To assess the impact of sea lice from salmon farms on the
survival of wild juvenile salmon, we collected two types of data sets,
one that tracks the infection dynamics of juvenile salmon migrating
past salmon farms and another that tracks the survival of infested
juvenile salmon collected from the field and reared in ocean
enclosures. From the data sets, we used maximum-likelihood and model
selection statistics to select and parameterize mechanistic models of
sea lice transmission and juvenile salmon survival. These models were
then coupled to estimate the mortality of wild salmon caused by
farm-origin lice. Below we offer a brief overview of the methods.
Further details appear in Supporting Text.
For 2 years (2004–2005), we studied the infection dynamics of parasitic sea lice on juvenile pink and chum salmon as they
migrated past active salmon farms, each containing ≈600,000 Atlantic salmon (Salmo salar). Three migration routes containing two, two, and three farms were surveyed for 40, 60, and 80 km, respectively. At 1- to
3-km intervals, we sampled ≈100 juvenile salmon as they approached and passed the salmon farms (Figs. 1 and 4). We used a nonlethal sea lice enumeration technique (33) to count the number of copepodid, chalimus, and motile lice on each fish, thus capturing the developmental progression of
To analyze these data, we extended an established spatial model of the stage-structured dynamics of sea lice infecting juvenile
salmon migrating past salmon farms (13). The model uses advection–diffusion–decay equations to describe the dispersion of planktonic larvae. For parasitic stages,
the infection dynamics on migratory juvenile salmon are described by the delay differential equations:
which track the mean abundances of copepodid (C), chalimus (H), and motile (M) lice, respectively. Salmon migrate at an average velocity, v, and encounter local densities of infectious planktonic copepodids (L), which then attach to host fish at rate β. The proportions of surviving copepodids and chalimi are sc and sh, respectively. The λ are the cumulative distances salmon travel during successive louse developmental stages (C, H, and M).
constrained the model by imposing independently estimated parameters
for the advection, development, and mortality of planktonic larvae.
Further, pink and chum data sets shared four parameters (larval
dispersion, louse demographic rates, and ratios of farm and ambient
louse production rates) in a composite likelihood function that spanned
the data sets of both host species. We modeled the occurrence of
infection events and subsequent louse survival as a Poisson-binomial
process (ref. 13;
Fig. 9, which is published as supporting information on the PNAS web
site) and used maximum-likelihood and model selection statistics to fit
and compare models. The models consisted of only ambient-origin lice,
only farm-origin lice, and both.
We analyzed survival data of infested and uninfested juvenile salmon collected from the same populations described in Transmission Dynamics. Details of the 2004 data can be found in ref. 34.
The 2005 data were collected similarly. The time-series analysis of
mortality events consisted of a likelihood-based comparison of survival
models that described how lice change in pathogenicity as they mature.
The best-fit survival model contained two parasitic stages, a
relatively benign pathogen (young chalimus lice) and a severe pathogen
(motile stages). The two stages induce mortality in their hosts at
rates α1 and α2, respectively. The first stage is divided into a series of n identically and exponentially distributed substages, where n is an estimated constant from the gamma distribution (35).
The survival model was then coupled to the transmission dynamics model by using the chain rule to map time to space. The coupled
model tracks changes in the abundance of the two pathogenic stages of lice (P1,i and P
2) as juvenile salmon migrate to sea:
where 1/μ1 is the mean duration of the first pathogenic stage, which has variance (nμ1)−1. Having arrived at the second pathogenic stage, lice die at rate σ, which represents the sum of natural parasite mortality
and parasite-induced host mortality rates (σ = μ2 + α2), which were not separately identifiable. However, σ could be estimated directly from the transmission dynamics data as σ
= v · (λm−λh)−1. The proportion of juvenile salmon at location x surviving sea lice infestation was then determined by:
0) = 1, and x
0 is the landward extreme of the study area. The quantity p is the proportion of P
1 parasites that survive natural parasite mortality to reach the P
2 stage. There are four parameters (α1, pα2, n, μ1) that were estimated from the survival data and two parameters (βs
c · v
−1, σ) estimated from the transmission dynamics data.