Introduction
A major long-term goal in biological oceanography is to understand the underlying mechanisms responsible for observed distribution and abundance patterns in marine organisms and to predict how these change in time and space. Observational data shows a high degree of seasonal and spatial variability in the large scale mean abundance patterns for some of the species of dominant mesozooplankton in the Georges Bank/Gulf of Maine region. The modeling effort in this study explores the extent to which this variability can be explained by the interaction of physical processes with zooplankton population dynamics. The focus of the present work is the distribution patterns of the copepod Calanus finmarchicus for the January-February (JF) and the March-April (MA) bi-monthly periods.
Authors
Wendy Gentleman(1)
Daniel Lynch(1)
Dennis McGillicuddy(2)
Cabell Davis(2)
(1) Dartmouth College, Hanover New Hampshire, U. S. A.
(2) Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, U. S. A.
MARMAP Characteristic Distributions of Calanus finmarchicus
Data courtesy of Carol Meise The Meise-O'Reilly log-transformed vertically integrated total abundance of stages CIII-CVI of Calanus finmarchicus was optimally estimated in order to map the data onto the Marmap1 domain. Resulting concentration fields for JF and MA are shown.
Figure 1:Tile locations for the MARMAP observational data.
January-February Key Features
Highest mean abundances are over Wilkinson and Jordan Basin. These basins are believed to be the sites at which the Calanus diapause. Thus, the higher values are attributed to the 'bottom source' of rising copepodites.
Figure 2:January-February log-transformed mean vertically-integrated abundance of stages CIII-CVI [log (#/10m2 +1)].
Figure 3:January-February total abundance of stages CIII-CVI plotted as concentrations [#/m3].
March-April Key Features
Gulf-wide, the concentrations have increased from JF values by a factor of 10. Here the plot of the concentration (Fig. 5) shows very high values along the tip of Nova Scotia and along the coast of the northern GOM. These may be a figment of the objective analysis/transformation of the data as there are no sampling sites this close to the coast (see Fig. 1). Also apparent are high on-bank concentrations and relatively lower concentrations along the northern flank and in the SCOPEX zone (from the Southern edge of Wilkinson Basin to the northern part of Great South Channel).
Figure 4:March-April log-transformed mean vertically-integrated abundance of stages CIII-CVI [log (#/10m2 +1)].
Figure 5:March-April abundance of stages CIII-CVI plotted as concentrations [#/m3].
Governing Equations and Numerical Model
We use the vertically integrated Advection-Diffusion-Reaction equation to couple realistic circulation with realistic stage-based population dynamics. Although zooplankton swimming speeds are comparable to vertical fluid speeds, they are negligible when compared with the horizontal fluid velocities. Thus, in 2-D, advective and diffusive transport are due entirely to the marine hydrodynamics. Under the assumption of fluid continuity, this equation is written:
Local Rate of Change = Rate of Advection + Rate of Diffusion + Reaction
where,
Advection=transport with the mean fluid motion
Diffusion=transport due to sub-grid fluid motions
Reaction=local generation or decay
is the instantaneous depth averaged concentration (quantity per volume) of stage p
is array 
of stage concentrations
is the local depth of the water
is the depth averaged fluid velocity
is the local horizontal diffusivity
is the populations dynamics source term for stage 
Advection due to the mean circulation is dictated by the bi-monthly vertically-averaged lagrangian residual velocity. These flow fields have been pre-computed using the results of the Dartmouth prognostic circulation model [Lynch et al., 1996a; Naimie, 1996]. Diffusion is due to the turbulent mixing that occurs on sub-grid scales. The horizontal diffusivities used in the model are the vertical average of the residual diffusivities pre-computed by the Smagorinsky closure in the Dartmouth prognostic circulation model [Lynch et al., 1996a; Naimie, 1996]. The diffusivities range from 1-900 m2/s with average on-bank values of 50 m2/s.
Figure 6:The finite element Marmap1 domain used to solve the ADR equation.
Reaction is due to the population dynamics. For this we use a staged-based model [as in Davis, 1984a,b] that includes fecundity (rate of egg production), molting (rate of development) and mortality (rate of death due to natural causes and predation). The stages are the 13 morphologically distinct stages (Egg, Naupliar Stages I-VI, and Copepodite Stages I-VI).
Table 1. Data for Calanus finmarchicus by stage 
C)
The reaction terms become
where where the factor 1/2 in the first term of the equation for R1 comes from the assumption that the sex ratio of adult Calanus finmarchicus is assumed 1:1 and both fecundity (e) and molting rates (g) are dependent upon the local temperature and food availability. If the development of the copepods is temperature-limited, these rates are described by the Belehradek's equation using appropriate parameters for Calanus finmarchicus. For 5oC, the molting rate for each stage is the reciprocal of the stage-durations listed in Table 1, and the fecundity rate is 2.95 eggs per day. A first approximation to the effect of food limitation is to reduce these development and/or fecundity rates in regions where there is a shortage of food supply for the copepod. Without modeling the predators, mortality rates are essentially unknowns as mortality (m) is dependent upon the predator concentrations, location and encounter rates.
Figure 7:JF vertically averaged temperature field used for population dynamics rate calculations
Passive Tracer Simulations
In these simulations, no population dynamics are employed. We examine how the mean physical transport alone affects the distribution patterns.
Effect of External Source Regions Inflow regions to the Gulf of Maine are of interest because they represent potential influxes of Calanus finmarchicus to the indigenous community on Georges Bank. One such potential source is the Scotian Shelf inflow. In this simulation, the spatial extent of the contribution of these potential source regions in examined for the JF bi-monthly period. Inflow boundaries were specified to have a constant concentration of 1.0 m-3 for all time while the concentrations elsewhere inside the domain were initially set to 0.0 m-3.
Figure 8:Results of inflow source region simulation. Although the influxes from the boundary of the domain do contribute to the Gulf populations of Calanus finmarchicus, in the course of 2 months, these do not make a significant contribution to the bank populations.
Effect of Differences in Seasonal Circulation Fields Some of the seasonal variability in the abundance of Calanus finmarchicus is attributed to the seasonal variability in the circulation fields. Here we compare the 'retentiveness' of the bank in each of the JF and MA periods. Given identical initial conditions of 1.0 m-3 on the bank (defined by the 100m isobath and the 69W longitude) is and 0.0 m-3 elsewhere in the domain, and identical boundary conditions of no-sources on inflow boundaries and no diffusive flux on outflow boundaries, the contrasting results of the two 2 month simulations are shown in Figures 9a and 9b.
Figure 9a:Results with the JF circulation field. The highest peak in concentration now lies at the southern tip of the bank and is being advected off the bank.
Figure 9b:Results with the MA circulation field. The peak concentration is further north than the JF results and remains well within the 60m isobath.
Because realistic inflow boundary conditions for the biologically active simulations are currently an unknown (and indeed the model can be used to test various hypotheses), the results of the simulations should not be compared with the MARMAP data in regions where these boundary conditions have a significant contribution. From this simulation, we see that this restricts comparisons to Georges Bank, the southern Gulf of Maine and the western part of the Northern Gulf of Maine.
MARMAP distributions as initial conditions This simulation used the JF MARMAP total abundance data (Fig. 3) for an initial condition. As the object was to see how the physical transport of the existing JF concentration contributes to the patterns seen in MA (Fig. 5), no sources were input at the boundaries or elsewhere in the domain.
Figure 10:Results for the JF circulation field for JF MARMAP initial conditions. The high concentration over Wilkinson basin has moved both eastward onto the bank and southward into the Great South Channel (GSC)/SCOPEX region, and the high concentration over Jordan Basin has been 'smoothed out' by the transport.
The transport of animals from the Gulf onto the bank (seen in Fig 10) due to the physical circulation during this 2 month period indicates that the dramatic increase seen in the on-bank MARMAP concentrations of Calanus from JF to MA, is not simply due to in-situ growth of the resident population.
The MARMAP data for MA does not show increased levels in the GSC. In fact, it has lower total concentrations in this region than are observed in the simulation without population growth. This implies that there must be relatively high mortality rates for the late-stage copepodites that are transported to the GSC.
Unlike the simulation results, the MARMAP data shows the peak concentration over Jordan Basin is maintained throughout MA. Thus, there must be some source (i.e. in-situ growth of the population, source regions external to the domain or a continued 'bottom source' from the rising CVs) to the Basin that replaces the animals removed by the physical transport.
Biologically Active Simulations
All of the following 2 month simulations were conducted with the JF physical fields. Boundary conditions were zero concentration on inflow boundaries and no diffusive flux on outflow boundaries. Initial conditions were adult concentrations matching the MARMAP total abundances for JF (Fig. 3) and all zero concentration in all other stages. These results are compared to the MA MARMAP distribution patterns (Fig 5).
No Mortality and Temperature-Limited Development Rates
As both the effect of food-limitation of the development rates and the mortality rates themselves are the least well defined parameters, this simulation was conducted assuming no mortality and optimal developments rates (limited only by the local temperature). Although unrealistic, this simulation represents the 'upper limit' for abundances of Calanus due to growth of the population found in JF.
Figure 11a:Total concentration of stages CIII-CVI [#/m3].
Figure 11b:Total concentration of naupliar stages NI-NVI [#/m3].
Figure 11c:Biomass of stages NI-NVI [mg C/m3]. Overlay is the generalized distribution of cod/haddock. Region 2 indicates the MA location of the early cod larvae.
Simulation concentrations are significantly higher than MARMAP except along the coast where they are much lower. We see that the GSC peak that occurred in the passive tracer results has been amplified by the growth of the population. It is quite evident from these results that mortality needs to be included in the population dynamics, and that, as discussed in the passive tracer experiments, this will necessarily have to be high in the GSC region. Although different in magnitude, the resulting concentration field looks very similar to the passive tracer simulation (Fig. 10). This is to be expected as distribution patterns in the biologically active runs will be nearly identical to the passive tracer runs if the population dynamics rates do not vary greatly in space and time. In addition, since the initial population was all adults, this self-similarity will be apparent in the individual stages until enough time has elapsed to complete one generation. At 5oC (the approximate average temperature for the JF period) the total generation time from egg to adult is roughly the same as the length of this simulation. Thus, the initial homogeneous adult population, has filled out all the stages by the end of the simulation. The nauplii represent the biggest component of the population (NI in particular) and these same nauplii are potential prey for larval cod (Northwest Atlantic Implementation Plan - NWAIP). In MA larval cod can ingest food on the order of 0.5mm - the same size scale of the Calanus finmarchicus nauplii. The NWAIP also indicates that the location of abundances or early cod larva in MA (region 2 on the overlay) coincide with the regions on the bank to where the population has been transported.
Mortality Varying by Stage and Depth and Temperature-Limited Development Rates Employing the hypothesis that the death rate is higher in shallower waters (i.e. on the bank) due to increased predator encounter rates, mortality was estimated to be a stage dependent quantity that varied inversely to depth. The mortality of individual stages was specified with the ratios (Egg: Nauplii: Copepodite: Adult = 1:5:2:1)
Figure 12a:Total concentration of stages CIII-CVI [#/m3].
Figure 12b:Total concentration of stages NI-NVI [#/m3]. The inclusion of mortality does reduce the overall abundances while still allowing some of the JF population to seed the bank for MA. However, it does not significantly change the 'self-similarity' of the adult abundances from the passive tracer abundances. Neither does the stage-dependent mortality appear to effect the similarity between stages (although the differences may not have been severe enough to be apparent in the results).
No Mortality and Development Rates Varying Spatially With Depth and Temperature
Employing the hypotheses that food concentrations increase with a decrease in water depth, and that the development rate can act as a surrogate for the effect of food-limitation, the temperature-limited development rates were reduced in deep water locations. For all depths greater than 250m, they were scaled to 1/10th their temperature-limited values. The scaling factor varied linearly with depth up to 50m, above which it was set to 1.0. No mortality was included in this simulation.
Figure 13a:Total concentration of stages CIII-CVI [#/m3].
Figure 13b:Total concentration of stages NI-NVI [#/m3].
The reduced growth rates had a significant effect on the distribution pattern of later-stage copepodites. The GSC peak present in other solutions does not appear here (in actual fact the over all concentrations in the GSC are still higher than MARMAP, but recall that mortality has not been included and the choice of development-reduction factor was somewhat arbitrary). The highest concentration of adults is now on bank, with a noticeable 'relative void' in the GSC area as per MARMAP. The GSC peak due to the transport is still evident in the naupliar abundances as is the high abundance of on-bank nauplii that are available for early cod larvae.
Conclusions
Both the seasonal physical transport and the population dynamics affect the distribution and abundance of Calanus finmarchicus in the Gulf of Maine
Inflow boundary regions do not have a significant contribution to the on-bank population during a 2 month simulation
Physical transport alone is capable of carrying the animals from the basins to the bank in the 2-month period from JF to MA.
Simulations indicate that the structure of this resulting on-bank population is dominated by the egg and naupliar stages. This means that high abundances of nauplii are available in the same region as the early cod larval are found during this bi-monthy period.
The results of the simulations with reduced development rates were more representative of the observational data, suggesting that the off-bank Calanus finmarchicus develop more slowly than at the temperature-limited rates
Accurate spatially and temporally varying values of the population dynamics rates, as well as the physical circulation parameters are needed to be able to interpret the distributional data.
Future Work
Closer examination of spatially varying fecundity, mortality and molting rates
Simulations using the staged-based MARMAP data as initial conditions
Study of other bi-monthly periods
Simulations with population dynamics and initial conditions representative of Pseudocalanus
3-D simulations that allow for study of stratification effects and variations in vertical structure.
Acknowledgments
We are grateful to Carol Meise and Jay O'Reilly for providing the observational MARMAP data; Chris Naimie for providing the physical circulation fields and to BIO for providing the objective analysis software. We also thank Monica Holboke and Drew Endy for their technical assistance.
Funding for this project was provided by the New Hampshire SeaGrant College Program and GLOBEC.
Bibliography
Davis, C. D.; Interaction of a copepod population with the mean circulation on Georges Bank; Journal of Marine Research; 42; 573-590; 1984a.
Davis, C. D. Predatory control of copepod seasonal cycles on Georges Bank; Marine Biology; 82; 31-40; 1984b.
Lynch, D. R., J. T. C. Ip, C. E. Naimie, and F. E. Werner; Comprehensive coastal circulation model with application to the Gulf of Maine; Continental Shelf Research; 16:7; 875-906; 1996a.
Lynch, D. R., M. J. Holboke, C. E. Naimie; The Maine Coastal Current: Spring Climatological Circulation; Continental Shelf Research; in press 1996b.
Meise, C. and J. E. O'Reilly; Spatial and seasonal patterns in abundance and age-composition of Calanus finmarchicus in the Gulf of Maine and on Georges Bank: 1977-1987; Deep Sea Research; in press 1995.
Naimie, C. E.; Georges Bank residual circulation during weak and strong stratification periods - Prognostic numerical model results; Journal of Geophysical Research; 101:C3; 6469-6486; 1996.
Northwest Atlantic Implementation Plan; US GLOBEC, June 1992.