	host–parasite models for louse-salmon dynamics, e.g. Anderson–May model [16] and extensions thereof to incorporate predation —effects of treatments on sea louse populations on farms [17] —parasite-mediated changes to predation [18]
partial differential equations	—continuous-time dynamics —spatially heterogeneous —deterministic	advection-diffusion models —sea louse dispersal from salmon farms along wild salmon migration routes [19]
matrix models (Leslie matrix, population projection matrix)	—linear system of difference equations —can include stochastic effects	age-structured population growth models —analysis of temperature-dependent sea louse demography [20]
regression models	—statistical —descriptive/correlational —can include spatial effects	GLM, GLMM, random effects, logistic regression —identifying epidemiological factors effecting sea lice abundance on salmon farms [21] —associations between aquaculture and sea louse infections on sea trout [22]
survival functions and hazard functions	—statistical —descriptive/correlational	survival analysis —impacts of sea lice on salmon survival in the NE Atlantic [3] —effects of salinity on sea louse survival on juvenile salmon [23]
stochastic processes	—discrete-time or continuous-time dynamics —stochastic —can include additional hierarchy	stochastic population growth models, e.g. stochastic Ricker model —hierarchical models of Pacific salmon productivity in relation to sea lice [24–26]
individual-based (or agent-based) model	—computer model —simulates actions and interactions of individuals within a system —can be deterministic or stochastic	predicting benefits of cleaner fish in control of sea louse populations [27]
numerical ocean-circulation model	—numerically solved complex dynamical system; includes hydrodynamic equations, three-dimensional transport and diffusion equations) —realistic model for oceanic motion	model for current, temperature and salinity patterns in marine environment —finite volume coastal ocean model (FVCOM) simulation of the spread of sea lice from salmon farms in British Columbia, Canada [28] —SINMOD simulation of sea louse and salmonid pancreatic disease virus in Norwegian fjords [29]