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

Abstract

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.

The relevance of larval biology on spatiotemporal patterns of pathogen connectivity among open-marine salmon farms

“…There were 21 vertical gridded layers with variable spacing from sea bottom to surface, with the highest resolution at the surface and bottom layers, and maximum inter layer spacing of 9% of the depth at mid column. Depth ranged between 3 m and 520 m (Cantrell et al 2018). Daily freshwater river discharge values were used (see Fig.…”

“…Hourly output from the hydrodynamic model was used by an offline particle-tracking model, in which each simulated particle represented a cohort of sea lice larvae. Each of these particles was coupled to a biological model that dictated the maturation and survivorship of the particle based on the salinity and temperature it encountered (Stucchi et al 2011;Cantrell et al 2018).…”

“…The details of the equations governing the biology of the sea lice larvae can be found in (Cantrell et al 2018). In short, particles where released as pre-infectious nauplii, which matured into infectious copepods at a rate that was temperature dependent.…”

“…Details of the methods used to calculate connectivity using the particle tracking releases can be found in Cantrell et al (2018). In brief, the infestation pressure (IP) each farm exerted on every other farm was estimated as follows: a cohort of sea lice was defined as 24 hours of particle pulses, and each of these groups was labelled as a "cohort release day" (CRD).…”

“…Thus, each CRD represents the entire life of a cohort of particles released from all farms on one particular day of the simulation ( Fig. 2 in Cantrell et al 2018).…”