Recent modeling efforts of Werner et al. (1993) and Lough et al. (1994) have focused on the Bank's circulation as it affects the distribution and transport of larvae spawned on the Bank. These studies identify a range of conditions (strength of physical forcing, spawning location, position in the water column, etc.) that result in larvae being retained on the Bank or advected to neighboring regions. We are extending our model-based studies to include trophodynamic aspects related to the feeding and growth of individual larvae within their broad-scale transport and distribution by the circulation. Our approach is to use an individual-based model (IBM) of larval fish trophodynamics coupled with a 3D circulation model on realistic topography. The essence of IBMs is a recognition that biological entities are not all equal (see Mangel and Clark, 1988; DeAngelis and Gross, 1992), and that variation can occur in egg quality, hatch size, prey encounter rates, prey capture success, predation risk, etc. Variation at each stage affects the ability of individuals to feed, grow, and survive. As a result, for example, the final frequency distribution of the sizes of survivors can be radically (and nonlinearly) different from the initial size distribution.
The core of our model is the ability to represent growth as the difference between the amount of food absorbed by a larva and the metabolic costs of its daily activities. This approach was introduced by Beyer and Laurence (1980 and 1981) in studies of winter flounder and Atlantic herring larvae. The food ingested is a function of such processes as the number of prey encountered, captured, eaten, and excreted, while the metabolic costs are a function of larval size, ambient temperature, swimming speed, etc. Larvae are assumed to die (of starvation) if their weight falls below a prescribed "death barrier". Using trophodynamic relationships derived from laboratory studies on the physiology and growth of Atlantic cod and haddock eggs and larvae, Laurence (1985) presented a model which included individual variation in hatch-size, prey density, prey size, and prey encounter rate.
We have extended Laurence's trophodynamic model by coupling it to a 3D circulation model on the realistic topography of Georges Bank. The circulation (Naimie et al. 1994) is used to derive trajectories for the transport of larvae (Werner et al. 1993), and their location each day determines the amount of food available based on the ambient prey concentration. At the present stage of model development, prey concentrations within appropriate size classes--which include Pseudocalanus spp. and Calanus finmarchicus eggs, nauplii, copepodite stages CI-CV and adults--are based on May plankton data from Laurence (1985) and February-March plankton data from Davis (1984 and 1987) and prescribed as "frozen" in time and vertically homogeneous within three regions of the Bank: northern flank, northeast peak, and the southern flank (Fig. 1). Present randomizations for individual larvae include the number of prey encountered each day (determined as a random deviate from a negative binomial distribution to represent prey patchiness; e.g., Winemiller and Rose 1993), and the success in capturing and ingesting the encountered prey (determined as a random deviate from a binomial distribution; Beyer and Laurence 1980). The contagion parameter in the negative binomial distribution, set to 1 in the examples shown here, defines the level of prey patchiness. Values on the order of 10 simulate encounters with randomly distributed prey and approximate a Poisson distribution (variance equal to the mean); decreasing values of the contagion parameter simulate greater patchiness (increased variance). In contrast to Laurence's formulation in which ingestion of a preferred prey size is considered, the prey biomass ingested by the larvae in our model is a combination of the eight specified prey items, with proportions of the ingested prey items determined by Kane's (1984) analysis of the gut contents of cod and haddock larvae.
Spawning is assumed to occur on the northeast peak, and the larvae drift passively southwestward with the circulation (Fig. 1). When all cod larvae are identical at hatch (specified here as the mean size at day 0 observed by Bolz and Lough 1988) and experience any of the prey densities prescribed within the three regions (deterministic case, Fig. 2), no larvae remain alive on the Bank after three days, with approximately a 10% loss of cod from the Bank during the egg stage due to the circulation. When the number of prey encountered and ingested by a larva are allowed to vary randomly about their expected values, such that (conceptually) some larvae encounter higher prey densities and some experience greater success at capturing and ingesting prey (stochastic case, Fig. 3), the results are quite different. A small percentage of larvae now survive for the entire 40 day simulation with a marked increase in the mortality due to starvation on the Bank between 15-25 days post-hatch. However, at the food densities defined in the model, all larvae remain very small (less than 5 mm in length or 50 ug in weight) after 40 days. The proportion of larvae lost off the Bank due to the circulation is about 20%, most of which occurs within the first 15 days post-hatch.
To achieve the growth rates (in weight) of about 10% per day that have been observed for cod on Georges Bank over the first two months by Bolz and Lough (1988) required a five-fold increase of the densities of the smallest prey items (eggs, nauplii, and copepodite stages C-I and C-II), illustrating the sensitivity of prey availability at first feeding. This factor is within the range of variability for estimates of zooplankton prey densities on Georges Bank, particularly during spring (Lough 1984). A survival rate of about 50% on the Bank was obtained in the deterministic case, with approximately equal losses due to starvation and advection off the Bank (Fig. 4), while in the stochastic case, on-Bank survival of about 70% was obtained, with almost all losses due to advection of larvae off the Bank, i.e., with less than 1% loss due to starvation. The trajectories and the amount of time spent in the various regions by the surviving larvae are also important in determining growth rates and larval sizes to day 40. For example, the resulting size distribution of cod larvae at the end of the deterministic simulation (Fig. 5) arises from the differing lengths of time spent by the larvae in the northeast peak and southern flank regions. The largest larvae (corresponding to those between 1500-3000 ug in Fig. 5) are those that spent the longest time in the northeast peak region, which was assigned to have a high proportion of small prey. The smaller larvae (associated with the mode centered at roughly 200 ug) are those that spent 20 days or more in the southern flank region, which had a lower proportion of small prey.
The sensitivity of haddock to low prey densities and its contrast with cod is illustrated in Figure 6 where the results of a fifteen-fold increase of the prey field is shown. Growth rates close to those observed for Georges Bank haddock (Bolz and Lough 1988) were achieved at these prey densities, which also produced a 30% survival rate of haddock larvae on the Bank (Fig. 6). No haddock survived on the Bank in the deterministic case when the prey concentration was increased by a factor of ten. The effect of random prey encounter and prey ingestion at these increased prey densities (not shown) was the same as that illustrated in Figure 3 for cod: a few haddock larvae persisted on the Bank for 30 days post-hatch, but they were extremely small in size (less than 5 mm in length or 30 ug in weight).
This preliminary sensitivity analysis demonstrates the significant differences that can arise in starvation mortality, growth rates, and losses due to advection off the Bank when individual variability is introduced in just two parameters: the number of prey encountered per day and the success at capturing and ingesting those prey. These results also suggest the extent to which spatial variability in prey distributions can influence the growth rates and resulting size distributions of larvae in different regions of Georges Bank. Variability in other parameters, such as the size distribution of larvae at hatch, undoubtably play a role. These results are also consistent with Laurence's (1985) original conclusion that haddock are more dependent on high densities of small prey items than are cod. While our trophodynamic relationships follow those of Laurence (1985), our model results also incorporate field-derived estimates of prey concentrations and distributions, and the observed prey sizes in the stomach contents of cod and haddock larvae.
In these examples we have considered only the effect of horizontal variations in prey concentration on larval growth. Analogous effects arising from vertical variations in the prey field concentration are likely and expected. Field studies have shown that stratification on Georges Bank can significantly influence the feeding and survival of larval cod and haddock (Buckley and Lough 1987). Up to 50% of haddock larvae (mean size 11.2 mm) from a well-mixed site in spring 1983 on Georges Bank had RNA/DNA ratios in the range observed in the laboratory for starved larvae. These field observations provide support for the hypothesis that haddock larvae require higher prey densities than cod and seem more adapted to spring conditions when prey are concentrated by stratification. A study of stratification variability on Georges Bank and its effect on larval fish is currently underway (U.S. GLOBEC News No. 3, 1993).
Our results suggest that two key aspects requiring detailed attention are an improvement in the spatial and temporal specification of the prey field, and better treatment of the details of the encounter rate and ingestion success of larvae with prey. Specifically: (1) The model's requirement of increasing the prescribed prey concentration by five to fifteen-fold to achieve growth and survival of larvae observed in the field is consistent with the range of (aggregated) prey concentrations reported by Lough (1984) and Buckley and Lough (1987). Increased prey aggregations of this magnitude were found in the vicinity of a pycnocline. Their studies also found that the mean depth of the larvae and/or the peak densities of larvae generally coincided vertically with the highest prey biomass indices, suggesting a larval behavioral component not considered in our calculations. In this regard, one of the crucial parameters in the model is the concentration of prey separated into size categories, and especially those sizes appropriate for the smallest larvae. Ideally, this parameter should be known in detail horizontally and vertically throughout the Bank, but in practice it is poorly known at some locations and unknown at most places. Analyses of historical small-mesh plankton samples and new information collected during the U.S. GLOBEC-Georges Bank field program should help provide additional details. (2) The different results between deterministic and stochastic simulations suggests the model is sensitive to small-scale prey distributions and to the ability of larvae to capture prey. Further work is needed to develop better representations of these processes, e.g., by including turbulence-dependent encounter rates (Rothschild and Osborn 1988) in place of the randomization routines, and laboratory studies to investigate capture success with different prey types and larval fish condition.
In conclusion, the ability to couple a larval fish trophodynamics model with a detailed model of the physical circulation on realistic topography, both of which operate at the scale of individual larvae, is providing a new tool for the development and exploration of the critical hypotheses regulating the variability of marine fish populations on Georges Bank. (F. E. Werner (University of North Carolina), R. I. Perry (Pacific Biological Station, Nanaimo), R. G. Lough (NMFS--Woods Hole), and D. R. Lynch (Dartmouth College) are U.S. GLOBEC funded investigators working on Georges Bank.)
Acknowledgements. We thank C. E. Naimie for providing us with the flow field and B. O. Blanton for his help in processing the particle trajectories.
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