© 2003 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
Evaluation of the Shepherd and Cushing (1980) model of density-dependent survival: a case study using striped bass (Morone saxatilis) larvae in the Potomac River, Maryland, USA
a University of Michigan, School of Natural Resources and Environment, Institute for Fisheries Research 212 Museum Annex Building, 1109 North University, Ann Arbor, MI 48109-1084, USA
b Coastal Fisheries Institute and Department of Oceanography and Coastal Sciences, Energy, Coast and Environmental Building, Louisiana State University Baton Rouge, LA 70803-7503, USA
*Correspondence to E. S. Rutherford; tel: +1 734 663 3554; fax: +1 734 663 9399. e-mail: edwardr{at}umich.edu.
Quantifying the degree of density-dependence in stock–recruit relationships is critical to understanding fish population dynamics. The Shepherd and Cushing (1980) model couples a simple model of density-dependent larval growth with a constant rate of mortality to predict numbers surviving to recruitment. The model has not been evaluated using field data, nor have its predictions been compared with those from other models. Here, the S&C model, an individual-based model (IBM), and a regression model are applied to 8 years of field data for striped bass larvae in the Potomac River, Maryland, USA, to predict larval carrying capacity (K) and percentage of recruitment lost as a consequence of density-dependent growth. The IBM and the regression model were corroborated by comparing their predictions of average growth rates of larvae and relative recruitment strengths to observed values for the 8 years of field data. Although the IBM and the regression model differed in their predictions of several important intermediate variables, both models predicted higher values of K and lower values of density-dependent growth than did the S&C model. Over the 8 years, the IBM and the regression model predicted an average of 0.3 and 1.8% recruitment lost as a result of density-dependent growth, respectively. In contrast, the S&C model predicted much higher recruitment lost (average of 27%). Slight differences in the assumed rate of mortality used in the S&C model resulted in values of carrying capacity similar to those predicted by the IBM and the regression model. Difficulties in estimating parameters of the S&C model from field data are discussed.
Keywords: density-dependence, larvae, model, otolith, recruitment, striped bass
Received 28 June 2003; accepted 3 July 2003.
 |
Introduction |
|---|
 Top Introduction MethodsResultsDiscussionReferences |
|---|
Lack of knowledge about the relationship between recruitment and spawning stock remains one of the central problems in fisheries science. The number of recruits produced by a spawning stock depends on the combined effects of density-independent and density-dependent factors. Whereas density-independent factors often dominate the interannual variation in recruitment, quantifying the density-dependent component is critical for understanding long-term population dynamics and for predicting sustainable harvest (Rose et al., 2001). Approaches for relating recruitment to spawners have evolved from fitting simple functional relationships between recruits and parent stock (Ricker, 1954; Beverton and Holt, 1957), to using regression analysis to predict survival rates of successive life stages from eggs to recruitment as functions of environmental variables (Kohlenstein, 1980; Tang, 1985; Crecco et al., 1986), to approaches that simulate growth, development, and survival processes of early life stages (Cushing and Harris, 1973; Shepherd and Cushing, 1980; Beyer, 1989; Shepherd, 1991). The early life stages of marine fish are thought to be the most likely stages during which recruitment variability is generated and when population regulation is exerted (Cushing, 1975; Beyer, 1989; Houde, 1989). Eggs and larvae are the stages of the life cycle associated with the greatest interannual changes in abundance, although Sissenwine (1984) argued that, in some species (e.g. Northwest Atlantic gadoids), cumulative mortality (the product of instantaneous mortality and stage duration) is greatest at the juvenile stage.
The Shepherd and Cushing (1980) model (S&C model) is a process-orientated recruitment model that combines density-dependent larval growth with a constant rate of mortality to predict survival to recruitment. The model provides a simple mechanism for predicting the magnitude of density-dependent regulation of recruitment. While the simplicity of the S&C model is appealing, it has not been applied rigorously to many systems, nor has it been evaluated against predictions from other models.
In this paper, we apply the S&C model to striped bass larvae in the Potomac River, Maryland, USA. The focus of the S&C model on larval growth and survival is appropriate for Potomac River striped bass. Striped bass recruitment in the Potomac River is highly variable from year to year, and it appears to be at least coarsely determined by the early larval stage, prior to larvae attaining 8 mm total length (Rutherford et al., 1997). Striped bass in the Potomac River have been the subject of an individual-based model (IBM) of recruitment (Rose and Cowan, 1993), a regression model of larval growth (Chesney, 1993), and multi-year field studies of early life stage growth and survival (Setzler-Hamilton et al., 1981; Rutherford et al., 1997). We therefore applied the S&C model, the IBM, and the regression model to 8 years of Potomac River field data, generating independent estimates of larval carrying capacity and percentage recruitment lost as a consequence of density-dependent growth. The consistency of the different models was then compared. The combination of multiple models and extensive field studies of striped bass recruitment provided an opportunity to assess rigorously the role of density-dependent larval growth in affecting striped bass recruitment, and to evaluate the utility of the S&C model.
|
Methods |
|---|
|
TopIntroductionMethodsResultsDiscussionReferences |
|---|
Overall approach
Rutherford et al. (1997) synthesized the extensive field data for striped bass larvae in the Potomac River that were collected during the 1970s and 1980s. The studies covered 8 years: 1976, 1977, 1980–1982, and 1987–1989. Striped bass larvae and zooplankton densities were monitored on surveys performed every 4–7 days (for convenience we refer to these as weekly) at six to eight stations in the lower portion of the river during April through June, the period of striped bass spawning and larval development. For each year, these data permitted estimation of striped bass abundances at hatching and at 8 mm, average growth and mortality rates, and weekly zooplankton densities. Daily water temperatures were recorded during the spawning season for each of the 8 years in the Potomac River (Setzler-Hamilton et al., 1981; Rutherford et al., 1997). From 1987 to 1989, otolith-based estimates of growth rates of individual striped bass were obtained, allowing estimation of striped bass abundance at hatching, abundance at 8 mm, and growth and mortality rates for weekly cohorts within each of those 3 years.
Using the field data, the S&C, IBM, and regression models were used to predict larval carrying capacity and the percentage of striped bass recruitment lost as a consequence of density-dependent growth for each of the 8 years. Each model was applied as if it was the only analysis to be performed; information obtained from one model was not applied or used to refine the other models. The approach used to apply the models is shown schematically in Figure 1.
|
The Shepherd and Cushing (1980) model
The S&C model combines an equation for weight-specific growth of an individual fish with an equation that describes the mortality of a cohort. The equation for growth of an individual fish assumes that growth rate depends on numbers present:
|
| (1) |
|
| (2) |
Shepherd and Cushing (1980) combine the equations for growth of an individual with the mortality equation to predict the number surviving to some final weight. They assume that individuals have to grow from some initial to some final weight (from W0 = 0.24 mg wet weight to W1 = 4.68 mg wet weight for striped bass), when recruitment is assumed to be set. Note that while the mortality rate is constant, the fraction of individual fish surviving to recruitment is density-dependent because abundance affects growth rate, which determines the time needed to grow from W0 to W1.
The result of combining the growth and mortality equations and integrating from W0 to W1, assuming an initial number (N0) of individuals, is an equation for the number surviving to W1 (denoted N1):
|
| (3) |
|
| (4) |
|
| (5) |
Application
We used field data to first estimate values of GMAX, m, N0, and N1 for each of the 8 years. GMAX is used to estimate T0 using Equation (5), and T0 and m are then used to estimate A using Equation (4) (Figure 1). Finally, these values are used in Equation (3) to estimate K, given specified values of W0 and W1. Note that in our application, the predicted N1 values (recruitment) using Equation (3) would agree exactly with the field-observed values of N1. By employing field data to specify N0 and N1, we used the S&C model to predict K. Using field estimates of N0 and N1, and the derived estimate of A, we computed the percentage of recruitment lost to density-dependent growth.
Values for m, N0, and N1 were estimated from the weekly abundance of striped bass larvae for each of the 8 years. Age of the larvae was determined by otolith increment analysis, and that age was assigned to cohorts within 3 days of their hatching date. Instantaneous daily mortality rates (m) were estimated for field data from exponential declines in abundance at age, and otolith-derived estimates of larval growth rate and stage duration. Estimated initial numbers of larvae (N0) were the intercepts of cohort-specific regressions of loge-transformed larval abundance on age. Abundances of larvae at 8.0 mm standard length (N1) were calculated from the exponential model
|
| (6) |
Values for GMAX were estimated from individual growth rates available for the years 1987–1989. Instantaneous weight-specific growth rates (G, d–1) were calculated for larvae in each year from 1987 to 1989 using estimates of growth in length back-calculated from otolith increments, and the lengths were converted to weight using the length–weight regression for striped bass larvae given by Houde and Lubbers (1986). GMAX was defined as the 75th percentile value of all observed G values for individual larvae. Growth rates were estimated for the periods 1976–1977 and 1980–1982 from changes in mean weight over time (estimated from changes in mean length). Cohorts in those years were distinguished by assigning ages and birthdate frequencies to larval lengths using an age–length key (Rutherford et al., 1997). GMAX values in those years were estimated by multiplying the average growth rate in each year by 1.15, because values in the period 1987–1989 were, on average, 15% higher than the mean values. The parameter A was estimated for each year assuming larval-stage durations T0 (i.e. growth at GMAX), and the observed instantaneous daily mortality rates m (Equation (4)).
The individual-based model
We used the IBM configured for Potomac River striped bass (Rose and Cowan, 1993) to estimate GMAX, A, K, and the percentage recruitment lost to density-dependent growth for each of the 8 years. Rose and Cowan (1993) described the IBM for Potomac River striped bass, and Cowan et al. (1993) and Rose et al. (1993) demonstrated its use for analysing the sources of recruitment variability and the effects of environmental water quality on survival of striped bass. The IBM, as used in this analysis, is summarized below.
The model began with egg abundance of striped bass introduced weekly during the spawning season, and followed individuals as they developed through egg, yolk-sac larval, and larval stages to a length of 8 mm. The model represented these dynamics on a daily time-step in a single well-mixed volume (4.0 x 106 m3), configured to represent the striped bass spawning and nursery area of the Potomac River (1052.5 x 106 m3). The total number of eggs produced in the field was multiplied by a factor (0.0038) to obtain the total number of eggs for the modelled volume. These eggs were then distributed in time on the basis of the percentage observed each week in the field data. Environmental conditions considered in the modelled volume were daily average water temperature, the fraction of the day where there is daylight, and the daily densities of four zooplankton prey types.
Each weekly influx of eggs, and the resulting yolk-sac larvae, was followed as a cohort. Development of eggs and yolk-sac larvae was dependent on water temperature, and they died based upon a constant rate of mortality plus a temperature-dependent mortality component. At 15°C, total mortality rates Z approximated 0.65 and 0.2 d–1 for eggs and yolk-sac larvae, respectively. The equations for temperature-dependent mortality of eggs (Ze) and yolk-sac larvae (Zy) are
|
| (7) |
|
| (8) |
Daily growth in weight (mg dry weight) of a larva was represented with a difference form of the bio-energetics equation
|
| (9) |
W is the daily change in weight, p the proportion of CMAX realized, E the fraction of consumption assimilated, CMAX the maximum consumption rate (mg d–1), Rtot the total metabolic rate (mg d–1), and t is the 1-day time-step. Assimilation fraction (E) was assumed constant at 0.7. CMAX and Rtot depended upon an individual's weight and temperature.
Maximum daily dry weight consumption rate (CMAX) depended upon an individual's weight and temperature:
|
| (10) |
Metabolic dry weight losses were determined as a routine component (Rr), which depended on larval weight and temperature, and an activity component, represented as a multiplier of routine metabolism for the period of feeding:
|
| (11) |
|
| (12) |
|
| (13) |
The proportion of CMAX realized by an individual on a given day (p) was computed on the basis of random encounters of a feeding individual with four types of zooplankton prey. The four prey types were rotifers (Eurytemora affinis nauplii, E. affinis copepodites, and adults) and cladocerans. Each prey type was defined by an average weight, average length, and equilibrium density, which were assumed to be constant over time. Equilibrium densities were the maximum allowed in simulations. Prey length determined reactive distances of striped bass larvae, and when combined with swimming speeds of the larvae, determined the numbers of each zooplankton type encountered. The number of each zooplankton type encountered was then adjusted for capture success to obtain the number potentially eaten. The actual number eaten was determined based upon an optimal foraging, diet-selection algorithm that permits an individual to consume mostly preferred prey types when preferred types are rare. Prey types were added to the diet in decreasing order of preference. Prey types were included in the diet until the optimal foraging rules indicated that adding the next prey type would not increase the individual's average consumption rate, or until consumption would exceed CMAX. The assumed weight of each prey item was used with the numbers actually eaten to compute the biomass consumed, which was summed over the four prey types to obtain total daily consumption by each larva. Total consumption was divided by maximum consumption for each larva on each day to obtain p.
Densities of each prey type (number l–1) were updated daily, based upon a modified version of a logistic equation:
|
| (14) |
The mortality of each feeding larva depended upon an individual's weight and length. Weight-dependent mortality was based upon laboratory experiments without predators, and was considered to be starvation-related. Larvae were allowed to lose weight, but not length. If the weight of an individual became less than some fraction (0.65 for feeding larvae) of the weight expected for an individual of that length, it was assumed to die. Length-based mortality was based on a regression relating mortality rate (ZL, d–1) to length using field estimates of mortality rates of age-0 striped bass (see Rose and Cowan, 1993). Probability of dying (1–exp–ZL) was evaluated daily on the basis of each individual's length:
|
| (15) |
Application
Two sets of simulations were performed for each of the 8 years: (1) model corroboration, and (2) estimation of GMAX, A, K, and percentage recruitment lost, for comparison with the S&C model results. Both sets of simulations used the same daily temperatures and weekly striped bass egg abundances, but differed in how zooplankton densities were represented.
The corroboration set of simulations was designed to evaluate the performance of the IBM (Figure 1). Each year was simulated using observed weekly egg abundances (proportional to N0) and daily temperatures. Observed egg abundances were multiplied by 0.0038 to scale field abundances to the modelled box. The eggs were then distributed in time in each simulated year on the basis of the percentage of eggs observed each week in the field samples.
The equilibrium zooplankton densities for each of the four types were specified for each day of the simulation by linear interpolation between values from successive cruises. We present here results based on computing the average density of each zooplankton type for the four stations surrounding the peak in striped bass larval abundance, reasoning that zooplankton at those stations would be most affected by striped bass larvae. We explored several other ways to collapse the zooplankton densities over stations (e.g. all stations, the single station with peak striped bass larvae, only stations in the turbidity maximum); all yielded similar results. Simulations were performed assuming density-independence (i.e. larval consumption CONt was not removed from the zooplankton population, and was set to zero in Equation (14)); thus, zooplankton densities in the simulations mimicked those observed in the field data. We compared IBM predictions of 8-mm abundance and average growth rate (G) with observed values for the 8 years. Rank correlation coefficients were computed between IBM-predicted and observed growth rates, and between predicted and observed 8-mm abundances. Rank correlation was used to compare trends in IBM predictions and field data across years. Similarity between IBM predictions and field data would increase confidence in the IBM.
The second set of simulations of the IBM was designed to generate estimates of maximum larval growth rate (GMAX) and survival (A) under density-independence, and larval carrying capacity (K) and the degree of density-dependence for comparison with the predictions of the S&C model (Figure 1). Zooplankton densities used were identical to those used in the corroboration simulations (i.e. the four stations surrounding the peak densities of striped bass). The difference was that zooplankton data from only the first few cruises before striped bass larvae arrived were used to specify the initial densities of each of the four zooplankton prey types in each year. Between one and two of the weekly cruises estimates of zooplankton density were used, depending on when striped bass larvae arrived each year. Simulations of the IBM were performed to estimate GMAX, A, and K for each of the 8 years. To estimate GMAX and A, model simulations were performed using the initial zooplankton densities as equilibrium densities and under density-independence (i.e. CONt set to zero). It was appropriate to turn off larval striped bass consumption of zooplankton in the IBM to simulate density-independence, because the mechanism of density-dependence proposed by the S&C model was density effects on growth, mediated through larval consumption. Zooplankton densities stayed at their equilibrium values throughout the simulations. GMAX was the predicted average growth rate, and A was the fraction surviving from hatching to 8 mm. The purpose of these simulations was to provide estimates of GMAX and A for use in later realistic IBM simulations that allowed for density-dependent larval effects on the zooplankton prey. Estimates of A with the observed N0 and predicted N1 were used to compute the percentage of recruitment lost to density-dependent growth.
K was estimated each year by starting with the initial zooplankton densities as equilibrium densities, but including density-dependence, so that realized zooplankton densities could potentially drop below their initial values. Simulations were repeated with weekly egg abundances incrementally increased until the predicted average growth rate equalled one-half of GMAX for that year. K was the number at hatching that resulted in one-half of GMAX. For some years, we stopped increasing egg abundance before reaching one-half of GMAX, because further increases in egg production resulted in too few survivors (<10) for accurate estimation of growth rate. For those years, K is reported as the highest hatching abundance that resulted in reasonable numbers (>100) of survivors. The actual K would be even larger than the values reported.
The regression model
The regression model of larval striped bass growth followed the daily growth and mortality of a single cohort of striped bass from hatching to 8 mm. Growth was based on data presented in Chesney's (1989) experimental studies on zooplankton density (PT, number l–1) and larval striped bass growth rate (G, d–1):
|
| (16) |
Application
Two sets of simulations, analogous to the simulations performed with the IBM, were performed with the regression model (Figure 1). The first set of simulations was for model corroboration. Simulations were performed that used daily interpolated zooplankton densities (under density-independence) for each year to predict average growth rate and the number surviving to 8 mm. As with the IBM, these predicted values were compared with observed values estimated from field data, using rank correlation. The second set of simulations was used to estimate GMAX, which was then used to estimate A. As with the IBM, initial zooplankton densities for each year were specified as the average of the four stations surrounding the striped bass peak, i.e. prior to the arrival of striped bass. GMAX was estimated as the average growth rate from simulations performed maintaining zooplankton densities at their initial average values (i.e. density-independence). Density-independent mortality rate (A) was estimated from larval-stage durations assuming that larvae grew at GMAX and field estimates of year-specific average mortality. As with the IBM approach, K was estimated for each year by incrementally increasing initial larval abundances with density-dependence allowed, until predicted zooplankton densities resulted in growth rates of one-half of GMAX for that year.
Comparisons among models
Estimates of GMAX, A, K, and the percentage of recruitment lost to density-dependent growth were compared among the three models for the 8 years. Rank correlation analysis was used with the IBM and regression model corroborations to evaluate whether model-predicted and -observed values of growth and 8-mm abundances showed similar year-to-year patterns. A two-sample Wilcoxon non-parametric test was used to test for significant differences among model predictions of GMAX, A, K, and percentage of recruitment lost across years. Model predictions for each parameter in each year were subtracted from each other, and the differences were tested for significance using the Wilcoxon test. Differences were considered significant at a level of 
=0.05. Agreement among different models in their estimates of K and the percentage recruitment lost would increase confidence in the general applicability of the S&C model.
|
Results |
|---|
|
TopIntroductionMethodsResultsDiscussionReferences |
|---|
IBM corroboration
IBM-predicted and field estimates of 8-mm abundances (Figure 2a) and growth rates (Figure 2b) were reasonably similar in their interannual patterns, although predicted growth rates were lower than observed ones. The rank correlation coefficients between predicted and observed values were 0.55 (n=8, p<0.10) for growth rates, and 0.57 (n=8, p<0.05) for the 8-mm abundances. In agreement with the field estimates, the IBM predicted relatively high recruitment in 1977 (observed value of 852) and 1982 (observed value of 990). For 1980, we simulated an episodic mortality of larvae in the model to reconcile observed vs. predicted 8-mm larvae abundance. Without the episode, the model greatly over-predicted 8-mm larvae abundance in 1980. Based upon field measurements of daily temperature data and a sudden disappearance of larvae, an episodic mortality was evident. Over all years, good recruitment was not simply a function of egg or hatching abundance; whereas 1977 had the highest initial abundance at hatching, 1982 had the fourth highest. Predicted growth rates in IBM simulations showed only moderately similar year-to-year variation around observed values, and predicted values were lower than observed for all 8 years (Figure 2b). On average, predicted growth rates (G = 0.075 d–1) were about one-half of observed ones (G = 0.14 d–1).
|
Regression model corroboration
Regression model predictions of 8-mm larval abundances (Figure 2a) and average growth rates (Figure 2b) also were qualitatively similar to observed values. The rank correlation coefficients between predicted and observed were 0.47 (n=8, p=0.11) for growth rates, and 0.71 (n=8, p<0.05) for 8-mm abundances. In agreement with the field data and the IBM, the regression model predicted relatively high recruitment in 1977 and 1982. Predicted growth rates in regression model simulations were similar to observed ones. On average, predicted growth rates were G = 0.16 d–1 in the regression model (G = 0.14 d–1 in the observed data).
Comparison among models
Predicted values of GMAX and A were generally lower for the IBM than for the regression model and for the field-derived parameters in the S&C model. IBM-predicted values of GMAX (range: 0.04–0.10 d–1) exhibited the least interannual variation, and were lower (Wilcoxon test, p<0.01) than regression model predictions for all years (range: 0.10–0.19 d–1), and less than the parameter values used in the S&C model (range: 0.09–0.20 d–1) for all years (Figure 3a). Predicted values of density-independent survival A from the IBM were significantly lower (p<0.01, often 10–100x lower) than those from the regression model in every year, and lower than the field-derived estimates of A included in the S&C model except for 1981 (Figure 3b). Regression model predictions and S&C model estimates did not differ for GMAX (p>0.55) or A (p>0.80).
|
Predicted values of larval carrying capacity (K) from the IBM and regression models were approximately 10- to 100-fold higher than those from the S&C model (Figure 3c). All models produced estimates of K that were different from each other (Wilcoxon test, p<0.01). The IBM and the regression model K values were on the order of 1011, 10–1000x higher than observed abundances at hatching. The results of the IBM and the regression model imply that carrying capacities for striped bass larvae were much higher than observed larval densities in the Potomac River, implying little chance of density-dependent growth. In contrast, the S&C model predictions of K were on the order of 108–1010, similar to, or only 10 times higher than, the observed abundances at hatching in many years, suggesting that density-dependent growth was more likely.
The IBM and regression models both predicted essentially no loss of recruitment attributable to density-dependent growth, whereas the S&C model predicted significant losses in many years (Figure 3d). IBM and regression model predictions were not significantly different from each other (Wilcoxon test, p>0.53), were less than 14%, and averaged 1.8 and 0.3% loss, respectively, for 8 years. The S&C model predicted significantly greater average losses of recruitment of 27% (range 3–75%) over 8 years than the regression model (p<0.001) or the IBM (p<0.02).
|
Discussion |
|---|
|
TopIntroductionMethodsResultsDiscussionReferences |
|---|
Our efforts to quantify density-dependent growth and survival in the larval stage of striped bass using the S&C model were complicated by difficulties in estimating the parameters GMAX and A, and by assumptions inherent in the model. Predicted values of K from the S&C model indicated that density-dependent effects could have had a significant impact on the numbers of late-stage striped bass larvae that recruited in some years during the 1970s and 1980s. Predicted values of K were similar in magnitude to abundances at hatching (Figure 3c), and potential recruitment lost to density-dependence ranged from 3 to 75% (Figure 3d). This prediction follows from the assumption that all larval growth at less than maximum rate is due to density-dependence. In contrast, predictions from the IBM and the regression model, both based upon bio-energetic calculations of larval density required to depress observed zooplankton densities, suggested no density-dependent effects. Predicted values of K from the IBM and the regression model were several orders of magnitude higher than abundances at hatching (Figure 3c), and the percentage of recruitment lost as a consequence of density-dependent growth was <14% for all years analysed (Figure 3d).
Despite differences in predictions of K, we believe that the values of K from the IBM and the regression model were more realistic than the values predicted from the S&C model. The individual-based and regression models were designed to simulate the growth of larval striped bass, and were developed using site-specific data for the Potomac River. The IBM was specifically developed to examine the effects of density-dependent growth (Cowan et al., 1993; Rose et al., 1993). Both the IBM and the regression model generated reasonable year-to-year patterns in 8-mm abundance and average growth rate. Further, both models generated similar values of larval carrying capacity, despite their differing in several important aspects. The IBM followed weekly cohorts within each year, included temperature effects, and was based on prey encounter and capture rates, whereas the regression model followed a single cohort in each year, did not include temperature effects, and was based upon laboratory and field correlations between growth rate and zooplankton density. The models also differed in their predictions of the absolute magnitudes of GMAX and A, the IBM consistently generating lower values of both. Despite these differences, the IBM and the regression model generated high estimates of K and low estimates of percentage recruitment lost as a consequence of density-dependent growth. We also explored alternative ways to treat the zooplankton data used in the models. For instance, we used weekly interpolated densities as equilibrium densities, and aggregated stations in a variety of ways, all resulting in similar predictions of larval carrying capacity for both the IBM and the regression model. Therefore, we have confidence in the conclusions based upon the IBM and the regression model that density-dependence had little effect on striped bass growth and potential recruitment during the 1970s and 1980s.
The S&C model's assumption that larvae grow at sub-maximal rates owing to density-dependent depletion of prey is too simplistic, and it results in overestimation of the role of density-dependent growth. Other equally plausible explanations for sub-maximal larval growth exist that do not require density-dependent prey consumption. Factors that promote variation in growth rate among individuals may explain the sub-maximal growth rates of most striped bass larvae. Larvae may grow at sub-maximal rates as a consequence of individual variation in metabolic scope for growth, capture success, or swimming ability, or because of spatial and temporal differences in contact rates between larvae and their zooplankton prey (Rothschild, 1986; Rothschild and Osborn, 1988; Mackenzie et al., 1990). The distribution of individual striped bass larval growth rates observed in the Potomac River during the years 1987–1989 supports the argument that prey densities and predator–prey encounter rates may vary greatly for individual larvae within each cohort, and that most larvae do not grow at rates achieved by the fastest-growing individuals. Chesney (1989) demonstrated wide variability in larval growth rates of striped bass (G values of 0.02–0.18 d–1), even under controlled laboratory conditions of light, temperature, and prey density. Limburg et al. (1997, 1999) demonstrated that cohort-specific growth rates of striped bass larvae in the Hudson River (G values of 0.07–0.56 d–1) varied in relation to the seasonal cladoceran bloom.
Another complication encountered with the S&C model was the difficulty in estimating GMAX from field data. Selection of the proper value for GMAX is critical for any of the models to predict density-dependence accurately. The IBM and the regression model permitted repeated simulations with only the initial number at hatching changing, thus permitting direct estimation of GMAX. Application of the S&C model requires estimation of GMAX from either field or laboratory data. Our estimation of GMAX as the 75th percentile of observed individual growth rates is, admittedly, somewhat arbitrary. Growth rates of fish larvae are currently measured more accurately than mortality rates, but determining the physiological maximum rate (GMAX) at which larvae may grow under different temperature and time-varying prey concentrations is a non-trivial and critical problem. Our review of the literature indicates that there are no laboratory studies of larval growth in striped bass under conditions that mimic those in nature. Ingestion rates of fish larvae determined in the laboratory rarely agree with field estimates, owing to differences in contact rates, turbulence, light, and perhaps other factors (Chesney, 1989; Mackenzie et al., 1990). Such fast-growing larvae in the field data actually may have encountered patches of zooplankton at densities much higher than observed mean densities. Therefore, we used a simple rule that GMAX was the 75th percentile of observed larval growth rates.
We also encountered difficulty in estimating values for A, the density-independent mortality rate, for the S&C model. Field data reflect the net effects of density-independent and density-dependent mortality, so determining what survival would have been without density-dependence is difficult. The IBM and the regression model allowed straightforward determination of A by simply running the models with interpolated zooplankton densities and no feedback between larval consumption and zooplankton densities. Field estimates for the years 1987–1989, when within-year cohorts were available, suggest a concave relationship between temperature and larval mortality. Similar patterns of mortality rate as a function of temperature (or day of year) were also predicted by the IBM. Secor and Houde (1995) quantified survival rates of hatchery-released cohorts, and identified an optimal temperature range for survival of yolk-sac larvae of 16–19°C. Yolk-sac larvae hatched outside this temperature range have poorer survival rates than larvae hatched within it. Survival rates of wild larvae in Chesapeake Bay and the Hudson River also vary seasonally, being high early, low in mid-season, and increasing later in the spawning season (Rutherford and Houde, 1995; Secor and Houde, 1995; Limburg et al., 1999).
We investigated the sensitivity of the predictions from the S&C model to uncertainty in the values of GMAX and A, then computed the values of A that would be needed to generate the larval carrying capacities predicted by the IBM. We assumed that we knew K (from the IBM) and then solved for A in Equation (3). In all but one year (1976), the estimates of A needed for the S&C model to generate the larger K values predicted by the IBM were only slightly different from the original values used for A (Table 1). A realistic value of A was not obtainable for 1976, because it required recruitment under density-independence to be less than recruitment with density-dependence (i.e. A * N0 < N1). Using the same values of GMAX (which determines stage duration) used in the original S&C model application, only slight changes in the field-based estimates of daily mortality rate (m) are required for the S&C model to generate the K values predicted by the IBM (Table 1). Therefore, the S&C model is very sensitive to the estimates of mortality rate included in the model. Given the difficulty of estimating A, the slight differences in A imposed for the sensitivity analysis lie within reasonable bounds of uncertainty of A, as interpreted from observed survival rates (Uphoff, 1989; Rutherford and Houde, 1995; Rutherford et al., 1997).
|
Although we felt that sensitivity analyses of IBM and regression model results would have been useful, we believed that a proper sensitivity analysis was beyond the scope of the current paper, and would have greatly expanded its length, and thereby possibly would have detracted from the major results. Also, given the types of models, we did not think that a sensitivity analysis would alter the major conclusions. We would expect that the more the variation imposed on model inputs, the greater would be the variation in model predictions, but the major results and differences among the models would remain. Because we did not have estimates of the uncertainty in many IBM or regression model inputs, a properly conducted sensitivity analysis would involve trying different levels of uncertainty in model inputs, lengthening and complicating the paper. Our "portmanteau" analysis of model predictions for 7 years provided a range of estimates given different starting conditions (eggs, temperatures, prey densities) and larval mortality rates. What gives us confidence is the extensive usage of field data in our analysis and the general consistency in model predictions of density-independent larval survival among the IBM and regression models.
In agreement with the IBM and the regression model, other sources of evidence also suggest that density-dependent growth and survival of striped bass larvae were minimal during the 1970s and 1980s. In theory, larvae can affect prey abundance when larval density is high, zooplankton density is low, and the instantaneous death rate of zooplankton is high (Heinle, 1969; Bollens, 1988). Relatively few examples of density-dependent growth exist for marine fish larvae (Jenkins et al., 1991; see Cowan et al., 2000 for a review). Cushing (1983) suggested that the growth rate of young haddock (Melanogrammus aeglefinus) larvae was unlikely to be influenced by any density-dependent consumption of their prey, but that the growth rate of post-larvae potentially could be influenced. Density-dependence in the egg and larval stages has not yet been demonstrated for striped bass, and density-independent events are thought to mould recruitment success (Ulanowicz and Polgar, 1980). However, most field studies of larval dynamics have been conducted during periods of low adult biomass, when larval densities are likely to be low, and the probability of observing density-dependent behaviour is slight (Shepherd and Cushing, 1990). Cowan et al. (2000) also concluded that density-dependence is unlikely in the larval stage because of low cohort-specific rates of consumption. Density-dependent effects on recruitment have been well documented for some species in juvenile life stages (Forney, 1977; Zijlstra and Witte, 1985; Van der Veer et al., 2000; see Cowan et al., 2000 for a review), although these examples usually are found in simpler ecosystems with few predator or prey species, or where habitat is limiting for suitable reproduction.
We explored the likelihood that carrying capacities of striped bass larvae may be exceeded at the high spawner biomass that now exists in Chesapeake Bay, given the dramatic recovery of the stock from its low levels in the 1980s, during which many of the 8 years of field data were collected. We estimated spawner biomass of striped bass for the Potomac River from published estimates for the Atlantic coast population (ASMFC, 2001), from historical estimates of the relative contributions of Chesapeake Bay spawners to the Atlantic coast population, and from the ratio (0.26) of Potomac River nursery area to the entire nursery area in Chesapeake Bay, as estimated from GIS-based analysis of historical nursery areas. Recent estimates of the relative contributions of Chesapeake Bay stocks to the Atlantic coast population are unknown, but they vary greatly depending on location, season, and year-class success (Fabrizio, 1987; Van Winkle et al., 1988). It was assumed that Chesapeake Bay stocks constituted most (60%) of the Atlantic coast population in 2000, because of good recruitment in 1989, 1993, and 1996, and because, historically, Chesapeake Bay fish contributed most to the Atlantic coast population following strong year classes (Van Winkle et al., 1988). To estimate egg production for the Potomac River, total spawner biomass was partitioned into age-specific biomass using age-specific data on catch rate from spawner survey samples (MDNR, 2000). We converted biomass-at-age data into estimates of egg production, making use of age-specific fecundity data (Mihursky et al., 1987), and then applied a range of rates of egg survival (10–50%; Olney et al., 1991) to estimate potential abundance at hatching of striped bass larvae.
Even under favourable conditions of high spawner biomass and good survival of eggs and larvae, the chances of observing density-dependent effects on larval growth and recruitment in Potomac River striped bass appear to be low. We estimated that some 120 600 spawning females and between 3.3x1010 and 1.6x1011 hatched larvae were present in the Potomac River during 2000. The spawner abundance in 2000 is approximately 10% of that needed to produce a larval hatching abundance that would reach the carrying capacities in the Potomac River estimated by the IBM and the regression model. It is likely that the Potomac River spawning population of striped bass has never been that abundant since commercial fisheries developed for the species, and with the re-opening of the fishery, such high spawner abundances are unlikely in the near future.
The S&C model provides an elegant mechanism to explain density-dependent regulation of fish recruitment, but it may be difficult to apply to field situations owing to problems of reliably estimating model parameters. Shepherd (1991) combined the effects of density-dependent larval growth from the S&C model with density-dependent mortality mediated through predator satiation at high densities of larval prey. This mechanism also may be difficult to confirm, because of the large errors inherent in estimating the rates of larval mortality. Based upon our analyses, we conclude that quantifying predator consumptive demand and prey supply through bio-energetic model analysis may provide a more fruitful approach to detecting density-dependence than can the S&C model.
|
Acknowledgements |
|---|
We thank Harry Hornick of Maryland Department of Natural Resources for information on striped bass spawning stock biomass in the Chesapeake Bay, and three anonymous reviewers for constructive comments that significantly improved the paper. Partial funding for the research was provided by the Electric Power Research Institute, Palo Alto, CA, USA.
|
References |
|---|
|
TopIntroductionMethodsResultsDiscussionReferences |
|---|
-
ASMFC. (2001) Stock Assessment Report for Atlantic Striped Bass. Atlantic States Marine Fisheries Commission, Striped Bass Technical Committee.
Beverton R. J. H. and Holt S. J. (1957) On the dynamics of exploited fish populations. UK Ministry of Agriculture and Fisheries, Fisheries Investigations Series 2, 19. 533 pp.
Beyer J.E. (1989) Recruitment stability and survival – simple size-specific theory with examples from the early life dynamics of marine fish. Dana 7:45–147.
Bollens S.M. (1988) A model of the predatory impact of larval marine fish on the population dynamics of their zooplankton prey. Journal of Plankton Research 10:887–906.
Chesney E.J. (1989) Estimating the food requirements of striped bass larvae, Morone saxatilis: the effects of light, turbidity and turbulence. Marine Ecology Progress Series 53:191–200.[ISI]
Chesney E.J. (1993) A model of survival and growth of striped bass larvae, Morone saxatilis, in the Potomac River, 1987. Marine Ecology Progress Series 92:15–25.[ISI]
Cowan K.A Jr., Rose J.H, Rutherford E.S, Houde E.D. (1993) Individual-based model of young of-the-year striped bass population dynamics. 2. Factors affecting recruitment in the Potomac River, Maryland. Transactions of the American Fisheries Society 119:757–778.
Cowan K.A Jr., Rose J.H, DeVries D.R. (2000) Is density dependent growth in young-of-the-year fishes a question of critical weight? Reviews in Fish Biology and Fisheries 10:61–89.[CrossRef][ISI]
Crecco V.A, Savoy T.F, Witworth W. (1986) Effects of density-dependent and climatic factors on American shad, Alosa sapidissima, recruitment: a predictive approach. Canadian Journal of Fisheries and Aquatic Sciences 43:457–463.
Cushing D.H. (1975) The natural mortality of the plaice. Journal du Conseil International pour l'Exploration de la Mer 36:150–157.
Cushing D.H. (1983) Are fish larvae too dilute to affect the density of their food organisms? Journal of Plankton Research 5:847–854.
Cushing D.H and Harris J.G.K. (1973) Stock and recruitment and the problem of density-dependence. Rapports et Procès-Verbaux des Réunions du Conseil International pour l'Exploration de la Mer 164:142–155.
Durbin A.G and Durbin E.G. (1981) Standing stock and estimated production rates of phytoplankton and zooplankton in Narragansett Bay, Rhode Island. Estuaries 4:24–41.[CrossRef][ISI]
Eldridge M.B, Whipple J.A, Bowers M.J. (1982) Bioenergetics and growth of striped bass, Morone saxatilis, embryos and larvae. Fishery Bulletin U.S. 80:461–474.
Fabrizio M.C. (1987) Growth-invariant discrimination and classification of striped bass stocks by morphometric and electrophoretic methods. Transactions of the American Fisheries Society 116:728–736.[CrossRef]
Forney J.L. (1977) Evidence of inter- and intraspecific competition as factors regulating walleye Stizostedion vitreum vitreum biomass in Oneida Lake, New York. Journal of the Fisheries Research Board of Canada 34:1812–1820.[ISI]
Heinle D.R. (1966) Production of a calanoid copepod, Acartia tonsa, in the Patuxent River estuary. Chesapeake Science 7:59–74.
Heinle D.R. (1969) Temperature and zooplankton. Chesapeake Science 10:186–209.
Hewett S. W. and Johnson B. L. (1987) A generalized bioenergetics model of fish growth for microcomputers. University of Wisconsin, Sea Grant Institute, Technical Report WIS-SG-87-245, Madison, WI.
Houde E.D. (1989) Subtleties and episodes in the early life of fishes. Journal of Fish Biology 35:Suppl. A, 29–38.[ISI]
Houde E.D and Lubbers L. (1986) Survival and growth of striped bass, Morone saxatilis, and Morone hybrid larvae. Laboratory and pond enclosure experiments. Fishery Bulletin U.S. 84:905–914.
Jenkins G.P, Young J.W, Davis T.L.O. (1991) Density dependence of larval growth of a marine fish, the southern bluefin tuna, Thunnus maccoyii. Canadian Journal of Fisheries and Aquatic Sciences 48:1358–1363.
Kohlenstein L. C. (1980) Aspects of the population dynamics of striped bass Morone saxatilis spawning in the Maryland tributaries of the Chesapeake Bay. PhD dissertation, Johns Hopkins University, Baltimore, MD. 127 pp.
Limburg K.E, Pace M.L, Fischer D. (1997) Consumption, selectivity, and use of zooplankton by larval striped bass and white perch in a seasonally pulsed estuary. Transactions of the American Fisheries Society 126:607–621.[CrossRef]
Limburg K.E, Pace M.L, Arend K.K. (1999) Growth, mortality and recruitment of larval Morone spp. in relation to food availability and temperature in the Hudson River. Fishery Bulletin U.S. 97:80–91.
Mackenzie B.R, Leggett W.C, Peters R.H. (1990) Estimating larval fish ingestion rates: can laboratory values be reliably extrapolated to the wild? Marine Ecology Progress Series 67:209–225.[ISI]
MDNR. (2000) Investigation of striped bass in Chesapeake Bay. Maryland Department of Natural Resources, Maryland Fisheries Service Performance Report to U.S. Fish and Wildlife Service for Federal Aid Project No. F-42-R-13, 1999–2000.
Mihursky J. A., Millsaps H., Wiley J. (1987) Fecundity estimates for Maryland striped bass. Report to Maryland Department of Natural Resources, Tidewater Administration. UMCEES Ref. No. 87-127 CBL. 24 pp.
Olney J.E, Field J.E, McGovern J.C. (1991) Striped bass egg mortality, production and female biomass in Virginia rivers, 1980–1989. Transactions of the American Fisheries Society 120:354–367.[CrossRef]
Plante C and Downing J.A. (1989) Production of freshwater invertebrate populations in lakes. Canadian Journal of Fisheries and Aquatic Sciences 46:1489–1498.
Ricker W.E. (1954) Stock and recruitment. Journal of the Fisheries Research Board of Canada 11:559–623.
Rose K.A and Cowan J.H. (1993) Individual-based model of young-of-the-year striped bass population dynamics. 1. Model description and baseline simulations. Transactions of the American Fisheries Society 122:415–438.[CrossRef]
Rose K.A, Cowan E.D Jr., Houde J.H, Coutant C.C. (1993) Individual-based modeling of environmental quality effects on early life stages of fishes: a case study using striped bass. American Fisheries Society Symposium 14:125–145.
Rose K.A, Cowan K.O Jr., Winemiller J.H, Myers R.A, Hilborn R. (2001) Compensatory density dependence in fish populations: importance, controversy, understanding and prognosis. Fish and Fisheries 2:293–327.[CrossRef]
Rothschild B.J. (1986) Biodynamics of the Sea(Harvard University Press, Cambridge).
Rothschild B.J and Osborn T.R. (1988) Small-scale turbulence and plankton contact rates. Journal of Plankton Research 10:465–474.
Rutherford E.S and Houde E.D. (1995) The influence of temperature on cohort-specific growth, survival and recruitment of larval striped bass, Morone saxatilis, in Chesapeake Bay, USA. Fishery Bulletin U.S. 93:315–332.
Rutherford E.S, Houde E.D, Nyman R.M. (1997) Relationship of larval-stage growth and mortality to recruitment of striped bass, Morone saxatilis, in Chesapeake Bay. Estuaries 20:174–198.[Medline]
Secor D.H and Houde E.D. (1995) Temperature effects on the timing of striped bass egg production, larval viability, and recruitment potential in the Patuxent River (Chesapeake Bay). Estuaries 18:527–544.[CrossRef][ISI]
Setzler-Hamilton E.M, Boynton W.R, Mihursky J.A, Polgar T.T, Wood K.V. (1981) Spatial and temporal distribution of striped bass eggs, larvae, and juveniles in the Potomac River estuary. Transactions of the American Fisheries Society 110:121–136.[CrossRef]
Shepherd J. G. (1991) Second-level models for larval growth and mortality, allowing for predation satiation and time- and size-dependence of predation rates. ICES CM 1991/MINI. 10 pp.
Shepherd J.G and Cushing D.H. (1980) A mechanism for density-dependent survival of larval fish as the basis of a stock–recruitment relationship. Journal du Conseil International pour l'Exploration de la Mer 185:255–267.
Shepherd J.G and Cushing D.H. (1990) Regulation in fish populations: myth or mirage? Philosophical Transactions of the Royal Society of London (B) 330:151–164.[CrossRef]
Sissenwine M.P. (1984) Why do fish populations vary. Exploitation of Marine Communities, Dahlem Conference (SpringerIn May R.M (Ed.). , New York)59–94.
Tang Q. (1985) Modification of the Ricker stock–recruitment model to account for environmentally-induced variation in recruitment with particular reference to the blue crab fishery in Chesapeake Bay. Fisheries Research 3:13–21.[CrossRef][ISI]
Tuncer H. (1988) Growth, survival and energetics of larval and juvenile striped bass (Morone saxatilis) and its white bass hybrid (M. saxatilis x M. chrysops). Masters thesis, University of Maryland, College Park.
Ulanowicz R.E and Polgar T.T. (1980) Influence of anadromous spawning behavior and optimal environmental conditions upon striped bass (Morone saxatilis) year-class success. Canadian Journal of Fisheries and Aquatic Sciences 37:143–154.
Uphoff J.H. (1989) Environmental effects on survival of eggs, larvae and juveniles of striped bass in the Choptank River, Maryland. Transactions of the American Fisheries Society 118:251–263.[CrossRef]
Van der Veer H.W, Bergahn R, Miller J.M, Rijnsdorp A.D. (2000) Recruitment in flatfish, with special emphasis on North Atlantic species: progress made by the Flatfish Symposia. ICES Journal of Marine Science 57:202–215.
Van Winkle W, Kumar K.D, Vaughn D.S. (1988) Relative contributions of Hudson River and Chesapeake Bay striped bass stocks to the Atlantic Coast population. American Fisheries Society Monograph 4:133–142.
Zastrow C.E, Houde E.D, Saunders E.H. (1989) Quality of striped bass (Morone saxatilis) eggs in relation to river source and female weight. Rapports et Procès-Verbaux des Réunions du Conseil International pour l' Exploration de la Mer 191:34–42.
Zijlstra J.J and Witte J.I. (1985) On the recruitment of 0-group plaice in the North Sea. Netherlands Journal of Zoology 35:360–376.
CiteULike 
Connotea 
Del.icio.us What's this?
| |||||||||||||||||||||||||||