Modeling parasite dynamics on farmed salmon for precautionary conservation management of wild salmon

Next-generation matrices for marine metapopulations: The case of sea lice on salmon farms

Classifying habitat patches as sources or sinks and determining metapopulation persistence requires coupling connectivity between habitat patches with local demographic rates. While methods to calculate sources, sinks, and metapopulation persistence exist for discrete-time models, there is no method that is consistent across modeling frameworks. In this paper, we show how next-generation matrices, originally popularized in epidemiology to calculate new infections after one generation, can be used in an ecological context to calculate sources and sinks as well as metapopulation persistence in marine metapopulations. To demonstrate the utility of the method, we construct a next-generation matrix for a network of sea lice populations on salmon farms in the Broughton Archipelago, BC, an intensive salmon farming region on the west coast of Canada where certain salmon farms are currently being removed under an agreement between local First Nations and the provincial government. The column sums of the next-generation matrix can determine if a habitat patch is a source or a sink and the spectral radius of the next-generation matrix can determine the persistence of the metapopulation. With respect to salmon farms in the Broughton Archipelago, we identify the salmon farms which are acting as the largest sources of sea lice and show that in this region the most productive sea lice populations are also the most connected. The farms which are the largest sources of sea lice have not yet been removed from the Broughton Archipelago, and warming temperatures could lead to increased sea louse growth. Calculating sources, sinks, and persistence in marine metapopulations using the next-generation matrix is biologically intuitive, mathematically equivalent to previous methods, and consistent across different modeling frameworks.

Estimating sea lice infestation pressure on salmon farms: Comparing different methods using multivariate state-space models

Sea lice are ectoparasites of salmonids, and are considered to be one of the main threats to Atlantic salmon farming. Sea lice infestation on a farm is usually initiated by attachment of the free-living copepodid stage derived from the surrounding water, frequently originating from adult lice on the same farm or from neighboring salmonid farms, referred to as internal and external sources, respectively. Various approaches have been proposed to quantify sea lice infestation pressure on farms to improve the management of this pest. Here, we review and compare five of these methods based on sea lice data from 20 farms located near Grand Manan island in the Bay of Fundy, New Brunswick, Canada. Internal and external infestation pressures (IIP and EIP, respectively) were estimated using different approaches, and their effects were modeled either by a unique parameter for all production cycles or by different parameters for each production cycle, using a multivariate state-space model. Predictive variables, such as water temperature and sea lice treatments, were included in the model, and their effects across production cycles were estimated along with those of other model parameters. Results showed that models with only EIP explained the variation in the data better than models with only IIP, and that models with unique IIP and unique EIP for all cycles were generally associated with the best model fit. The simplest, fixed lag method for calculating infestation pressure had the best predictive performance in our models among the methods studied.

A Next-Generation Approach to Calculate Source-Sink Dynamics in Marine Metapopulations

In marine systems, adult populations confined to isolated habitat patches can be connected by larval dispersal. Source-sink theory provides effective tools to quantify the effect of specific habitat patches on the dynamics of connected populations. In this paper, we construct the next-generation matrix for a marine metapopulation and demonstrate how it can be used to calculate the source-sink dynamics of habitat patches. We investigate the effect of environmental variables on the source-sink dynamics and demonstrate how the next-generation matrix can provide useful biological insight into transient as well as asymptotic dynamics of the model.

The Use of Kernel Density Estimation With a Bio-Physical Model Provides a Method to Quantify Connectivity Among Salmon Farms: Spatial Planning and Management With Epidemiological Relevance

Connectivity in an aquatic setting is determined by a combination of hydrodynamic circulation and the biology of the organisms driving linkages. These complex processes can be simulated in coupled biological-physical models. The physical model refers to an underlying circulation model defined by spatially-explicit nodes, often incorporating a particle-tracking model. The particles can then be given biological parameters or behaviors (such as maturity and/or survivability rates, diel vertical migrations, avoidance, or seeking behaviors). The output of the bio-physical models can then be used to quantify connectivity among the nodes emitting and/or receiving the particles. Here we propose a method that makes use of kernel density estimation (KDE) on the output of a particle-tracking model, to quantify the infection or infestation pressure (IP) that each node causes on the surrounding area. Because IP is the product of both exposure time and the concentration of infectious agent particles, using KDE (which also combine elements of time and space), more accurately captures IP. This method is especially useful for those interested in infectious agent networks, a situation where IP is a superior measure of connectivity than the probability of particles from each node reaching other nodes. Here we illustrate the method by modeling the connectivity of salmon farms via sea lice larvae in the Broughton Archipelago, British Columbia, Canada. Analysis revealed evidence of two sub-networks of farms connected via a single farm, and evidence that the highest IP from a given emitting farm was often tens of kilometers or more away from that farm. We also classified farms as net emitters, receivers, or balanced, based on their structural role within the network. By better understanding how these salmon farms are connected to each other via their sea lice larvae, we can effectively focus management efforts to minimize the spread of sea lice between farms, advise on future site locations and coordinated treatment efforts, and minimize any impact of farms on juvenile wild salmon. The method has wide applicability for any system where capturing infectious agent networks can provide useful guidance for management or preventative planning decisions.

Statistical modelling of sea lice count data from salmon farms in the Faroe Islands

Fiskaaling regularly counts the number of sea lice in the attached development stages (chalimus, mobiles and adult) for the salmon farms in the Faroe Islands. A statistical model of the data is developed. In the model, the sea-lice infection is represented by the chalimus (or mobile) lice developing into adult lice and is used to simulate past and current levels of adult lice-including treatments-as well as to predict the adult sea lice level 1-2 months into the future. Time series of the chalimus and adult lice show cross-correlations that shift in time and grow in size with temperature. This implies in situ the temperature-dependent development times of about 56 down to 42 days and the inverted development times (growth rates) of 0.018 up to 0.024 lice/day at 8-10°C. The temperature dependence DT=α1T+α2α3=17,840T+7.439-2.128is approximated byD1T=105.2-6.578T≈49 days at the mean temperature 8.5°C-similar to DchaT=100.6-6.507T≈45 days from EWOS data. The observed development times at four sites for a year (2010-11) were 49, 50, 51 and 52 days, respectively. Finally, we estimate the sea lice production from fish farms to discuss approaches to control the sea lice epidemics-preferably by natural means. This study is useful for understanding sea lice levels and treatments, and for in situ analysis of the sea-lice development times and growth rates.

Using state-space models to predict the abundance of juvenile and adult sea lice on Atlantic salmon

Sea lice are marine parasites affecting salmon farms, and are considered one of the most costly pests of the salmon aquaculture industry. Infestations of sea lice on farms significantly increase opportunities for the parasite to spread in the surrounding ecosystem, making control of this pest a challenging issue for salmon producers. The complexity of controlling sea lice on salmon farms requires frequent monitoring of the abundance of different sea lice stages over time. Industry-based data sets of counts of lice are amenable to multivariate time-series data analyses. In this study, two sets of multivariate autoregressive state-space models were applied to Chilean sea lice data from six Atlantic salmon production cycles on five isolated farms (at least 20 km seaway distance away from other known active farms), to evaluate the utility of these models for predicting sea lice abundance over time on farms. The models were constructed with different parameter configurations, and the analysis demonstrated large heterogeneity between production cycles for the autoregressive parameter, the effects of chemotherapeutant bath treatments, and the process-error variance. A model allowing for different parameters across production cycles had the best fit and the smallest overall prediction errors. However, pooling information across cycles for the drift and observation error parameters did not substantially affect model performance, thus reducing the number of necessary parameters in the model. Bath treatments had strong but variable effects for reducing sea lice burdens, and these effects were stronger for adult lice than juvenile lice. Our multivariate state-space models were able to handle different sea lice stages and provide predictions for sea lice abundance with reasonable accuracy up to five weeks out.

Association between sea lice (Lepeophtheirus salmonis) infestation on Atlantic salmon farms and wild Pacific salmon in Muchalat Inlet, Canada

Growth in salmon aquaculture over the past two decades has raised concerns regarding the potential impacts of the industry on neighboring ecosystems and wild fish productivity. Despite limited evidence, sea lice have been identified as a major cause for the decline in some wild Pacific salmon populations on the west coast of Canada. We used sea lice count and management data from farmed and wild salmon, collected over 10 years (2007–2016) in the Muchalat Inlet region of Canada, to evaluate the association between sea lice recorded on salmon farms with the infestation levels on wild out-migrating Chum salmon. Our analyses indicated a significant positive association between the sea lice abundance on farms and the likelihood that wild fish would be infested. However, increased abundance of lice on farms was not significantly associated with the levels of infestation observed on the wild salmon. Our results suggest that Atlantic salmon farms may be an important source for the introduction of sea lice to wild Pacific salmon populations, but that the absence of a dose response relationship indicates that any estimate of farm impact requires more careful evaluation of causal inference than is typically seen in the extant scientific literature.

Lessons from sea louse and salmon epidemiology

Effective disease management can benefit from mathematical models that identify drivers of epidemiological change and guide decision-making. This is well illustrated in the host-parasite system of sea lice and salmon, which has been modelled extensively due to the economic costs associated with sea louse infections on salmon farms and the conservation concerns associated with sea louse infections on wild salmon. Consequently, a rich modelling literature devoted to sea louse and salmon epidemiology has been developed. We provide a synthesis of the mathematical and statistical models that have been used to study the epidemiology of sea lice and salmon. These studies span both conceptual and tactical models to quantify the effects of infections on host populations and communities, describe and predict patterns of transmission and dispersal, and guide evidence-based management of wild and farmed salmon. As aquaculture production continues to increase, advances made in modelling sea louse and salmon epidemiology should inform the sustainable management of marine resources.

Wild juvenile salmonids in Muchalat Inlet, British Columbia, Canada: factors associated with sea lice prevalence

The Muchalat Inlet, British Columbia, is among the most westerly points at which aquaculture is practiced in Canada. In this paper, we summarise data from over 18000 wild fish sampled at 16 sites over an 8 yr period, between 2004 and 2011. The most prevalent wild species was chum salmon Oncorhynchus keta (82.4%), followed by Chinook O. tshawytscha (10%) and coho O. kisutch (4.3%). However, inter-annual and seasonal variation was evident, and smaller numbers of other Pacific salmon and stickleback species were sporadically observed. A high percentage of wild salmon (~95%) had no sea lice parasites present, with less than 1% of the fish hosting a mobile-stage sea louse. Of the data for which sea lice species were recorded, just over 96% of samples were identified as Lepeophtheirus salmonis. Logistic regression models assessed the association between the presence of lice and a range of independent variables. These models indicated a significant degree of spatial variation, much of which could be explained in terms of salinity levels. There were also important variations through time, both over the season within a year and across years. In addition, coho salmon were significantly more likely (odds ratio = 1.65; 95% CI = 1.20-2.3) to be infected than chum salmon. The protective effect of low salinity was most clearly seen at values lower than 15 psu, although this was dependent on fish species.

Modelling the impact of temperature-induced life history plasticity and mate limitation on the epidemic potential of a marine ectoparasite

Temperature is hypothesized to contribute to increased pathogenicity and virulence of many marine diseases. The sea louse (Lepeophtheirus salmonis) is an ectoparasite of salmonids that exhibits strong life-history plasticity in response to temperature; however, the effect of temperature on the epidemiology of this parasite has not been rigorously examined. We used matrix population modelling to examine the influence of temperature on demographic parameters of sea lice parasitizing farmed salmon. Demographically-stochastic population projection matrices were created using parameters from the existing literature on vital rates of sea lice at different fixed temperatures and yearly temperature profiles. In addition, we quantified the effectiveness of a single stage-specific control applied at different times during a year with seasonal temperature changes. We found that the epidemic potential of sea lice increased with temperature due to a decrease in generation time and an increase in the net reproductive rate. In addition, mate limitation constrained population growth more at low temperatures than at high temperatures. Our model predicts that control measures targeting preadults and chalimus are most effective regardless of the temperature. The predictions from this model suggest that temperature can dramatically change vital rates of sea lice and can increase population growth. The results of this study suggest that sea surface temperatures should be considered when choosing salmon farm sites and designing management plans to control sea louse infestations. More broadly, this study demonstrates the utility of matrix population modelling for epidemiological studies.

Allee effect from parasite spill-back

The exchange of native pathogens between wild and domesticated animals can lead to novel disease threats to wildlife. However, the dynamics of wild host-parasite systems exposed to a reservoir of domesticated hosts are not well understood. A simple mathematical model reveals that the spill-back of native parasites from domestic to wild hosts may cause a demographic Allee effect in the wild host population. A second model is tailored to the particulars of pink salmon (Oncorhynchus gorbuscha) and salmon lice (Lepeophtheirus salmonis), for which parasite spill-back is a conservation and fishery concern. In both models, parasite spill-back weakens the coupling of parasite and wild host abundance-particularly at low host abundance-causing parasites per host to increase as a wild host population declines. These findings show that parasites shared across host populations have effects analogous to those of generalist predators and can similarly cause an unstable equilibrium in a focal host population that separates persistence and extirpation. Allee effects in wildlife arising from parasite spill-back are likely to be most pronounced in systems where the magnitude of transmission from domestic to wild host populations is high because of high parasite abundance in domestic hosts, prolonged sympatry of domestic and wild hosts, a high transmission coefficient for parasites, long-lived parasite larvae, and proximity of domesticated populations to wildlife migration corridors.