Sea lice as a density dependent constraint to salmonid farming. Electronic supplementary material

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1 Sea lice as a density dependent constraint to salmonid farming Electronic supplementary material Peder A. Jansen a,1,*, Anja B. Kristoffersen a,d,*, Hildegunn Viljugrein a,e, Daniel Jimenez a, Magne Aldrin b, f and Audun Stien c a Norwegian Veterinary Institute, PO Box 750 Sentrum, N-0106 Oslo, Norway; b Norwegian Computing Center, PO Box 114 Blindern, N-0314 Oslo, Norway; c Norwegian Institute for Nature Research, Fram High North Research Centre for Climate and the Environment, NO Tromsø, Norway; d Department of Informatics, University of Oslo, PO Box 1080, Blindern N-0316 Oslo, Norway; e Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biology, University of Oslo, PO Box 1066 Blindern, N-0316 Oslo, Norway; f Department of Mathematics, University of Oslo, PO Box Corresponding author: Peder.jansen@vetinst.no Contents ESM Introduction 2 ESM Methods 2 ESM Discussion 14 ESM References

2 ESM Introduction Sea lice infections of salmonids in Norwegian coastal waters are dominated by the salmon louse (Lepeophtheirus salmonis), but may also be by the generalist copepod Caligus elongatus [1, 2]. The salmon louse is a marine ectoparasitic copepod of salmonids that feeds on host surface tissues. The ectoparasite has 10 morphologically distinct stages [3]. The three youngest stages are non-feeding and planktonic, of which the third stage, the copepodid, is the infective stage. The copepodid attaches to the salmonid host and develops into the first of four feeding chalimi stages which are fixed to a position on the host by a frontal filament. The fourth chalimus stage subsequently develops into two preadult stages and finally adult reproductive males and females, all of which are mobile and may move about on the host. Adult female lice produce 2 egg strings which remain attached to the female as they develop and finally hatch as planktonic larvae. Female fecundity and development times of all stages depend on water temperature [4]. The generation time for L. salmonis and C. elongatus at a temperature of 10 C, i.e. from egg extrusion in the female to mature adults have developed, is approximately 40 and 50 days for males and females, respectively [5]. Due to multiple species of parasitic lice on farmed salmonids, infections are termed sea lice in the following. In this Electronic supplementary information (ESM) we present data and methodology in more detail. We also critically discuss underlying assumptions for our data analyses. ESM Methods Data and data processing Operators of Norwegian salmonid farms need a license to operate a specific farm site. All licences are featured with an identity code and geo-references in the aquaculture licence register of the Directorate for Fisheries [6]. All marine farms holding salmonids are also required to report key production statistics to responsible authorities on a monthly basis. This includes data on fish stocks, water temperatures and data regarding sea lice infections and counter measurements to infections [7]. These data are featured in a database hosted by the Norwegian Food Safety Authority (NFSA), and which was downloaded for this study in May The following is a step by step description of the present processing of data from the NFSA database. 2

3 Salmonid stock data. The present study includes monthly data from the NFSA database covering 1442 marine salmonid farms, i.e. farms holding Atlantic salmon (Salmo salar) or rainbow trout (Oncorhynchus mykiss) in coastal marine waters. The data extends over 108 months from January 2002 to December Data on the total number of fish and the mean weight of the fish on farms were processed further. These data are represented in the NFSA database either as 0 (no fish on the farm), numbers to represent mean fish size and numbers of fish on given farms, or there was no report of data (denoted by NA). NA indicates either a missing report or no fish on the farm [8]. To identify presumably missing data, and to impute values for these data, the following processing procedures were followed: (I) Short gaps in the data corresponding to 1 2 NA enclosed by positive reports were identified. There were totally 330 gaps of 1 NA and 79 gaps of 2 consecutive NA in the data. Gaps always included both the total number of fish and mean fish weight. (II) The identified short gaps in the data were imputed by 0 (no fish on the farm) when numbers before and after the gap were considered to represent different cohorts of fish. The criteria for imputing zero were: i) when fish weight was > 250g before and < 250g after the gap; ii) when fish weight was > 3500g before and < 1000g after the gap; iii) when the number of fish increased by more than 20% from before and after the gap. Imputations of 0 for NA were conducted for a total of 69 records. (III) All other gaps of 1 2 NA were imputed by the mean of the number of fish, and by the mean fish weight, of the enclosing non-zero values. Imputations of non-zero values for NA were conducted for a total of 340 records for each of the two variables. After imputation of fish stock data, the dataset covered records of fish stock numbers and mean weights, of which 409 records (0.6%) were imputed. The reason for imputing data was that short gaps of missing data would imply that disproportionately much of the data would have to be discarded since time dependencies and time lags were included in the statistical analyses (see below). Sea lice data. Sea lice infection in fish farms is subject to detailed regulations (7, 9), which are enforced by the NFSA. The regulations specify maximum thresholds to sea lice abundance on farms and a compulsory reporting system for sea lice counts. With regard to 3

4 infection thresholds, sea lice are separated into adult females or other mobile stages (comprising of preadults and adult males). Maximum threshold abundances are set to 0.5 adult females or 3 mobiles per fish in the period January 1 st August 31 st, and 1 adult female or 5 mobiles per fish in the period September 1 st December 31 st. When threshold infections are exceeded, it is mandatory for the salmonid farmers either to reduce sea lice abundance by applying medical treatment or to slaughter their fish. For the salmonid farmers to be able to comply with the regulations, and for the NFSA to enforce them, the maximum threshold infections are accompanied by regulations on compulsory counting of sea lice and reporting of such counts. Counting and reporting procedures were changed in August 2009 and details of these procedures before and after changes are tabulated in table S1. Table S1. Procedures, as instructed by the authorities, for counting and reporting sea lice infections on farmed salmonids in Norway. Procedures were changed as of August Counting and reporting Period procedures Before August 2009 From August 2009 Count frequency at > 10 C Bi-weekly Weekly different ranges of 4-10 C Bi-weekly Bi-weekly temperature < 4 C Not required Not required Sample size pen (fish per pen) No. pens % of farm pens 2 Reporting The net-pen sample with the highest mean abundance of adult female lice 3 The farm sample, i.e. the mean of mean net-pen samples, with the highest mean abundance of adult female lice 3 1 One net-pen is to be sampled every time as a reference 2 All net-pens are to be counted for every two rounds of sampling 3 Adult female lice are the main rule, but when the abundance of mobile sea lice is above legal thresholds, then such a sample should be reported 4

5 Data on mean counts of adult female and mobile sea lice were processed as a sum of the two categories for the present analyses (i.e. adult females + adult males + pre adult mobile stages). According to regulations, every fish stock record should have been accompanied by reported sea lice counts, but some counts of lice were missing. Of fish stock records, 1925 (3%) sea lice reports were missing (NA). Missing sea lice reports were imputed as follows: (I) As the mean of sea lice reports enclosing gaps of NA sea lice reports (637 imputations). (II) Equal to the sea lice report from the previous month, when the NA was found in the last month before the stock of fish was removed from the farm (452 imputations). (III) Zero was imputed for NA whenever all sea lice reports in previous months from the given stock of fish were 0 (836 imputations). After missing sea lice counts were imputed, each monthly record of a fish stock was accompanied by a sea lice count. The dataset with imputed sea lice counts was used in all figures both in the main paper and in the ESM. For the statistical analyses using count reports of sea lice as the dependent variable, however, the imputed records were discarded from the data (table S2). Nevertheless, imputed data were used in the time lagged explanatory variables using sea lice counts (see below). Figure S1 shows the monthly number of farms holding salmonids and the total standing stock of farmed salmonids in the data. 5

6 700 Farm holdings (#) e+5 Biomass (tonnes) 6e+5 5e+5 4e+5 3e Year Figure S1. Monthly numbers of farms holding salmonids (upper panel), and the total biomass of the stocks of farmed salmonids (lower panel), from January 2002 December Table S2. Summary statistics describing variables entered in the regression analyses. LBD refers to local biomass density of farmed salmonids. The North-region, Mid-region and South-region are tabulated separately (continuous variables are entered as mean (5 th percentile, 95 th percentile)). Total dataset South-region Mid-region North-region No. salmonid farms No. salmonid stocks No. observations Sea lice count (20 fish; t -1) 20.5 (0, 94) 24.8 (0, 110) 22.7 (0, 96) 9.2 (0, 44) Temperature (ºC, t) 9.1 (4.0, 15.7) 10.0 (4.5, 16.8) 8.9 (4.4, 14.6) 7.5 (3.0, 12.8) Mean fish weight (kg, t) Medical treatments (t -1) 2.0 (0.13, 4.9) 0: : (0.14, 4.6) 0: : (0.13, 5.2) 0: : (0.13, 4.9) 0: : 1145 LBD (t-1) 1.4 (0.2, 3.4) 1.8 (0.32, 3.8) 1.5 (0.4, 3.1) 0.64 (0.05, 1.5) Atlantic salmon 0: 4475 Cleaner fish (t -1) 1: : : : : : : : 748 1: : : : 521 1: : : 48 6

7 Regression analyses of farm level data, dependent variable The main goal of the present study was to identify factors that contribute to explain the reported sea lice counts from salmonid farms. The count reports of sea lice represent means of counts of lice on 20 fish (before August 2009) or means of multiple net-pen means of lice on 10 fish (table S1). Hence, to construct a dependent variable of an integer count to be used in the statistical analyses, all sea lice reports were multiplied by 20 and rounded off to the nearest integer (table S2). The resultant integer counts then represent an estimate of the number of sea lice on 20 fish on given farms in given months. The estimated sea lice numbers (excluding imputed counts) were used as the dependent variable in the regression analyses. Sea lice counts from before and after counting procedures were changed in August 2009 were processed similarly. Disregarding these changes was justified by the fact that separate analyses of the data from before and after changes were implemented did not qualitatively alter results (table S4). Simulations of the counting and reporting procedures do, however, suggest that the early procedures (before August 2009) gave expectations of higher sea lice reports than the late procedures, when sampling lice from the same farm population of fish (Anders Løland, Norwegian Computing Center, personal comment). This implies that the apparent increases in peak infections in 2009 and 2010 may be slightly under-estimated. However, note that this increase in peak infections was not observed in the North-region. Predictor variables Count reports of sea lice in previous months. Sea lice development times and longevity depend on temperatures. Mobile stages may survive for many months, depending on water temperatures [4]. It was therefore expected that counts of sea lice on given farms in given months correlate with counts in previous months. Exploring these time series correlations in sea lice counts in the regression models (see below) gave significant effects of sea lice counts extending over time lags of 4 months. Regional differences. To account for possible regional differences in the population dynamics of sea lice in a north to south gradient, the dataset was subdivided into three geographic regions (figure 2 in the main paper); i) the North-region (all farms north of 67 degrees latitude), the Mid-region (farms between latitudes 67 degrees - 62 degrees 35 min), and the South-region (all farms south of 62 degrees 35 min latitude). 7

8 Medical treatment. Medical treatments against sea lice are mandatory to report as the number of treatments applied on a given farm and month [9], but without specifying type of treatment. During the years 2002 to 2008, in feed treatment by Emamectin benzoate and bath treatments by pyrethroids accounted for 100 % of treatments against sea lice in Norway [10]. Here we constructed a dichotomous variable of medical treatments where non-zero integers in the NFSA database were given value 1 (medical treatment applied on the given farm in the given month). This amounted to 8333 records of medical treatment for the study period (table S2). All other records were given the value 0 (no treatment), 840 records of which were NA according to the fish stock data. Water temperature. Water temperatures are to be reported from a depth of 3 meters. Compared to the fish stock data, 402 reports of water temperatures were missing. Furthermore, 318 records of water temperatures were of the value 0 C and 40 records of the value 1 C, both of which are suspiciously low temperatures. These missing and suspicious water temperatures were imputed by: (I) Inverse distance weighted average water temperature of farms within a seaway distance of 40 km. This accounted for 617 imputations. (II) For farms with no neighbouring farms according to (I), the mean of water temperatures reported from the given farm and month in previous years was imputed. This accounted for 143 imputations. Monthly water temperatures for the South-, Mid-, and North- regions are shown in figure S3. Water temperatures were log (temperature + 0.6) transformed based on pre analyses using gam.nb and splines, compared to log transformed and linear variants of the variable. Also the final model was tested with linear and log transformed temperature. Log transformed temperature models gave lowest AIC values. 8

9 20 Water temperature ( C) Year Figure S3. Mean monthly water temperature for the North-region farms (blue line), Midregion farms (red line) and South-region farms (yellow line) covering January 2002 December Mean fish weight. Mean fish weight was log transformed for the regression analyses assuming a non-linear effect of fish weight on sea lice population dynamics. Local biomass density (LBD). LBD estimation is described in the main paper. Cleaner fish. A counter measurement to sea lice infections involves the use of cleaner fish to prey on the lice. The cleaner fish that are used are wild caught fish of the family Labridae. The use of cleaner fish on salmonid farms is mandatory to report as a dichotomous variable (usage vs. non-usage). Compared to the fish stock data, 388 reports on cleaner fish were missing. For missing reports on cleaner fish, the value from the previous non-missing report for the given stock of fish was imputed. When no previous report existed, the value 0 (no cleaner fish) was imputed. In total, 9984 records indicated usage of cleaner fish in the study period (table S2). 9

10 The use of cleaner fish was significantly associated with high sea lice counts in the farm level regression models. We do not anticipate high sea lice counts to be promoted by the use of cleaner fish. The use of cleaner fish was excluded from further farm level regression analyses since inclusion did not contribute to insight into forces influencing sea lice abundance. Freshwater exposure. Data on salinity in coastal waters are fragmentary. Hence, we estimated a proxy for salinity expressing relative exposure to freshwater for given farm sites. Freshwater run off through river catchments that drain into the sea along the coast were obtained from the data base Regine, which is supported by the Norwegian Water Resources and Energy Directorate ( First a raster dataset (5 x 5 km grid) expressing outflow volumes of freshwater to coastal waters was generated using the ArcView extension Spatial Analyst (ESRI). This raster dataset was then extrapolated into the coastal area using the function focal statistics in Spatial Analyst accounting for a height and width of 15 grid cells. Values in the final raster dataset were extracted for each salmonid farm site. The resultant freshwater exposure value for each farm gradually decreased as the distance to the sources of freshwater outflow increased. Eventually, these data were only used to identify the 50% of farms with the least exposure to freshwater for a ZINB regression analysis of a subset of the data. Finally, variables designed to account for additional seasonal trends and time trends are described in the main paper, and shown graphically in figure S5. Table S2 summarises statistics for variables entered in the regression analyses. 10

11 South region Mid region North region Sea lice counts 6 Low LBD Medium LBD High LBD Medical treatment reports Local biomass density Year Figure S4. Monthly mean counts of mobile stages of sea lice (upper panel), proportion of farms reporting medical treatments against sea lice (mid panel) and mean local biomass of farmed salmonids (lower panel) for the South-region, Mid-region and North-region. For each month the curves are plotted separately for farms located in areas with low (< 33.3 percentile), median ( percentile) and high (> 66.6 percentile) local biomass of farmed salmonids. Choice of regression model. Given the high level of over dispersion in the sea lice data (variance-to-mean ratio = 114.6), negative binomial variance models were more appropriate than Poisson models. Furthermore, zero inflated negative binomial distribution (ZINB) models gave better fits to the data than negative binomial models, as shown by comparably lower AIC values. Including farm specific time lags in sea lice counts in the ZINB model gave the lowest AIC value (table S3). The ZINB model yields explanatory covariates for two 11

12 distinct processes: i) a count process which includes the possibility of a zero count and ii) a binary process generating either a positive or a zero count. Figure S5. Seasonal trends (left panel) and time trends (right panel) for the negative binomial count model (upper panel) and the logistic model for excess of zero counts (lower panel). The seasonal trends were comprised of 4 sine and 4 cosine functions with periodicities of 12, 6, 4 and 3 months, respectively. The time trends were comprised of 5 b-splines (see methods in the main paper). 12

13 Table S3. The number of parameters and the AIC statistics for different statistical models explaining reported sea lice counts. Number of AIC AIC parameters NB full model ZINB full model ZINB without region ZINB only 3 sea lice lag ZINB only 2 sea lice lag ZINB only 1 sea lice lag ZINB without sea lice lag ZINB without temperature ZINB without weight ZINB without medical treatment ZINB without a seasonal trend ZINB without a time trend ZINB without LBD ZINB without Atlantic salmon ZINB with linear temperature ZINB with linear weight Zero-inflated negative binomial (ZINB) model. For the zero-inflated negative binomial distribution the probability of observing a sea lice count of y is, p p ( Y = 0) ( Y = y) = = k p + (1 p) µ + k Γ (1 p) Γ ( y + k) y k µ k ( k) y! ( µ + k) k y, k + k = 1, 2,... (1) 13

14 Here p is the probability of observing a zero count originating from the Bernoulli process and [k/(μ + k)] k is the probability of observing a zero count from the NB. Similar to μ being linearly related to covariates via the logarithmic link function, log(µ ) = a + b j X j (2) j the logit function (ln[p/(1 - p)]) was used to linearise the relationship between p and potential covariates [11]. logit ( p) = a + b j X j (3) j The relationship given in equation (3) was used to define the Bernoulli component of the mixture model. These models were fitted to the data using maximum likelihood as implemented in the zeroinfl function in the pscl package (v.1.02) in R (for further information on fitting zero-inflated mixture models see [11]). Fitted models were compared using AIC (table S3).. ESM Discussion Sea lice abundance as a proxy for infection rate Since our data are not infection rates, but rather a measure of sea lice abundance, we use the sea lice counts as a proxy for sea lice infection rates. Sea lice abundance is determined by opposing forces of infection rates and mortality, where the temporal and spatial variability in mortality is mainly determined by antiparasite interventions. In the present analyses of aggregated data, a constant average abundance of infection may appear if the treatment frequency is tuned to compensate for variability in infection rates. Overcompensation in the treatment frequency may cause a negative relationship between infection rates and abundance of infection, while a constant or less than compensatory response in the treatment frequency will cause infection rates and abundances of infection to show positive covariation (figure S6). We therefore reason that if the density of hosts in surrounding waters is a main determinant of local infection rates, high densities of hosts should result in high sea lice abundances and/or on average greater treatment efforts to control sea lice infections. At the individual fish farm level, chemotherapeutic treatments are expected to cause high sea lice mortality rates over a short time period after treatment and result in reduced abundances of infection. The 14

15 subsequent rate of increase in the sea lice abundance at a farm will, however, be determined by the infection rate. In our analysis of the time series of individual farm data we therefore expected a positive effect of the density of fish in surrounding waters on sea lice abundance, when the autoregressive within farm sea lice abundance, and effects of chemotherapeutic treatment events and other factors known to influence sea lice mortality and infection rates were controlled for. Infection rate Figure S6. Potential patterns in the relationship between the annual average infection rate, abundance of infection (red lines) and treatment frequency (blue lines). The figure visualises the case where treatment frequency compensates for increases in infection rate leading to an approximately constant average abundance (dotted lines), the case with overcompensation in treatment frequency causing a decline in abundance of infection with increasing infection rates (dashed lines), and the case where variability in the treatment frequency does not compensate for variability in the infection rate leading to a positive relationship between annual abundance of infection and the average infection rate (full line). The schematic figure is based on simulations of the model A t = (Λ+A t-1 exp(-μ))(1-ηi t ), where A t is the abundance of infection at time t, Λ is the infection rate, μ is the natural sea lice mortality rate and η is the efficiency of the antiparasite treatment, and I t is a 0/1 indicator variable. Each simulation was run with a fixed infection rate Λ, and the number of treatments being a linear function of Λ (sum(i)=a+bλ). The plotted lines gives the across simulations pattern in the relationship between Λ, the treatment frequency and the average abundance of infection over the latter half of the simulation runs. 15

16 Data quality The present data cover large numbers of sea lice count reports and stock statistics of farmed salmonids extending over many years and a wide spatial distribution. This yields possibilities for powerful analyses of the governing factors for sea lice abundance on farmed salmonids, given adequate quality of the data. A weakness with regard to the quality of the present data is that sea lice counting and reporting mostly are done by farm staff, so skill and practises in all procedures leading up to the reported counts may vary between farms [12]. There is also a relatively complex set of rules regarding sampling, counting and reporting procedures which have changed over time. The fact, for example, that for every month the mean number of lice from the sample with the highest mean should be reported, implies that the data are biased with regard to estimating true population sizes of sea lice. Hence, the presented estimates of sea lice densities should only be regarded as relative densities. Nevertheless, we have no reason to believe that anything but random noise is introduced in the data by varying skill and practises between farms in counting and reporting procedures [12]. Hence, we consider the consistent effects in the present data of host density and water temperatures on the population dynamics of sea lice to be robust results. There were also gaps of missing data and imputations of data were conducted. However, the proportion of imputed data was low and imputed data on sea lice counts were excluded from the dependent variable. We argue therefore that the imputations are unlikely to have biased results. One possible source of bias in the sea lice counts is related to the legal abundance thresholds, above which treatment or slaughtering of the fish stock is mandatory. The sea lice counting and reporting regulations are enacted to enable the authorities to control the salmonid farming industry with regard to abundance thresholds. This implies that farms may have to report sea lice counts that demand costly control measurements. If this introduces bias to the data, then it would apply to the high counts. We would argue that this potentially reinforces the main conclusion of our analysis since it would reduce counts more in the most affected areas with high local densities of farmed salmonids. 16

17 Possible confounders and pseudo replication of data The present ZINB regression analyses on determinants of sea lice counts include a large number of potentially interplaying variables, many of which may affect sea lice counts in opposing directions. Moreover, the dataset has a nested structure of subsequent salmonid cohorts on given farm sites, which were not accounted for in the full ZINB regression model. The present large dataset, however, allows for analyses of subsets of data to check for the consistency of main effects across possible confounders. Table S4 reports from analyses of different subsets of the data where only one random cohort per farm site was included in 10 model estimations; all records where cleaner fish were used were excluded; 50% of the farm locations estimated to be most strongly exposed to freshwater were excluded; or data only up to August 2009 were included. In all of these analyses we have a consistent positive effect of LBD on the abundance of sea lice infection and, we would argue, that other parameter estimations are not substantially affected. Hence, it is not likely that confounding between predictor variables would alter the main conclusions from our analysis. 17

18 Table S4. Parameter estimates for the ZINB model for subsets of data. The column representing one random cohort per farm tabulates the maximum range of confidence intervals (estimated parameter ± 2 SE) based on 10 runs of the model. Subsets of data excluding the use of cleaner fish (No cleaner fish); extending only to August 2009; or excluding 50% of farms based on high influence of freshwater (Salinity), are tabulated with standard errors in brackets. Negative Binomial Cohort No cleaner fish Time Salinity (25619, 26982) (n = 47107) (n = 47159) (n = 26979) Intercept [0.73, 2.02] 1.40 (0.11) 1.55 (0.10) 1.64 (0.14) North-region [-0.24, ] (0.02) (0.02) (0.03) South-region [-0.022, 0.13] (0.017) (0.02) 0.13 (0.02) Sea lice count (t -1) [0.0075, ] (0.0002) (0.0002) (0.0003) Sea lice count (t -2) [0.0018, ] (0.0002) (0.0002) (0.0002) Sea lice count (t -3) [0.0004, ] (0.0002) (0.0002) (0.0002) Sea lice count (t -4) [ , ] (0.0002) (0.0002) (0.0002) log(temp (ºC) + 0.6; t) [0.39, 0.95] 0.62 (0.04) 0.52 (0.04) 0.55 (0.05) log(fish weight (kg); t) [0.20, 0.27] 0.24 (0.01) 0.23 (0.01) 0.21 (0.01) Med. treat. (bin; t -1) [-0.27, -0.09] (0.02) (0.02) (0.02) LBD (t -1) [0.092, 0.16] 0.13 (0.01) 0.14 (0.01) 0.10 (0.01) Atlantic salmon [0.02, 0.29] 0.19 (0.03) 0.21 (0.03) 0.17 (0.05) log(theta) [-0.43, -0.31] (0.01) (0.01) (0.01) Zero Inflation model intercept [1.77, 3.98] 3.04 (0.24) 2.88 (0.23) 3.22 (0.33) North-region [0.62, 1.09] 0.73 (0.05) 0.69 (0.05) 0.59 (0.07) South-region [0.39, 0.83] 0.56 (0.04) 0.49 (0.04) 0.19 (0.06) Sea lice (bin; t -1) [-2.72, -2.30] (0.05) (0.04) (0.06) Sea lice (bin; t -2) [-0.93, -0.47] (0.05) (0.05) (0.06) Sea lice (bin; t -3) [-0.63, -0.18] (0.05) (0.05) (0.06) Sea lice (bin; t -4) [-0.52, -0.14] (0.04) (0.04) (0.06) log(temp (ºC) + 0.6; t) [-1.32, -0.49] (0.10) (0.09) (0.13) log(fish weight (kg); t) [-0.19, ] (0.01) (0.01) (0.02) Med. treat. (bin; t -1) [0.094, 0.55] 0.27 (0.07) 0.35 (0.06) 0.37 (0.07) LBD (t -1) [-0.36, -0.17] (0.02) (0.02) (0.03) Atlantic salmon [-0.90, -0.17] (0.05) (0.05) (0.10) 18

19 Table S5. Intercept and regression coefficient with standard error (SE) for the linear regression y = y 0 + ax in figure 3 in the main paper, where y represents sea lice abundance (Ab), mean monthly proportion of farms reporting the use of medical treatment (MT) or cleaner fish (CF). Statistics are tabulated for the whole of Norway (tot) and the three geographic regions separately. y Intercept SE Regression coefficient SE Ab tot Ab North Ab Mid Ab South MT tot e -5 MT North MT Mid e -5 MT South e -5 CF tot CF North e e -5 CF Mid CF South

20 ESM references 1. Bristow, G. A. & Berland, B A report on some metazoan parasites of wild marine salmon (Salmo salar L) from the west-coast of Norway with comments on their interactions with farmed salmon. Aquaculture 98, (doi: / (91)90395-n) 2. Bjørn, P. A. & Finstad, B Salmon lice, Lepeophtheirus salmonis (Krøyer), infestation in sympatric populations of Arctic char, Salvelinus alpinus (L.), and sea trout, Salmo trutta (L.), in areas near and distant from salmon farms. ICES J. Mar. Sci. 59, (doi: /jmsc ) 3. Schram, T. A Supplementary descriptions of the developmental stages of Lepeophtheirus salmonis (Krøyer, 1837) (Copepoda: Caligidae). In Pathogens of Wild and Farmed Fish: Sea Lice (eds. G. A. Boxshall & D. Defaye), pp New York, NY: Ellis Horwood. 4. Stien, A., Bjørn, P. A., Heuch, P. A. & Elston, D. A Population dynamics of salmon lice Lepeophtheirus salmonis on Atlantic salmon and sea trout. Mar. Ecol. Prog. Ser. 290, (doi: /meps290263) 5. Costello, M. J Ecology of sea lice parasitic on farmed and wild fish. Trends Parasitol. 22, (doi: /j.pt ) 6. Directorate of Fisheries Havbruksregisteret (In Norwegian). See 7. Ministry of Fisheries and Coastal Affairs Luseforskriften (In Norwegian). See html&emne=luseforskrift*&. 20

21 8. Kristoffersen, A. B., Viljugrein, H., Kongtorp, R. T., Brun, E. & Jansen, P. A Risk factors for pancreas disease (PD) outbreaks in farmed Atlantic salmon and rainbow trout in Norway during Prev. Vet. Med. 90, (doi: /j.prevetmed ) 9. Norwegian Food Safety Authority Luseforskriften. Forskriftsveileder for akvakulturnæringen (In Norwegian). See orskriften_for_fiskeoppdrettere_ Norwegian Institute of Public Health Økt bruk av midler mot lakselus i norsk fiskeoppdrett i fjor (In Norwegian). See 5,2675:1:0:0:::0:0&MainLeft_5565=5774:0:15,2675:1:0:0:::0:0&Area_5774=5544: 88347::1:5776:1:::0: R Development Core Team 2009 R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. 12. Heuch, P. A., Gettinby, G., Revie, C. W. Counting sea lice on Atlantic salmon farms -- Empirical and theoretical observations. Aquaculture 320, (doi: /j.aquaculture ) 21