Parasite management in aquaculture exerts selection on salmon louse behaviour

Abstract The evolution of pest resistance to management strategies is a major challenge for farmed systems. Mitigating the effects of pest adaptation requires identifying the selective pressures imposed by these strategies. In Atlantic salmon (Salmo salar) aquaculture, barriers are used to prevent salmon louse (Lepeophtheirus salmonis) larvae (copepodids) from entering salmon cages. These barriers are effective against shallow‐swimming copepodids, but those swimming deeper can pass underneath and infest salmon. Laboratory experiments suggest that depth regulation in copepodids is a variable behavioural trait with a genetic basis. We used biological–hydrodynamic dispersal models to assess how this trait variation alters the dispersion of lice through the ocean environment and into farms. The dispersal of copepodids with 3 behavioural phenotypes (deep, mean or shallow) was modelled over winter–spring and spring–summer periods in a Norwegian fjord system with intensive aquaculture. The infestation pressure of each phenotype on barrier cages was estimated from their modelled depth distributions: copepodids deeper than 10 m were predicted to successfully pass underneath barriers. The deep phenotype was the most abundant below 10 m and reached infestation pressures 3 times higher than that of the mean phenotype. In contrast, the shallow phenotype infestation pressure reached less than half that of the mean phenotype. These differences in relative fitness indicate that barriers can impose strong directional selection on the swimming behaviour of copepodids. The strength of this selection varied seasonally and geographically, with selection for the deep phenotype stronger in winter–spring and at coastal locations than in spring–summer and within fjords. These findings can be applied across farms to slow louse adaptation, by limiting barriers during situations of strong selection, although this must be balanced against trade‐offs to short‐term efficacy. More broadly, our study highlights new ways in which dispersal models can address evolutionary questions crucial for sustainable parasite management in aquaculture.


| INTRODUC TI ON
Farming is inextricably tied to evolutionary processes, and this is particularly true for pest management (Thrall et al., 2011). Pest populations are not static, but often adapt to control measures, such as pesticides, biological control and crop rotation (Georghiou & Saito, 1983;Krysan et al., 1986;Levine et al., 2002;Tomasetto et al., 2017;Whalon et al., 2008). The long-term efficacy of pest management strategies can be safeguarded against resistance if they are coordinated according to evolutionary principles (Barzman et al., 2015;Stear et al., 2001;Zhan et al., 2015). For example, combining multiple treatments and maintaining treatment-free refuges can slow pest adaptation, by reducing the overall strength of selection imposed on the pest population (Carrière et al., 2010;REX Consortium, 2013;Rimbaud et al., 2018). Identifying selection pressures imposed by a management strategy is therefore a key step towards ensuring the durability of that strategy. Are certain traits selected for? How strong is this selection? Is selection heterogeneous across space or time?
These questions are particularly salient for salmon aquaculture. The ectoparasitic copepod Lepeophtheirus salmonis (salmon louse) presents a major challenge to the sustainable growth of the salmon aquaculture industry (Torrissen et al., 2013). The productivity and welfare of farmed salmon are adversely affected by louse infestations, as well by the methods used to treat infestations (Finstad et al., 2000;Grimnes & Jakobsen, 1996;Overton et al., 2019;Wagner et al., 2008). Outbreaks of lice on farms also impact wild salmonid populations (Bjørn et al., 2001;Krkošek & Hilborn, 2011;Krkošek et al., 2013). Given the size and value of the salmon aquaculture industry (FAO, 2018), there has been considerable incentive for the development of effective louse controls. The efficacy of chemical pesticides has declined significantly in many areas, due to rapid adaptation by salmon lice (Aaen et al., 2015). As a consequence, farms have reduced chemical use and shifted to various nonchemical strategies, including 'depth-based preventions' (Barrett et al., 2020;Coates et al., 2021). Unlike other major nonchemical strategies, which treat salmon already infested with lice, depth-based preventions reduce the chances of copepodids (the infective, transmissive larval stage of lice) infesting a salmon cage in the first place. Copepodids typically aggregate at shallow depths in the water column, which is where infestations are most likely to occur (Penston et al., 2008;Salama et al., 2018;. The most widely used approaches to depth-based prevention (and those with the strongest evidence of efficacy) are cage barriers technologies (Barrett et al., 2020). Barriers encircling the upper levels of a sea-cage impede larval access from surface waters, whilst leaving deeper parts of the cage open to allow sufficient water circulation (Grøntvedt et al., 2018;Stien et al., 2018;Wright et al., 2017). Although depth-based preventions can reduce infestations by 75% or more, some copepodids manage to pass underneath these barriers and infest a cage (Geitung et al., 2019;Oppedal et al., 2017;Stien et al., 2018). The depth of infective copepodids is a product of environmental forces (such as currents and hydrodynamic mixing; Johnsen et al., 2014) and their vertical swimming behaviour in response to cues such as pressure, salinity and light (Coates et al., 2020;Crosbie et al., 2019;Heuch et al., 1995). Individual variation in swimming behaviour-and hence depth-is regularly observed in small-scale experimental columns (Bricknell et al., 2006;Crosbie et al., 2019;Heuch, 1995). Coates et al. (2020) found a significant effect of family on this variation: lice from some families were more likely to aggregate at the bottom of columns than others. Differences were consistent when columns were pressurized to simulate the conditions found at a range of depths down to 10 m. Overall, higher pressures stimulated an increased frequency of upwards swimming, but the strength of this response varied strongly between families. There was no clear evidence of environmental or maternal effects accounting for this variation, pointing to at least some heritable component to vertical swimming behaviour in copepodids, although more research is needed to quantify this (Coates et al., 2020).
Assuming a genetic element to this behavioural variation, if depth-based preventions select for louse copepodids that occur deeper in the water column (those that pass underneath barriers), adaptive responses are likely to ensue. To assess this possibility, it is first essential to determine whether the inter-family variation observed in experimental columns (Coates et al., 2020) translates to differences in depth in the natural environment. Differences in the distribution of families might be diluted by the much larger scale of the natural water column or by environmental factors such as currents and salinity. Experiments using large scale, in situ columns (e.g. as used in Tang et al., 2011) is one approach for testing this, but performing sufficient replicates with this method across a realistic range of natural conditions would be prohibitively costly and time- consuming. An alternative approach is to use computer simulations to model louse distributions over large spatial and temporal scales.
Sea lice dispersal models predict the dispersion of larvae through the environment and are powerful tools for researching and monitoring louse transmission dynamics Johnsen et al., 2016;Murray & Gillibrand, 2006). By predicting the infestation pressure of farm outbreaks on wild salmonid populations, these models inform decisions on how salmon aquaculture is managed across Norway (Myksvoll et al., 2018Vollset et al., 2018). Here, we use a louse dispersal model for a novel, evolutionary purpose: to predict the strength of selection imposed on lice by the widespread use depth-based preventions. Practical applications of this model include informing decisions on how preventative strategies can be coordinated across farms to protect against resistance.
Our first aim was to assess whether inter-family variation in swimming behaviour influences the vertical and horizontal dispersion of copepodids in the natural environment. To do so, we converted behavioural data (from Coates et al., 2020) into new parameters for a Norwegian lice dispersal model and tracked the effect of different behaviours on the spatial distribution of larvae in three dimensions.
We then used these outputs to estimate the strength of selection that depth-based preventions might impose on louse behavioural phenotypes. Finally, we examine how the strength of this selection varies over time and space.

| Salmon louse biology
There are eight stages in the Lepeophtheirus salmonis life cycle (Hamre et al., 2019). The first three (two nauplius stages and one copepodid stage, referred collectively here as 'larvae') are planktonic and can be transported on currents for tens of kilometres . Nauplii are noninfective, whereas copepodids will seek out and attach to a host, whereupon they will complete the life cycle as a parasite.
Since larvae are nonfeeding, copepodids have a limited time window to find a host before their yolk reserves are depleted . It is through the dispersive copepodid phase that salmon lice are transmitted to farms from the external environment.

| Methods overview
Experimental data on copepodid distributions (from Coates et al., 2020) were converted into parameters for the swimming behaviour of different copepodid phenotypes. These parameters were then incorporated into a lice dispersal model, to simulate the vertical and horizontal distribution of each phenotype through the study area.
The modelled abundance and depth of copepodids were used to predict the efficacy of depth-based preventions, for each phenotype at various spatial and temporal scales. We estimated the relative fitness of each phenotype based on their success at infesting farms using depth-based preventions. Finally, selection gradients were calculated (from a regression of phenotype against relative fitness) to predict the strength of the selection imposed by prevention strategies.

| Constructing behavioural parameters from experimental data
Based upon the findings of Coates et al. (2020), we parameterized vertical swimming behaviour to reflect (1) that copepodids regularly alternate between 'swim' and 'sink' states and (2) that the probability of a copepodid being in a state is a function of its depth and its genetic background. Using data from Coates et al. (2020), we calculated the proportion of copepodids in 'swim' and 'sink' states, for each family tested and for each simulated depth (0, 5 and 10 m). We designated copepodids in the top and bottom of columns into 'swim' and 'sink' states, respectively; of the remainder in the middle of columns, we assigned half to each state. We assumed that the proportion of individuals in one state at a given point in time is equal to the probability of any one individual being in that state. In our dispersal model, lice were assigned a probability of moving up (p z ) or down (1−p z ) at each timestep, which was dependent on the particles' depth (z) and family background (Coates et al., 2020). We modelled 3 distinct behavioural phenotypes, reflecting variation between families: mean, deep and shallow phenotypes. For the mean phenotype, we calculated the mean p z across all (n = 37) families tested in Coates et al. (2020). For the deep phenotype, we took the 4 families with the lowest p z values (consistent across depths) and calculated the mean of these values. We did the same for the 4 families with the highest p z values to give us the shallow phenotype (Table 1). In this way, we captured the mean swimming behaviour, and the behaviours of the ~10% deepest-distributed and ~10% shallowest-distributed families.
We then constructed separate probability curves that best fit the p z values for each family, using a Michaelis-Menten type equation: Values of p 0 and p 10 (the probability of swimming at 0 and 10 m depth); and K M (the value of z at which p z = p 10 2 ) are given in Table 1 (see Figure S1 for curve fits).
Louse larvae avoid low-salinity water close to the surface by actively swimming down to more saline depths (Crosbie et al., 2019).
We included this behaviour in our model, based on Sandvik et al. (2020). When lice resided in water with a salinity <31 ppt, Equation 1 was overridden by a new function: where the probability of swimming downwards (p d ) is a function of salinity (s, in ppt). As s decreases from 31 to 23 ppt, the likelihood of downwards swimming increases linearly to 1. When salinity is <23 ppt, lice will always swim down.
At every timestep (δt = 120 s) in the dispersal model, a value of p z (or p d ) was calculated for each individual louse particle according to its family, depth and surrounding salinity. Realized swimming state was drawn from a Bernoulli distribution given by p z . For example, if p z = 0.75, a particle would have a 75% chance of moving up and a 25% chance of moving down. (1) The probability of copepodids swimming upwards (p z ), for 3 behavioural phenotypes and at 3 depths (z; 0, 5 and 10 m) In keeping with the standard simulation, all simulations also included random vertical movement to simulate fine-scale hydrodynamic mixing. This was given by the random walk: where δw R is the random velocity, D is the diffusion coefficient (10 −3 m 2 s −1 ), and the random number R is drawn for every particle each timestep from a normal distribution with a mean of 0 .

| Lice dispersal model
These behavioural parameters were incorporated into a salmon lice dispersal model. The full parameterization of this model is described in detail elsewhere Johnsen et al., 2016;Myksvoll et al., 2018). In brief, at most . In particular, the model predictions coincide well with observations during periods of strong forcing (for instance, strong wind episodes) and therefore recreate circular patterns important for estimating louse distribution and transport distances (Dalsøren et al., 2020).
The particle-tracking model simulates the transport of particles (representing planktonic louse larvae) through the study area, as driven by the ocean circulation model. Particles were released from positions corresponding to farm locations. Their dispersal was simulated using the 4 th order Runge-Kutta scheme, solving for the Lagrangian equation of motion. The horizontal and vertical position of particles was calculated using a 120 s timestep and saved every hour. The water's surface acted as a reflecting border, whereas the shoreline was set as a nonreflecting border. The particles were given no depth limitation.
Particles were simulated to have the life history and behaviour of lice. Particles were released as 'nauplii' and underwent temperature-dependent development, becoming 'copepodids' at 40 degree-days . The lifespan and infectivity of copepodids were parameterized as a function of age and temperature in accordance with Skern-Mauritzen et al. (2020).
Background mortality was set at a constant rate of 17% day −1 (as estimated by Stien et al. 2005). Particles were given the ability to move up and down the water column (with a velocity of 0.5 mm s −1 ), according to our new behavioural parameters. The predicted infestation pressure from the particle-tracking model in the Hardangerfjord area correlates strongly with infestation levels observed using sentinel cages ) and on wild salmon (Johnsen et al., 2021;Myksvoll et al., 2018).

| Simulation
To reflect seasonal effects on the dispersion of different louse families, we ran simulations for two periods: 1 January-31 March 2018 ('winter-spring') and 1 May-31 st July 2018 ('spring-summer'). The average water temperature, as experienced by lice particles during the simulations, was 4.5°C in winter-spring and 11.6°C in springsummer. In winter-spring, the surface salinity remained relatively high (32-33 ppt) through the study area ( Figure 1a). In springsummer, on the other hand, surface salinity was lower, particularly further into the fjord system (25 ppt; Figure 1b).
In each simulation, 5 particles (each representing 100 lice) were released every hour from each of 144 farm sites in the area ( Figure 1c) to test inter-family differences in dispersion. Particles were modelled with the behaviour of either the mean, deep or shallow phenotype, in separate simulations. A total of 6 simulations were run (3 phenotypes × 2 seasons).
The first month was used as a spin-up period (i.e. particle data not considered in further calculations), to allow time for lice to develop into copepodids. We plotted the vertical distributions of copepodids with a 1 m resolution. The simulated horizontal distribution of lice was given by the average concentration of infestive copepodids per grid cell. The duration and infestation level of the copepodid stage was parameterized as a function of age and temperature, in accordance with (Skern-Mauritzen et al., 2020). The hourly concentration of infective copepodids at farm sites were averaged over the 2-month simulation period to estimate the average infestation pressure on farms (assuming no cage barriers).

| Estimating barrier efficacy and relative fitness of phenotypes
To estimate the infestation pressure on farms, assuming they were using 10-m-deep cage barriers, we multiplied the farm infestation pressure by the proportion of copepodids deeper than 10 m. These values were assumed to provide a good metric of fitness, as the survival and reproduction of lice are dependent on the copepodid encountering a host, the vast majority of which are found on farms 2D t (Dempster et al., comparing farm stocks with estimates of wild population size). For each season and location, the barrier cage infestation pressure of each phenotype was divided by that for the mean phenotype, to calculate the relative fitness of each phenotype (relative to the mean phenotype). To assess for spatial variation in copepodid distribution and infestation pressure, we repeated the above for clusters of 10 farms in each of 3 different locations in the simulation area: inner-fjord, mid-fjord and coastal locations (see Figure S2).

| Calculating the selection gradient to estimate selection strength
One approach to quantifying the strength of selection is to calculate the linear selection gradient (β), which is the slope of a linear regression of phenotype against relative fitness (Lande & Arnold, 1983). We used p 10 values (the probability of a copepodid being in the 'swim' state at 10 m depth, Table 1) for the 3 phenotypes as a metric of phenotype, and the relative (to mean phenotype) fitness as described above. Linear

| Vertical and horizontal distributions
In all simulations, copepodids were most abundant close to the surface and diminished in number with increasing depth (Figure 2).
Copepodids were distributed higher in the water column in winterspring than in spring-summer: 73% of copepodids in winter-spring, and 61% in spring-summer (averaged across phenotypes) occurred in the top 5 m. Vertical distributions differed between behavioural phenotypes. Lice modelled with the deep phenotype were found at a greater abundance in deeper water than the other phenotypes ( Figure 2). In winter-spring, for example, 75% of deep phenotype copepodids were found in the top 7 m of the water column, whereas 75% of the shallow phenotype occurred in just the top 4 m.
In both periods, the average horizontal transport distance was highest for the shallow phenotype (25.1 km in spring-summer, 37.8 km in winter-spring) and lowest for the deep phenotype (23.0 km and 36.8 km), although differences between phenotypes were small. These are the average distances from the release position during the entire copepodid lifespan.

| Infestation pressure
In spring-summer, the infestation pressure (number of infective copepodids per grid cell per hour) at farms was similar for each phenotype.
In winter-spring, the average infestation pressure across all farms was highest for the deep phenotype (22% higher than the mean phenotype) and lowest for the shallow phenotype (12% lower than the mean phenotype). Differences between phenotypes were consistent for inner-fjord, mid-fjord and coastal farm locations (Figure 3). Overall, copepodids tended to reach higher concentrations further into fjords, with the infestation pressure at inner-fjord locations more than double that at coastal sites ( Figure 3). The total infestation pressure in winterspring was only ~1% of that in spring-summer.

| Efficacy of depth-based preventions
Of the infective copepodids occurring at farm sites, we calculated the percentage that were below 10 m depth. These percentages were highest for the deep phenotype and lowest for the shallow phenotype, at all places and times. In spring-summer, 16% of deep phenotype copepodids were deeper than 10 m, which was 1.6 and 2.5 times higher than for the mean and shallow phenotypes, respectively ( Figure 4). In winter-spring, these percentages were lower, but the differences between phenotypes were even greater. In winterspring, 11% of deep phenotype copepodids were below 10 m, which was 2.5 and 6.2 times higher than for the mean and shallow phenotypes, respectively (Figure 4).
In spring-summer, copepodids at inner-fjord locations were more likely to occur below 10 m (e.g. 35% of the deep phenotype) than coastal locations (10% of the deep phenotype; Figure 4). The relative differences between phenotypes were greatest at coastal sites, however, with the percentage of deep phenotype lice more than twice that for the mean phenotype in spring-summer. In winter, the percentage of each phenotype below 10 m was similar across the three farming locations.

| Relative fitness and selection gradients
We multiplied the infestation pressure on farms by the proportion of lice deeper than 10 m, to predict the infestation pressure on farms using depth-based preventions. For each season and farm location,  Figure 5).

F I G U R E 3
In winter-spring, the fitness of the deep phenotype was approximately 3 times that of the mean phenotype and 9 times that of the shallow phenotype. The standardized selection gradients indicate strong directional selection (|β µ | = 4.5; |β σ | = 0.95; Figure 5).

| Efficacy of depth-based preventions
The % efficacy of depth-based preventions was lower in springsummer than in winter-spring (Figure 4). This was due to lower salinity at the surface, resulting from increased freshwater input during the spring melt (Figure 1; Asplin et al., 2020). Louse larvae move deeper in the water column to avoid brackish water (Bricknell et al., 2006;Crosbie et al., 2019); since this behaviour was included in our model, more copepodids (regardless of phenotype) sank below 10 m during times of low salinity. This was most pronounced in spring-summer at inner-fjord sites, where a relatively thick, stable brackish layer accumulated ( Figure 1). Experimental trials have shown that seasonal and spatial variation in salinity has a strong effect on the efficacy of depthbased preventions (Geitung et al., 2019;Oppedal et al., 2019).
The predicted efficacy of depth-based preventions differed for louse behavioural phenotypes, with these strategies being less effective against the deep phenotype. Although the absolute difference in It must be noted that we used an unconventional approach to estimate these selection gradients. Fitness is usually scored on a continuous scale (e.g. the number of offspring produced), and the selection gradient is calculated using a data point for every individual in the population. In our system, individual fitness is binary: individuals either infest a cage (if they are deeper than 10 m at a farm site) or they do not infest a cage. We instead used data points representing the mean relative fitness of each phenotype, which should produce a slope representing the whole population ( Figure 5).

| Possible evolutionary response by lice to depth-based preventions
Taken alongside preliminary evidence that swimming behaviour has a genetic component (Coates et al., 2020), our results support the hypothesis that directional selection by depth-based preventions could shift the vertical distribution of the louse population. Similar shifts towards deeper distributions have evolved in other planktonic crustaceans in response to selection by predators (Cousyn et al., 2001;Gliwicz, 1986;De Meester, 1993, 1996. In lice, adaptation could lead to populations becoming resistant to barrier cages . Strong selection can drive rapid evolution, provided that the trait under selection is heritable (Falconer & Mackay, 1996).
The magnitude of our selection gradients |β| suggests that widespread use of barriers cages could drive a sizeable evolutionary response, even if genetic variation plays only a small role in the population's phenotypic variation. The breeder's equation Falconer & Mackay, 1996) provides a simplified illustration of this. Assuming swimming behaviour has a relatively low heritability (h 2 = 0.05; Visscher et al., 2008;Hansen et al., 2011), the estimate of winter-spring selection (S = β = −7.4) shifts the population's p 10 phenotype by R = −0.37. This is a greater change, in just one generation, than the difference in p 10 between mean and deep phenotypes (−0.18). Further research is needed to estimate the heritability of this behavioural trait, that is, to calculate the degree to which it is determined genetically, rather than by external factors. If heritability is high, then the industry must look towards evolutionarily informed strategies for managing lice across the farm network.
The average horizontal transport distance was slightly longer for the shallower phenotypes, as might be expected from increased wind-driven dispersal near the surface .
However, the differences were relatively small (1-2 km, or <9%) and the temporal averaged patterns of horizontal dispersal were very F I G U R E 5 Relative fitness of copepodid phenotypes (relative to mean phenotype) in (a) winter-spring and (b) spring-summer, and at different farm locations. Phenotypes given as p 10 values ( Deep ← Phenotype ( p 10 ) → Shallow similar for phenotypes (Figure 3). Reductions in larval transmission distance or increases in the distance between farms can impact the lice connectivity of farms. However, these changes in distance generally need to be much larger (tens of kilometres) to significantly alter the connectivity network .

| Variation in infestation pressure
The infestation pressure (# infective copepodids grid −1 hour −1 ) across all depths in winter was only ~1% of that in spring (Figure 3) this was assuming all farms release identical quantities of larvae, simulations with more realistic releases of larvae have also found higher infestation pressures within fjords Sandvik et al., 2020). In this context, the point of interest was the differences in infestation pressure between phenotypes, within each season and location. In winter-spring, lice of the deep and shallow phenotypes reached infestation pressures ~1.2 times and ~0.9 times that of the mean phenotype, respectively. This suggests that even in the absence of depth-based preventions, there may be some directional selection for the deep phenotype during winter-spring. During this period, temperatures were warmer deeper in the water column, which shortens the development time to the copepodid stage and improves the attachment success of copepodids Skern-Mauritzen et al., 2020). Despite the advantages of occupying warmer water, copepodids in the laboratory do not adjust their depth in response to temperature, but rather aggregate at the surface, regardless of temperature (Crosbie et al., 2020). This suggests that over the copepodids' evolutionary history, the benefits of being near the surface, where wild salmonids typically swim (LaBar et al., 1978;Plantalech Manel-La et al., 2009;Rikardsen et al., 2007;Strøm et al., 2018), outweighed benefits of temperature-seeking behaviour. Today, however, many emerging depth-based preventions shift farmed salmon into deeper water Frenzl et al., 2014;Geitung et al., 2019;Glaropoulos et al., 2019;Korsøen et al., 2012). If these strategies become widespread, deep-swimming copepodids in winter-spring would benefit from both improved temperatures and an increase in host availability.

| Spatial and temporal variation in selection
Although barrier cages consistently selected for the deep phenotype, the strength of this selection varied temporally and spatially.
Selection was stronger in spring-summer than in winter-spring, and stronger at coastal sites than at inner-and mid-fjord locations ( Figure 5). The differences in relative fitness were an effect of surface salinity. In our model, salinity avoidance overrode other behaviours and was identical for all phenotypes. This meant that where a thick brackish layer was present (most pronounced at inner-fjord sites in spring), copepodids of all phenotypes were driven into deeper water, and the difference in fitness between phenotypes was reduced.

| Applications
Our results can be applied under a framework of evolutionary principles to coordinate louse management strategies across farms in ways that protect their durability against resistance (Barzman et al., 2015;McEwan et al., 2016;Onstad et al., 2013;Zhan et al., 2015).
Leaving large portions of the pest population unexposed to a selective pressure reduces the overall strength of selection on the population. These refugia can slow the rate of evolution or even halt it, if resistant phenotypes are lost (through genetic drift or fitness costs) as fast as they are selected for (Kreitzman et al., 2018). In the Pacific, large wild salmonid populations act as a refugia, providing a valuable 'evosystem service' to farms (Kreitzman et al. 2018). In the Atlantic, where farmed hosts greatly outnumber wild hosts (Dempster et al.), refugia can instead be farms that are left untreated through space or time (McEwan et al., 2015;REX Consortium, 2013). Deciding which farms do not receive the management strategy is a challenge, however, as there are multiple factors to consider. These include the connectivity of farms, the efficacy of the strategy and the strength of selection for resistant phenotypes.
Management strategies should be prioritized at farms that are highly connected in the network, that is, those receiving large quantities of lice from nearby farms and/or transmitting large quantities to new farms. Using effective prevention strategies at these sites essentially removes crucial nodes from the connectivity network and disrupts louse transmission through the area . However, this relies on the strategy being effective. Our simulations predicted spatial and temporal variability in barrier efficacy. Using barriers at farms that are highly connected in winter-spring and on the coast is expected to have a greater effect on louse transmission than those in spring-summer and in fjords.
Our model results also highlighted a trade-off between efficacy and selection pressure. Where barriers were more effective, they also imposed a stronger selection pressure, which may accelerate the evolution of resistance. Imposing strong selection at too many well-connected farms also risks facilitating the spread of resistant genotypes through the population. Co-ordinating management strategies is a complex process that must strike a balance between short-term (minimizing infestation) and long-term (extending the durability of the strategy) goals. To find an optimal approach, dispersal models need to be combined with epidemiological and evolutionary models (e.g. Groner et al., 2016;McEwan et al., 2016;Samsing et al., 2019).

| Limitations
It is important to remember that we have not directly measured selection on farms, but have rather used a model to simulate the depth distribution and likely selection strength. A model-based approach has logistical advantages but also some limitations, which highlight areas for future research and development. Firstly, lice particles were not modelled with phototactic behaviour, as in most previous version of the model (e.g. Johnsen et al., 2016;Sandvik et al., 2020). Coates et al. (2020) performed their behavioural assays in the dark, and so it is not known if phototaxis is influenced by family effects or pressure cues. Differences in depth between phenotypes might be amplified if there is also genetic variation in phototaxis, and selection could also act on this variation (Cousyn et al., 2001;Gliwicz, 1986;King & Miracle, 1995).
A second limitation is that our models assumed a background mortality rate of 17% day −1 , taken from a study on a captive louse population (Stien et al., 2005). In nature, larval mortality at certain times of the year is likely to be much higher than this due to predation by planktivores (Brooker et al., 2018). Predation rates not only vary seasonally and geographically, but also with depth, potentially influencing the infestation pressure of copepodid phenotypes through space and time.
A third limitation is that our model did not capture the finescale hydrodynamic processes that occur immediately around sea cages. For example, turbulence around cages with lice skirts can pull water down from 2.5 m and underneath 5 m skirts (Frank et al., 2015). Similarly, pressure differences can cause upwelling inside cages (Frank et al., 2015). These processes might affect the probability of different phenotypes passing underneath cage barriers. They might also influence how salmon semiochemicals are transported out of cages, which copepodids are attracted to over short distances (Bailey et al., 2006;Fields et al., 2017 et al., 2018) and so in reality, surface salinities might be lower and drive lice deeper than the model predicts. This may explain why our estimates of barrier efficacy ( Figure 4) were slightly higher than those reported from experimental trials, when comparing similar areas and seasons (Geitung et al., 2019;Oppedal et al., 2017;Wright et al., 2017). By under-estimating the effect of salinity on copepod depth, we may have over-estimated the importance of behavioural phenotype, particularly at farms with a thick brackish surface layer. Other model simplifications included a fixed diffusion coefficient for vertical mixing (whereas mixing is in fact weaker with stronger stratification) and fixed larval salinity tolerance. There may be some genetic variation in salinity tolerance (Andrews & Horsberg, 2020), which would further complicate the vertical distribution of genotypes in the presence of salinity gradients.

| Broader implications
A number of studies have used new data on salmon louse biology to update lice dispersal models, and compare their predictions with those from previous versions of the model (Crosbie et al., 2019(Crosbie et al., , 2020Johnsen et al., 2014;Skern-Mauritzen et al., 2020). These have largely been concerned with more accurately predicting the transmission of lice through the environment. What has not been addressed is that larval traits included in these simulations might vary within the louse population. We have shown that dispersal models can also be used to address evolutionary questions. This can have potentially valuable applications for salmon aquaculture: insight into the strength of selection imposed by management strategies can be used to inform policy decisions aimed at mitigating the effects of louse evolution, to preserve the efficacy of these strategies. More broadly, physical barriers and other spatial manipulations have long been staples in terrestrial pest management (Boiteau & Verson, 2001), but using these strategies in an aquatic environment comes with unique challenges. Our findings suggest that preventative methods in aquaculture are not necessarily immune to adaptive ability demonstrated by pest species.

CO N FLI C T S O F I NTE R E S T
None declared.