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.

Timing and probability of arrival for sea lice dispersing between salmon farms.

Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. With a free-living larval stage, sea lice can disperse tens of kilometres in the ocean between salmon farms, leading to connected sea louse populations that are difficult to control in isolation. In this paper, we develop a simple analytical model for the dispersal of sea lice (Lepeophtheirus salmonis) between two salmon farms. From the model, we calculate the arrival time distribution of sea lice dispersing between farms, as well as the level of cross-infection of sea lice. We also use numerical flows from a hydrodynamic model, coupled with a particle tracking model, to directly calculate the arrival time of sea lice dispersing between two farms in the Broughton Archipelago, British Columbia, in order to fit our analytical model and find realistic parameter estimates. Using the parametrized analytical model, we show that there is often an intermediate interfarm spacing that maximizes the level of cross-infection between farms, and that increased temperatures will lead to increased levels of cross-infection.

Ecological responses to blue water MPAs.

Marine protected areas (MPAs) can contribute to protecting biodiversity and managing ocean activities, including fishing. There is, however, limited evidence of ecological responses to blue water MPAs. We conducted the first comprehensive evaluation of impacts on fisheries production and ecological responses to pelagic MPAs of the Pacific Remote Islands Marine National Monument. A Bayesian time series-based counterfactual modelling approach using fishery-dependent data was used to compare the temporal response in the MPAs to three reference regions for standardized catch rates, lengths, trophic level of the catch and species diversity. Catch rates of bigeye tuna, the main target species (Kingman/Palmyra MPA, causal effect probability >99% of an 84% reduction; 95% credible interval: -143%, -25%), and blue shark (Johnston MPAs, causal effect probability >95%) were significantly lower and longnose lancetfish significantly higher (Johnston MPAs, causal effect probability >95%) than predicted had the MPAs not been established, possibly from closing areas near shallow features, which aggregate pelagic predators, and from 'fishing-the-line'. There were no apparent causal impacts of the MPAs on species diversity, lengths and trophic level of the catch, perhaps because the MPAs were young, were too small, did not contain critical habitat for specific life-history stages, had been lightly exploited or experienced fishing-the-line. We also assessed model-standardized catch rates for species of conservation concern and mean trophic level of the catch within and outside of MPAs. Displaced effort produced multi-species conflicts: MPAs protect bycatch hotspots and hotspots of bycatch-to-target catch ratios for some at-risk species, but coldspots for others. Mean trophic level of the catch was significantly higher around MPAs, likely due to the aggregating effect of the shallow features and there having been light fishing pressure within MPAs. These findings demonstrate how exploring a wide range of ecological responses supports evidence-based evaluations of blue water MPAs.

Modeling Pathogen Dispersal in Marine Fish and Shellfish.

In marine ecosystems, oceanographic processes often govern host contacts with infectious agents. Consequently, many approaches developed to quantify pathogen dispersal in terrestrial ecosystems have limited use in the marine context. Recent applications in marine disease modeling demonstrate that physical oceanographic models coupled with biological models of infectious agents can characterize dispersal networks of pathogens in marine ecosystems. Biophysical modeling has been used over the past two decades to model larval dispersion but has only recently been utilized in marine epidemiology. In this review, we describe how biophysical models function and how they can be used to measure connectivity of infectious agents between sites, test hypotheses regarding pathogen dispersal, and quantify patterns of pathogen spread, focusing on fish and shellfish pathogens.

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.