Connectivity of lobster populations in the coastal Gulf of Maine Part I: Circulation and larval transport potential

ecological modelling 210 (2008) 193 211 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/ecolmodel Connectivity of lobster populations in the coastal Gulf of Maine Part I: Circulation and larval transport potential Huijie Xue a,, Lewis Incze b, Danya Xu a, Nicholas Wolff b, Neal Pettigrew a a School of Marine Sciences, University of Maine, Orono, ME 04469-5706, United States b University of Southern Maine, United States article info abstract Article history: Received 20 June 2006 Received in revised form 11 July 2007 Accepted 26 July 2007 Published on line 12 September 2007 Keywords: Lobster population Larval transport Circulation Model Gulf of Maine The remarkable increase of Homarus Americanus (lobster) abundance in recent years has resulted in record landings throughout the states and provinces along the perimeter of the Gulf of Maine. A considerable amount of data on various life stages of lobsters has been collected for research, management and conservation purposes over the past 15 years. We have used these data sets to develop models that simulate lobster populations from newly hatched larval stage through settlement and recruitment to the fishery. This paper presents a part of the synthesis study that focuses on the early life history of lobsters. A coupled biophysical individual based model was developed that considers patterns of egg production (abundance, distribution and timing of hatch), temperature-dependent larval growth, stage-explicit vertical distributions of larvae, and mortality. The biophysical model was embedded in the realistic simulations of the physical environment (current and temperature) from the Gulf of Maine Nowcast/Forecast System. The predominant direction of larval movement follows the cyclonic Gulf of Maine Coastal Current (GMCC). Results show relatively low accumulation of planktonic stages along the eastern Maine coast and high accumulation along the western Maine coast. In years when the eastern branch of the GMCC turns offshore southeast of Penobscot Bay, more particles accumulate downstream of the branch point. Interannual variability is also apparent in development times that vary as a function of year-to-year water temperature variation. The larval stages tend to remain relatively near shore, but the final planktonic stage (the postlarva) resides near the sea surface, and the prevailing southwesterly winds in summer cause eastward and offshore drift of postlarvae. Thus, more settlement might take place earlier in the potentially long postlarval stage, and the timing and strength of the southwesterly winds are important in determining the population of potential settlers. 2007 Elsevier B.V. All rights reserved. 1. Introduction The lobster (Homarus americanus) fishery is the most lucrative coastal fishery in the Gulf of Maine (Fig. 1), now comprising more than 80% of total commercial landings of all species of fish and shellfish in the state of Maine. During the past decade, regional landings were more than double the previous longterm mean and appear to be due in significant measure to an Corresponding author. Tel.: +1 207 5814318; fax: +1 207 5814388. E-mail address: hxue@maine.edu (H. Xue). 0304-3800/$ see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2007.07.024

194 ecological modelling 210 (2008) 193 211 Fig. 1 Map of the Gulf of Maine and adjacent shelf/slope regions. Heavy contours are the coastline, 200 and 2000 m isobaths. Thin lines are 50, 100, 1000 and 3000 m isobaths. At the seaward edge, two subsurface banks (Georges and Browns Bank, both with water depth < 100 m) limit exchanges between the Gulf of Maine and the Atlantic Ocean. Several geographic references are labeled, including the deep basins (Jordan, Wilkinson and Georges); PB stands for Penobscot Bay. The shaded island at the mouth of the Bay of Fundy is Grand Manan Island. increase in abundance (Steneck and Acheson, 1997; Incze et al., 2006) as well as some increase in effort (Fogarty, 1998). A close examination of temporal and spatial patterns of abundance argues against a simple explanation for these increases, which have been variously attributed to conservation of reproductive females, large subsidies in the form of bait, favorable water temperatures and decreased predation from groundfish (see Drinkwater et al., 1996; Incze et al., 2006). Variations in larval transport, survival, and settlement can be added to the list of possible contributing factors (Wahle et al., 2004). When normalized by the area of coastal shelf less than 100 m deep, lobster landings in western Maine began increasing earlier than in eastern Maine (early versus late 1980s), though large portions of both regions attained similar areaspecific landings of approximately 3300 kg/km 2 /year by the late 1990s. The two ends of the coast have the lowest areaspecific yields and may be recruitment limited. Compared to other areas of the coast, the area east of Penobscot Bay receives a lower supply of planktonic postlarvae (the last pelagic stage in the early life of lobsters) and lower benthic settlement densities (both measured as number per unit area: Incze and Naimie, 2000; Steneck and Wilson, 2001; Incze et al., 2006). Data on temporal variability in the early life stages of lobsters come from two general sources. The first is a time-series of observations from 1988 to present of postlarval abundance off Seabrook, New Hampshire; the second is a time-series of the same length for settlement density off Boothbay Harbor, Maine (Incze et al., 2006). Both show high interannual variability and some multi-year trends, such as a period of low abundance from 1995 to 2000 followed by consecutive years with high abundance. A series of good or poor settlement years can influence multi-year trends in landings (Wahle et al., 2004). The data set does not begin early enough to know whether the increased landings of the 1990s were due to a shift in the pattern of postlarval supply and settlement in earlier years, but it is clear that such shifts occur and that there is a tight coupling between postlarval abundance and settlement (Incze et al., 1997, 2000; Wahle and Incze, 1997). The second source of data is a short series (2000 2004) of settlement densities from seven collection areas from Grand Manan Island, Canada to western Maine (Fig. 1). Those data reveal a lowsettlement year that is apparent at all sites, thus indicating a large-scale influence on recruitment (Incze et al., 2006). Good settlement years also are widespread, with some differences in specific patterns among sites. The highest settlement densities are generally west of Penobscot Bay and taper off farther to the west. The spatial pattern of postlarval abundance along the coast is similar to the along-coast pattern of settlement, substantiating studies in mid-coast Maine that show a strong correlation between postlarval supply and benthic settlement (Incze et al., 1997, 2000; Wahle and Incze, 1997). The goal of our research is to build a coupled physicalbiological model of lobster recruitment in the Gulf of Maine, focusing on coastal regions. Our prime objectives are to describe and predict patterns of transport of planktonic lobster stages, and thereby understand patterns of connectivity between various regions of the Gulf. For example, what is the spatial relationship between egg production and settlers? To what extent do variations in circulation affect this relationship? These questions are of general interest in understanding the dynamics of coastal marine populations with pelagic larvae (Cowen et al., 2006), and the capacity to answer these questions is of practical use in the management of living resources. In this paper we describe patterns of connectivity based on circulation, temperature-dependent rates of larval development, and dispersion, with and without mortality. This relatively simple approach lets us examine potential transport pathways (no mortality) and quantitative patterns for meroplankton transport (with mortality) in a complex coastal current system with strong horizontal gradients in transport and temperature. In particular, it allows us to evaluate gradients in transport along the coast as well as inshore offshore exchanges. In a subsequent paper, we will examine the more complex case where egg production varies spatially (along the coast and with depth) and temporally (over the hatching season). In both papers we compare 3 years with different along-shelf transport patterns. 1.1. Lobster early life history Larval lobsters hatch from eggs that are attached to pleopods on the adult females. Hatching along the coast of Maine occurs from June through September, with a peak in mid-july. Hatching in the Canadian portion of the Gulf of Maine begins and peaks later, perhaps by as much as 1 month depending on location. Planktonic development includes three larval stages and one postlarval stage. Postlarvae are competent to settle approximately halfway through their development (Cobb et al., 1989) but can delay settlement if suitable benthic habitat is not found (Lawton and Lavalli, 1995). Development of all stages is temperature-dependent (MacKenzie, 1988; Incze et al., 1997; Incze and Naimie, 2000) and 2 3 weeks or more may be

ecological modelling 210 (2008) 193 211 195 required from hatching to competent postlarvae (Annis et al., 2007). During this time, larvae and postlarvae can be carried considerable distances by the residual circulation (Harding and Trites, 1988; Harding et al., 2005; Incze and Naimie, 2000), but transport is highly dependent on where hatching occurs and on variability of the transport system itself. The vertical distribution of larvae is not well resolved, but there are enough data to show that distributions throughout the upper mixed layer (generally the upper 15 m) are common (Harding et al., 1987 and Incze et al., unpublished data). Postlarvae are concentrated in the upper 2 m, with most (average = 65%) of their time spent in the upper 0.5 m (Annis, 2005). Incze et al. (2003) estimated a mortality rate averaged across all planktonic stages of approximately 0.07 day 1. Recent calculations indicate that the rate is highest in the first larval stage (Incze et al., unpublished data). 1.2. Gulf of Maine circulation The Gulf of Maine and the adjoining Bay of Fundy are well known for a nearly resonant semidiurnal tide (Garrett, 1972; Greenberg, 1983) and strong tidal currents. The residual (or low frequency) circulation, driven by a combination of inflowing shelf and slope waters, river runoff, wind, heat fluxes, and tidal rectification (e.g., Bigelow, 1927; Hopkins and Garfield, 1979; Loder, 1980; Smith, 1983; Ramp et al., 1985; Brooks, 1985; Xue et al., 2000), is of a magnitude similar to the tidal currents. The Gulf of Maine Coastal Current (GMCC) is a part of the cyclonic (anticlockwise) near-surface circulation of the Gulf. It is particularly prominent during summer months, 5 30 cm s 1, when lobster larvae are in the water column. The branch of the GMCC from Grand Manan Island to Penobscot Bay (known as the Eastern Maine Coastal Current, EMCC) is generally the most coherent and vigorous part of the GMCC. In summer, the EMCC often bifurcates in the vicinity of Penobscot Bay (Pettigrew et al., 1998, 2005) with the major portion of the transport turning offshore and contributing to the cyclonic gyre around the Jordan Basin and a southward flow into the central Gulf. The portion of the EMMC that continues southwestward along the coast combines with the outflow from Penobscot Bay to constitute the Western Maine Coastal Current (WMCC). Recent observations suggest that the continuity of the EMCC and WMCC varies from year-to-year, the two being more disconnected in some years (e.g., 1998) and more connected in others (e.g., 2000: Pettigrew et al., 2005). In years when the two currents are less connected, offshore flow near Penobscot Bay is strong and the WMCC is weak. In contrast, when the cyclonic circulation encompasses the entire Gulf there is relatively little offshore transport, and transport along the western Maine coast nearly matches that of the EMCC. Thus, it is important to understand the role of the coastal current system in larval transport, and especially how variability in the coastal current system modifies connection between the east and west. 1.3. Transport and development of planktonic larvae and individual based models To depict pathways of planktonic larvae in the water and describe simultaneous larval development along the pathways, individual based models (IBMs) with coupled biology and physics are often applied (e.g., Bartsch et al., 1989; Werner et al., 1996, 2001; Page et al., 1999). In these models, Lagrangian trajectories of either passive particles or particles with prescribed behaviors (swimming, diel migration, etc.) are computed by complex hydrodynamic models. A numerical technique called random walk is often employed to simulate dispersion due to sub-grid scale processes (Csanady, 1973; Hunter et al., 1993; Visser, 1997). Furthermore, particles are equipped with the ability to sense the environment so that growth may vary according to feeding environment and physical factors such as light and temperature. Using a simple IBM imbedded in a climatological circulation model, Incze and Naimie (2000) calculated trajectories of larval lobsters in the Gulf of Maine. These early calculations identified a number of research needs, including the incorporation of mortality and dispersion, improvement in the estimations of development times, and realistic simulations of temporal and spatial variations in currents. 2. Method We developed a coupled biophysical model to describe lobster population connectivity and interannual variability along the coastal Gulf of Maine. The biophysical model includes a larval individual based model (IBM) coupled with the operational circulation model of the Gulf of Maine Ocean Observing System (www.gomoos.org and Xue et al., 2005). The larval IBM incorporates stage-specific, temperature-dependent growth rates, and simple ontogenetic changes in vertical distribution. Spatial distributions of egg production, time-dependent hatching and mortality rates are applied as post-processing steps. Of these, we consider only the effects of mortality in this paper. The following sections detail the coupled biophysical model. 2.1. Ocean circulation model The circulation model used in this study is the operational model of the Gulf of Maine Ocena Observing System (GoMOOS). It is based on the Princeton Ocean Model (Mellor, 2003) in an orthogonal curvilinear grid that has 180 120 horizontal grid points (Fig. 2) and 22 sigma levels in the vertical to map the Gulf of Maine, Georges Bank, Scotian Shelf, and the adjacent slope region with realistic topography down to a depth of 3000 m. The horizontal model resolution varies from 3 to 5 km. The GoMOOS operational model is initialized and forced at the open boundaries with daily nowcasts of velocity, surface elevation, temperature, and salinity from the Regional Ocean Forecast System (http://polar.ncep.noaa.gov/cofs/). Surface forcing, including heat, moisture and momentum fluxes, is obtained from the National Center for Environmental Prediction (NCEP) NAM 221 AWIPS Grid (http://www.nco.ncep.noaa.gov/pmb/products/nam/). Daily freshwater inputs from the Gulf s six major rivers (St. John, Penobscot, Kennebec, Androscoggin, Saco and Merrimack) are obtained from the US Geological Survey. The circulation model also includes six tidal constituents (M 2,S 2,N 2,K 1,O 1, and P 1 ) and employs SST assimilation using a simple optimal interpolation algorithm (Xue et al., 2005).

196 ecological modelling 210 (2008) 193 211 Fig. 2 Model grid of the Gulf of Maine Nowcast/Forecast System. Shaded areas represent the coastal shelf region (water depth < 100 m), where hatching takes place in the model. Locations of GoMOOS buoys E and I are denoted by asterisks. 2.2. Particle-tracking algorithm A particle-tracking subroutine (Berntsen et al., 1994) is embedded in the circulation model to simulate transport and dispersion of particles in the water. A random walk term is used to approximate the effects of sub-grid scale processes upon particle trajectories. The random walk formulation is based on the advection-dispersion equation, in which the overall transport of particles during a time interval t results from an advective component (model-resolved flows) and a dispersive component that accounts for the unresolved flows. The advective component is calculated for each particle by interpolating the 3D flow field to the particle s position, which carries the particle to its new position at the next time step. Since there are always sub-grid scale processes that cannot be resolved by discrete velocity fields, a numerical technique must be employed to simulate particle dispersion due to unresolved fluctuations in the velocity fields. In a Lagrangian framework, this is idealized by superimposing a random walk for each particle, analogous to the turbulence diffusion term in the Eulerian frame. The equation that describes the particle position can be written as X i (t + t) = X i (t) + V i (t) t + Z i (t) (1) where X i (t) is the position vector of the ith particle at time t; V i (t) is the local current velocity; and Z i (t) is a vector representing sub-grid scale turbulent dispersion. In the circulation model, effects of sub-grid scale processes on the velocity field are approximated by the turbulence diffusion terms. Scale analysis leads to the use of an ad hoc random walk in the form of (A H /l x, A H /l y, K H /l z ){R} t to represent effective dispersion. Here A H and K H are horizontal and vertical diffusivity, respectively; l x, l y, and l z are turbulence length scales; and {R} is a random process with zero mean and standard deviation of 1. A more commonly used random walk formula is derived based on the central premise that the ensemble average of the squared particle displacement increases at the rate of 2K, Fig. 3 Daily averaged horizontal diffusivity (A H )atthe depth of 1 m in logarithmic scale for 1 July 2004. The values range from 20 m 2 s 1 to about 200 m 2 s 1 along the fronts. The basic features remain unchanged at 15 m but with smaller magnitude. As well, the features are similar from day to day but with small variations in magnitude. where K is the diffusivity (Taylor, 1921). Hence, the change in position for an individual particle is given by (2K t) 1/2 {R}. The scheme (also known as naïve walk ) is known to cause particles to accumulate in areas of small diffusivity. Hunter et al. (1993) showed that if K varies linearly the centroid of a spreading normal distribution moves with a velocity K in the direction of increasing diffusivity. Following Hunter et al. (1993), Visser (1997) used the following formula such that the dispersion due to sub-grid scale processes is approximated by two terms: a definite movement in the direction of increasing diffusivity and a random movement that has a zero mean and a variance of 2K t with K evaluated at the half point of the definite movement. Z i (t) = K t + R{0, 2r 1 K( X i (t) + 1/2 K( X i (t) t)) t} (2) Here R{0, 2 } is a random process with zero mean and variance of 2, r = 1/3 if the random numbers are drawn from a uniform distribution between 1 and +1. For this study, the horizontal diffusivity (A H ) is set equal to the horizontal viscosity (A M ) (Prandtl number = 1), which is calculated using the Smagorinsky (1963) mixing scheme. The vertical diffusivity and viscosity are calculated according to the 2nd order turbulence closure scheme of Mellor and Yamada (1982). Since the particles move at fixed depths at any given time, only horizontal diffusivity (A H ) is used in the calculation, which ranges from 20 m 2 s 1 in most places to about 200 m 2 s 1 in frontal zones, occasionally reaching 400 m 2 s 1 in isolated spots (Fig. 3). The horizontal mixing numbers based on Smagorinsky (1963) are usually used in models to insure numerical stability and smooth solutions, which may overestimate the actual mixing strength of unresolved sub-grid scale processes. Nevertheless, they are used due to the lack of any other information to parameterize sub-grid scale mixing. Although the bulk of experiments in this study use the ad hoc formula above, sensitivity experiments using naïve

ecological modelling 210 (2008) 193 211 197 Table 1 Lobster development rates and the currency (PASD, see text) used in the biophysical model to record development in each stage Stage 1: 1.0 PASD < 2.0 D1 = (851(T 0.84) 1.91 ) 0.4 PASD = 1 + t/(d1 86400) Stage 2: 2.0 PASD < 3.0 D2 = (200(T 4.88) 1.47 ) 0.4 PASD = 2 + t/(d2 86400) Stage 3: 3.0 PASD < 4.0 D3 = (252(T 5.3) 1.54 ) 0.4 PASD = 3 + t/(d3 86400) Stage 4: PASD 4.0 D4 = 0.5 (0.358833T 2 14.316T + 156.895) 0.4 PASD = 4 + t/(d4 86400) D is duration, in days; T is water temperature, in C; and t is the model time step, in seconds ( t = 216 s in these runs). walk, the formula of Visser (1997) and variations of Eq. (2) are conducted to compare the magnitudes of random walk (see Section 6). As advection is the dominant transport process, the overall conclusions (especially the aggregated results at the analysis scale see Section 4 for the definition of analysis scale) are unaffected by the differences associated with the random walk term. 2001 2002 (December 2001 through February 2002) was relatively mild (3-month averaged air temperature derived from National Data Buoy Center buoys in the Gulf of Maine was 2.7 C above the mean of the period from 1984 to 2005 and the second warmest for the period). In contrast, the winters of 2.3. Larval IBM The coupled biophysical modeling focuses on the coastal shelf. Ten super-particles are released at each model node where water depth 100 m (the shaded areas in Fig. 2), resulting in a total of 21,740 particles per experiment. Each super-particle is independently subjected to the random walk term and each represents a large number of individual larvae that are maintained at stage-specific depths and develop at stage-specific, temperature-dependent rates. Development is divided into five stages: 1 3 are the first three larval stages; 4 is the early postlarval stage; and a numerical value of 4.5 is chosen to represent postlarvae that are midway through their development and competent to settle. Development rates are from the equations of MacKenzie (1988) for larval stages and Incze et al. (1997) for postlarvae, except that the original stage durations are multiplied by 0.4 to reflect recent findings that development in the field is more rapid than the previous laboratory results indicate (Incze and Naimie, 2000; Annis et al., 2007). In the model, a currency in terms of proportional accumulative stage days (PASD) is carried forward for every super-particle to record larval and postlarval development (Table 1). Super-particles maintain a depth of 15 m below the surface during larval stages 1 3 and rise to 1 m depth when they molt to stage 4. 2.4. Numerical experiments The coupled biophysical model was run for the years 2002, 2003 and 2004, which offered contrasting flow conditions of the GMCC as follows: a strong discontinuity between east and west; high flow-through, or continuity from east to west; and intermediate conditions, respectively (Fig. 4). Similar flow regimes were observed during 1998, 2000, and 2001 (Pettigrew et al., 2005). Comparisons between the modeled temperature and velocity with in situ observations at GoMOOS buoys I and E (EMCC and WMCC, respectively) show good agreement and are discussed in detail by Xue et al. (2005). Mechanisms driving interannual variability of the circulation are being investigated and will be detailed in a separate study. However, analysis of model results suggests that one of the possible mechanisms is the strength of convective mixing in winter. The winter of Fig. 4 Monthly mean circulation at 5 m for (a) July 2002, (b) 2003, and (c) 2004, showing contrasting flow conditions along the coast. Only the vectors in the area with water depth < 1000 m are shown.

198 ecological modelling 210 (2008) 193 211 2003 and 2004 were the two coldest in the period from 1984 to 2005, with 3-month averaged temperature anomalies of 2.6 and 1.7 C, respectively (Raineault and Xue, submitted). Severe cooling tends to reduce the subsurface density difference between the basins in the east and west (Jordan and Wilkinson, Fig. 1), which is consistent with the recent result of Pringle (2006) based on analysis of hydrographic data in the Gulf of Maine and the NCEP reanalysis of meteorological forcing. In summer, the sea level is higher along the coast than in the interior basins so that it gives arise to a generally cyclonic circulation in the Gulf of Maine. In years like 2002, higher sea level extends into the northwestern quadrant of the Gulf (not shown), which resulted in an upcoast pressure gradient force hence offshore turning of the coastal current. Accompanying with the decrease in density gradient between basins, the sea level slope in July between Jordan and Wilkinson basin was also smaller in 2003 with the dynamic low in Jordan basin extended into the northwestern quadrant of the Gulf. This may be related to the fact that westerly winds in 2003 and 2004 were weaker than normal during the spring and summer, while they were stronger than normal during spring 2002 and close to normal during summer 2002. In fact, the monthly averaged wind was from the east in May 2003. Easterly wind tends to enhance the southwestward coastal current and the connection between the east and west. Similar responses have been seen in recent years both in the model and in observations (Cousins et al., 2006). Super-particles were released three times each month (on the 1st, 11th and 21st) from June through September, resulting in a total of 36 experiments for the 3 years. Each release was carried forward in time for 2 months. Daily positions of all particles and their corresponding stages (1 4.5) were stored in large data arrays for post-processing. Post-processing can include the initial weighting of each super-particle to reflect the spatial and temporal distribution of hatching (that is, the number of newly hatched larvae represented by each superparticle on the day of its release, and the changing number per release over the course of the season). These results will be presented in a subsequent paper focusing on biological patterns. Post-processing also included mortality, which we evaluate here. The approach of incorporating hatching density and mortality rate in post-processing gives us flexibility to alter rates and conditions in future analyses without rerunning the full model. Both of these variables can be modified to test different scenarios (for example, climate-, disease- or fishing-induced changes in egg production and distribution), or to improve estimates with new information. 3. Larval trajectories The entire database of particle trajectories from various experiments is available at http://rocky.umeoce.maine.edu/ synthesis lobster.html. These results were first studied without post-processing, which provides the best view of predicted trajectories and potential connections among different parts of the lobster population. Model runs captured many known features of the coastal circulation, including variable flow at the mouth of the Bay of Fundy and interannual variations of the GMCC. For exam- Fig. 5 Trajectories of larvae (without mortality) released west of Nova Scotia near Digby Neck [blue box in (a)] on 11 June in (a) 2002, (b) 2003 and (c) 2004. Daily locations between 11 June and 10 August are recorded. Larval stages are color-coded: stage 1 in black, 2 orange, 3 blue, 4 green, and 4.5 (postlarvae competent to settle) magenta. ple, some of the particles released off southern Nova Scotia entered the Bay of Fundy, while others took a shortcut across the mouth of the bay and joined the Eastern Maine Coastal Current (Fig. 5). Particles generally did not converge on the eastern Maine coast. In contrast, many tended to aggregate in the vicinity of Penobscot Bay even during the year when the coastal current system flowed more continuously from east to west. Another important characteristic is that the postlarvae (stage 4 and greater) exhibited more apparent eastward drift, as they were close to the surface and more susceptible to transport by the southwesterly winds that prevail between June and September. The possible rotation of winds near shore as a result of local diurnal pressure gradient changes (sea-breezes) is not resolved in the present model. Significant divergence of flow at various points along the outer edge of the current and convergence with land along the western section of the Maine coast conform to numerous satellite-tracked drifter trajectories (J. Manning, personal communication).

ecological modelling 210 (2008) 193 211 199 Fig. 6 Similar to Fig. 5, but for particles released around (a) Grand Manan Island, (b) the eastern Maine coast, (c) Penobscot Bay region, and (d) western Maine coast on 11 July 2003. The release areas in (b) and (d) appear to be smaller as they are limited by the distance between the coast and the 100 m isobath. Fig. 5 also shows different trajectories for particles released in the same area during the same calendar period in the 3 years, suggesting interannual variations in larval delivery in response to the variable circulations patterns seen in Fig. 4. During the year with strong discontinuity between east and west (2002), particles appeared to be concentrated in the midcoast area, with a small number of them reaching the western shore in the coastal zone. During the flow-through years (2003 and 2004), particles originating at the Digby Neck release site reached the western coast of the Gulf of Maine, particularly in 2004. Although 2003 was a stronger flow-through year at the junction of the EMCC and WMCC, the flow regime west of Digby Neck favored transport into the Bay of Fundy, thereby decreasing inputs to the Maine coast. The exact paths of particles were highly dependent on the release location and time (cf. Figs. 5 and 6). Nevertheless, particles released farther to the east (as in Fig. 6) tended to stay on the offshore side of the coastal current, consistent with the notion that water adjacent to the coast is constantly pushed offshore by plume waters from various rivers along the coast (Pettigrew et al., 2005). grids are units chosen according to scientific and management considerations, but they are not formal management zones. 4.1. Zone averaged stage durations By tracking individual particles released in the analysis grids and their model stage transitions, the mean duration of each larval stage can be determined for particles originating in various grids. The estimated mean durations were further averaged for the three experiments in any given month and 4. Connectivity To summarize the role of the GMCC in distributing lobster larvae or other plankton along the Maine coast and how this varies from year-to-year, analyses of model results were focused on a scale of management interest, a total of 15 analysis grids including Maine s seven Lobster Management Zones (LMZs; Fig. 7). This is a practical scale for aggregating model results in geographic terms readily understood by the industry and management, and it avoids too much focus on small-scale patterns or results where prediction is less reliable. The other Fig. 7. Analysis grids of the biophysical model results are delineated by the 15 polygons. Red polygons A G are Maine s Lobster Management Zones; others are: BB (Browns Bank); GB (German Bank); DG (Digby Neck); FN (Bay of Fundy); GM (Grand Manan); NH (New Hampshire); MB (Massachusetts Bay) and OCC (Outer Cape Cod).

200 ecological modelling 210 (2008) 193 211 Fig. 8. Average duration time for particles released in zones A G in different months of the year for 2002: (a) June, (b) July, (c) August, and (d) September. Stages are color-coded: black (1); orange (2); green (3); and blue (4 up to the point of competence to settle). are shown in Fig. 8 for the seven Maine LMZs in 2002. The averaged stage durations are important because they determine the timing when larvae reach postlarval stage and rise to near the surface where wind effects can modify connection patterns. Particles originating in the eastern LMZs, especially zones A and B, generally took longer to develop to the postlarval stage than those originating farther to the west. The differences varied from as much as 6 days in early summer to about 2 days in the fall. The patterns shown in Fig. 8 are complicated by the fact that larval development is not isochronal across stages even at constant temperature (Table 1). In addition, larvae are transported through areas of characteristically different temperature along and across the shelf, and there is seasonal warming and cooling (Fig. 9). Stages 2 and 3 had longest durations from the June releases, ranging from 16 days in the east to 12 days in the west. Corresponding (longest) durations for Stage 1 range from 12 to 8 days in the east and west, respectively. Adding together the duration times for stages 1, 2, and 3, larvae released in June, July, August and September, averaged for all zones, took 40, 24, 18 and 16 days, respectively, to reach stage 4. Releases thus reached postlarval stage around mid-late July, late July-early August, late August-early September, and late September, respectively. Note that SST peaked in August in the west (Fig. 9a) and August September in the east (Fig. 9b), the duration time for stage 4 increased with August releases and more so with September releases. Though not shown, the averaged durations needed to reach postlarva stage increased by 2 days from 2002 to 2003 and another Fig. 9 Monthly averaged temperature at 1 m and 20 m depths from GoMOOS buoys (a) E and (b) I for the summer months of 2002, 2003 and 2004.

ecological modelling 210 (2008) 193 211 201 2 days from 2003 to 2004 in response to the lower temperatures. 4.2. Connectivity matrices Connectivity was expressed as the percentage of particles released from one analysis grid that arrived at another grid at the end of a 2-month integration period regardless of the stages of development. Note that the initial releases were restricted to locations where water depth is 100 m (Fig. 2), whereas the tally at the end of the 2-month integration periods included all depths within the analysis grids. Connectivity matrices were calculated for each month using the output from all three releases in that month. A small proportion of particles encounter the landward boundary of the model. In the first set of experiments (Fig. 10), when a particle came in contact with a landward boundary it stopped and ceased development. These particles were included in the Fig. 10 Connectivity matrices [% of particles in each analysis grid on y-axis (sink) originating from each analysis grid on the x axis (source), see text] for particles released in each month (June September) in 2002, 2003, and 2004. Particles contacting the landward boundary remained there in this experiment. Analysis grids are defined in Fig. 6.

202 ecological modelling 210 (2008) 193 211 Fig. 10 (Continued ). tally used to calculate connectivity and account for a slightly conservative estimate. The diagonal elements of the connectivity matrices represent the percentage of particles remaining within their initial release grid (i.e., measures of retention at the analysis grid-scale). Elements below the diagonal describe the transport of particles in the direction of the cyclonic (anticlockwise) coastal current, while those above the diagonal were transported eastward, presumably by wind-driven drift and mesoscale circulation features (see below). Column summation is almost always less than 100% due to loss of particles to areas outside the analysis grids. Relatively high local (LMZ- and other grid scale) retention (20 40%) was found in all runs in this set of experiments. Among all analysis grids, FN and OCC had highest retention rates, followed by Zone D. Particles originating in the Browns Bank grid (BB) had almost no arrivals in the US grids, whereas the other Canadian grids sometimes did. Overall, particles initiated in Canadian grids in June had higher per-

ecological modelling 210 (2008) 193 211 203 Fig. 11 Monthly average wind vectors in summer 2002 (blue), 2003 (red) and 2004 (green), based on data from all NDBC and GoMOOS buoys (http://www.ndbc.noaa.gov/maps/northeast.shtml) inthe Gulf of Maine. centages reaching US grids than did later releases. Zones from D westward often received large percentages of particles from eastern (upstream) release grids. Note grid NH often had smaller accumulations than those of grid MB, as the percentages were not adjusted for differences in size and shape of the analysis grids. Eastward transport of particles from the Maine coast to grids BB and GB occurred with June and July releases in all 3 years, as well as with initial releases in August 2002 and 2003 and September 2003. This eastward transport occurred across the open gulf during the postlarval stage (see Figs. 5 and 6) as a result of Ekman drift, for which we examined the prevailing wind in the summer. Fig. 11 shows the monthly mean wind vectors averaged from all National Data Buoy Center (NDBC) and GoMOOS observations in the Gulf of Maine. Because postlarvae are not abundant until July, winds in June are less important than in other months. Prevailing southwesterly winds in July and August (Fig. 11) resulted in eastward drift of postlarvae to grids BB and GB for those hatched along the Maine coast in June and July of all 3 years (see Fig. 10). This eastward transport persisted for particles released in August 2002 because winds remained from the southwest in August and September 2002, but it stopped for September releases as the wind changed to primarily from the north in October. On the other hand, eastward transport of larvae to BB and GB was enhanced with September releases in 2003 as the southwesterly wind intensified in October 2003, whereas there was no transport from the US coastal grids to BB and GB with August and September releases in 2004 as winds during September and October of that year were primarily from the north. A smaller-scale, eastward transport of particles also occurred within zones D, E, F, and G in all months of 2002 and in August and September of 2004 (e.g., in Fig. 10 and 12, particles originating in G contributed to postlarvae in zone F in all months, zone E in some, and zone D once). Brooks (1994) showed that river plumes tend to form back eddies that can generate northeastward flow near shore. For example, the author showed that the Kennebec/Androscoggin plume generates a northeastward flow near shore that sometimes reaches the mouth of Penobscot Bay (zone D). Differences in river discharges among 2002, 2003, and 2004 summers were very small according to USGS gauge measurements (http://water.usgs.gov/cgi-bin/daily flow?me). Another factor that affects the size and strength of the back eddy is the southwestward flowing coastal current, which was strong in the modeled condition of 2003 and of intermediate strength in 2004 (Fig. 4). The effect of lagging transport near shore was simulated in a second set of experiments, in which when a particle came in contact with the landward boundary, random kicks acted upon it to bring the particle back to the water. Once it was in the water, the particle might be grounded again if the local current was shoreward (and kicked out again), or it might be transported away from the landward boundary at subsequent time steps. Connectivity matrices for this set of experiments are shown in Fig. 12 for June and August. As in the first set of experiments (Fig. 10), FN emerged again as the grid with the highest local (grid-scale) retention. However, local retention rates (10 30%) were generally lower in this set of experiments, and downstream transport was relatively more important. The grid immediately downstream sometimes had a higher percentage of particles than the originating grid. Although more particles originating from grid BB reached various Maine LMZs in this experiment, this transport occurred mostly with June releases. The contribution of particles from grid GM to the Maine coast was also apparent in this second set of experiments. Zone G appeared again as a bottleneck in downstream transport such that particles originated from the eastern grids ended at grid G in several instances (more so in 2002). Recirculation within zones D, E, F, and G discussed above ( back eddies ) was again found in June and August 2002 as well as August 2004. 5. Mortality Mortality (which we modeled at 7% day 1 ) can be applied in one of two ways: (1) randomly eliminating 7% of the remaining super particles daily; or (2) applying an artificial weight to each super particle (W 0 at time zero) and decreasing it by 7% day 1. The first approach results in a rather small number of particles after 2 months (21,740 0.93 61 = 260). Since the elimination process is random, it can be imposed on the trajectories repeatedly in separate trials. Ten trials were conducted, two of which are shown in Fig. 13. The small number of particles is not ideal for depicting the randomness of trajectories for different trials because they appear to have quite distinct pathways. Fig. 13 shows the two visually most different trials among the 10, while a composite of the ten (not shown) recovers the majority of variability in the trajectories seen in Fig. 6. When taking the second approach, the weight decreases daily by a factor of 0.93 to 0.01 of the initial weight (W 0 ) after 2 months. To calculate the number of postlarvae in any of the analysis grids, one needs to know the days needed to reach stage 4.5. Fig. 8 shows that it takes about 22 44 days to reach stage 4.5, which is equivalent to a weight ranging from

204 ecological modelling 210 (2008) 193 211 Fig. 12 Connectivity matrices, similar to those defined in Fig. 10, but for experiments in which particles coming in contact with the landward boundary received random kicks to bring them back to the water at subsequent time steps. Only June and August releases are shown. 0.20 to 0.04W 0. For example, Fig. 14 shows the locations and number of days needed for the same super particles as in Fig. 6 to reach stage 4.5. Note that the distribution is much more restricted (closer to shore) than that shown in Fig. 5, and that the relative weights of the particles are much greater (11 14 ) than at the end of 2 months. The continuing decrease in numbers and progressive transport offshore by the prevailing southwesterly winds suggest that recruitment would benefit from postlarvae settling as soon as possible after they attain competency to do so (stage 4.5 by our definition here). Recall that these conclusions apply to the case where W 0 is homogeneous in all areas with water depth 100 m.

ecological modelling 210 (2008) 193 211 205 Fig. 13 Similar to Fig. 6 but with random elimination of 7% super particles daily to approximate mortality. (a) and (b) are two separate trials for particles released around Grand Manan Island, (c) and (d) the eastern Maine coast, (e) and (f) the Penobscot Bay region, and (g) and (h) the western Maine coast, respectively. 6. Sensitivity to sub-grid scale dispersion To estimate the variability of trajectories associated with different parameterizations of sub-grid scale dispersion, trajectories for the 1 July 2004 release were computed using several variations of Eqs. (1) and (2) (Table 2). Since the mouth of the Bay of Fundy is an area with strong gradients in diffusivity (see Fig. 3), we compared the trajectories of particles released west of Nova Scotia near Digby Neck (Fig. 15). Advection determines the overall direction of the trajectories, i.e., to follow the primary circulation features such as the GMCC and the gyre at the mouth of the Bay of Fundy. Drift of the centroid associated with the gradient of A H modifies the trajectories slightly (Fig. 15e). The envelope is noticeably wider with onshore/offshore drifts on the shoreward/seaward side of the GMCC. Random Walk adds further spreading of the trajectories. Experiment c (A H = 200 m 2 s 1 ) greatly overestimates the dispersion associated with sub-grid scale processes as the modeled A H is 20 m 2 s 1 in most locations (Fig. 3). Experiment h, on the other hand, shows the smallest dispersion as (A H / x) t is about 80 times smaller

206 ecological modelling 210 (2008) 193 211 Fig. 14 Time (days) and location for super particles to reach stage 4.5 when released near (a) Grand Manan Island, (b) the eastern Maine coast, (c) the Penobscot Bay region, and (d) the western Maine coast on 11 July 2003. The initial release locations are indicated by the black boxes. Colors denote development time: black (24 days or less), orange (25 26 days), green (27 28 days), blue (29 30 days), magenta (31 32 days), and red (33 days or more). Histograms show the distributions of development times for each release. than 2A H t. Differences between the other four experiments are small, hardly distinguishable in a Monte Carlo sense. Results of the sensitivity experiments are again aggregated into the analysis scale, and the connectivity matrices are shown in Fig. 16. Note that Fig. 16 shows the results of a single release on 1 July 2004 in contrast to the average of three releases for any given month shown in Fig. 10. Overall, differences between panels in Fig. 16 reflect the differences seen in Fig. 15, with the two determinant experiments (a and e) showing the least amount of dispersion. Relatively more dispersion is seen in the experiment using the ad hoc random walk (h), even more in experiments b, d, f, and g, and most in experiment c with a constant A H of 200 m 2 s 1. On the other hand, the differences between experiments h and g are mostly of the same order as the differences seen in random trials (not shown, but reaching 3% for twin experiments of g). The only noticeable difference is for the particles released in zone E, for which a significant portion arrives at zone F in experiment, b, d, f and g in contrast to having the majority ending in zone G in experiment a, e, and h. Nevertheless, the overall conclusions remain the same for all experiments: (1) relatively high local retention at the analysis scale, (2) advection by the GMCC is the predominant transport process, and (3) for this release, Table 2 List of sensitivity experiments using different formulas to approximate particle dispersions due to sub-grid scale processes Exp. a Advection only: X i (t + t) = X i (t) + V i (t) t Exp. b Advection + random walk (RW) (aam = 20 m 2 /s): X i (t + t) = X i (t) + V i (t) t + R{0, 2r 1 A H t} 1/2, A H = 20 m 2 /s Exp. c Advection + RW (aam = 200 m 2 /s): X i (t + t) = X i (t) + V i (t) t + R{0, 2r 1 A H t} 1/2, A H = 200 m 2 /s Exp. d Advection + RW (model estimated aam) also known as naïve walk: X i (t + t) = X i (t) + V i (t) t + R{0, 2r 1 A H t} 1/2, A H from the circulation ( ) model Exp. e Advection + drifting of centroid: X i (t + t) = X i (t) + V i (t) t + A H X i (t) t Exp. f Visser (1997): X i (t + t) = X i (t) + V i (t) t + A H t + R{0, 2r 1 A H ( X i (t) + 1/2 A H t) t} 1/2 Exp. g Modified Visser: X adv = X i i (t) + V i (t) t, X h = ( X i i (t) + X adv )/2, X hh = ( X h + A i i i H ( X h i ) t/2) X i (t + t) = X i (t) + V i (t) t + A H ( X h i ) t + R{0, 2r 1 A H ( X hh ) t} 1/2 i Exp. h Advection + the ad hoc RW: X i (t + t) = X i (t) + V i (t) t + ( AH x i + A H y j ) R(r 1 ) 1/2 t R represents a random process with zero mean and variance of r (e.g., r = 1/3 if R is a uniform distribution between [ 1, 1]).

ecological modelling 210 (2008) 193 211 207 Fig. 15 Trajectories of larvae released near Digby Neck (the blue box in (a)) on 1 July 2004 in experiments with different formulas of random walk as listed in Table 2. zones E and F appear to have low connection with the zones to the east. 7. Summary A coupled biophysical IBM was used to simulate transport and development of lobster larvae in coastal regions of the Gulf of Maine. The IBM simulated larval development according to stage-specific, temperature-dependent growth rate and depth. Meanwhile, pathways of larvae were calculated using a Lagrangian particle-tracking algorithm with current fields and turbulence dispersion from the Gulf of Maine Nowcast/Forecast System (Xue et al., 2005). Larvae were assumed to maintain a fixed depth at 15 m during stages 1 3, whereas postlarvae (stage 4) were at 1 m depth. Simulations were conducted in the modeled physical environment corresponding to hatching seasons in 2002, 2003 and 2004. The modeled GMCC, in response to the real-time wind, surface heat flux, river discharge, tides and open-ocean forcing, displayed a range

208 ecological modelling 210 (2008) 193 211 Fig. 16 Connectivity matrices, similar to those defined in Figs. 10 and 12, but associated with the sensitivity experiments listed in Table 2.

ecological modelling 210 (2008) 193 211 209 of circulation regimes over the simulation years. The GMCC regimes varied from little east west continuity, with most of the EMCC turning offshore and a weak WMCC (e.g., 2002), to a highly connected flow-through (2003). Similar contrasting flow conditions have been directly observed in 1998 and 2000 (Pettigrew et al., 2005). The numerical experiments thus investigated a realistic range of flow conditions in evaluating influence of GMCC interannual variability on lobster settlement patterns. Although the trajectory of any individual particle is highly susceptible to flow conditions affected by instantaneous wind, stratification of the water column, interactions with river plumes, and other factors, the prevailing pathways for planktonic stages of lobster larvae can be predicted given the characteristics of the GMCC. For example, the model predicts two distinct pathways near the mouth of the Bay of Fundy, with one bypassing the Bay to arrive at the coast of Maine directly, and another circulating cyclonically in the Bay and often being entrained in the cyclonic eddy in the outer Bay. The predominant direction of larval movement is southwestward following the cyclonic coastal current system, but the within-year and interannual variations substantially modify the generalized expectations. Accumulation of particles is relatively low along the eastern Maine coast, whereas the western Maine coast appears to receive particles (larvae) brought from the east by the coastal current system. These results describe the general tendency of water motion to distribute lobster larvae (or similar plankton) along the shelf when they originate everywhere where water depth is 100 m. The patterns will be further modified by spatial and temporal differences in hatching patterns. There is a significant amount of retention in most zones, indicating considerable potential for local recruitment in populations. In years when the EMCC turned offshore southeast of Penobscot Bay, more particles tended to accumulate in zones C and D. A small portion of particles from zones A, B and C, especially those closer to the coast (inside the 50 m isobath), were able to reach the western Maine coast, while most particles that originated in deeper water (50 100 m depth) tended to veer offshore. Interannual variability was apparent in development times. As the water temperature decreased from 2002 to 2003 then to 2004, the averaged duration needed to reach postlarvae increased by 2 4 days. The potential contribution from egg hatching even farther afield, in Canadian waters, was also investigated. Those hatching on Browns Bank had limited impact on the total number of modeled postlarvae along the US coast, while those from the Grand Manan region reached as far as the western shore of the Gulf. These connectivities describe only the potential pathways, however, as mortality reduces the numerical impact of all super-particles over time. Egg production patterns also vary and must be factored into any population-level modeling. Wind is the primary factor responsible for eastward drifting of postlarvae across vast regions of the open gulf. Transport of larvae by offshore branches of the EMCC and by the WMCC also contributes to the eastward flux of later stages in some locations and years. When larvae develop to stage 4 and move to near the surface they become part of the easterly movement driven by the prevailing southwesterly winds. Relative timing and strength of the southwesterly wind are thus important in determining the likelihood and the percentage of larvae originated from the Maine coast that potentially settle around German Bank and Browns Bank. An interesting implication of this eastward drift is that it leads to a circular larval transport assemblage. Local retention rates are relatively high especially if the land boundary is assumed to be sticky. Downstream transport becomes more important if the larvae are randomly reinjected into the water column after they encounter the land boundary. Due to the limited resolution of the present model, processes near the coast (<10 m deep and <2 grid scales from shore) were not well resolved. Neither simulation fully resolves transport processes along the complex shoreline of our modeled area. Both approaches have interpretive value, however, and together they allow one to estimate the proportion of particles that converge on the near-shore environment as a result of circulation. The circulation model, which represents a substantial step forward in transport and population modeling in the Gulf of Maine region, is in transition to higher-resolution simulations ( 1 km in the horizontal and 30 sigma levels in the vertical), which will enable us to refine the estimates of near-shore transport in the future. The simple mortality algorithm used in this study (7% day 1 for all stages) results in about 4 20% of larvae developing to postlarvae that are competent to settle (stage 4.5), depending on how long development takes. This number would be further reduced during the time required for postlarvae to settle, and many probably never do (Incze and Wahle, 1991; Incze et al., 2000, 2003), in part because they are located over deep water where settlement appears to be low (Incze et al., 2006). The initial postlarval population appears relatively close to the coastline (Fig. 14), but postlarvae drift farther offshore and continue to disperse and become less abundant the longer they remain in the water column (as in Fig. 5). The transport pathways depicted in these model results are useful for considering potential sources of postlarvae as well as patterns of gene flow (where relatively small numbers still count). For example, it seems that postlarvae in the southern Gulf of Maine might come from a variety of potential source regions (e.g., Fig. 5) that varies among years (Fig. 4). The patterns also are very useful for considering transport pathways for other constituents of the water column, including holoplanktonic species. The next addition to this model should evaluate the quantitative relationships between egg production and settlement in lobsters around the Gulf of Maine, which requires that we introduce data on egg production, which is not evenly distributed around the Gulf. This study represents the first quantitative and spatially explicit analysis of early life history data and coupled biophysical recruitment processes for lobsters for the entire coastal Gulf of Maine. Further refinements of the coupled biophysical model should include better information on the vertical distribution of larvae and mortality rates, and increased resolution of near-shore flows. Additional Lagrangian boundary conditions and alternative random walk models also should be tested in future renditions of the model. Though only approximations of the first order for growth and vertical movement have been included in the study, the individual based modeling approach offers advantages to allow ontogenetic details about the targeted organism. Unlike