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On the Ability to Detect the Influenceof Spawning Stock on RecruitmentC. Phillip Goodyear a & Sigurd W. Christensen ba U.S. Fish and Wildlife Service , National Fisheries Center-Leetown , P.O. Box 700, Kearneysville, West Virginia, 25430,USAb Environmental Sciences Division , Oak Ridge NationalLaboratory , Oak Ridge, Tennessee, 37831, USAPublished online: 08 Jan 2011.

To cite this article: C. Phillip Goodyear & Sigurd W. Christensen (1984) On the Ability toDetect the Influence of Spawning Stock on Recruitment, North American Journal of FisheriesManagement, 4:2, 186-193, DOI: 10.1577/1548-8659(1984)4<186:OTATDT>2.0.CO;2

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North American Journal of Fisheries Management 4:186-193, 1984 ¸ Copyright by the American Fisheries Society 1984

On the Ability to Detect the Influence of Spawning Stock on Recruitment

C. PHILLIP GOODYEAR

U.S, Fish and Wildlife Service National Fisheries Center-Leetown

P.O. Box 700

Kearneysville, West Virginia 25430

SlGURD W. CHRISTENSEN

Environmental Sciences Division

Oak Ridge National Laboratory Oak Ridge, Tennessee 37831

ABSTRACT

Simulated observations of spawning stock size, recruitment, and two random environmental vari- ables were obtained from a density-independent Leslie matrix model. Recruitment to Age 1 was directly proportional to population fecundity but strongly influenced by the effects of the random environmental variables. The simulated observations were subjected to mnltiple regression analysis which detected the influence of the random environmental variables but did not reliably detect the influence of spawning stock. These results indicate that multiple regression is unreliable in detect- ing the influence of stock on recruitment when annual variations in recruitment are primarily due to environmental factors.

A classical problem in fisheries management is the question of whether or not recruitment substantially depends on the size of the spawning stock. The answer to this question is central to scientifically based fisheries management strat- egies. If recruitment is independent of the size of the spawning stock, it is sensible to manage to maximize yield per recruit or to prevent "growth overfishing" (Cushing 1977, p. 118), but managing to maintain spawning stock can be a secondary consideration. If recruitment does de- pend on stock size, however, managing for max- imum sustainable yield (MSY) or optimum sus- tainable yield (OSY) especially for the prevention of "recruitment overfishing" is a more appro- priate objective.

The emerging significance of this dichotomy was recognized by Cushing:

In the past it was often assumed that recruit- ment failure was, if not inconceivable, unlike- ly. In recent years, however, the failures of some pelagic fisheries have been recognized as being due to recruitment over fishing and even some demersal stocks have been threatened

with such recruitment failure. The change of

• Publication No. 2253, Environmental Sciences Di- vision, Oak Ridge National Laboratory.

attitude that is taking place is the recognition of the possibility of the decline in recruitment due to fishing.

(Cushing 1977, p. 131)

It is important, from both a scientific and a management point of view, to ascertain whether or not maintenance of spawning stock size is important to the maintenance of recruitment.

Declining recruitment and declining fishing yields can sometimes be interpreted as being due to recruitment overfishing or to other man-in- duced stress without recourse to formal statis-

tical tests (e.g., Salo and Stober 1977). Such tests, however, are being applied with increasing fre- quency to attempt to detect and quantify the re- lationship between spawning stock and recruit- ment (Sommani 1972; Lett et al. 1975; Marcy 1976; Chevalier 1977; Parrish 1977; Smith 1977; Kohlenstein 1980; Ecological Analysts Inc. 1981; Yoshiyama et al. 1981). Because the effect of environmentally induced variation on survival from the egg stage to recruitment very often plays the dominant role in the determination of year- class strength, multiple regression techniques often are used. The advantage of this approach is that some of the effect of environmental vari-

ables can be removed from the data set, which increases the chance of detecting a relationship

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SPAWNING STOCK INFLUENCE ON RECRUITMENT 187

between spawners and recruits. However, as not- ed by McFadden (1963), multiple regression can sometimes be misleading when applied to eco- logical problems.

The purpose of this paper is to examine the ability of regression techniques to detect a rela- tionship between stock size and recruitment for the case where recruitment is directly propor- tional to the number of eggs produced by the spawning stock, but strongly modulated by den- sity-independent variation in first-year survival.

METHODS

Simulated observations of spawning stock size, population fecundity, and two random environ- mental variables were obtained from a Leslie

matrix model in which the number of 1-year-old recruits is given by:

N,,t+, = SoCtqtE. (1)

where

So = the deterministic steady-state, first- year survival,

ct and q, = annual survival deviations associ- ated with temperature (C) and flow (Q), respectively,

E• = the total egg production by the stock in year t.

The values ofc and q are varied for each year of the simulation; thus, the survival fraction from eggs to Age 1 for a given year is the quantity s0ctqt.

The life history parameters utilized in this study correspond to those estimated for the Hudson River striped bass (Morone saxatilis) population (Table 1). The total annual mortality was as- sumed to be 0.40 for each age class, and the value of So was determined for the stable age distri- bution using the methods of Vaughan and Saila (1976) and Van Winkle et al. (1978). Fifteen age classes were considered in the model and all fish

were assumed to die by the end of the 15th year. The value of E was determined for each year of the simulation as the sum of the products of the age-specific fecundities (Table 1) and the simu- lated number of individuals in each age class.

The value of c, for each simulated year was computed as:

2 c• - (2)

1 + e

where C• = the simulated temperature for the year t.

Table 1. Life history data used in the simula- tion model described in the text. Data corre-

spond to the Hudson River striped bass popu- lation as compiled in Christensen et al. (1982).

Survival

Age Weight (kg) rate Eggs per fish

1 O.Ol 0.6 0.0

2 0.10 0.6 0.0 3 0.46 0.6 1.4 x 104 4 1.17 0.6 2.3 x lO a

5 1.75 0.6 5.5 x 10 a 6 2.67 0.6 1.2 x l0 s

7 3.75 0.6 2.5 x 10 • 8 5.82 0.6 5.8 x l0 s 9 6.55 0.6 7.9 x l0 s

l0 7.55 0.6 8.8 x 10 •

l 1 8.05 0.6 9.9 x 10 • 12 9.36 0.6 1.0 x 106 13 10.32 0.6 1.1 x 106

14 9.68 a 0.6 1.1 x 106 15 9.81 a 0.0 1.3 x 106

a The unexpected pattern in the numbers may simply reflect inaccuracies due to small sample size. The sample size is 2 l for Age 12 but drops to I each for ages 13, 14, and 15.

The values of Q were randomly drawn from a normal distribution with a mean C of 5.0 (ar- bitrary units, e.g., øC) and variance 1.0. Although they are suitable for the type of analysis we are performing here, both the form of Equation 2 and the distribution of C are arbitrary. The com- puted deviations in survival from Equation 2, however, are consistent with the observed trend for strong year classes of striped bass to be pro- duced following below-normal winter tempera- tures (Ulanowicz and Polgar 1980). The form of Equation 2 is such that if the temperature is av- erage, ct will equal 1.0 and there will be no effect from temperature on survival. As temperature falls, survival increases asymptotically to twice the average. Higher-than-average temperatures act to depress survival.

The value of qt for each simulated year was computed as:

2

q• 1 + e-(Q, ,•) (3)

where Q, = the simulated flow for the year t. The values of Qt were randomly drawn from

a normal distribution with a mean Q of 15 (ar- bitrary units; e.g., hundreds of m3/second) and variance 1.0. As before, both the form of the equation and the distribution are arbitrary. Again, however, the deviations in survival computed

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188 GOODYEAR AND CHRISTENSEN

1000

z H

¸

Ioo

I 6 7• 8 9 10111 2 3 41S

20 60 100 140 180 220 260 300 340 380 420

YEAR

Figure 1. Plot of the population trajectory for the simulation described on p. 188. The population was simulated for 440 years. Data from the last 400 years of the simulatiou were divided into 20 periods of 20 years each and analyzed with multiple regression techniques.

from Equation 3 are consistent with the obser- vation that year-class strength is positively cor- related with river discharge in striped bass (Ulan- owicz and Polgar 1980). At mean flow conditions, qt equals 1.0 and there is no effect of flow on average survival. Below-average flow depresses survival and above-average flow increases sur- vival asymptotically to twice the average.

The model was initiated with the stable age distribution and 440 years of simulated obser- vations were produced. Data from the first 40 simulated years were discarded to eliminate the effects of the initial conditions. The remaining 400 years of data were segregated into 20 periods of 20 years each (Fig. 1). For each simulated year, an index of spawning stock, the current year's egg production, the simulated abundance of Age- 1 recruits, and the simulated values of the en- vironmental variables Q and T were output for later statistical analysis. The index of spawning stock was the total biomass of fish older than

Age 4. The intention here is to probe the ability of

multiple regression techniques, as convention- ally used, to detect the influence of stock size on recruitment. An investigator using multiple regression typically will do the following: (a) as- semble a collection of variables that are avail-

able, and which may be thought or suspected to be relevant; (b) enlarge this collection by adding transformations (i.e., logarithmic) of some or all of the variables; (c) obtain one or more statistical models, often based on traditional fisheries models, which include various combinations of the variables from step (b); (d) perform regres-

sion analyses of the models in (c), often using some algorithm for selecting variables to include or exclude in successive thais; and (e), based on statistical measures of goodness-of-fit of the models and of significance of the variables, select a best combination of model and variables. As-

suming stock size did not emerge as important in the analysis, it is common to (t) state that variation in recruitment did not appear to be influenced by variation in stock size. A final step often taken is to strengthen the statement of con- clusion (t) by omitting the variation aspect; e.g., (g) it may be stated that stock size did not appear to influence recruitment, or that recruitment is independent of stock size, or a mathematical model for recruitment that ignores stock size may be used.

Because this investigation is based on a sim- ulation model, it is possible to use external knowledge (which an investigator of real-world populations would lack) to simplify this process. An additive model, suitable for linear regression, can be obtained from the underlying model (Equation 1) by taking the log, of both sides:

log,N•: log,So + log,c + log,q + log,E (4)

This corresponds to the regression equation

Y = bo + b•X• + b•X• + b•X• + error (5)

where Y = log,N,, X,: log,c, X2 = log,q, X3 =

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SPAWNING STOCK INFLUENCE ON RECRUITMENT 189

Table 2. Correlations (r) among the variables available for regression based on 400 years of sim- ulated observations. The lower triangular matrix gives the results from untransformed data; up- per triangular matrix, the log-transformed data. a

Simulated

temperature Simulated flow Variable Recruit Stock index Eggs (C) (Q)

Recruits -- 0.28** 0.37** -0.52** 0.64** Stock index 0.25** -- 0.84** 0.11' -0.05

Eggs 0.36** 0.82** -- 0.10 - 0.02 C -0.55** 0.11' 0.10 -- 0.02

Q 0.60** -0.06 -0.03 -0.00 -

a*p<0.05,**p< 0.01.

IOgeE, and b0, b, b2, and b3 are coefficients to be estimated by regression. Therefore, the natural logarithm of the simulated number of Age-1 recruits was used as the dependent vari- able Y. An investigator would not have measures of c or q which represent the effect of the envi- ronmental variables (temperature and flow, re- spectively) on survival, but likely would have measures of the variables themselves (C and Q) and would try various transformations in the course of the analysis. To find the best variables to use for Xi and X2 in Equation 5, knowing that 1OgeC and 1Ogeq are ideal but unavailable to the investigator, the correlations of log,c and 1Ogeq with the corresponding untransformed and IOge, exponential, sine, and square root transformed values of C and of Q, respectively, were deter- mined. The untransformed values of C and Q were most strongly correlated (r > 0.95,398 df) with 1OgeC and IOgeq. As a consequence, the values of Q and C were employed for X• and X2 without transformation in the regression analysis. Final- ly, the investigator would not have estimates of E, the actual egg deposition by the spawning stock, because these data are not available from field

samples. It is, however, common practice to use estimates of stock size based on catch data as a

surrogate for egg production in such analyses. The index of spawning stock, therefore, was se- lected to represent egg production in the regres- sion analysis, and X3 in Equation 5 was logeS.

RESULTS

The correlations among the variables available for the regression analysis are presented in Table 2. The lack of a perfect correlation between the index of parental stock size and the annual pro- duction of eggs is the result of different egg pro-

duction rates per unit biomass in the different age classes that contribute to the spawn and some egg production by age-classes 3 and 4. The index of spawning stock was selected to represent egg production in the regression analysis because data on actual egg deposition by spawning stocks are generally unavailable from field data.

The index of spawning stock was found to be significant in only 3 of the 20 cases, when con- sidered along with temperature and flow in the multiple regression equation (Table 3). Further examination of these three cases revealed that if

either flow or temperature were eliminated from the regression model, the parental stock index was no longer significant. The 20 fitted relation- ships between log of recruitment and log of spawning stock at mean flow and mean temper- ature were plotted along with the underlying true model (Fig. 2). The slope of the true relationship was underestimated in every case and, not un- expectedly, considerable scatter was evident.

In the simple regression case (with the random variables excluded from the regression), the number of recruits to age-class 1 appeared to be independent of the size of the spawning stock in all but 1 of the 20 cases (Table 3). An exami- nation of this single case revealed that the sig- nificant regression was spurious because the regression coefficient was negative, whereas the underlying model specifies a positive effect.

In contrast to these results, the multiple regres- sion models detected the effect of temperature and flow on the number of Age- 1 recruits very clearly. Both factors were found to be significant at the 0.01 level of probability in each of the 20 cases (Table 3). It is evident, also, that the ad- dition of the parental stock index resulted in little improvement in the overall regression for any of the 20 cases.

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190 GOODYEAR AND CHRISTENSEN

Table 3. Values of t or F and of r s and results of tests of significance for the regression coefficients. • The natural logarithm of the simulated number of recruits was the dependent variable for all regressions. The independent variables were the natural logarithms of the stock index (stock or SI), temperature (C) and flow (Q). Each case represents 20 data points, resulting in 400 points for the total set.

Stock included b Random only • Stock only

t (16 df) t (17 df) (18 df)

Case Stock C Q r 2 C Q r 2 F r •

1 0.27 12.76'* 7.27** 0.95 - 13.13** 7.93** 0.95 0.99 0.05 2 1.87 -15.42'* 10.45'* 0.95 -14.29'* 10.22'* 0.94 0.14 0.01 3 1.51 4.39** 6.59** 0.80 -4.00** 6.18'* 0.77 1.07 0.06 4 3.36** 6.42** 11.06'* 0.90 -5.29** 8.39** 0.84 0.41 0.02 5 1.87 7.76** 10.91'* 0.93 7.06** 10.24'* 0.91 0.07 0.00 6 0.05 -7.41'* 11.54'* 0.95 -7.63** 11.93'* 0.95 0.06 0.00 7 0.78 -6.32** 7.48** 0.87 -6.37** 7.61'* 0.86 0.31 0.02 8 -0.74 -10.69'* 9.27** 0.95 -11.66'* 9.55** 0.95 3.10 0.15 9 1.01 -4.50** 9.03** 0.86 -4.51'* 9.03** 0.85 0.21 0.01

l0 0.56 -5.77** 6.08** 0.88 -5.87** 6.45** 0.88 1.99 0.10 11 0.70 9.85** 9.75** 0.92 10.21'* 10.09'* 0.91 1.63 0.08

12 1.15 8.64** 8.74** 0.91 8.90** 8.68** 0.90 0.00 0.00 13 2.02 -6.72** 5.64** 0.78 -5.89** 4.86** 0.72 0.12 0.01 14 1.31 - 10.93'* 10.43'* 0.95 - 12.60'* 11.03'* 0.94 7.36* 0.29 15 0.38 10.73'* 10.67'* 0.93 -11.66'* 11.07'* 0.93 1.95 0.10 16 2.14' 7.86** 10.99'* 0.93 -7.26** 10.45'* 0.91 1.26 0.06 17 0.44 -7.99** 9.72** 0.91 -8.31'* 9.97** 0.91 0.17 0.01 18 0.47 9.25** 8.03** 0.92 -9.50** 9.11'* 0.92 0.72 0.04 19 2.37* 8.84** 8.27** 0.89 -7.56** 7.15'* 0.85 0.88 0.05 20 -0.43 -16.05'* 10.46'* 0.96 17.90'* 11.20'* 0.96 3.64 0.17

Total

set 20.71' -34.18'* 36.20** 0.87 -22.34** 24.43** 0.73 33.31'* 0.08

a,p < 0.05; **P < 0.01. Regression equation: Y = bo + b•SI + b2 C q- b3Q + Regression equation: Y = bo + b•C + b2Q + error. Regression equation: Y = b0 + b,SI + error.

error.

When the entire 400 simulated observations

were simultaneously employed in the regression, the parental stock index was found to be signif- icant when temperature and flow were included (R 2= 0.87) and when considered alone (R 2= 0.08; Table 3). Also, the inclusion of the stock index caused a rather substantial improvement in the fitted regression equation (from R 2 = 0.73 tO R 2 = 0.87) when all 400 simulated observa- tions were used.

As a check on the simulation and regression procedures, the entire process was repeated, us- ing log• E rather than log• S, and with the form of the effects of Q and C modified so that they affected survival in a log normal manner. In this special (and trivial) case, where all the assump- tions of the regression procedure were met, all of the variation was accounted for, and correct and significant estimates of all regression coef- ficients were obtained.

DISCUSSION

The random variables, temperature and flow, employed in this analysis could account for about 90% of the variability in simulated recruitment to Age 1 in the model population. In contrast, the variability in parental stock size appeared to be totally unrelated to the variability in number of young produced when considered alone, and was infrequently picked out as having a signifi- cant influence when the effects of the random

variables were included in the regression equa- tion. Although this simulation was performed without density-dependent mechanisms, similar results would be expected for many situations where density-dependent mortality exists, par- ticularly if it is low. Such a situation could be natural in some stocks or could result from sus-

tained high levels of fishing mortality. The importance of this obervation is that the

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SPAWNING STOCK INFLUENCE ON RECRUITMENT 191

15.5

14.0

I• 0 1• 5 ]3.8 13.5 14 0

LOG e OF SPAWNZN6 STOCK INDEX

Figure 2. Plots of the 20 fitted relationships between the natural logarithms of recruitment and the natural logarithms of spawning-stock size at mean flow and mean temperature. The underlying true relationship is given by the dashed line.

underlying model would have the effect of dou- bling the number of young produced if the parent stock size were to double, and would halve the number of young if the parent stock were to de- cline by one-half. The fitted models, on the other hand, could lead to the incorrect conclusion that reductions in stock size would not lead to re-

duced recruitment. The proper management strategies are different for these two situations and the difference is important.

The difficulty in detecting the influence of stock size on recruitment in our example was the result of the relative power of the random variables (compared to egg production) to influence year- class strength and the error associated with the use of the spawning stock index as a surrogate for the population fecundity. Since reproduction was spread across a number of age classes, both egg production and the stock index were buffered against rapid change. Thus, the year-to-year vari- ation in the stock index and its influence on year- class strength were necessarily small compared to the effects of the random variations. Reducing the effect of the environmental variables on year- class strength would not have helped, because it is just this variation in year-class strength which causes the stock in the model to vary at all. (Ex- trinsic factors causing stock sizes to change from year to year, such as varying fishing mortality,

would in principle make the influence of stock size easier to detect, but in practice also would likely reduce the accuracy of stock-size esti- mates.) Also, because no simple transformation of the random variables would result in an exact

correspondence of the regression model with the underlying model, the effects of the random vari- ables could not be completely extracted. The combined effects of these factors acted to reduce

the probability of detecting the influence of the population size on recruitment. When the time series was sufficiently long that the stock size varied over a fairly wide range, as was the case with our 400-year data set, then the importance of the stock size became apparent.

In this model study, we were able to directly examine the relationship between the environ- mental variables and their functional represen- tation in the regression model to determine the most appropriate transformation to employ. In contrast, important environmental variables that are measured in the field would most often be

correlated with the activity of some agent of mor- tality. The functional relationship between the measured environmental variable and the activ-

ity of the agent of mortality would determine the appropriate transformation that should be ap- plied. It is doubtful that an investigator would have any prior knowledge of the functional form relating the environmental variable to its effect on the survival rate. Furthermore, it is unlikely that any transformation will perfectly fit the real- world situation. Such phenomena would tend to mask the ability to detect the influence of paren- tal stock size on recruitment in populations that are characterized by large variations in year-class strengths caused by density-independent envi- ronmental factors.

It should be noted, also, that in our example the variables employed in the regression con- tained no sampling error, which is not the case in a real-world situation. The occurrence of sam-

pling error likely will further compound the problem.

Walters and Ludwig (1981), in the context of simple linear regression (i.e., with stock but with- out environmental variables), demonstrated that large errors in measurements of stock size could lead to an incorrect conclusion that recruitment

is independent of spawning stock. They recom- mended not trusting models based on such an assumption, unless it was known that spawning stocks had been measured with errors "less than

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192 GOODYEAR AND CHRISTENSEN

+30% or so." Because of the multiple-aged na- ture of the striped bass, spawning stock size is a poorer surrogate for egg production than would be the case with, say, salmon. Nevertheless, the use of log spawning stock size as a surrogate for log egg production in the regressions meets the "_+ 30% or so" criterion of Walters and Ludwig (R 2 = 0.7) and still leads to a failure to detect the true relationship between stock and recruit- ment. This can be attributed to the effects of the

random (environmental) variables in our under- lying model. The active, adaptive management techniques recommended in Smith and Walters ( 1981), Walters ( 1981 ), and Ludwig and Walters (1981), would improve the ability to detect the influence of spawning stock.

In summary, the lack of an observable rela- tionship between size of spawning stocks and the recruits they produce should not be taken as an indication that recruitment is truly independent of the size of the reproductive stocks. Although such may be the case, managing a fishery under this assumption when it is not true could con- tribute to the decline (perhaps extinction) of the population. This obervation would seem to argue for management schemes that preserve at least some minimum spawning stock whenever the dynamics of the population are not well under- stood.

ACKNOWLEDGMENTS

We thank L. W. Barnthouse, J. Boreman, J. C. Goyert, P. Rago, W. Van Winkle, and D. S. Vaughan for their thoughtful comments on the manuscript. Sigurd W. Christensen's contribu- tion was supported by the U.S. Environmental Protection Agency, Of•ce of Research and De- velopment, Of•ce of Environmental Processes and Effects Research, under Interagency Agree- ment EPA No. 79-D-X0533 with the U.S. De-

partment of Energy (DOE No. 40-740-78), under contract W-7405-eng-26 with Union Carbide Corporation.

REFERENCES

CHEVALIER, J.R. 1977. Changes in the walleye (Stizo- stedion vitreum vitreum) population in Rainy Lake and factors in abundance, 1924-75. Journal of the Fisheries Research Board of Canada 34:1696-1702.

CHRISTENSEN, S. W., C. P. GOODYEAR, AND B. L. K•R•C. 1982. An analysis of the validity of the utilities' stock-recruitment curve-fitting exercises and "prior

estimation of beta" technique. Volume III. On the impact of entrainment and impingmerit on fish populations in the Hudson River estuary. ORNL/ NUREG/TM-385/V3 (NUREG/CR-2220 1V3) Oak Ridge National Laboratory, Oak Ridge, Ten- nessee, USA.

CUSHING, D. H. 1977. The problems of stock and recruitment. Chapter 6, Pages 116-133 in J. A. Gulland, editor. Fish population dynamics. John Wiley and Sons, New York, New York, USA.

ECOLOGICAL ANALYSTS, INC. 1981. Pittsburgh power plant cooling water intake structures 316(b) dem- onstration. Prepared for Pacific Gas and Electric Company. Ecological Analysts, Inc., Sparks, Maryland, USA.

KOHLENSTEIN, L.C. 1980. Aspects of the population dynamics of striped bass (Morone saxatilis) spawning in the Maryland tributaries of the Ches- apeake Bay. Doctoral dissertation, Johns Hopkins University. Publication PPSE T-14, Johns Hop- kins University Applied Physics Laboratory, Bal- timore, Maryland, USA.

LETT, P. F., A. C. KOHLER, AND D. N. FITZGERALD. 1975. Role of stock biomass and temperature in recruitment of southern Gulf of St. Lawrence At-

lantic Cod, Gadus morhua. Journal of the Fish- eries Research Board of Canada 32:1613-1627.

LUDWIG, D., ANvC. J. WALTERS. 1981. Measurement errors and uncertainty in parameter estimates for stock and recruitment. Canadian Journal of Fish- eries and Aquatic Sciences 38:711-720.

MARCY, B.C. JR. 1976. Early life history studies of the American shad in the lower Connecticut River and the effects of the Connecticut Yankee Plant.

Pages 141-168 in D. Merriman andL. M. Thorpe, editors. The Connecticut River ecology study: The impact of a nuclear power plant. Monograph I, American Fisheries Society, Bethesda, Maryland, USA.

MCFADDEN, J. T, 1963. An example of inaccuracies inherent in interpretation of ecological field data. American Naturalist 97:99-116.

PARRISH, R. H. 1977. An assessment of environ- mentally related variation in the recruitment of the California Current stock of Pacific mackerel

(Scomberjaponicus) and its implications for man- agement. Doctoral dissertation, Oregon State Uni- versity, Corvallis, Oregon, USA.

SALO, E. O., ANY Q. J. STOBER. 1977. Man's impact on the Columbia River stock of salmon. Pages 36- 45 in W. Van Winkle, editor. Assessing the effects of power-plant-induced mortality on fish popu- lations. Pergamon Press, New York, New York, USA.

SsnlTH, A.D. M., AND C. J. WALTERS. 1981. Adaptive management of stock-recruitment systems. Ca- nadian Journal of Fisheries and Aquatic Sciences 38:690-703.

SSnITH, LLOVV L. JR. 1977. Walleye (Stizostedion vit- reum vitreum) and yellow perch (Perca fiavescens) populations and fisheries of the Red Lakes, Min-

Dow

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ded

by [

McG

ill U

nive

rsity

Lib

rary

] at

11:

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3 N

ovem

ber

2014

SPAWNING STOCK INFLUENCE ON RECRUITMENT 193

nesota, 1930-75. Journal of the Fisheries Research Board of Canada 34:1774-1783.

SOMMANI, P. 1972. A study on the population dy- namics of striped bass in the San Francisco Bay estuary. Doctoral dissertation, University of Washington, Seattle, Washington, USA.

ULANOWICZ, R. E., AND T. T. POLGAR. 1980. Influ- ences of anadromous spawning behavior and op- timal environmental conditions upon striped bass (Motone saxatilis) year class success. Canadian Journal of Fisheries and Aquatic Sciences 37:143- 153.

VAN WINKLE, W., D. L. DEANGELIS, AND S. R. BLUM. 1978. A density-dependent function for fishing mortality rate and a method for determining ele- ments of a Leslie matrix with density-dependent parameters. Transactions of the American Fish- edes Society 107:395-401.

VAUGHAN, D. S., AND S. B. SAILA. 1976. A method for determining mortality rates using the Leslie matrix. Transactions of the American Fisheries

Society 105:380-383. WALTERS, C.J. 1981. Optimum escapements in the

face of alternate recruitment hypotheses. Cana- dian Journal of Fisheries and Aquatic Sciences 38: 678-689.

WALTERS, C. J., AND D. LUDWIG. 1981. Effects of measurement errors on the assessment of stock-

recruitment relationships. Canadian Journal of Fisheries and Aquatic Sciences 38:704-710.

YOSHIYAMA, R. M., W. VAN WINKLE, B. L. KIRK, AND D. E. STEVENS. 1981. Regression analyses of stock-recruitment relationships in three fish pop- ulations. ORNL/NUREG/TM-424 (NUREG/CR- 1836). Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA.

Dow

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