G. Law - Scallop Population Modeling

Interdisciplinary Fisheries and Coastal Ecology Research at Rutgers University, Cook College Campus, NJAES

C. Grant Law • Scallop population models

11/28/2007: As a momentary distraction from thesis revision, I thought it would be fun to share a couple animations I put together for my defense presentation. I've always found it a bit awkward trying to describe how I build dispersal kernels out of my transport simulation results, so I thought it would be easier to just show the process as it unfolds. In case you aren't in the know, a dispersal kernel is the distribution of transport distance probabilities for dispersing seeds/larvae/eggs/whatever. I alter the concept slightly, in a way that is (I believe) far more intuitive, by building spatial probability-of-settlement maps. In these animations, you will see the dispersal kernel evolving over the course of the simulation. Each particle used in building the dispersal kernel has a weight value that it contributes to nearby stations. These values are accumulated by the stations, then at the end of the run, the values are all normalized to the maximum possible weight sum. The weights themselves are a function of the position within the release, decreasing with spatial and temporal distance from the center of the release pattern. The weights are further modified by the age of the particles themselves, increasing linearly from zero to their full values in 42 days. The weights are represented visually in these animations by the transparency of the disks surrounding the particles. The diameters of the disks increase according to a turbulent diffusion function, and represent the area over which each particle searches for stations to donate their weight vales to. Using the early positions of the particles in the construction process helps the final dispersal kernels develop the kurtotic shape found in real-world terrestrial dispersal kernels. In my models the particles are eliminated when they reach 42 days of age, but in these animations they hang around over the entire run (I didn't have enough time to get that part programmed). The first animation shows the larval retention that is typical for Georges Bank dispersal kernels. The second animation demonstrates the profound impacts initial release conditions can have on transport pathways. You can't tell from this one dispersal kernel, but the full set shows major interannual shifts in Browns Bank dispersal kernels between the Gulf of Maine and outer Georges Bank -- the latter being especially associated with Scotian Shelf crossover events. What are the ecological consequences of this variability?

6/29/2007: Here's a cool figure -- this plots the total volume of Northwest-Atlantic shelfwater (defined as having a salinity less than 34 psu) from 1980 to 2004, along with a measure of connectivity throughout sea scallop habitat (the black line is the 2-year running average of the shelfwater volume, which is plotted in gray, and the red line is the 3 year running average of connectivity, which is plotted in pink). The shelfwater volume was calculated using bimonthly climatologies (see my webpage on environmental variability). Total connectance is the sum of all connections between larval sources and their sinks. These data suggest a significant inverse correlation between these two metrics -- most likely because increases in shelfwater volume push the shelf-slope front further offshore, thereby reducing it's ability to snatch-up and move my virtual scallop larvae. What this means for sea-scallops (and all the other larval dispersers in this system) is that recruitment variability may be strongly tied to the current state of the shelfwater system. I've done correlation analyses between shelfwater variability and a couple of environmental indices -- the Noth-Atlantic Oscillation (NAO), which is the east coast version of El Nino, and the Atlantic Multi-Decadal Oscillation (AMO), which is based on changes in the mean Atlantic temperature. The correlation between NAO and shelfwater is strongest with an offset of about 5 to 6 years (NAO anticipates shelfwater volumes), generating an r- value from .38 to .51, depending on the manner in which you express NAO (running-means, winter months only, etc.). This means we can infer the state of the shelfwater system in the past, based on historical NAO data. It also allows us to predict what may happen to the shelfwater system as a result of global warming. Some climatologists expect NAO values to increase as global temperatures rise, so we may then infer that shelfwater volumes will increase as well. This figure suggests that the connectivities between shelf populations may suffer as a result. It is hard to predict exactly what this situation might produce, but one possibility is a decrease in local sea scallop populations' ability to rebound from disturbances -- a requirement for sustainable fishery activities.

6/10/2007: The following figures are derived from my most recent set of bio-physically coupled model runs (June 2007), designed to simulate transport potentials for sea scallop larvae during fall spawning events (1980 through 2003). The circulation model (Quoddy) is forced by historically derived spatio-temporally varying wind fields, historically derived density fields, and M2 tides. The individual larvae are programmed to drift at 30m depth during the day, then ascend and drift at 5m depth at night. Animations of the larval transport trajectories (ground-truthed using NOAA drifter buoys - plotted in magenta - during the same time period as the simulation) can be accessed from the following links: 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003.

This figure shows the mean flowfield generated by Quoddy, using a general set of density gradients, tides, and the winds from 2001. The magenta vectors show the surface currents, and if you look closely, you'll see little black vectors underneath that show the vertically integrated flow. The Georges Bank gyre is present, but the southwestern section appears weak. The Gulf of Maine gyre is also present, along with several expected fronts. Mean flowfield figures are also available for the Mid-Atlantic Bight and Cape Hatteras.
After the simulations are complete, transport trajectories followed by virtual larvae are used to construct dispersal kernels -- probability maps showing the likely destinations of larvae carried by the currents. This figure shows several dispersal kernels throughout the domain. The probability values are log transformed to better resolve the low probability components of the dispersal kernels. Color transparency scales with probability. For a video containing the full set of 667 mean dispersal kernels, cick here.
This movie file contains figures for self-seeding potential demonstrated in the 24 runs from 1980 to 2003. The values are the proportion of the larvae produced in each area that eventually settle in the same area at the end of the run. Self-seeding is an important factor in whether or not a local population is persistent. Population managers value persistent populations not just as a consistent supply of fishable resource, but also as a source of larvae which may be transported to nearby areas. In the context of marine reserves, the areas which have high self-seeding potential may be more valuable than others. This is especially true if the self-seeding potential varies from year to year, suggesting that the area may also provide a source of larvae to downstream populations.
Here are the mean self-seeding potentials by area.
And here are the standard deviations of self-seeding potentials by area. Again, in terms of effective marine reserve placement, areas which have high levels of both self-seeding and variability may be most valuable.
This movie file contains figures for source area demonstrated in the 24 runs from 1980 to 2003. In this case, the values displayed are the number of distinct areas in the domain which contribute larvae to a particular station. In other words, this is a measure of how many nearby populations contribute larvae to each particular sub-population. Populations living in areas with high source area values are more likely to rebound after being over-fished.
Here are the mean source areas by area.
Here are the standard deviations of source area by area.
This movie file contains figures for source area anomalies demonstrated in the 24 runs from 1980 to 2003.
This movie file contains figures for sink area demonstrated in the 24 runs from 1980 to 2003. In this case, the values displayed are the number of distinct areas in the domain to which larvae from a particular station are contributed. In other words, this is a measure of how many nearby populations recieve larvae from each particular sub-population. Populations living in areas with high sink area values are likely to be important sources of larvae for other populations.
Here are the mean sink areas by area.
Here are the standard deviations of sink area by area.
This movie file contains figures for sink area anomalies demonstrated in the 24 runs from 1980 to 2003.

1/23/2006: The data displayed below are generated from the integration of a circulation model, an individual-based model of larval behavior, and a spatially explicit demographic model. All the subpopulations are exactly the same in all respects, except for their connectance to each other via larval dispersal. In the next few months, I'll be running simulations from 1980 through 2004 with a variety of larval behaviors, setting the population model to accurately represent sea scallops, and expanding the range of environmental factors effecting population growth.

This figure links to a video showing the currents from the circulation model used to generate larval transport trajectories. The purple vectors represent surface currents. The black vectors occasionally peeking out from under the purple vectors show the vertically integrated velocities. The model is forced by spatially varying winds (from NCEP/NCAR Reanalysis, 4x daily), M2 tides, and a slope of 0.123 cm/km along the entire northeastern boundary. The only open boundary is located on the southern side, from the shore to halfway out to the southeast corner. (I've been told by some that it is not entirely obvious what geography is being represented in this image. You are looking at the east coast of North America, from the base of the Florida Peninsula north to Nova Scotia.)
This figure links to a video showing the paths of the larvae. The larval release positions are at about 4x the density of the stations used in the population model. This, plus the hexagonal arrangement, allows me to use 7 larvae per release to evaluate transport from each station -- one on the station itself, and 6 placed equidistant around it. This arrangement allows spatial variability in flow to effect the final transport calculation. To get a sense of how wind variability effects transport, a new set of larvae is released on a daily cycle for 15 days. By releasing on a daily cycle instead of a tidal cycle, the starting positions of the larvae are influenced by the shape and magnitude of the local tidal oscillations, adding an additional source of variability. For this simulation, the larvae are programmed with diel vertical migrating behavior, and settle after drifting for 49 days.
The connectivity matrix generated from the above run is displayed here. Because the 301 stations are not arrayed in a straight line, I can't really infer much about spatial transport patterns from the splotches in this figure (at least not with any confidence). I can, however, see that some stations appear to be more self-seeding than others (red spots along the diagonal).
Here we can see the spatial distribution of stations which are primarily self-seeding (meaning that larvae tend to fall back onto the heads of their parents).
Colors for this figure scale with the total area each station provides larvae to. In other words, the larvae released from the red stations traveled further and/or spread out more than the those released from the blue stations. In practical terms, this figure is a measure of how valuable the various subpopulations are for recolonizing other populations after disturbances.
This figure is the reverse of the above figure, showing the total area of stations providing larvae to each station. Red stations are likely to be much more robust in their ability to recover after a disturbance.
As the title suggests, this figure shows the population sizes for each subpopulation (301) and demographic subset (16) plotted on a log-scale, while growing under the connectance patterns defined by the above matrix.
The slopes of the previous figure's data are plotted here. Notice how some of the slopes appear to pop-up from one stable state to another near the end of the run (cool!)
This figure places the end slopes plotted above in their appropriate places. The yellow regions on Georges & Browns Banks are the second highest set of slopes in the above figure. The red regions are the highest set of slope values. The slopes which slide up to the higher slope value near the end of the run are all located just southwest of Georges Bank (a couple of them are orange in this figure).

�2007 C. Grant Law • To IMCS • To Rutgers

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