Developing models for investigating the environmental ...and further increase is forecasted (FAO 2012). Salmonid species account for over a tenth of the pro-duction by value (FAO 2008),

AQUACULTURE ENVIRONMENT INTERACTIONSAquacult Environ Interact

Vol. 4: 91–115, 2013doi: 10.3354/aei00077

Published online July 18

INTRODUCTION

Globally, aquaculture production has increased ata rate of 6.9% yr−1 to current levels of 63.6 × 106 t,and further increase is forecasted (FAO 2012).Salmonid species account for over a tenth of the pro-duction by value (FAO 2008), and within Scotland,Atlantic salmon Salmo salar dominates the produc-tion with over 158 000 t produced in 2011 (Walker etal. 2012). Total salmon production in Scotland hasexperienced a 5-fold expansion since the early

1990s, whilst over the last decade, the number oflicensed sites has decreased, indicating that thetotal output per site is increasing. Currently, over80% of Scotland’s At lantic salmon production occurson farms licensed to stock over 1000 t. This trend forlarger farm size is likely to continue as new produc-tion methods are continually being developed,enabling farms in Scotland to meet requirements forconsents granted by the Scottish Environmental Pro-tection Agency (SEPA) to stock up to 2500 t. Produc-tion methods also exist in Norway which make it

© The Crown 2013. Open Access under Creative Commons byAttribution Licence. Use, distribution and reproduction are un -restricted. Authors and original publication must be credited.

Publisher: Inter-Research · www.int-res.com

*Email: [email protected]**Both authors contributed equally to this manuscript

REVIEW

Developing models for investigating the environmental transmission of disease-causingagents within open-cage salmon aquaculture

N. K. G. Salama*,**, B. Rabe**

Marine Scotland Science, Marine Laboratory, Torry, Aberdeen, AB11 9DB, UK

ABSTRACT: Global aquaculture production continues to increase across a variety of sectors,including Atlantic salmon production in Scotland. One limitation to the expansion of open-cageaquaculture is disease-induced stock losses as well as the potential for disease agents from farmsinteracting with other farms and possibly with wild salmonids. Epidemiological studies of disease-agent transmission often omit environmental transmission of organisms, although this process isan integral part of parasite spread and incidence. Within the aquatic environment, water move-ments enable pathogens and parasites to potentially be transmitted over long distances. As patho-gens and parasites are transported, their status can change; they can degrade or, in the case of sealice, develop into an infectious stage. A combination of biological and physical models is requiredto understand the transmission of disease-causing organisms. Here we propose a set of compo-nents that have been implemented in a range of modelling studies of sea lice dispersal, anddescribe how such attributes have been used in developing a study in one of Scotland’s largestfjordic systems. By developing descriptive simulation model frameworks, which are validatedusing physical and biological observations, alternative methods of integrated pest managementcan be investigated and developed. The identification of dispersal routes of sea lice and establish-ment of potential farm−farm connections can inform sea lice management.

KEY WORDS: Disease transmission · Environment · Modelling · Multi-disciplinary · Dispersion ·Sea lice

OPENPEN ACCESSCCESS

Aquacult Environ Interact 4: 91–115, 2013

possible for farms to stock more fish (Fiskeridirek-toratet 2011). Within Scotland, there is an aspirationfor a sustainable 50% increase in finfish aquaculturebetween 2009 and 2020 (Baxter et al. 2011). A dom-inating factor in restricting the increase of stockingon individual farms is their environmental impact,largely governed by dispersal conditions of the sur-rounding environment and the degradation ofchemicals and waste associated with fish farming(SEPA 2011). This could be resolved by relocatingproduction into areas where environmental impactis reduced due to the characteristics of the location(e.g. locations with greater flushing rates). However,relocating could lead to variation in disease trans-mission properties of the locality, and altered pro-duction systems (such as larger, more isolated sites)potentially leading to increased pathogen-inducedproduction losses and altered disease risk due toincreased pathogen transmission distances (Murrayet al. 2005, Salama & Murray 2011).

Infectious disease has an impact on farmed salmonwelfare (Turnbull et al. 2011), which subsequentlyaffects fish productivity due to increased mortality orreduced growth rates. For example, infectious salm -on anaemia (ISA) can cause 90% mortality over sev-eral months (Rimstad et al. 2011). This loss due tomortality can have significant productivity impactsand therefore economic consequences (Murray &Peeler 2005). Globally it was estimated that diseasemanagement across all aquaculture sectors costs€2.25 billion yr−1 (Subasinghe et al. 2001), with out-breaks of notifiable diseases having additional costsdue to a range of factors including those associatedwith destocking, surveillance and interruption inproduction. An estimated loss to the Scottish salmonindustry of over €23 million was incurred due to anISA outbreak in 1998–99 (Hastings et al. 1999),whilst the costs of the recent 2008/09 ISA outbreak inthe Shetland Islands (Murray et al. 2010) are still tobe established. The 2007–09 outbreak of ISA in Chilere sulted in the economy losing an estimated €1.5 bil-lion (Mardones et al. 2011). (Note that for consis-tency, currencies are converted at rates of 0.75 forUSD, and 1.15 for GBP to €1.00, as of February 2013.)

Pathogens and parasites are ubiquitous in the nat-ural environment and can be transmitted to farmedfish from wild sources (Murray 2009). Once an inci-dence occurs on a farm, if untreated, disease canspread through the farmed population. It can mag-nify the size of the infective agent population andcreate a greater infection pressure, which may thenbe transmitted back into the open environmentwhere it could infect wild hosts (Murray 2009).

Fish pathogens and parasites have been reportedas having impacts both on farmed (e.g. Mardones etal. 2011) and potentially on wild salmonid species(Costello 2009a, Krkošek et al. 2011) when they arepresent within the environment. Aquaculture com-panies make efforts to treat against pathogenic dis-ease agents, e.g. by providing vaccination againstviral diseases (Secombes 2011) and treatmentsagainst sea lice (Rae 2002). A range of integratedpest management (IPM) strategies are used to man-age disease in salmon aquaculture, including biolog-ical controls such as using wrasse as ‘cleaner fish’ forlice reduction (Treasurer 2002, 2012) and undertak-ing production in designated aquaculture productionzones, such as farm management areas (FMAs) as isthe case in Scotland (CoGP Management Group2010), Bay management areas (BMAs) in Canada(Chang et al. 2007), neighbourhoods in Chile (Kris -toffersen et al. 2013) and Single Bay Management inIreland (Jackson 2011), whereby farms coordinateproduction methods such as stocking, fallowing andapplying treatments, termed chemical fallowing, tominimise disease transmission.

Predicting and assessing the potential risks fromthese disease-causing agents is a substantial chal-lenge that requires considerable understanding of thebiology of the agent and the host of interest, and theirinteraction with the physical environment, includingthe processes involved with transporting agents fromsources to potential host populations. The develop-ment of coupled biological−physical models makes in-vestigating such interactions possible. These can beused to predict dispersal patterns leading to exposureof susceptible individuals to infectious particles, as-sisting understanding of the host− disease agent sys-tem of interest, and aiding the development of moreappropriate management practices in the aquacultureproduction of farmed fish. In order to build a model-ling tool to investigate agent dispersal, a multi-disci-plinary approach is required to develop and validatethe model. The outcomes of the model can be used todirect field sampling efforts efficiently and to testmanagement scenarios. Here we outline a possibleframework for the development, assessment and useof such models to investigate the transmission of dis-ease-agent dispersal by the physical environment.

FRAMEWORK COMPONENTS

The schematic in Fig. 1 (with examples in Table 1)represents important components to develop meth-ods for investigating the environmental transmission

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Salama & Rabe: Developing disease agent modelling investigations

of disease-causing agents. The hydrodynamic model(1) requires information relating to model forcing andinput (2). Once a hydrodynamic model is created, itshould be validated using oceanographic observa-tions (3) to assess whether the model portrays thephysical system. The hydrodynamic model is coupled(4) with a particle-tracking model (5), which accountsfor the biological agent and as such requires biologi-cal parameterisation (6). Using this combined modelwill provide a range of computational outputs (7),which can highlight estimated locations or densitiesof biological particles within the model system. Aswith the simulated oceanographic estimates, the bio-logical outputs also need validation (8). Should themodel be fit-for-purpose, the system can be investi-gated (9) such as by measuring connectivity betweensites within the system, and then interpreted (10) sothat the simulated system is placed in context withthe real world. Finally, the results of the simulationcan be applied (11), e.g. by determining manage-

ment practices based on site relation. It must benoted that throughout and at each stage, assump-tions and limitations (12) exist and sensitivity analy-ses need to be conducted. This paper reviews someof the methods which have been used in previousstudies to develop environmental transmission mod-els of disease agents of salmon produced by aquacul-ture. We demonstrate how we have adopted suchprinciples in developing a biological and physicalmodelling approach with biological validation thatcan be used to assess the hydrodynamic movementsof parasite particles and how such principles arebeing applied to study the dispersal of the ectopara-site Lepeophtheirus salmonis in a Scottish loch.

ROLE OF THE ENVIRONMENT IN DISEASE

Disease triangle

Disease is usually considered to be the result of theecological interaction between at least 2 biologicalorganisms (host and agent) and their abiotic environ-mental conditions (Fig. 2). However, the physicalmovement of agents in the environment plays animportant role in infectious disease risk in aquacul-ture. Aspects of the host−disease agent interactionhave long been investigated in fish cultivationthrough immunological, physiological and epidemio-logical studies. Much of the scientific work con-ducted within aquaculture infectious disease epi-demiology concentrates on the relationship betweenhost and pathogenic disease agents. Scales rangefrom molecular (e.g. Schiøtz et al. 2008) to genetic(e.g. Vallejo et al. 2010), individual (e.g. Wagner etal. 2008) and population level, both empirically(e.g. Wallace et al. 2008) and theoretically (e.g.Werkman et al. 2011). However, anthropogenic fac-tors (Murray et al. 2002) and aspects of the environ-ment (Murray et al. 2010) are risk factors in transmis-sion of pathogens such as Infectious salmon anaemiavirus (ISAV) as well as other pathogens such as thedisease agent of Pancreas Disease (PD; Viljugreinet al. 2009) and ectoparasitic sea lice (Amundrud &Murray 2009, Asplin et al. 2011, Stucchi et al. 2011).

The disease triangle (Fig. 2) (Stevens 1960) repre-sents the interactions among host, disease agent(such as micro- or macroparasites) and the environ-ment. The area covered by the intersection of all 3represents the severity of the infection; thus, alteringthe intensity of any component alters the severity ofdisease expression. An interaction of a susceptiblehost with a pathogenic disease agent in favourable

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Fig. 1. Framework of components to develop methods for investigating the environmental transmission of disease-

causing agents


Table 1. Summary of the components highlighted in Fig. 1 and how several studies have addressed such principles. Note that the assump-tions and limitations are limited to 1 example, due to the vast array of implicit and explicitly described possibilities. T: temperature, S: salinity

No. Component Region (modelling study)

Scotland − Loch Linnhe(Salama et al. 2013)

Scotland − Loch Torridon & Shieldaig

(Amundrud & Murray 2009)

Scotland − Loch Fyne

(Adams et al. 2012)

Norway − Hardangerfjord

(Asplin et al. 2011)

Canada − BroughtonArchipelago

(Stucchi et al. 2011)

1 Hydrodynamicmodel

Proudman Oceano-graphic Laboratory

Coastal Ocean ModellingSystem (POLCOMS)

Georgia-Fuca system (GF8)model

Finite VolumeCoastal Ocean

Model (FVCOM)

Bergen OceanModel (BOM)

Finite VolumeCoastal Ocean

Model (FVCOM)

2 Model inputand forcing

Seasonal variation of Tand S at open boundary;

seasonal variation offreshwater input (adjoin-ing lochs); tidal diamonds

at open boundary;seasonal variation of

atmospheric parameters;measured winds;

bathymetry

Tidal elevations fromPOLCOMS; measured

winds; freshwater input(river); densities fromoffshore conductivity,

temperature and depth(CTD) samples; bathymetry

T and S nudging atopen boundary;freshwater input

(rivers); tidal forcingat open boundary;measured winds;

bathymetry

Coastal PrincetonOcean Model/

Norwegian ecologi-cal model system;

river runoffs;atmospheric modelforcing; bathymetry

Tidal forcing fromtide gauge records;North Pacific modelat open boundaries;

freshwater input(rivers); measured

winds; initial 3-dimensional T and Sfields; bathymetry

3 Oceanographicvalidation

Current, T, S, elevation data

UK hydrographic tidecharts and current data

Current and S data Current data Current data

4 Model output Surface velocities Surface velocities Upper layervelocities

Upper layervelocities

Surface velocities

5 Particle-track-ing model

Amundrud & Murray(2009)

Simplified from Murray &Gillibrand (2006)

Amundrud &Murray (2009)

Ådlandsvik &Sundby (1994)

Particle-trackingfunction in FVCOM

6 Biologicalparameters

Larvae maturation (10%h−1), Stien et al. (2005);

larvae mortality (1% h−1),Stien et al. (2005)

Larvae maturation (10%h−1), Stien et al. (2005);

larvae mortality (1% h−1),Stien et al. (2005)

Larvae maturation(more rapid

development thanAmundrud &Murray 2009);

larvae mortality(e−0.01t, no hostsdie after 14 d),

Adams et al. (2012)

Larvae maturation(10% h−1), Stien

et al. (2005); avoidS <20 (Heuch et al.

1995); limited to10 m depth

(Davidsen et al.2008); diel migration(Heuch et al. 1995)

Lice developmentcoefficients, derived

from Stien et al.(2005); lice mortalitycoefficient is salinitydependent (Johnson& Albright 1991b);vertical migration

(±5.5 m h–1),Gillibrand & Willis(2007); limited to

10 m depth

7 Output Particle location, age,trajectories; relativeparticle residency in

each grid over simulation

Particle location, age,trajectories; relative particle residency in

each grid over simulation

Source, destinationand dispersal timeof each successful

particle

Particle locations Copepodid concen-tration in the surface

layer

8 Biologicalvalidation

Sentinel cages; planktontows; lice counts from

farms

Sentinel cages Plankton tows; licecounts from farms

Sentinel cages Plankton tows; wildfish survey

9 Investigation Connectivity maps,connectivity probability

Role of variable winds indispersal, role of mortality

Connectionprobability,

graph/networkanalysis

None None

10 Interpretation Limitations, usefulness Winds influence dispersal;mortality does not alter

relative density

Caveats andlimitations, future

plans

Distance lice cantravel from release

Spatial associationsobserved

11 Application Model use in a largersystem, policy advice

Principles used in furtherdevelopment for larger

systems

Assisting in makingmanagement

decisions relating tosites in Loch Fyne

Determining role ofvariable conditionsin dispersing lice

Investigate crediblesea lice interactionsbetween wild and

farmed salmon

12 Assumptions &limitations

Short model runs Small study region No diel movement No plankton tows No sentinel cagedata


environmental conditions is required for an expres-sion of disease within a host. Therefore, by removingor minimising at least 1 of the segments of the trian-gle, disease is prevented. Whilst more widely used inphytopathology since its inception in the 1960s(Stevens 1960), the disease triangle has been appliedto aquaculture (Snieszko 1973). This concept wasamended to the disease pyramid or tetrahedron con-cept (e.g. Zadoks & Schein 1979) combining an axisfor time and the anthropogenic interactions that leadto pathogenic disease progression (Scholthof 2007);both factors often simply alter the condition or stateof the agent, host or environment. This framework isoften seen as inappropriate in veterinary or humanmedicine, as the individual has the mobility to avoidinhospitable conditions and also due to the endother-mic nature of humans and livestock with highlydeveloped immune systems. This allows for mam-mals to mitigate environmental conditions to preventdisease transmission (Moore et al. 2011). Therefore,the environmental component is less important todisease progression. However, fish produced underaquaculture are held in pens, which restrict the indi-viduals’ ability to avoid exposure to pathogens andparasites but allow free flow of pathogens betweenthem (Frazer 2009). Additionally, fish immune sys-tems are less sophisticated than those of mammals(Tort et al. 2003) and therefore altering the host sta-tus aspect of the concept framework is less of anoption in disease prevention in fish. Thus environ-mental conditions coupled with reduced immunolog-ical prevention play an important role in pathogenicdisease progression in aquaculture fish production(Magnadottir 2010).

Environment

‘Environment’ is a broad term usually used todescribe the physical and biological factors that, byworking on host and pathogen, may influence dis-ease incidence and severity, such as temperature(e.g. Becker & Speare 2004, Jokinen et al. 2011),salinity (e.g. Powell et al. 2001, Bricknell et al. 2006),water chemistry (e.g. Green et al. 2005), planktonblooms and nutrient availability (e.g. Leonardi et al.2003). The environmental conditions can alter thepredisposition of hosts to disease. A range of environ-mental impacts on the immune systems of commer-cial farmed fish is found in the literature (e.g. Bow-den 2008, Magnadottir 2010) and as such would leadto altered disease status. Water temperature hasbeen demonstrated to alter the leukocyte numbers insalmon smolts which will in turn alter the hosts’ sus-ceptibility to pathogenic diseases (Pettersen et al.2005). Salm onids change growth hormone levels inre sponse to varying salinity, temperature, pollutantsand other stresses related to aquaculture (McGeer etal. 1991, Deane & Woo 2009). Changes in salinity canlead to susceptibility of salmon to amoebic gill dis-ease due to changes in gill cell ionoregulation(Roberts & Powell 2003). Chemicals such as ammoniacan increase susceptibility to disease in Chinooksalmon Oncorhynchus tsha wy t scha (Ackerman et al.2006), as can varying pH for infection in Coho salmonO. kisutch (McGeer et al. 1991). Atlantic salmon Salmosalar fry exposed to Infectious pancreatic necrosisvirus (IPNV) suffer higher mortality levels as tempera-ture in creases between 12.5 and 15°C (Dams gård etal. 1998). In addition, other characteristics of an indi-vidual’s environment that can lead to disease symp-toms include stocking density, chemical environ-ment, feed levels, genetic fitness/ conditioning, diseasecondition and infection history (Snieszko 2006).

However, in aquatic ecosystems, the environmentalso transports, disperses and inactivates pathogenicagents which may initiate a disease. The environ-ment is critical in the occurrence and persistence ofinfectious disease and may result in disease out-breaks far from the initial source. For example, mar-ine pathogens have been reported as being trans-ported up to 11 000 km yr−1 (McCallum et al. 2003),causing far-reaching disease outbreaks. Scheibling &Hennigar (1997) and Scheibling et al. (2010) linkedthe transport of amoebic pathogens of sea urchins tolarge-scale oceanographic and meteorological pro-cesses. While this may be exceptional, transmissionof pathogens over kilometres with water movementappears fairly common; for example, IPNV has been

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Disease agent

Environment

Host

Disease

Fig. 2. Simple disease triangle demonstrating the relation-ships among host, disease agent and environment in causing

disease (Stevens 1960)


isolated 19.3 km from its source at an infected hatch-ery (McAllister & Bebak 1997), and outbreaks of dis-eases such as PD and ISA are related to water cur-rents (Aldrin et al. 2010).

The fluidity of the aquatic environment may resultin greater connectivity between fish farm sites overlarge distance, much greater than those in terrestrialanimal production systems. However, it must benoted that occasionally some airborne pathogens canbe transmitted over large distances as was the casefor Foot-and-mouth disease virus (Schley et al. 2009)and vector borne pathogens such as Bluetonguevirus (Szmaragd et al. 2009). Within both terrestrialsystems and aquaculture, infection occurs throughthe introduction of an infected individual andlocalised transmission. Transport pathways throughhydrodynamic movements are able to transmitpatho genic agents between fish farms (Frazer 2009,Amundrud & Murray 2009) and also from wild fish tofarms and vice versa (Johansen et al. 2011, Kurath &Winton 2011) over far-reaching distances. Hydrody-namic disease transmission between farms has beendemonstrated as a risk factor for ISA (e.g. McClure etal. 2005, Gustafson et al. 2007, Aldrin et al. 2010,2011) and PD (e.g. Kristoffersen et al. 2009, Vilju-grein et al. 2009, Aldrin et al. 2010). Proximity isreported as being a risk factor for ISA transmission inNorway (Lyngstad et al. 2008), whilst the 2007–09ISA outbreak in Chile demonstrated spatial cluster-ing of infectious farms surrounding an initial out-break farm (Mardones et al. 2009). Hydrodynamictransmission was shown to be important for sea licetransmission (e.g. Amundrud & Murray 2009, Salamaet al. 2013).

The ability of disease agents within the environ-ment to remain viable and cause disease changesdepending on the environmental conditions. Forexample, sea lice Lepeophtheirus salmonis maturefrom nauplii to infective copepodids dependent onwater temperature (Stien et al. 2005) and remaininfective de pendent on salinity (Bricknell et al.2006), with lice exposed to salinities <30 havingsurvivability described as being ‘severely compro-mised’. Salinity has also been demonstrated as anenvironmental determination of viability for patho-gens such as certain strains of Viral haemorrhagicsepticaemia virus (VHSV), which survives longer infreshwater than seawater (Hawley & Garver 2008),as does a similar aquatic rhabdovirus Infectioushematopoietic necrosis virus (IHNV), which alsodegrades at a higher rate at higher temperatures(Barja et al. 1983). Salinity plays a role in pathogenviability such as IPNV degrading in conditions of

salinities >30 (Toranzo & Metricic 1982). Aeromonassalmonicida has higher degradation at high salinity(Rose et al. 1990), and Salmonid alpha virus (SAV)has been recorded to cause PD in salmon only atsalinities between 16 and 34 (McLoughlin et al.2003). Temperature also dictates the time for whichVHSV remains infective, with temperature increasedfrom 4 to 20°C leading to a decrease in viability(Hawley & Garver 2008). Graham et al. (2007)reported that the optimal temperature for SAV iswithin the range of 10 to 15°C, whilst it becomesinactive below 4°C and above 20°C. Additionalaspects of the physical environment such as ultravi-olet exposure lead to inactivation of pathogens suchas ISAV, VHSV and IPNV, which at (mean ± SD) 33± 3.5, 7.9 ± 1.5 and 1188 ± 57 J m−2, respectively,become no longer infective (Øye & Rimstad 2001).Exposure is sensitive to sunlight and to the mixingregime in surface waters (Suttle & Chen 1992, Mur-ray & Jackson 1993). Exposure to ozone has beenrecorded to inactivate IPNV at 1944 (mg s) l−1 andISAV at 1.4 (mg s) l−1 (Liltved et al. 2006). The pH ofthe aquatic environment also determines the viabil-ity of disease agents, for example as pH increasesfrom 6.8 to 8, the degradation of IPNV becomesgreater (Toranzo & Metricic 1982). The level of via-bility changes when the environmental factors arecompounded, such as salinity and temperature inthe case of IHNV (Barja et al.1983) and A. salmoni-cida (McCarthy 1977).

Biological hazards also exist for pathogens in theaquatic environment. For example, bacteriophagesplay a role in altering the presence of microorgan-isms (Murray & Eldridge 1994), with bacteriophagenumbers found to increase in water where Aero mo -nas salmonicida was present (Mackie et al. 1935).Viruses are sensitive to virucidal bacteria, grazingprotozoa and filter feeding animals in the plankton(e.g. salps, Sutherland et al. 2010) or benthos (e.g.mussels, Faust et al. 2009). Such filter feeders canalso consume bacteria and larval parasites such assea lice (Molloy et al. 2011).

The elements of time and anthropogenic interven-tion are widely acknowledged in aquaculture by theuse of fallowing strategies, treatment and harvestingtimes as described in the Code of Good Practice(CoGP) for Scottish finfish aquaculture (CoGP Man-agement Group 2010). Anthro pogenic intervention indisease transmission includes aspects such as thera-peutic treatment, management intervention, stockingpolicy, harvesting and culling, pathogen and diseasedetection and control. Long-distance anthropogenicinvolvement in transmission of disease-causing

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pathogens can occur, with shipping movementsresponsible for transport of viruses (Lawrence 2008),and well boats spreading ISAV more locally (Murrayet al. 2010) as well as management practices influ-encing the transmission of IHNV in Pacific Canada(Saksida 2006). Trade movements are also a substan-tial contributor to disease transmission processes(e.g. Green et al. 2009). Although anthropogenicintroduction of disease agents can have a substantialrole in disease incidence, here we only concentrateon methods of investigating the introduction of dis-ease agents through transport within the physicalenvironment.

Localised dispersal through the environment haspreviously been recognised as a transmission route ofISAV and has led to the development of disease man-agement areas (DMAs) partly based on simplifiedtidal excursion (TE) distances (Scottish Executive2000), which categorise groups of farms in relation totheir separation to another farm cluster where theirTE distances do not overlap. During a recent ISA out-break in the Shetland Islands (Murray et al. 2010),the application of DMAs was useful in controllingISA transmission and prevented disease spread out-with the initial outbreak area and subsequent eradi-cation (Allan 2012). Simplified hydrodynamic modelframeworks have demonstrated that the TE-basedDMAs remain valid for rapidly degrading pathogenssuch as ISAV, al though more conserved pathogenssuch as IPNV and Aeromonas salmonicida (Salama &Murray 2011), as well as sea lice (Murray et al. 2005),have the potential to be transmitted over much far-ther distances especially with increased tidal currentspeeds and where farms are increased in size(Salama & Murray 2013). Additionally, for control ofnon-colloidal or passively dispersed disease-causingagents such as salmon lice, FMA boundaries relate inpart to the simple TE concept; however, basic hydro-dynamic principles may not be appropriate becauseof the complexity of the characteristics of sea lice dis-persal and infection.

An additional complexity when studying the role ofthe environment in disease transmission is its con-stant changes. These changes occur in the short termthrough weather events (Marcos-López et al. 2010);such as sunny periods altering predisposition to gilldisease (Mitchell & Rodger 2011), seasonal and long-term climatic changes which are perceived to in -crease the risk of parasitic (Karvonen et al. 2010) andpathogenic (Peeler & Taylor 2011) infections in aqua-culture. Therefore, long-term studies capturing envi-ronmental change and alterations in pathogen statusare required.

These examples of the impact of the environmentalconditions on the success of disease agents demon-strate that the role of the environment needs to beconsidered in developing transmission models, andhighlights that it would be inappropriate to directlysubstitute a model developed for one specific agentdirectly for another. However, modifications of mod-els can be undertaken as demonstrated by the devel-opment of a circulation model in Pacific Canada(Foreman et al. 2009) which has formed the basis fora study of IHNV dispersal (Foreman et al. 2012) andalso sea lice (Stucchi et al. 2011).

MODELLING ENVIRONMENTAL TRANSMISSION OF DISEASE AGENTS

Overall principles

Models are a useful way to supplement informationrelating to systems where empirical observations andpractical experimentation is unsuitable due to factorssuch as cost, ethical and methodological restrictions.Therefore, obtaining such data would be preferablebut not always achievable. Models run diverse sce-narios within a system and act as tools to reproduceinterlinked processes under different conditions.They help us understand problems and questionsrelating to the system of interest. A model can repre-sent a conceptual setting, verbal description, simpli-fied physical representation or a description in quan-titative mathematical relations (Jopp et al. 2011).Chassignet & Verron (2006, p. 19) state that ‘modelsprovide an experimental apparatus for the scientificrationalization of (ocean) phenomena’. Jørgensen &Bendoricchio (2001) wrote that a model can offer adeeper understanding of the system than a statisticalanalysis. Therefore models yield a much better man-agement plan for how to solve the focal environmen-tal problem. They further stated that models are builton all available tools simultaneously, which includestatistical analyses of data, physical-chemical-eco-logical knowledge, the laws of nature and commonsense, among others.

Model development relies on a multi-disciplinaryapproach depending on the overarching questions.Sammarco & Heron (1994) stated that the multiple-team approach comprises the most effective meansby which to solve a highly complex, multi-facetedscientific problem, such as dispersal in the marineenvironment. Large-scale modelling efforts requirespecialised scientists from different fields to worktogether to complement their statistical, geographi-

97


cal or computer science expertise (Jopp et al. 2011).Multi-disciplinary projects bring together differentexpertise to best evaluate and interpret questionsand results.

Gallego et al. (2007, p. 125) wrote that ‘modelsshould be as simple as possible but as complex asnecessary’. Murray (2008, after Jørgensen 1988)described a simple relationship: more complex mod-els allow more detailed inference. However, thiscomes at a cost of additional parameters and in -creased uncertainty. Available data might motivatethe choices and complexities. The challenge is toselect the most appropriate model for your task,which will depend on forcing, boundary conditionsor validation data. Gallego (2011) suggested that bio-physical models, for example, can be used to comple-ment experimental and observational studies in themarine field since they do not suffer from some of theproblems of observational methods like poor spatialor temporal coverage or instrumentation failure.

It is important to acknowledge that models canonly represent reality up to a certain degree; they aresimplified versions of the real world, include assump-tions and limitations and require sensitivity analyses.Scenarios need to be validated for reliable results.The type of validation data, to ensure that the modelgenerates robust results, depends on the model andwill be described below. Also, an additional consider-ation is that the more detailed the model, the morecomputing power is required.

Murray (2008, 2009) provided summaries of vari-ous modelling approaches such as: susceptible infec-tious removed (SIR) type models, statistical models ofsurveillance, hydrodynamic models and network ana -lysis. These can be used in addressing the transmis-sion of pathogens in the aquatic environment.

Types of models

Types of models include, for example, conceptualor physical, stochastic or deterministic, and scientificor management models. Models can answer scien-tific questions, and their results can then be used asdecision-support tools. In the case of disease trans-mission in the aquatic environment, we can applyepidemiological models (SIR models), structuredpopulation models, simple/specialised models (e.g.TE) or more complex models (e.g. coupled biologi-cal−physical models dispersing pathogens within asystem under more realistic forcing conditions).Starting with disease dynamics, the model choiceneeds to consider how and if the model deals with

environmental transmission and whether classicalSIR models are appropriate. Specialised models fill aniche while hydrodynamic models need to be intro-duced for physical− biological connections for morecomplex scenarios and studies. Outcomes can beinterpreted and evaluated with results passed on todecision makers.

Epidemiological models

Models within epidemiological studies are used toinform prevention mitigation and control methods torestrict pathogen transmission between populations.This allows for key components to be identified andincorporated, and variables explored. The term mod-elling within an epidemiological context can describethe process of statistical modelling (using observedor experimentally derived data and simulation) orprocess modelling (informed through available data).Simulation modelling emphasis within traditionalepidemiology has relied on direct contact or trans-mission (β) between infectious (I) and susceptible (S)individuals (Anderson & May 1979), which is oftendensity dependent. The βSI infectious process doesnot necessarily account for the influence of the envi-ronment. Obviously the term β can encapsulate ele-ments of the environment. The complexity of the roleof the environment in disease transmission is high-lighted by Ögüt (2001) who demonstrated that epi-demiological model outcomes vary determined bychanging the interactions of disease parameter val-ues. Werk man et al. (2011) applied a stochastic SIS(Susceptible – Infectious – Susceptible) model to in -vestigate spread of disease between farms, empha-sizing the effects of local and long-distance contactsand different fallowing strategies. Murray (2009)analysed simple SIR epidemic models going beyonddensity-dependent transmission and concluded thatappropriate models need to be selected depending,among other factors, on the disease. The generalassumption of using such Kermack-McKendrick-based models (Kermack & McKendrick 1927) is thatthe agent is spontaneously transmitted from an in -fected individual to a susceptible individual througha probabilistic function.

In cases where infected and susceptible individualsdo not come into direct contact, the transmissibilitycomponent between individuals by the environmentcan be undertaken using expansions of the Kermack-McKendrick-type models and allowing for an envi-ronmental component which becomes ‘infected’ andthen ‘infects’ susceptible individuals. For example,

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this has been applied to investigate the role of aquaticenvironments in human waterborne diseases. Thisapproach has been considered as a secondary sourceof infection (e.g. Eisenberg et al. 2002, Tien & Earn2010) in which the pathogen sheds from the popula-tion, accumulates in the water and decays with time.Further amendments to this model can be imple-mented whereby the environmental compartmentundergoes movement using simplified hydrody-namic approximations (e.g. Murray et al. 2005,Salama & Murray 2011, 2013), to enable the estab-lishment of general principles of the role of hydrody-namics and pathogen transmission and infection.However, to develop specific dispersal characteris-tics, the derivation of β can become complex andrequires additional modelling. For example, establish-ing that the transmission of Foot-and-mouth diseasevirus was transmitted aerially in terrestrial animalproduction (Schley et al. 2009) required combiningmeteorology and epidemiology, whilst for specificdispersal in aquatic environments, detailed oceano-graphic particle dispersal models are required to, forinstance, assess the dispersal of parasitic sea lice in asmall sea loch, fjords and archipelagos (Amundrud &Murray 2009, Asplin et al. 2011, Murray et al. 2011,Stucchi et al. 2011). Using such methods highlightsthe potential long-distance dispersal of infectiousagents, without the presence of an infected class ofindividuals in close proximity to a susceptible popu-lation, and allows for identification of where risk oftransmission may occur, should a susceptible class bepresent.

Host−parasite modelling

SIR-type models applied for pathogens (viral, fun-gal, bacterial and oomycete agents) describe the sta-tus of the host in relation to the disease-causingagent (Anderson & May 1979); however, this model-ling structure may be inappropriate for more com-plex macroparasite life cycles such as those of hel -minths (e.g. Gyrodactylus salaris) and arthropods(e.g. Lepeophtheirus salmonis). For such systems, thenumber of parasites determines the deleteriouseffects on the host and the level of transmission fromthe host. Additionally, it is likely that there is unevendistribution amongst the host population harbouringparasites, resulting in variable transmissibility fromhosts within the population. Krkošek (2010) de scribedthat the key difference between the structure of mod-els required for pathogens and parasites is that themodels are required to account for the variation in

life cycle such that parasites tend to have a free- living phase. During this free-living phase, the organ-ism (as discussed in the previous subsection) canundergo maturation and mortality and can be trans-ported through the aquatic environment. These com-ponents of the life history require consideration inmodel development. The general structure of suchmodels follows the principles described by May &Anderson (1979), whereby the model represents thepopulation dynamics of the parasite (or stages of theparasite life cycle or components of the populationimportant to transmission of the agent such as femalestages), and includes the host population dynamics.

Such methods of coupled delayed-differential ordifferential equations models have been used instudying sea lice parasitism for approximately adecade with a simple lice population model devel-oped by Tucker et al. (2002) parameterised usingdata obtained from experiments, as were stage-struc-tured models accounting for pre-infective, infective,chalimus, pre-adult and adult stages (Stien et al.2005). Models have also been developed to addressquestions relating to lice on farmed and wild fish, forexample the transmission of lice from externalsources (Krkošek et al. 2010) resulting in an assess-ment of the motile numbers of lice per farmed fish.Frazer et al. (2012) described a model representingthe population dynamics of free living and all settledstages to establish potential host density thresholdsinfluencing outbreaks. Revie et al. (2005) developeda stage-structured model for lice on farmed salmonaccounting for mortality and time in stage as well asrecruitment from external sources acting as an initi-ating condition and within farm population develop-ment. The model assesses the population progressionof 4 classes within the population (chalimus, pre-adult, adult and gravid females) and takes account oftreatment efficacies. This model was developed foran assessment of the Scottish industry and has sincebeen applied to farms in Norway (Gettinby et al.2011).

To account for an aspect of environmental trans-mission of lice through the environment, an alter-nate stage-structured model involving developmentthrough the copepodid, chalimus and motile stageswas developed and takes into account spatial compo-nents of modelled transmission from farms to wildsalmon (Krkošek et al. 2005) which was developedfurther by including host mortality and addresses theover-dispersion of lice loads on hosts (Frazer 2008).

May & Anderson (1979)-type models are not theonly methods for estimating sea lice population dy -namics on farmed fish; for example, there are empir-

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ical models, such as those developed by Rogers et al.(2013), which determine the number of motile lice asa function of lice reproduction, environmental factors(temperature and salinity), management interven-tions and host surface area. Groner et al. (2013)recently developed a computational, agent-basedapproach to understanding sea lice parasitism andhow this can be mitigated using cleaner fish.

Specialised, simple models

Aquaculture farms in Scotland, Norway, Chile,Canada and Ireland are mostly located in sea lochs,fjords or archipelagos which show estuarine circula-tion patterns due to their fjord-like features. Spe-cialised, coarse, simplified models are usually run onsmaller spatial and shorter temporal scales. Somemodels may be based on 30 d current measurements,to resolve the main tidal constituents, or do not in -clude atmospheric forcing. Some simplistic dispersalmodels are only based on diffusion and tidal diamonds(symbols for direction and speed of tidal streams fromBritish Admiralty charts) and give a general idea ofparticle dispersal without taking into account thelarger area, dynamics and conditions (currents,wind) at the specific time and site. TE (Scottish Exec-utive 2000) or simplified box models are examples(Gillibrand & Turrell 1997).

Previously, models on smaller scales for specificScottish sea lochs have reproduced accurate patternsof hydrodynamics (e.g. Gillibrand 2002, Gillibrand &Amundrud 2007, Amundrud & Murray 2009). How-ever, added detail may be required to reflect addi-tional biological complications such as vertical move-ment in the water column, and a full 3-dimensional(3D) model may be necessary such as the case of seascallop dispersal (Gilbert et al. 2010). Other animals,such as sea lice that we describe later on, remain pre-dominantly in the surface layers (Hevrøy et al. 2003).

Environmental assessment planning uses simplisticmodels within aquaculture. For example, maximumconsented biomass in Scotland is determined usingSEPA models (e.g. DEPOMOD, CODMOD, AutoDE-POMOD) that assess the benthic impact on the envi-ronment and the spread around farms (Cromey et al.2009, Weise et al. 2009). Mayor et al. (2010) andMayor & Solan (2011) demonstrated that the use ofhydrodynamic dispersal of treatments and chemicalsfrom fish farms can be used to ascertain the impacton the benthic community and demonstrated athreshold in farm size whereby further stocking sizeleads to no further degradation of the biota. These

passive dispersal models derived for chemical disper-sal could be used to predict dispersal patterns for col-loidal pathogens; however, for parasites with morecomplex ecology and biology, detailed coupled bio-logical−physical models are required.

Coupled biological−physical models

The development of biological−physical modelsfollows the general sequence displayed in Fig. 1. Notevery step is required for every application, but ahydrodynamic and particle-tracking model, bothinfluenced by forcing/parameters, lead to some out-put while validation of both models is essential. Forpathogen modelling, connectivity analysis, interpre-tation thereof and applications (such as informingpolicy) are important parts.

General requirements for hydrodynamic circula-tion models (Component 1, see Fig. 1) (dependingon varying complexities) are forcing and inputs (e.g.bathymetry) (2) and oceanographic validation data(3). Forcing for the hydrodynamic model can includeseasonal variations of meteorological variables fromclimatologies or high-resolution wind models, fresh-water input, tides, or realistic winds during specificvalidation periods (see Table 1 for specific examplesfor different study areas). Tides at the open bound-aries can be derived from measurements, tidal dia-monds from sea charts or fed in from coastal oceanmodels. For more complicated circulation patterns,a spin-up of the model (the time taken for an oceanmodel to reach a state of statistical equilibriumunder applied forcing) might be necessary beforecertain scenarios are run. Hydrodynamic modelscan predict, among other variables, sea surfaceheight, currents and water property distributions(e.g. temperature and salinity). Some examples ofpopular existing circulation models that are used bydifferent re search groups and can be set up for therelevant study area include POLCOMS (http:// cobs.noc. ac. uk/ modl/ polcoms/), FJORDENV (Stigebrandt2001) or the Finite Volume Coastal Ocean Model(FVCOM: http:// fvcom.smast.umassd.edu/FVCOM/),to name a few. Depending on the de sired outcome,time scales range from short event time scales tomulti-annual. The physical oceanography compo-nent needs to be described accurately to provide avalid basis for the particle-tracking model. Modeloutput needs to be validated against oceanographicmeasurements (3). These include, for example, cur-rent velocity (from moorings or drifters), sea surfaceheight or temperature and salinity from different


suitable sites within the model domain. Measure-ments should preferably be made during the sametime period that is being modelled, although histori-cal data can fill in gaps.

Hydrodynamic model output (4) or simplified cur-rents are the basis for particle-tracking models (5). Inaddition, knowledge of the biology of the particles (6)(e.g. plankton, larvae or pathogens) is required. If theparticles do not have any swimming behaviour, thenpassive neutrally-buoyant particles are used. Morecomplex models include locomotory abilities result-ing in horizontal or vertical swimming, sinking orother behaviour within the water column. The impli-cations of active particles would lead to a differentspatial spread. Biological parameters representinglife cycle behaviour need to be incorporated if neces-sary (e.g. the incorporation of temperature or salinitydependency). These biological−physical models rep-resent the interplay between physical processes suchas turbulent motion or advective processes resultingfrom currents generated by winds, tides and biologi-cal processes (Gallego 2011). To determine howhydrodynamics affect the transmission of material,particles need to be followed as they are movedaround. Dispersal of pathogens can be modelled bytracking particles with the help of different algo-rithms. These particle-tracking models are widelyused, and the term ‘particle’ is interchangeable withe.g. pathogen, larva, plankton or molecule. Particle-tracking models can be customised (Amundrud &Murray 2009) or developed using open-source codeslike FVCOM. They are a well-established tool todetermine dispersal of chemical discharges (e.g.Navas et al. 2011) and biological larval dispersal (e.g.North et al. 2008) but are less often used to evaluatethe dispersal of disease-causing agents; however, theprinciples are similar.

Depending on the scenario, particles are releasedfrom a point source at once or continuously. Releasesites can represent sources at farm sites, wild sourcesor fictional new locations of outbreaks. Knowledge ofparticle input is essential to obtain a realistic outputfor comparisons between model predictions and dataobservations. Each particle can be considered as apacket of particles or as a super-individual. Boundaryconditions within discrete models must be desig-nated to reflect the reality of the system. For exam-ple, boundaries can be absorbing (whereby particlesthat hit the boundary are removed causing a de -crease of particles in the system) or reflecting (parti-cles bounce back in to the system), or boundaries canbe sticky such that accumulation occurs when cur-rents push particles towards the shore (Soetaert &

Herman 2009). For example, open sea−sea bound-aries could be absorbing representing particles beingadvected out of the system and leaving the modeldomain, whilst land−sea boundaries could be stickyboundaries as is the case for accumulation of zoo-plankton (Archambault et al. 1998) including sea licein Scottish lochs (Penston et al. 2004). This is due tothe no-slip condition of viscous flow and no flowalong the boundary, which is widely described in thefluid dynamic literature (for example Goldstein 1965,Kundu & Cohen 2002).

The output of particle-tracking models (7) willshow particle distributions, possibly different lifestages after the set run-time or at intermediate timesteps. Trajectories of particle movements can be plot-ted as well as areas of higher density (and thereforehigher risk if evaluating diseases). Biological valida-tion data (8) are a requirement to test the outputs ofthe model. Plankton samples or use of sentinel fish inthe case of sea lice modelling will test the modelresults with respect to sea lice occurrence (Amun -drud & Murray 2009, Penston & Davies 2009, Pert2011). Interactions (connectivity) (9) between differ-ent sites can be evaluated and then be interpreted(10). These results can be applied (11), for examplewith regard to the effectiveness of managementareas, if in existence.

Limitations (12) of coupled biological−physicalmodels can include any or all of the below amongstmany more: simplified reality with regard to coast-line, bathymetry, currents, biology or behaviour; alack of data on disease prevalence; effects of treat-ments on disease prevalence; effects of the difficultyin quantifying husbandry practices at farms (e.g. bio-security practices); effects of rare or difficult to pre-dict events such as storms; unknown factors; varyingtime scales; or limited validation data. Uncertainmodel assumptions and parameters need to be eval-uated to ensure confidence; therefore, sensitivityanalyses to result in robust predictions are a require-ment. Considerable work on the need to combinebiological and physical models and reduce limita-tions has been done but more work is still required.

By combining these physical and biological model-ling principles, it is possible to provide a structurethat enables an assessment of the transmission anddispersal of pathogenic agents through the aquaticenvironment. To summarize: the main purpose ofmodels in studying disease transmission in aquacul-ture is to predict the spatial and temporal spread ofdisease in order to help the industry and regulators.The study of the potential dispersal of the ectopara-sitic sea lice, which is a concern to the salmon aqua-

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culture industry, exemplifies the use of this model-ling approach. Developing a modelling framework ofsea lice transmission and investigating scenarios mayaid an understanding of transmission characteristicsand assist in informing future sea lice management.

SHARED PRINCIPLES TO STUDY SEA LICE TRANSMISSION

Ectoparasites which are of concern to the sustain-ability of both wild and farmed salmonid industries(Rosenberg 2008) are the ubiquitous copepodids ofthe family Caligidae, predominantly of the generaCaligus and Lepeophtheirus, commonly called sea orsalmon lice. Sea lice management costs the globalsalmonid aquaculture industry in the region of €305million yr−1, which is some 6% of the overall salmonglobal production value (Costello 2009b). In Scot-land, the species of concern are dominated by thesalmonid specialist L. salmonis (Krøyer) and the gen-eralist fish parasite C. elongatus (von Nordmann).Sea lice graze upon salmonid hosts causing skinabrasions which can lead to osmotic irregularities(Boxaspen 2006); there is also the potential that liceact as a vector for pathogens to cause secondaryinfections (e.g. Jakob et al. 2011). The cost to outputratio of sea lice management in Scotland is reportedto be the highest of the salmon-producing countriesat 0.25 € kg−1 (Costello 2009b). Around 98% by vol-ume of Scottish farms work towards a voluntaryCoGP guideline (CoGP Management Group 2010) inorder to minimise the numbers of lice settled onfarmed fish, demonstrating the significance theindustry places on mitigating against sea lice infec-tion. The use of chemical pesticides and in-feedthera peutants represents the predominant cost asso-ciated with sea lice control. These have been usedsince the industrialisation of aquaculture in Scotland(Rae 2002).

Because lice are demonstrating aspects of resist-ance to some of these chemical applications (Murray2011), alternative means of control need to be devel-oped, in addition to wider issues related to the influ-ence of pesticide use on the surrounding biota (e.g.Mayor et al. 2010). Such methods include developingalternate structural zones of production by position-ing of farms in discrete management areas which hasbeen demonstrated to aid disease control (Werkmanet al. 2011) and can be used as a successful IPM toolfor lice management (Brooks 2009). These structurescan be informed through dispersal modelling. How-ever, modelling is not the only intervention being

developed. For example, biological controls such asthe use of cleaner fish, commonly wrasse species(Treasurer 2012), and the potential for using licepathogens have been investigated (Treasurer 2002)as well as using integrated multi-trophic aquacultureapproaches such as using mussels to filter planktoniclarval lice (Molloy et al. 2011, Bartsch et al. 2013).Selective breeding (Jones et al. 2002) and geneticmanipulation (e.g. Gjerde et al. 2011) for traits whichenable salmon to be less susceptible to sea lice arealternate ways of minimising the risk posed by lice tofarmed salmon. Methods such as fallowing (Bron etal. 1993) and single year class production (Butler2002) have been demonstrated to diminish sea licerisk. The importance of alternative IPM strategies isevident by their inclusion in the CoGP, e.g. by desig-nating separated FMAs of a single year class, withfallowing between cycles. Novel methods for theintegration into IPM continue to be developed, suchas using chemical layers on the water surface (Boxas-pen & Holm 2001) and stimulating the jumpingbehaviour of salmon to aid with exposing lice to suchchemicals (Dempster et al. 2011). A thorough reviewof the study of sea lice is provided in a work edited byJones & Beamish (2011), and ongoing research ispresented through international sea lice conferenceseries and subsequent proceedings (Roth & Smith2011, Boxaspen & Torrissen 2013).

Sea lice have complex characteristics compared tomicroparasites such as their life cycle and ability toremain predominantly near the surface (Hevrøy et al.2003). The reported life cycle of Lepeophtheirussalmonis consists of 10 stages and 5 phases (Johnson& Albright 1991a); the nauplius (2 stages) and cope-podid (1 stage) are planktonic phases, whilst thechalimus (4 stages), pre-adult (2 stages) and adult (1stage) phases are completed on a host. The naupliusstage is non-pathogenic, whilst the copepodid phaseposes a risk of infection to salmonids. Caligus speciessuch as C. elongatus have a similar life cycle but lacka pre-adult phase (Piasecki 1996). However, a recentstudy has indicated that a Lepeophtheirus speciesshares a similar life cycle to that of Caligus species,which may indicate that there are corresponding lifecycles across the family (Venmathi Maran et al.2013). In terms of transmission of lice, both speciesare of interest during their nauplius and copepodidstages; however, the phases that cause harm to fishoccur after attachment. The development throughthe phases is highly dependent on water tempera-ture. Sea louse larval development time increaseswith lowering temperature (Johnson & Albright1991a,b). The life cycle at 10°C ranges between 40

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and 50 d for L. salmonis (Johnson & Albright 1991b),of which the nauplius stage lasts 3.6 d, and 40 d for C.elongatus (Piasecki & MacKinnon 1995), of which3.8 d are as non-infectious nauplii. The mortality rateassociated with copepodid stage lice appears to bestrongly associated with salinity. Stien et al. (2005)reported that above a salinity of 30, mortality occursat a rate of approximately 0.01 h−1. However, Brick-nell et al. (2006) estimated that at similar salinity,mortality is 0.058 h−1, this doubles to around 0.1 h−1 ata salinity of 26 and to around a salinity of 0.5 h−1 at 25and below. Johnson & Albright (1991b) estimated amortality rate of 0.029 h−1 at 10°C and a salinity of 30.

Dispersal during the planktonic phase dictates thelocations of lice accumulation, which may pose a riskto salmonids. As the lice are mainly in the surfacelayer, dispersal is strongly dictated by wind forcingsas well as by tidal conditions and surface circulation(Amundrud & Murray 2009). Therefore, under vary-ing conditions, accumulation could potentially occurnear the source of lice or at some distance.

Applying the principles to sea lice

Over the last decade there has been a growingamount of research, through the combination of epi-demiological and oceanographic methods, assessingthe role of the aquatic environment in transportingdisease agents (see Stephenson 2005). Althoughhydrodynamic connectivity is demonstrated to be arisk factor in the spread of various pathogenic dis-eases, to aid direct comparisons across a range ofstudies, we standardise by describing methods asso-ciated with investigating the dispersal of sea lice. Inthis manuscript, we consider sea lice dispersal stud-ies of Asplin et al. (2011), Amundrud & Murray(2009), and Stucchi et al. (2011), which are compiledin a recent book edited by Jones & Beamish (2011), inaddition to a recent study by Adams et al. (2012).Note that this is not a complete list of the sea lice dis-persal modelling studies; there are others, such asthe work in Ireland (Jackson et al. 2012), which areomitted merely in order to constrain this review. Weapply the characteristics of the framework presentedin Fig. 1 to highlight that, although different ap -proaches have been used, the studies share commoncomponents as part of the development process. Wethen demonstrate how we applied such principles inundertaking an ongoing research project to study sealice dispersal (Salama et al. 2013). Note that descrip-tions of each paper are kept to a minimum for brevityin Table 1.

Study comparison

Each of the studies used a hydrodynamic modelwith (FVCOM) being used for Broughton Archipel-ago (BA; Stucchi et al. 2011) and Loch Fyne (LF;Adams et al. 2012), Bergen Ocean Model (BOM) inHardandgerfjord (HF; Asplin et al. 2011) and theeighth format of the Georgia-Fuca system (GF8)model of Loch Torridon (LT; Amundrud & Murray2009). All hydrodynamic models are 3D models,which provide vectors for movements of parasite rep-resentative particles; however, they vary consider-ably in the methods of calculating these vectors andtheir structure. For example, there is a difference inthe fixed grid used by the GF8 and BOM models ver-sus the variable triangular grids of the FVCOM mod-els. The fixed grid models vary in size, with 100 ×100 m for GF8 and 800 × 800 m for BOM. TheFVCOM models vary, with the LF model comprising943 nodes, whereas BA uses over 46 000 nodes,demonstrating the degree in difference in domainsize of the various models. The models are also runfor varying times. LT ran for 14 d, HF 20 d, BA 31 dand LF 1 mo for each month of the year betweenMarch 2011 and February 2012.

The models require input (e.g. bathymetry) andforcings (e.g. atmospheric data). HF uses an atmos-pheric model determined by meteorological data, alower-resolution North Sea coastal model at the openboundary and over 60 freshwater river inputs. The LTand LF models use simplified tidal elevations at theopen boundary, they have fewer river inputs, and LTis forced using uniform directional winds, whereasLF has measured winds and temperature and salinitynudging at the boundary. BA uses a similar numberof recorded river flows as LT and LF; however, it isalso supplemented with estimates for the other riversin the system. The open boundary uses an openocean model, and wind forcings are derived fromseveral meteorological stations in the system.

The outputs of each of the models include esti-mates of the abiotic environment such as tempera-ture, salinity and currents. To assess the modelledpredictions, oceanographic observations are under-taken using methods such as current profilers asoccurred in BA and HF, or conductivity, temperature,depth (CTD) measurements as used in LF.

Each of these studies used vectors obtained fromthe hydrodynamic model and input particles into thesystem which are monitored by using a particle-tracking algorithm. The format of the particle-track-ing component has slight variations such that the LTstudy used a method described by Murray & Gilli-

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brand (2006), also applied at LF. The BA study used aparticle-tracking package as part of FVCOM, whilstthe HF model incorporates a model presented inÅdlandsvik & Sundby (1994). The approaches alsovary in the detail of biological parameters associatedwith the particles; each of the studies applied matu-ration conditions derived from Stien et al. (2005), butconsidered mortality in a range of ways. LT simplyuses a constant mortality rate, LF uses the same mor-tality rate as Amundrud & Murray (2009) but after14 d, a free living particle dies. The HF work does notinclude a mortality term, whereas BA uses variablemortality dependent on salinity and egg develop-ment as well as maturation between age stages. Fur-thermore, in HF and BA, particles avoid low salinity.Vertical migration of particles is included as part ofthe BA and HF models, but is omitted by LT and LF.

Each of the models produces relative particle con-centrations and locations in the surface layer over thecourse of the simulation, which allows the potentialfor biological validation of the predictions. In LT,counts of lice on sentinel caged fish and planktontrawls demonstrated an increasing gradient of licecounts as predicted by the model. Similar use ofcaged fish was developed in HF, but comparisonmethods are still ongoing. Plankton trawls wereattempted in LF and BA but resulted in low occur-rences of planktonic lice and therefore could not beused to validate the models. However, non-0 countswere observed in regions predicted to have lice; sim-ilarly, the BA study also involved wild fish trapping,which resulted in 0 lice counts being observed inregions where modelled concentration were pre-dicted to be low and thus demonstrate some corre-spondence of agreement between observations andmodel predictions.

The development of sufficiently accurate modelsallows for investigations of dispersal and transmis-sion to be undertaken. For example, in LF, an assess-ment of the hydrodynamic connectivity among farmsindicated distinct networks of groups of farms andalso how the grid resolution impacts on the hydrody-namic simulations. Variable wind directions wereinvestigated in LT to assess their influence on disper-sal patterns; continual release versus single eventrelease was investigated using the HF system, whilstin BA the diel migration of copepodid lice was con-sidered to assess what role this may have on disper-sal patterns.

The process of developing methods to investigatesea lice dispersal requires interpretation of outputs inorder to make the model applicable. The results fromBA indicate that the model predicted spatial differ-

ences in lice levels which could be assessed by thecounts of lice corresponding to the spatial difference,as was the observation with LT. The results of LTindicate that wind direction has a strong influence onlice dispersion. In LF, relationships between farmswere obtained and the most important nodes in thenetwork were highlighted. HF demonstrated thepotential dispersal distances of lice released fromfarms. The application of the results from LT and HFindicates that accumulation does not necessarilyoccur at the release point, allowing some assessmentof the role of long-distance interaction that lice mayhave with wild fish populations. Such a model willallow for the potential capacity for lice in a region orsystem to be established and modes of transmissionidentified among farms in a system to aid sea licemitigation measures. The highlighting of specificfarms in LF as being important connections in a net-work could be applied to allow targeted treatmentsand surveillance at these influential sites. The resultsof the BA study are expected to contribute to large-scale/area-wide management strategies.

Model limitations

At each of the stages, there are assumptionswhich lead to limitations. For example, the resolu-tion and grid structure of models may limit the accu-racy of the hydrodynamic vectors, along with thevertical resolution of the model. There is a limitationon the collection/availability of wind data to forcemodels. Likewise, gaining all the information onfreshwater input can be highly resource intensive orinaccurate. The use of wider ocean models or tidalconditions at open boundaries depends on the studyarea, and various degrees of accuracy in space andtime occur. In assessing the model predictions, bio-logical and oceanographic recordings can only betaken at a limited number of locations and times,which could make the conclusions of any model todata assessments spurious; therefore, site locationand replication must be an important considerationof study design. The biological parameters takeaccount of reported means, whereas in reality therewill be substantial variation within the population.With highly complex systems, computational effi-ciency becomes an issue; therefore, time resolution,particles tracked, and run time and number of itera-tions have to be considered, and it must be decidedwhether trade-offs in these could influence the sim-ulation results. Assumptions have to be made wheninterpreting limited simulation times and applying

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them to general system characteristics forapplying management strategies. As withany investigation, the researcher needs toconsider whether efforts are focused onimportant areas and do not ignore anunknown which may have more influenceon the model output. Interpreting the model-ling results to the real world with stochasticevents needs ca veats, especially within anarea as controversial as sea lice on salmon(Bocking 2012) where public opinion ispolarised. Although research is still ongoing,it could be the case that these developmentswill provide information to support sustain-able aquaculture industries, such as devel-oping management strategies, developingproduction zones, determining treatmenttiming and order and identifying criticaltreatment thresholds.

CASE STUDY OF LOCH LINNHE

Study system

In developing a study of sea lice dispersalmodel for Loch Linnhe, Scotland, Salama etal. (2013) used procedures consistent with theprinciples outlined in Fig. 1, using both com-plementary and alternative processes to thoseof previous studies.

The basis for undertaking a study of Loch Linnhewas to assess whether it was possible to scale-up themethods of Amundrud & Murray (2009), developedfor the smaller Loch Torridon and Shieldaig system,to one of Scotland’s largest fjordic systems (Fig. 3).This allows an assessment of whether these princi-ples of biological−physical modelling of sea lice canbe applied to other, more complex systems. LochLinnhe has 2 FMAs (CoGP Management Group 2010)containing 10 active salmon farms with side lochscontaining additional salmonid farms. The system con -tains farms that are consented to stock almost a tenthof Scotland’s Atlantic salmon production output.

In the past, research in Loch Linnhe included phys-ical oceanography (e.g. Allen & Simpson 1998), and itwas the site of an extensive study in the early 1990swhich incorporated simulation modelling (e.g. Rosset al. 1993) and plankton ecology (e.g. Heath 1995). Itacted as a site for assessments of environmentalchange through anthropogenic activities such as theconstruction of artificial reefs (e.g. Wilding 2006) andindustrialisation (e.g. Pearson 1975, Pearson et al.

1982), whilst fish farms within Loch Linnhe havebeen used as trial sites for sea lice treatment investi-gations (Corner et al. 2008). A multi-disciplinaryassessment of ectoparasitic sea lice is on-going inLoch Linnhe, and a brief description of the relevantmodel components applied in Loch Linnhe is pro-vided below.

Model components

For the Loch Linnhe system, the Scottish Asso -ciation for Marine Science ran and validated thehydrodynamic Proudman Oceanographic LaboratoryCoastal-Ocean Model System (POLCOMS), differingfrom variable FVCOM applications and being similarin structure to BOM and GF8 (1), for different timeperiods (Ivanov et al. 2011). A 4 yr spin-up of this 3Dhydrodynamic model established consistent density−velocity arrays. The model system with 365 × 488nodes spans over 60 km from the Firth of Lorne andSound of Mull in the SW to the opening of Loch Eil

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Fig. 3. Loch Linnhe on the west coast of Scotland, showing multi- disciplinary sampling stations for biological and physical model vali-dations (WLR: water level recorder, ADCP: acoustic doppler current

profiler, RDCP: recording doppler current profiler)


near Corpach in the NE, catching the prevailingwinds due to its SW−NE orientation. This 3D baro-clinic model resolves 100 m in the horizontal andincludes a variable vertical resolution with smallersteps in surface and bottom boundary layers (s-coor-dinates) to resolve the important surface layer wheresea lice exist. Specific model scenarios for 1 test caseand with a number of 2 wk validation periods havebeen run to date with time intervals ranging from 15to 30 min.

Model forcing (2) during the model set-up includedtides (tidal diamonds at the model boundary at theFirth of Lorne and Sound of Mull), seasonal varia-tions of freshwater inputs from rivers and adjoininglochs (Lochs Etive, Creran, Leven, A’Choire and Eil),seasonal variations of temperature and salinity at theopen boundary and seasonal variations of atmos-pheric parameters (e.g. wind speed and direction,pressure). Specific runs were forced using measuredwind (speed and direction) from multiple weatherstations around the loch (Fig. 3). These wind meas-urements were extrapolated onto a regular grid thatthen forced the hydrodynamic model for 2 wk valida-tion periods. Since the complicated orography aroundLoch Linnhe channels air flows, wind measurementsat different locations around the loch are essential forthe most realistic wind forcing. Scenarios so far in -clude four 2 wk periods in May and October 2011and 2012, with further validation periods due tooccur in 2013. Accurate bathymetry is re quired aspart of the model input to represent e.g. the sills, nearshore areas and islands. Good bathymetry data existfor Loch Linnhe, but the coarse model grid leads tosome simplifications (see limitations below).

To develop dispersal models of sea lice, the surfacelayer velocities from the hydrodynamic model wascombined post-simulation (4) to reduce computa-tional overheads with a particle-tracking model (5),which not only followed the movements of lice parti-cles, but had biological characteristics (6) of matura-tion, similar to all other mentioned models, and mor-tality, similar to all but the Norwegian study.

For the Loch Linnhe sea lice project, the particle-tracking model (5) follows an existing, tested modelset-up (Murray & Amundrud 2007, Amundrud &Murray 2009) previously used in a smaller system inLoch Torridon. The outcomes from the POLCOMSruns (4), notably the surface currents, are used tomove the particles that represent planktonic lice. Dif-ferent model runs can be set up either using a pointor continuous release from different source points.Surface current vectors, representing advection, areoverlaid by diffusion. A fourth-order Runge-Kutta

solver for the Lagrangian equation of motion is usedhere including a random-walk stochastic element.Diffusion values are varied between 0.1 and 1 m2 s−1,a rate, which according to Turrell (1990), is represen-tative of Scottish sea loch diffusion (for more detailssee Salama et al. 2013).

In addition, lice change due to maturation andmortality (6). In the Loch Linnhe dispersal model,nauplii mature to infectious copepodids at a defaultrate of 10% h−1. Maturation occurs at approximately9.6 d at 5°C, 3.6 d at 10°C and 1.9 d at 15°C. Mortal-ity depends on salinity, increasing rapidly as salinitydrops to less than 29 (Bricknell et al. 2006). For LochLinnhe, we use a default decay value of 1% h−1

(Johnson & Albright 1991a). For sea lice, the agestatus depends on development rates as a functionof temperature. The model of Stien et al. (2005) isused here to describe the time for immature louseparticles to become infectious mature particles. TheLoch Linnhe model does not currently take realistictemperature and salinity into account due to compu-tational overheads, but these could be implementedto provide more realism. The number of particles re -leased at each site within the model domain and atthe boundary was originally determined as a pro-portional function of farm-consented biomass; how-ever, this has since been modified to account for liceinput based on a voluntarily provided transformedweighting for farms. Limited data exist to determinethe position of wild salmonids in the loch; therefore,randomly allocated release points are used to obtain distribution of lice from potential wild sources inaddition to releases at freshwater boundaries where,due to salinity variation, lice on wild fish are likelyto be dislodged. Model runs last for 2 wk, duringwhich particles are released continuously. Ideally,longer releases and repeats of scenarios would bedesirable and might be implemented in the future.A sticky wall is implemented at the interface be -tween land and water which is consistent with pas-sively dispersed material in sea lochs and anabsorbing boundary at sea−sea interfaces. The agestatus of sea lice depends on development rates as afunction of temperature, so we use the model ofStien et al. (2005) here to describe the time forimmature louse particles to become infectiousmature particles. Although there are suggestionsthat lice have the ability to undertake small-scalemovements (Pike and Wads worth 1999), the licehere are assumed to be passive and remain in thesurface layer, as used with LT and LF, and do notundertake diel migration, as is the case in HF andBA.

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The particle-tracking model produces particle dis-tribution fields from different sources of lice as out-puts (7). This helps to identify areas of varying riskfor sea lice accumulation or potential interactionbetween lice and farmed/wild fish under differentforcing conditions within Loch Linnhe.

The model produces particle tracks of each of the~45 000 particles over the simulation and recordstheir age. From this, we produce distribution maps(see an unvalidated example output in Fig. 4) pre-senting the relative particle-per-unit-time of eachlouse stage experienced at each grid cell over theentire simulation. As the input numbers into the sys-tem are relative, and not absolute, no prediction ofnumbers of lice can be made at each grid cell, merelythe relative level compared to other grid cells.

To date it appears that there is a level of correspon-dence between model-simulated distributions (Sala -ma et al. 2013) using farm-consented biomass as aproxy for input, and a similar correspondence assess-ment using weighted lice information provided bythe farms (not presented). Using this model, we haveinvestigated (9) the level of connectivity betweenfarms in 2011, and this investigation for 2012 is ongo-ing to measure whether these connectivity patternsoccur consistently. Should a regular network patternarise, it could be possible to interpret (10) the rela-tionships between groups of farms, and such infor-mation could be applied (11) to manage sea lice onfarmed salmon in Loch Linnhe.

Field validation

For the model to be informative, the simulation out-puts need to be evaluated against field observations.A field work component to collect the relevant phys-ical and biological data is included in this study(Fig. 3). To validate the hydrodynamic model output(3), measurements of currents, sea surface height,temperature and salinity were taken during the cor-responding model validation periods by current pro-filers, CTDs, water level recorders and a multi- parameter data buoy. Drifters were deployed at a fewsites to test the surface currents under realistic condi-tions. Within Loch Linnhe, the hydrodynamic modelreproduces the hydrodynamic conditions well. Vali-dation data are collected during the validation peri-ods. Other studies (e.g. Adams et al. 2012) have usedsimilar instrumentation and data from historical andrecent measurements.

To assess the model and outputs of regions of theloch with higher and lower particle occurrence, accu-rate lice inputs are required. The particle distributionfrom a test scenario was used to identify areas poten-tially providing adequate variation in lice distribu-tions. In those locations, plankton samples for pas-sively dispersed lice (similar to BA, LT, LF) werecollected, and sentinel caged salmon, using similarmethods to HF, were deployed for sampling infectivelice stages (8). Bongo nets were used to sampleplanktonic nauplii and copepodids in the surface

layer whilst sentinel cages were stockedwith 50 smolts, and sea lice counts weretaken after a 1 wk exposure. This procedurewas repeated with a new batch of salmon forthe second week (more details in Salama etal. 2013). These methods have proved usefulin sampling plankton lice levels (e.g. Pen-ston et al. 2011) and attached lice (Pert 2011)in Torridon and Shieldaig, and the latter issimilar to sentinel cage fish work in Norway(Bjørn et al. 2011). A description of compar-ing observed sea lice data from tows andcaged fish to simulated distributions is givenby Salama et al. (2013).

As with all model studies, assumptionsare made at each stage to minimise com-plexity whilst capturing important features;however, this may limit the accuracy of theoutcome (12). For example, due to resolu-tion constraints, all side lochs are omitted,except Loch A’Choire. Due to the 100 mhorizontal model resolution, there is a smalldiscrepancy between the model and reality

107

Fig. 4. Unvalidated results of Loch Linnhe particle dispersal showing high and low regions of particle density


leading to a few features in the topography beingsimplified or omitted, for example Shuna Island. It isassumed that the surface velocities from the hydro-dynamic model are accurately portrayed. This limitsthe likelihood of having lice disperse at differentstrata in the water column, which could lead toalternate dispersal patterns due to vertical variationsin the current field. It is assumed that freshwaterinputs and tides are replicated well for simulationtimes, although they are based on seasonal cyclesand tidal diamonds at the open boundaries. Thismay limit the study, as stochastic or unusual eventscould occur during the study period of interest. Themeteorological data collected from a few sites areused to extrapolate across the entire system, butcould limit the study should the recordings behighly localised and not represent the far-field.These assumptions are not only made during theLoch Linnhe study, but are consistent with theassumptions in the previously described models.The time resolution is assumed to be an adequatetrade-off between short-time resolving of the veloci-ties, which would be computationally expensive,and unrealistic longer time steps. It is assumed thatrunning the model to produce 2 wk simulations foreach spring and autumn of 2011, 2012, 2013 willcapture sufficient patterns that describe the consis-tent patterns experienced within Loch Linnhe. Theoceanographic assessments made at several loca-tions throughout the system are assumed to bereflective of the conditions throughout the loch andthat the replication would capture any variationin modelled to observed conditions. The particle- tracking algorithm contains a defined stochastic ele-ment and fixed dispersive coefficients for ease ofcalculation, as was the case in previous studies. It ispossible that this limits the accurate dispersal condi-tions by individual lice in the system which wouldexperience variable dispersion. Sensitivity analyseswere undertaken to evaluate a range of diffusivityparameters.

The biological components are simplified for afixed growth and mortality rate based on the meanrates calculated from experimental studies; it isassumed that these results are valid in the field andthat the fixed mean actually reflects the conditionsexperienced by individuals in nature. No level ofvariable mortality based on salinity- or tempera-ture-induced maturation is included, as it isassumed that a mean rate will encapsulate the con-ditions experienced by the majority of lice individu-als. Lice are also assumed to stay within the surfacelayer, and no diurnal movement is included. As it is

impossible to track the numerous eggs that arereleased from a gravid female, it is assumed thatpackets of lice can represent the dispersal distribu-tions effectively without causing computationalissues. This may result in not capturing sufficientvariability of lice dispersal. The outputs of themodel are assumed to portray the mean conditionsexperienced over the simulation, but it could be thecase that transmission risk weighting could beapplied at differing times of the simulation toreflect potential changes in risk, for example lowerrisk just after farm treatments. Such treatment mayreduce the usefulness of the study should importantfeatures be omitted. The biological assessment canonly be taken at a limited number of locations dueto finite resources. It is assumed that the locationsselected are not anomalies but reflect the likelyconditions of the system.

Making interpretations based on limited replica-tions could be spurious; therefore, this can be limitedthrough replication over time. The potential applica-tions of such dispersal results are assumed to notalter future dispersal, for example taking out animportant node in the network through successfulsurveillance and treatment could alter the structureof the network and change the relationships betweenfarms. However, although it will certainly be the casethat the model over-simplifies and misses out possi-bly influential unknown characteristics and causeslimitations in the possible accuracy of the dispersalcharacteristics experienced by sea lice in LochLinnhe, it appears that the model has sufficient detailto allow for simulation outputs to be created whichhave a level of correspondence with the biologicalreports of planktonic and settled sea lice sampledfrom the environment (Salama et al. 2013).

This is an ongoing, multi-disciplinary project in -vestigating sea lice dispersal within the large LochLinnhe sea loch. It incorporates the characteristicsof previous sea lice dispersal studies. Through thedevelopment of such modelling studies, it could bepossible to develop accurate methods of studyingtransmission of pathogenic and parasitic organismsthrough the aquatic environment, which could beused in providing information for greater IPMapproaches.

DISCUSSION

Here we have highlighted some principles thathave been applied to developing and undertakingstudies of the environmental transmission of sea lice,

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and have demonstrated how the framework is ap -plied to an ongoing study of sea lice dispersal in LochLinnhe, Scotland. Although the framework could beapplied to any disease agent of interest, here we con-centrate on sea lice due to their importance to theaquaculture industry (control measures for sea liceare a substantial production cost, which can impacton the economic sustainability of salmon aquacul-ture). Furthermore, there is a long-standing debateabout the role of sea lice with regard to the surviv-ability and recruitment success of migratory Atlanticsalmon (e.g. Jackson et al. 2013, Krkošek et al. 2013,Skilbrei et al. 2013), as well as the role of salmonfarms in contributing to the levels of sea lice in theenvironment (e.g. Penston et al. 2011, Middlemas etal. 2013).

Although sea lice control is seen as an importantissue by a substantial number of stakeholders andresearchers from across broad disciplines, there areconsiderable gaps in knowledge related to sea licemanagement that are currently being explored (Box-aspen & Torrissen 2013). A range of IPM measureswill be required, and sea lice dispersal models con-tribute to such approaches. Assessing the role ofenvironmental variability on the dispersal and accu-mulation of lice in the environment is important as itwill enable the ability to highlight areas where larvallice numbers and therefore likely the risk to salmonlice interactions is elevated. By identifying theseregions, it may be possible to provide information onoptimal locations of farms to minimise transmission oflice between sites. Additionally, connectivity assess-ments could highlight potential zonation informationfor aquaculture production, as regions where coordi-nated production strategies such as FMAs and BMAshave helped manage pathogenic and parasitic dis-eases. The network structure that arises from someconnectivity assessment could help inform the orderin which treatments occur, such as targeting the mosthighly connected nodes first to avoid re-infectionthrough the system. Should it be the case that farm-derived lice have an impact on the success of out-migratory salmon, then it may be possible to use suchmodels to help determine future farm site locationssuch that lice do not accumulate in areas where wildfish are known to congregate or along migrationpaths.

Substantial gaps must be overcome in order tothoroughly develop such models. All studies de -scribed short snap shots in time and did not addresshow the dispersal patterns may alter over longertime scales beyond the timeframes considered inthe aforementioned studies, and general properties

may require further observations. Should the aim ofsuch model developments be to aid the conservationof wild fish, then further information is needed as towhere and how long migratory fish reside, andtherefore field observations need to be incorporated.An additional requirement is that the implications ofchanges in production methods need to be incorpo-rated, such as changes in chemical usage and effi-cacy, demand for production influencing stockingdensities, and the removal and addition of new sitesto systems, which may influence dispersal patterns.As such, studies need to account for these changeswhich could be innumerable and potentially highlyinfluential.

In order to parameterise the model with more accu-racy, biological and physical characteristics in thefield need developing. For example, the sea licebehaviours used in previous studies are derived fromlaboratory trials and may not be reflected in the field.Likewise, these models are using parameters associ-ated with Lepeophtheirus salmonis and may not bevalid for other Caligidae species such as those inChile. Additionally, the models do not thoroughlydescribe the life cycle of salmon lice, for example theLoch Linnhe project only attempts to describe 2stages, nauplii and copepodids, and does not accountfor the other life stages. This requires the integrationof biological population models with the coupled biological−physical models.

A major requirement is an assessment of whetherthe accumulation of larval lice in areas of higher con-centration results in increased transmission risk tofish, and if so what effect this may have on fishhealth, and possibly mortality. It is difficult to cur-rently determine the link between presence of dis-persed lice and impact on health.

Oceanographic and atmospheric model develop-ments are needed that include larger-scale oceanand atmospheric forcings, ideally in near-real time athigh temporal resolution to achieve higher accuracyand link long-distance dispersal routes between systems. The smaller, fjord-based models may berestrictive in determining the possible transmissiondistances.

The characteristics highlighted (Fig. 1) and de -scribed (Table 1) demonstrate that although differentmethods exist for approaching environmental trans-mission modelling studies, there are shared princi-ples. Highlighting these principles may act as a guideto develop best practices for studying environmentaltransmission of disease agents in order to provideinformation to help manage pathogenic and parasiticdiseases.

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Acknowledgements. This review was developed as part ofthe Scottish Government-funded project AQ0040. We thankthe editor and 4 anonymous reviewers for their helpful com-ments. We also thank Marine Harvest Scotland, Scottish SeaFarms, the Linnhe-Lorne Fisheries Board, the LochaberFisheries Trust and District Board, the Scottish Associationfor Marine Science, the Crown Estate, crew and supportingscientists, colleagues at Marine Scotland Science, land own-ers, the Underwater Centre and Aggregate Industries forhelp with weather stations and moorings and for providingfish, data, advice and support.

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Editorial responsibility: Bengt Finstad, Trondheim, Norway

Submitted: October 29, 2012; Accepted: June 5, 2013Proofs received from author(s): June 26, 2013

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