Hydrodynamic connectivity, water temperature, and salinity are major drivers of piscirickettsiosis prevalence and transmission among salmonid farms in Chile

Piscirickettsiosis is one of the most im portant diseases affecting farmed salmonid in Chile. Several studies have demonstrated the survival of Piscirickettsia salmonis in seawater and the horizontal transmission from infected to non-infected fish; however, the extent of waterborne transmission between farms has not been quantified. In this study, we used a stochastic hydrodynamic connectivity-based disease spread model to determine the role of hydrodynamic connectivity and the effect of seawater temperature and salinity on the dynamics of piscirickettsiosis in the Los Lagos region of Chile. Results demonstrate that environmental dynamics play a major role in disease prevalence.Thestrongestdeterminantsofpiscirickettsiosis prevalence were the number of infected farms in upstream watersand theextentofdiseaseoutbreaksin upstreamwaters(totalmortality), followedbyseawater salinity and temperature. In farms downstream from infected farms, observed disease prevalence 25 wk into the farming cycle was close to 100%, while in farms with little or no exposure to upstream, infected farms, prevalence reached only ~10% by the end of the farming cycle (Week 56). No previous studies have quantified the scales of connectivity associated with piscirickettsiosis or provided risk metrics of waterborne transmission of the disease among farms; these are a novel aspect of this research. The above knowledge regarding the use of the epidemiological model will allow industry and regulators to better target disease control strategies for more effective control of piscirickettsiosis in the study area.

ABSTRACT: Piscirickettsiosis is one of the most important diseases affecting farmed salmonid in Chile. Several studies have demonstrated the survival of Piscirickettsia salmonis in seawater and the horizontal transmission from infected to non-infected fish; however, the extent of waterborne transmission between farms has not been quantified. In this study, we used a stochastic hydrodynamic connectivity-based disease spread model to determine the role of hydrodynamic connectivity and the effect of seawater temperature and salinity on the dynamics of piscirickettsiosis in the Los Lagos region of Chile. Results demonstrate that environmental dynamics play a major role in disease prevalence. The strongest determinants of piscirickettsiosis prevalence were the number of infected farms in upstream waters and the extent of disease outbreaks in upstream waters (total mortality), followed by seawater salinity and temperature. In farms downstream from infected farms, observed disease prevalence 25 wk into the farming cycle was close to 100%, while in farms with little or no exposure to upstream, infected farms, prevalence reached only ~10% by the end of the farming cycle (Week 56). No previous studies have quantified the scales of connectivity associated with piscirickettsiosis or provided risk metrics of waterborne transmission of the disease among farms; these are a novel aspect of this research. The above knowledge regarding the use of the epidemiological model will allow industry and regulators to better target disease control strategies for more effective control of piscirickettsiosis in the study area.

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The pressure of infection of Piscirickettsia salmonis (inset) among farmed salmonid populations is controlled by oceanographic conditions including hydrodynamic connectivity, seawater temperature, and salinity.

INTRODUCTION
Aquaculture of seawater salmonid species (hereinafter referred to as 'salmon') has expanded rapidly in the last 2 decades to become the second-largest in the world, with an annual production of over 900 000 t (SERNAPESCA 2018a). However, the rapid expansion in the number of marine farms and total salmonid biomass has coincided with an increased prevalence and severity of many diseases (Figueroa et al. 2019).
In Chile, one of the most devastating pathogens of farmed salmon is Piscirickettsia salmonis, a Gramnegative intracellular bacterium that causes sal monid rickettsial syndrome (SRS) or piscirickettsiosis. In salmon-farming countries in the Northern Hemisphere, such as Canada (Cusack et al. 2002) and Norway (Olsen et al. 1997), the prevalence of piscirickettsiosis is relatively low, whereas in Chile, it is a leading cause of mortality (Rozas & Enriquez 2014, SERNAPESCA 2016, 2018b and high use of antibiotics (Miranda et al. 2018). Estimates of economic losses due to P. salmonis infections since 1990 range be tween 10 million and 700 million USD annually (Cvita nich et al. 1995, Cabezas 2006, Rozas & Enriquez 2014, Maisey et al. 2017. The route of transmission of P. salmonis is not completely understood, although penetration of salmon skin and/or gills by P. salmonis has been reported to result in the onset of infection in experimental animals (Smith et al. 1999(Smith et al. , 2004. Waterborne (horizontal) transmission of P. salmonis has also been demonstrated in the absence of parasites or vectors in coho salmon held in seawater and freshwater (Cvitanich et al. 1991). Prolonged survival (14−40 d) of the bacterium in seawater has also been reported in several studies (Lannan & Fryer 1994, Olivares & Marshall 2010. Waterborne transmission of P. salmonis from fish to fish within and across farms has therefore been recognized as the main route of infection (Almendras & Fuentealba 1997, Fryer & Hedrick 2003, but the extent of waterborne transmission be tween farms has, to date, not been quantified in Chile. Currently, piscirickettsiosis prevention and control strategies include vaccination, antibiotics (i.e. florfenicol and oxytetracycline), and alternative treatments with immunomodulators and immunostimulants of variable effectiveness (Rivas-Aravena et al. 2013, Valenzuela et al. 2015. Piscirickettsiosis control strategies in Chile also include coordinated stocking and a fallowing period of 3 mo after harvesting under well-defined areas of coordinated management (SERNAPESCA 2008(SERNAPESCA , 2009. Physical separation of farms or groups of farms is an important disease prevention and control mechanism in open net pens in marine aquaculture (Salama & Murray 2013). A minimum safe distance among farms of 1 nautical mile (nmi) has been recommended in Chile. Furthermore, a surveillance zone of 5 nmi around farms is also applied in the event of a disease outbreak (MINECOM 2002).
It is increasingly recognized that the emergence, prevalence, and severity of diseases is driven by complex pathogen−host and environment interactions (Callaway et al. 2012, Engering et al. 2013, Groner et al. 2016. Several risk factors, both biotic (age and species) and abiotic (water temperature, salinity, sunlight, hydrodynamic connectivity), along with farming practices (stocking date, fish density, vaccination, smolt quality) are known to contribute to the onset and progression of fish diseases (Lannan & Fryer 1994, Murray 2013, Rees et al. 2014, Price et al. 2017, Estévez et al. 2019. To design effective disease prevention and management strategies, the complex and often fluid relationships among host−pathogen and environmental drivers of the disease need to be well understood (Mardones et al. 2018).
Over the years, significant effort has been de voted to the development of models for investigating the environmental transmission of pathogens within open-cage salmon aquaculture (Salama & Rabe 2013). These models include compartmental infectious disease models, also known as SIRs (susceptible− infectious− recovered) (Amundrud & Murray 2009, Aldrin et al. 2011, hydrodynamic and particle tracking models coupled with network analysis techniques (Amundrud & Murray 2009, Viljugrein et al. 2009, 2018, MODS 2012, Salama & Rabe 2013, Stene et al. 2014b, Foreman et al. 2015a, Samsing et al. 2016, agent-based models (Alaliyat et al. 2019a), and statistical methods (Viljugrein et al. 2009, Rees et al. 2014, Stene et al. 2014b. The proximity to diseased farms has been recognized as a major risk factor for the onset of diseases such as infectious salmon anemia virus, salmon pancreas disease virus, hematopoietic necrosis virus, and piscirickettsiosis (Gustafson et al. 2007, Lyngstad et al. 2008, Murray et al. 2010, Mardones et al. 2011, Rees et al. 2014, Stene et al. 2014a, Foreman et al. 2015b. Physical distance, along with ocean current speed and direction, ultimately determine connectivity among farms, and studies have also demonstrated that transport of pathogens by ocean currents can often better explain horizontal disease transmission be tween farms than geographic proximity alone (e.g. Euclidean and seaway distance) (Viljugrein et al. 2009, Stene et al. 2014b. Only a few models have explicitly evaluated the role of connectivity among farms in the transmission of piscirickettsiosis (Salama & Murray 2012, Rees et al. 2014. In most of them, pathogens are typically assumed to have a fixed survival time outside the host (e.g. assuming an exponential decay rate) and passively drift with ocean currents. The effect of changes in oceanographic conditions, such as seawater temperature and salinity, on the survival of pathogens are rarely considered (Alaliyat et al. 2019a). The main objective of this study was to determine the influence of oceanographic conditionsspecifically hydrodynamic connectivity among farms, seawater temperature, and salinity -on the dispersal and prevalence of piscirickettsiosis at salmon farms in the Los Lagos region of southern Chile.

MATERIALS AND METHODS
Cultured salmon records (production and sanitary conditions) were combined with oceanographic modeling data (seawater temperature, salinity, and hydrodynamic connectivity among farms) to explore environmental drivers of piscirickettsiosis in the Los Lagos region of southern Chile (Fig. 1).

Aquaculture data
Salmon aquaculture data from January 2015 to December 2016 (~103 wk in total) containing weekly re cords of fish population and mortality due to piscirickettsiosis were obtained from the National Fisheries Service of Chile (SERNAPESCA). The data were associated with 217 fish farm sites and 318 production cycles in the Los Lagos region. Mortality due to piscirickettsiosis was confirmed by certified laboratories through analysis of dead-fish tissue (brain, liver, or muscles) with PCR or indirect fluorescent anti body test (IFAT), following procedures defined by SERNAPESCA (2018d).
Pre-processing of the aquaculture data included re moval of incomplete or incorrect records of fish weight (75 cases removed) and cage population (12 cases removed), using data validators defined by the Fundación para la Transferencia Tecnológica of Universidad de Chile (SERNAPESCA 2017a,b). Rare events of high mortality reported attributable to piscirickettsiosis were also removed to avoid skewed parameterization of the stochastic model due to low representativeness. These large mortality events were identified and removed from the data set using the 98 th percentile technique, which corresponded to cumulative observed mortalities in farms located in upstream waters above ~600 000 deaths per farm in the previous 6 wk. As a result, 10 650 mortality records attributed to pis ci rickett si osis were included in the subsequent analysis. Cultured species in cluded Salmo salar (At lan tic salmon), Oncorhynchus kisutch (coho or Pacific salmon), and O. mykiss (rainbow trout). Over 70% of the records were associated with Atlantic salmon.

Oceanographic model data
Predictions of seawater temperature, salinity, and water currents (speed and direction) were generated hourly by the calibrated Near-Real-Time Sparse Hydrodynamic Ocean Code (NRT SHOC, Herzfeld 2006) hydrodynamic model of the Los Lagos region. Details of the construction and validation of the hydrodynamic model from which connectivity matrices were derived are outlined in Herzfeld (2018) and Steven et al. (2019). Briefly, the hydro dynamic model was implemented on a fine-scale (600 m horizontal; 1−50 m vertical resolution) 3D grid of the Los Lagos inland sea and nested within a regional shelf and global ocean model (Oke et al. 2008) to allow for ac curate inshore propagation of circulation and water properties. Atmospheric  Hydrodynamic Ocean Code (Herzfeld 2006) fluxes were computed from the ACCESS-G global meteo rological model, and daily river discharges for the 22 major river catchments in the region were simulated using the GR4J rainfall-runoff model (Perrin et al. 2003) with a snow component (Nepal et al. 2017). The output from the hydrodynamic model was combined in the connectivity tool CONNIE3 (CONNectivity InterfacE v3, https:// connie. csiro.au/) with particle tracking techniques for assessing the connectivity between farms. A snapshot of the model predictions in the study area is shown in Fig. 2. At each farm location, the depth-weighted predictions of mean seawater temperature and salinity were calculated for the upper 20 m of the water column. Subsequently, weekly mean values were calculated to match the temporal scale of SERNAPESCA records. The hydrodynamic connectivity among farms was predicted weekly during the study period (2015− 2016) from particle release and tracking simulations representing the passive transport (drift due to ocean currents) of Piscirickettsia salmonis in seawater. To perform the simulations, a particle behavior model was developed to represent the survival of P. salmonis in seawater: where k is the exponential mortality timescale (2.5 d) ac cording to Almendras & Fuentealba (1997), P. salmonis 0 is the particle abundance of P. salmonis at t 0 , and t is the time after release in days. We assumed P. salmonis cells to be unattached to suspended solids, and settling velocity was assumed to be negligible.
There is a paucity of information on the incubation period of P. salmonis in salmonoids prior to the appearance of symptoms of disease. Three published reports quote incubation periods from 2−25 d , Almendras et al. 1997. Large variability in the reported incubation period of P. salmonis may be due to several factors, including virulence of the strain of bacteria, concentration of the pathogen in seawater, route of infection, and host immunity status. For this study, we hypothesized that farms reporting mortality attributed to P. salmonis in the SERNAPESCA records were carriers of the disease and actively shedding pathogens into sea water for at least 3 wk (21 d) prior to reported mortalities. We also hypothesized that at the beginning of the disease cycle on a farm the number of infected salmon would be low, and therefore P. salmonis shedding rates. With progression of the disease, bacteria shedding rates are expected to increase with the increase in the total number of infected fish. During the recovery phase, shedding rates decrease in response to treatment with drugs or natural recovery from disease. To estimate the transport and dispersal of P. salmonis, a conservative ap proach was used. The release of particles (i.e. representing the bacteria) from infected farms changes in equal increments of 100 particles d -1 in the range of 100 to 700 particles d -1 on Day 1 up to Day 7, respectively, which represents the beginning of the infection cycle. Thereafter, a constant rate of 700 particles d −1 were released from Days 8−15. After Day 15, the re lease of particles was decreased linearly to 100 particles d −1 until Day 21, which represented the recovery phase of the disease. For simulations, particles were seeded at a depth of 3 m below the sea surface, which was considered the salmon swimming depth in the cages. This seeding rate adequately captures dispersal statistics, while maintaining relatively rapid computational rates. Following seeding, particles were tracked individually using a 4th-order Runge-Kutta ordinary differential equation solver, which uses linear interpolation to find the horizontal velocity at the required depth and time.
As the first step, simulations of particle release and tracking were replicated weekly for each farm in the study area to calculate potential pathogen connectiv- Fig. 2. Surface water temperature and surface current vector field for Los Lagos region, southern Chile, at midnight on 1 December 2015, generated by the hydrodynamic SHOC model (Herzfeld 2006) ity matrices among farms. The result of these simulations were weekly connectivity matrices in the form of 217 × 217 arrays, with rows corresponding to release sites (source farms) and columns corresponding to destination sites (sink farms). Each matrix element then represented the total number of P. salmonis particles arriving from each source or up stream farm to each sink or downstream farm. The potential connectivity between farms was defined as the dispersal potential of P. salmonis cells between farms, assuming all farms were shedding the bacteria into seawater, which was effectively the worst-case scenario. As explained below, potential connectivity matrices were corrected by the number of farms re porting pisci rickett si osis and the scale of a disease outbreak to provide a more realistic estimation of the risk of waterborne infection among farms.

Risk metrics of waterborne infection
Two exposure metrics of waterborne infection with P. salmonis were estimated from the combined analysis of potential connectivity matrices and mortality records due to piscirickettsiosis: the number of upstream shedding farms (UI f ) and the cumulative exposure to waterborne infection from upstreaminfected farms (CE m ).
UI f was predicted weekly through each farming cycle by cross-comparing the potential connectivity matrices (that identify upstream farms) with the mortality records attributed to piscirickettsiosis (that identify farms potentially shedding P. salmonis into seawater). Given that disease outbreak episodes can last for several weeks or more, observed mortalities due to piscirickettsiosis could be the result of cumulative exposure to multiple farms shedding the bacteria through variable periods. We assumed that infected farms located in upstream waters can influence disease dynamics in downstream farms for up to 6 wk. This time window of influence, or w' max , ac counts for (1) the time for transmission, which was limited to 30 d, (2) the incubation period of the disease (up to 25 d), and (3) the time between manifestation of first symptoms and mortality at downstream farms. Infected farms in upstream waters were counted each week they appeared in w' max (i.e. a maximum of 6 times for any farm). UI f was estimated from the following: (2) where w is the current week monitored, f is the farm monitored (at a downstream position), f' represents the farms in the connectivity network, w' is the week monitored in the past, f' max is the total number of farms in the connectivity network, C f' ,f,w−w' is hydrodynamic connectivity -specifically, the number of arriving particles to farm f that were released from farm f' at week w' , and M f' ,w−w' is the mortality observed in the upstream farm f' at week w'(ind. wk −1 ) CM is a discrete variable that takes the value of 0 when mortality and/or hydrodynamic connectivity equals 0, or 1 in any other case.
CE m was computed as the cumulative product of the hydrodynamic connectivity calculated from the particle release experiments and the mortality attributed to piscirickettsiosis in upstream farms throughout w' max . CE m is considered a proxy for the pressure of infection of P. salmonis from upstream-infected farms, and was estimated from: (3) CE m indirectly integrates other common metrics that are used to quantify infection pressure from nearby farms, such as the distance between farms (Euclidean and seaway distance) and the biomass concentration of cultivated fish (t km −2 ). In the computed connectivity, the released particles were counted as many times as they entered the cell grids where downstream farms were located. The latter condition allows a more realistic estimation of risk of waterborne transmission; nonetheless, the drawback of this simulation setup is that it did not allow us to normalize the connectivity values, specifically, of the number of arriving particles by the total number of released particles, which would be desirable to cancel the 'particles' unit of CE m . As a result, the units of CE m are number of dead fish × arriving hydrodynamic particles.

Data exploration
An exploratory analysis based on the calculation of prevalence ratios (or attributable risk) was carried out to explore environmental conditions (exposures) as risk factors of piscirickettsiosis on the fish farms in the Los Lagos region. The prevalence ratio expresses the proportion of farms reporting mortality due to piscirickettsiosis to the total number of farms exposed to a risk factor, in this case, temperature, salinity, and hydrodynamic connectivity among farms. The statistical significance of the observed differ- ences in prevalence ratios was tested using a chisquared test that compares the observed to expected values assuming no relationship between exposure and disease outcome. Only results with a probability of a Type I error (rejecting a true null hypothesis) lower than 5% are reported in the results. Prevalence ratios were computed using R (version 3.6.2, R Studio version 1.2.5033); specifically, the function 'epi.2by2' of the 'epiR' package (Stevenson et al. 2013).
Threshold values (CE m,thr , T thr , S thr ) were defined at regular intervals within the predicted range of each risk factor to discriminate (and to bin) exposed from unexposed cases (e.g. mortality records above and below 15°C) and estimated prevalence ratios. This approach al lowed us to determine the existence of threshold values of CE m , seawater temperature and salinity at which piscirickettsiosis prevalence was significantly different (higher or lower).

Stochastic model
A stochastic, state-based, time-dependent epidemi o logical model was developed to understand the dynamics of piscirickettsiosis over a fish farm production cycle. The model was built by combining mortality records attributed to piscirickettsiosis and the connectivity metrics defined above. The model assumes that each week, the fish at a farming site could be in one of the following 3 disease states: disease-free (F ), infected (I), or recovered (R). F indicates that no fish mortality due to piscirickettsiosis has been observed throughout the farming cycle, whereas R indicates that although fish mortality due to piscirickettsiosis has not been reported in the present week, such deaths had occurred earlier in the production cycle. In total, there were 6 possible transitions between disease states: F→I, I→R, R→I, F→F, I→I, and R→R. A schematic of the model is shown in Fig. 3. F was transient; all farms started in F and could move to a state of I and R. I and R are the recur-rent states, as it is not possible to return to F.
The likelihood of a farm reporting mortality due to piscirickettsiosis was related to the disease status of the farm in the previous week along with the following 4 covariates: (1) the number of farms in upstream waters that reported mortality and were therefore assumed to be shedding P. salmonis into seawater (i.e. UI f ); (2) the mortality due to piscirickettsiosis in the upstream farms corrected by the hydrodynamic connectivity (i.e. CE m ); (3) the week of the year that the farms were stocked with salmon smolts; (4) the depth-weighted predictions of mean seawater temperature and (5) salinity. The model parameters were estimated to maximize the likelihood (or probability) of the model generating the observed data. This was achieved using a Monte Carlo Markov chain approach, which considered all plausible stochastic pathways between time observations. At this point, the model only focuses on the role of environmental conditions and precludes the influence of other relevant covariates such as the fallow period, stocking density, stocking weight, stocking date, fish species, vaccination status, antibiotic treatments, and the influence of other viral and parasite co-infections.

Production statistics and sanitary conditions at fish farm sites
Descriptive statistics of the 318 salmon production cycles are presented in Table 1. The average (±SD) length of the fish farm cycles was 48.2 ± 25.3 wk (max.: 89 wk). The variability in farming cycle length was mostly due to differences in the intrinsic growth rates among salmonid species (e.g. Oncorhynchus kisutch have the shortest production cycle), temperature dependencies, and harvesting due to disease outbreaks. Farm stocking and harvesting occurred throughout the year, although most harvesting was concentrated between September and March. The average fish population was 817 059 ± 319 037 ind. farm −1 .
The average weekly fish mortality attributed to pisci rickettsiosis was highly variable, reaching a maximum of 6.2% wk −1 (~52 000 fish week −1 farm −1 ). This estimate does not account for massive outbreaks filtered from the data set, which were as high as 34.2% of the farm population. The cumulated mortality due to piscirickettsiosis in up stream farms averaged 8143.7 fish within the monitored w' max (max. 209 641 fish). CE m associated with farms reporting mortality 268 Fig. 3. Stochastic representation of piscirickettsiosis dynamics at salmon farm sites. The model includes 3 disease states (boxes) and 6 possible weekly state transitions (arrows). p F , p I , and p R represent the probability of being infected (I) at week w having been in a disease-free (F), I, or recovered (R) state at week w − 1 due to piscirickettsiosis in w' max averaged 4.1 × 10 4 ± 9.4 × 10 4 dead fish × arriving hydrodynamic particles (max.: 6.3 × 10 5 ).
According to the predictions of potential hydrodyna mic connectivity, farms were connected weekly to an average of 15.3 ± 22.5 farms (including infected, non-infected, and non-operating farms). The connectivity decreased to 2.45 ± 4.26 farms (max.: 36) when considering only those farms located in upstream waters reporting mortality attributed to piscirickettsiosis. When considering w' max (i.e. 6 wk in the past), the number of upstream farms reporting mortality attributed to piscirickettsiosis (i.e. UI f ) was 15.6 ± 23.2 farms (median: 6 farms) and reached up to 190 farms in the most ex treme cases considered in the analysis. It is important to recall that in the case of UI f , each farm was counted every week it was both reporting mortality due to piscirickettsiosis and connected hydrodynamically with a downstream farm (i.e. up to 6 times farm −1 ).

Oceanographic conditions at fish farm sites
Summary statistics of the observed variability in pre dicted oceanographic conditions (temperature and salinity) at the fish farm sites are summarized in Table 1. Over the study period (2015 to early 2017), the depth-weighted predictions of mean surface salinity and temperature within the upper 20 m of the water column at fish farm sites were 12.0 ± 1.5°C and 31.6 ± 1.8 PSU, respectively. Seawater temperatures ranged from 7.2−17.1°C and decreased with increas-ing latitude (Fig. 4A). The highest predicted seawater temperatures were in the areas of high water residence time (e.g. Reloncaví Sound, Comau Fjord, and Riñihué Fjord), whereas the lowest values were at farms along the western side of the Gulf of Corcovado (Fig. 4C).
In contrast, salinity increased towards the southwest, with the lowest values (~18 PSU) at farms on the continental side of the inner sea of Chiloe where fresh water inputs are mostly concentrated (e.g. Relon caví Fjord, Comau Fjord, and Riñihué Fjord, Chaitén), and the highest values at farms along the east coast of Chiloe Island. This pattern agrees with field observations reported in Steven et al. (2019) and references therein.

Observed fish mortality attributed to piscirickettsiosis
The risk of waterborne transmission of piscirickettsiosis among farms was estimated by a combined ana lysis of potential connectivity matrices and recorded mortality data for the years 2015 and 2016. The observed prevalence of piscirickettsiosis organized by week of the farming cycle is shown in Fig. 5. As evident from Fig. 5A, the observed prevalence of piscirickettsiosis increased progressively over the farming cycles, reaching almost 100% by Week~60. Due to the low number of cases, no significant differences were found in observed prevalence after Week 60. Disease prevalence increased through spring (Weeks 37−50) and peaked in early summer (Fig. 5B). 4.1 × 10 4 ± 9.4 × 10 4 0−6.3 × 10 5 Temperature (T ) predicted at fish farms sites throughout the study period (°C) 12.0 ± 1.5 7.2−17.1 Salinity (S) predicted at fish farms sites throughout the study period (PSU) 31.6 ± 1.8 18.1−33.5 a A single farm is counted as many times it is predicted in upstream waters in w' max (max. 6 times farm −1 ) Table 1. Summary statistics of salmon fish farm cycles considered within the study (n = 318) and observed variability in oceanographic conditions. w' max : window of influence

Role of upstream infection, water temperature, and salinity
The observed prevalence of piscirickettsiosis over the 318 farming cycles is presented in Fig. 6. Mortal-ity records were grouped using threshold values as described in Section 2.4 and only included production cycles that showed a significant difference (p < 0.05) in observed prevalence ratios between exposed and unexposed groups. The observed piscirickettsiosis prevalence in creased over the farming cycle independently of the oceanographic conditions (salinity, temperature, and connectivity). Nonetheless, as observed in Fig. 6A,C,E, a relatively faster increase in the pre va lence of piscirickettsiosis was observed for CE m compared to temperature or salinity. The prevalence of piscirickettsiosis became significantly higher after Week 10 in those farming cycles ex posed to waterborne infection (i.e. with CE m > CE m,thr ), independently of the CE m,thr value selected to group the data (exposed vs. unexposed cases).
The observed piscirickettsiosis prevalence in the farms not exposed to waterborne transmission (CE m = 0) was low, reaching only ~10% by the end of the farming cycle (Weeks 54−56) (Fig. 6B). These records were associated with isolated inshore farms with little or no exposure to upstream farms. This observation underscores the important role of hydrodynamic connectivity in the transmission of piscirickettsiosis among farms in the Los Lagos region. As evident from Fig. 5B, in the unexposed farms (CE m,thr = 0), low prevalence of disease could potentially be due to localized sources of infection at the farms.
The likelihood of observed mortality being driven by waterborne pathogens increased when higher CE m,thr values were used, as only the cases associated with the highest CE m values remain in the exposed group. As evident in Fig. 6A, no meaningful difference in disease prevalence was observed when data were grouped using CE m,thr values > 5000. For the unexposed farms (CE m < CE m,thr ) the prevalence of pis cirickettsiosis increased as increasingly higher CE m,thr values were used to discriminated exposed and unexposed farms. These observations suggest that the exposure level to waterborne infection re quired to trigger infection and mortality at downstream farms is relatively low.
As observed in Fig. 5C,D, the prevalence of piscirickettsiosis increased with predicted salinity in the study area (26−32 PSU). In farms where salinity was greater than 32 PSU, the disease prevalence was over 90% by the end of the farming cycle (Week 58), whereas below this salinity the maximum pre - valence of the disease was 75%. At Week 37 of the production cycle, the observed prevalence in farms with predicted salinity above 26 PSU was ~74% compared to a maximum of 29% at salinity below 26 PSU. Piscirickettsiosis prevalence also increased with seawater temperature (Fig. 5E,F). At Week 36 of the farming cycle, the observed prevalence of piscirickettsiosis at seawater temperature above 9°C was as high as 70% (Fig. 6E), while below this temperature it was as high as 20% (Fig. 6F). At Week 41, the prevalence of piscirickettsiosis in farms exposed to seawater temperatures above 15°C was up to ~88% and decreased to ~65% below this threshold.

Stochastic model
A stochastic model was built to predict the role of risk factors on the incidence of piscirickettsiosis (UI f , CE m , temperature, salinity and stocking week of the year). Results show that disease dynamics simulated by the model fit with the observed prevalence patterns shown in Fig. 5. The increase in the probability of a farm being infected over the farming cycle stabilizes around Week 40, as observed in Fig. 5. The model also replicated the influence of model covariates on piscirickettsiosis disease dynamics. The co variates that influence the probability of piscirickettsiosis infections, in descending order of importance, were (1) UI f in w' max (depends on distance among farms, speed and current direction), (2) CE m , followed by (3) salinity, and finally (4) temperature.
The influence of risk factors (covariates) on piscirickettsiosis dynamics were evaluated one at a time. A slight increase in the probability of piscirickettsiosis infection was predicted with an increase in the seawater temperature at the fish farm sites (Fig. 7A).
The model correctly predicted an increase in the prevalence of piscirickettsiosis with an increase in salinity from 20−32 PSU (Fig. 7B). In general, the probability of disease increased more rapidly at higher salinity, reaching > 60% toward the end of the cycle (Week 58) at 32 PSU. At Week 40 of the production cycle, the predicted probability of disease was 56% at 32 PSU compared to ~26% at 20 PSU. The overall influence of salinity on the prevalence of disease was higher than temperature, which agrees with observed prevalence ratios shown in Fig. 6E,F. However, low salinity values (< 25 PSU) were only observed occasionally in areas heavily influenced by freshwater inputs (Fig. 3); the minimum average salinity predicted at the fish farm sites was around 25 PSU.
In this study, 2 metrics related to hydrodynamic connectivity (UI f and CE m ) were incorporated into the stochastic model. These are not independent factors, as CE m depends on the number of upstream farms reporting mortality attributed to piscirickettsiosis as well as the strength of hydrodynamic connectivity between farms, which hinders the establishment of the individual role of each risk factor. As observed in Fig. 7C, the model fits suggested that piscirickettsiosis was more likely to be prevalent when farms were exposed to an increasing number of infected farms in upstream waters. The transition from states of F to I (probability greater than 50%) was predicted much earlier (~Week 15−20) in farms exposed to more than 100 upstream infected farms in w' max compared to farms exposed to 10 or less upstream infected farms in w' max , where the probability of recovery was much higher.
The stochastic model fits also suggested an increase in piscirickettsiosis incidence with an in crease in fish mortality in the upstream farms as expressed by CE m (Fig. 7D). However, the impact of CE m is predicted to be meaningful only at values above 5 × 10 5 , which is rather considered an artefact of analyzing one factor at a time and assuming a constant value for the rest of the co variates, particularly the number of upstream in fected farms (in this case fixed at 20), as ex plained above. Finally, the stochastic simulations covering all 4 seasons indicated that the week of the year for stocking salmon smolt had little influence on the predicted incidence of piscirickettsiosis (Fig. 7E).

Application of the stochastic model to predict risk
To evaluate the performance of the developed stochastic model, we applied it to the reported disease prevalence data set (318 farming cycles) for the Los Lagos region (Fig. 8). Two scenarios were considered: (1) exposure to upstream farms reporting fish mortality due to piscirickettsiosis and (2) farms which were not exposed to upstream infected farms as predicted from our hydrodynamic connectivity model (represented by CE m ). The CE m value for the exposed scenario was set equal to 1 × 10 4 (maximum feasible predicted CE m = 2 × 10 6 in the study period Week of the production cycle and area), while temperature and salinity were set to 10°C and 31.5 PSU. The stocking date of farms was set at Week 30 of the year, and the number of upstream infected farms was assumed constant for the entire farming cycle and set at 100. It is important to mention that the latter value can be achieved by multiple combinations of upstream infected farms (e.g. 16 farms shedding P. salmonis into upstream waters in the 6 wk w' max ). The observed disease prevalence frequency was very similar to the probability curve of being infected over the production cycle (blue dotted curve vs. solid red line in Fig. 8). The predicted probability of disease-free cycles for farms exposed to upstream infection rapidly declined from the stocking time to Week 25 of production. The pro bability of the farms that were exposed to upstream infected farms being infected closely matched with the recorded disease prevalence. The rate of probability change from the onset of the farming cycle was slightly higher than the observed pre valence. The ob served and predicted prevalence plateaued at about the same week (Week ~40) at a value close to 90% (Fig. 8B).

DISCUSSION
Spatial management is increasingly considered as an important tool for protecting fish health and reducing disease outbreaks , Murray & Gubbins 2016, Alaliyat et al. 2019b). Hydro dynamic models combined with particle tracking models can provide information on the risk of being exposed to pathogens from neighboring farms. In this study, we combined weekly mortality records attributed to piscirickettsiosis with hydrodynamic model data to establish relationships beyond areas of coordinated management and across the entire connectivity network in the Los Lagos region. We built on pre vious knowledge by analyzing how the number of infected farms in upstream waters, the strength of hydro dynamic connectivity, and the scale of disease outbreaks (inferred from fish mortality at individual farms), along with seawater temperature and salinity, explain the prevalence of piscirickettsiosis. The purpose of building this model was to identify piscirickettsiosis risks in space and time.
As evident from the results of this study, during the period of analysis (2015−2016), < 2% of the farming cycles were found to be disease-free until harvesting. Furthermore, during 2015 and 2016, the mortality in extreme disease outbreak events was observed to be as high as 34.2% of the population. This suggests that none of the current disease prevention and control strategies are completely effective.
This study suggests that disease dynamics in upstream farms (in terms of the number of infected sites and mortality per farm), hydrodynamic connectivity, salinity, and water temperature have complex interactions that ultimately determine the risk of infection. The stochastic model we developed allows for further exploration of these interactions. Despite complex interactions between on-farm disease dynamics and the physical environment (ocean currents, temperature, and salinity), our model successfully demonstrated the relative importance of factors that influence the probability of infection. In order of relevance, the covariates that have the most influence on the probability of infection are (1) the number of upstream infected farms, (2) the intensity of singlefarm disease outbreaks (represented by fish mortality), (3) salinity, and (4) temperature. Further understanding of the interactions between these risk factors may help to target and determine more effective disease management and control strategies. The results are consistent with previous studies where the risk of transmission of piscirickettsiosis has been reported to be influenced by water temperature, salinity, and proximity to infected farms (Rees et al. 2014, Price et al. 2017.

Hydrodynamic connectivity is a major driver of disease
Passive dispersal of salmon pathogens such as hematopoietic necrosis virus, infectious salmon anemia, and sea lice from farm to farm via ocean currents has been well documented (Gustafson et al. 2007, Jansen et al. 2012, Kristoffersen et al. 2013, Salama & Murray 2013, Foreman et al. 2015b, Murray & Gubbins 2016. In this study, the prevalence of piscirickettsiosis at farms exposed to upstream infection was observed to be 60% at Week ~15 and increased to > 90% after Week ~25 of the production cycle. In comparison, in unexposed farms, the observed prevalence of piscirickettsiosis was 60% at Week 30 and reached a maximum of 78% towards the end of the production cycle at Week 60 (Fig. 6A). This observation suggests that hydrodynamic connectivity among farms is the major driver of the disease, and that farms in the Los Lagos region are significantly inter-connected through ocean currents.
A second conclusion that arises from statistical analysis is that the level of exposure in terms of upstream infected farms required to trigger piscirickettsiosis infection and mortality at downstream farms appears to be relatively low compared to the maximum range of exposure predicted in this study. A similar conclusion is apparent from the stochastic modeling results applied to historic piscirickettsiosis disease outbreak data. Nonetheless, further research is necessary to characterize the precise level of exposure required to trigger infections in disease-free farms and potential carriage of bacteria from one production cycle to the next.
It is noteworthy that the piscirickettsiosis incidence on the farms that did not show strong hydrodynamic connectivity with our model also increased, over time, with an increase in reported mortality in upstream farms (Fig. 6B). This is most likely due to an underestimation of the connectivity within this study, as very conservative bacteria shedding rates and survival time of bacteria in the environment were used. Also, high Piscirickettsia salmonis load in the water is ex pected to result in a larger impact area or greater connectivity than estimated. Furthermore, the probability of piscirickettsiosis depends on the exposure dose of P. salmonis (Garcés et al. 1991), which is expected to increase with an increase in the rate of disease prevalence in the upstream farms.
The disease prevalence in the farms with very low or no hydrodynamic connectivity to upstream farms was low, increasing only to ~10% by the end of the farming cycle (Weeks 54−56) (Fig. 6B). We explored the records of these farms, which were a small group of farms located inshore in isolated areas with little to no hydrodynamic connectivity with surrounding farms. The fact that the observed prevalence of piscirickettsiosis in farms not exposed to upstream infection (i.e. CE m = 0) is considerably low suggests that the major route of disease transmission is the passive movement of waterborne P. salmonis via ocean currents. The source of infection in the isolated farms is most likely to be localized, such as a lapse in sanitation conditions or by carriers of the disease (e.g. wild fish have been reported to be the carrier of P. salmonis; Contreras-Lynch et al. 2015). Further research is required to establish the causes of disease outbreaks in isolated farms, as this information is vital for understanding the mechanism of transmission and control of P. salmonis.

Role of temperature and salinity
The results of this study suggest that temperature and salinity are positively correlated with fish mortality due to piscirickettsiosis. At Week 36 of the farming cycle, the observed prevalence of piscirickettsiosis at below 9°C water temperature was ap proximately 20%, whereas at temperatures above 9°C, disease pre valence increased by up to 70% (Fig. 6C,D). At Week 41, the prevalence of piscirickettsiosis in farms exposed to temperatures above 15°C was up to ~88% and decreased to ~65% below this threshold. A positive correlation between seawater temperature and piscirickettsiosis has been re ported previously (Rees et al. 2014).
The results of this study also suggest a higher prevalence of piscirickettsiosis (74%) at salinity > 26 PSU compared to a much lower prevalence (< 29%) at salinity < 26 PSU. Despite the higher mortality observed with an increase in water temperature and salinity, the mechanisms involved remain unclear, and further work is required to determine the role of temperature and salinity on disease dyna mics. For instance, this association may be due to the increased metabolic activity of both host and pathogens at higher water temperatures (Schulte 2015). It is also possible that other indirect factors which in duce stress in farmed fish, such as high salinity, low oxygen availability (controlled by ocean current speed and solubility), and coinfection with ectoparasites such as sea lice Caligus rogercresseyi, may also influence disease onset and severity (Lhorente et al. 2014, Montory et al. 2018. Atlantic salmon infected with C. rogercresseyi have been reported to have re duced immunity to P. salmonis (Lhorente et al. 2014). Furthermore, sea lice have been reported to survive better at salinity > 20 PSU (Groner et al. 2016) and a significant association between the abundance of adult C. rogercresseyi and high mortality rates in sal mon due to piscirickettsiosis has also been re ported in Chilean farms (Arriagada et al. 2019).
The hydrodynamic model predictions showed that salinity and temperature vary considerably, both seasonally and among farms (Fig. 4). Sea surface temperature increases in summer in a north-east direction within the study area, while salinity increases in a south-east direction due to freshwater inflow from rivers and streams. Consequently, the risk of piscirickettsiosis associated with changes in temperature and salinity is expected to vary significantly throughout the year and across different locations in the Los Lagos region.

Model limitations and future research
In building the stochastic model, several assumptions were made. First, a homogeneous disease-state condition was assumed at the fish farms (i.e. all fish in the same disease state at the same time). The scale of disease outbreaks can range from single individuals in cages to the entire farm population over time. Second, for the sake of simplicity, covariates (the number of upstream infected farms, associated mortalities, temperature, and salinity) were assumed constant over the farming cycle. Third, we used piscirickettsiosis-induced mortality as a proxy for the pressure of infection from source farms (P. sal mo nis shedding) assuming a 6 wk w' max . Potential bias associated with using mortality data as a surrogate of bacteria prevalence in water was offset by initiating particle release computational experiments 3 wk prior to mortality being recorded at the farm to account for the incubation period of piscirickettsiosis. Finally, the particle model representing piscirickettsiosis survival in seawater assumed a constant exponential decay rate of 2.5 d (50% re duction in ~0.25 d) (Lannan & Fryer 1994, Almendras & Fuentealba 1997. This decay rate may be conservative, given more recent estimates of survival time as long as 8 wk by Olivares & Marshall (2010) and S. A. Contreras-Lynch et al. (unpubl. data). The implications of longer survival time of P. salmonis in seawater are that the scales of connectivity among farms are possibly much larger than predicted by our model. This might explain the discrepancy in the observed infection rate of ~70% in non-connected farms. The assumption of a constant decay rate of piscirickettsiosis in seawater may need to be reviewed, as new evidence shows that decay rates vary significantly with temperature and salinity (S. A. Contreras-Lynch et al. unpubl. data). Incorporation of environmental dependencies of decay rates into particle release experiments would further improve the representation of the hydrodynamic dispersion of piscirickettsiosis in seawater. Finally, the development of new risk metrics could explicitly account for pathogen concentrations in seawater and apply a minimum infectivity dose for the disease to occur. Such thresholds have been reported for fish diseases like infectious salmon anaemia (Raynard et al. 2001, McBeath et al. 2015, infectious pancreatic necrosis virus (Smail et al. 2006), and the amoebic gill disease (Morrison et al. 2004), but the information on the infectious dose and shedding rates for piscirickettsiosis are relatively unknown.
Despite some degree of uncertainty and the potential improvements that could be made with availability of new data, the developed model corresponds well with the recorded piscirickettsiosis dynamic data in the study area and therefore can be consid-ered robust. This model could be used to explore the likely success of interventions and risk mitigation measures aimed at reducing exposure to waterborne infections. Potential connectivity matrices calculated in this study allowed us to identify farms that are highly connected i.e. receiving and spreading infection from and to other sites (stepping stones); source of pathogens to surrounding farms (super-spreaders) at high risk of being infected (super-sinks); and those isolated from the network which show a very low incidence of piscirickettsiosis. The characterization of farms according to their behavior in a 2-dimensional space (source versus sink) can potentially im prove disease management by allowing prioritized pathogen and parasite control efforts at high-risk farms.
As part of this research project, we have developed an interactive online application that simulates piscirickettsiosis dynamics at salmon farming sites in the Los Lagos region using the R package 'shiny' (https:// oa-csirochile. shinyapps. io/ water borne-srs-transmission-risk/); step-by-step instructions for using the application are provided. This web-based program allows users to investigate piscirickettsiosis dynamics as a function of oceanographic conditions, and is expected to support communication among academia, the public, and industry sectors.

Conclusions
Spatial planning and management tools can be effectively used to reduce disease risks in the absence of robust disease-specific information (Sala ma & Murray 2011). The present study aimed to develop new risk prediction models that could underpin the development of better risk management plans such as the identification of areas of high disease risk and the development of disease management strategies. At a regional scale, the developed model can help in the identification and isolation of farms in high disease dissemination areas or the selection of new farm locations with low connectivity. This may also assist in the development of area-based disease control measures such as coordinated stocking, harvesting, and fallowing. In the event of disease outbreak, models can also help in the designation of quarantine zones based on connectivity criteria rather than distance. A farm-scale model could assist in de termining the size and density of farms in an area with high connectivity, early detection of the disease on farms, and evaluation of disease management strategies such as drug treatment or early harvesting in the event of disease outbreaks. Collectively, the imple-mentation of improved risk mitigation strategies could lead to earlier control of disease outbreaks and reduced mortality.