Modeling Mussel Larval Dispersal Patterns

At large spatial scales, the larvae of M. galloprovincialis are dispersed as passive particles and their dispersal patterns and range of dispersal can be linked closely to hydrogeographic data [68 (link)]. Thus, the probability of M. galloprovincialis dispersing beyond the already established range in southern Africa was inferred by individual-based Lagrangian Particle Simulations (LPS). Data for currents were derived from the Hybrid Coordinate Ocean Model (HYCOM), a daily high-resolution product forced by wind speed, wind stress, heat flux and precipitation [69 (link)]. This model can resolve oceanic eddies, meandering currents, filaments and fronts [69 (link)], important mesoscale processes required to simulate accurately dispersing larvae (e.g., [70 (link)]). The LPS covered two separate coasts where the northern range limits are presently defined: (1) the west coast from Capulo (Angola; 8.00° S) to Walvis Bay (Namibia; 23.00° S) and (2) the southeast coast, from St Francis Bay (South Africa; 34.00° S) to Beira (Moçambique; 20.00° S). Both coastlines were gridded so the cells would match the spatial resolution of HYCOM (0.08° x 0.08°). Passive particles simulating drifting larvae were released from each coastal cell on a daily basis throughout the spawning season of M. galloprovincialis (from May to July and from October to January; [71 (link)]). The particles were allowed to drift for 30 and 90 days, which are the average and upper end (when metamorphic delay occurs) Pelagic Larval Duration (PLD) known for Mytilus spp. [68 (link),72 (link)–75 (link)]. In these experiments, the geographical position of each particle was determined every two hours using the local bilinear interpolation of HYCOM’s velocity fields. The aggregated trajectories allowed the production of a connectivity matrix between every pair of cells, by determining the number of temporal steps that a particle released from cell i crossed cell j, divided by the number of steps simulated per particle (30 days PLD * 12 steps per day). To account for inter-annual variability, simulations were run individually for each year for a 5-year period (2008 to 2012), and the mean connectivity matrix was calculated by averaging the annual matrices. The null hypotheses of no correlation between the connectivity matrices performed with contrasting PLDs (30 and 90 days) for both west and southeast coasts were tested using Mantel non-parametric test based on 9999 permutations.
Niche modeling analysis, niche divergence tests and dispersal simulations were performed in R [76 (link)] using the packages: adehabitat, dismo, gbm, gstat, mda, parallel, raster, SDMTools and vegan.