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ParentProgeny Relation andEstimation of Optimum Yield forAmerican Shad in the ConnecticutRiverCharles H. Walburg aa U.S. Bureau of Sport Fisheries and Wildlife , Yankton , SouthDakota , USAPublished online: 09 Jan 2011.
To cite this article: Charles H. Walburg (1963) ParentProgeny Relation and Estimation ofOptimum Yield for American Shad in the Connecticut River, Transactions of the American FisheriesSociety, 92:4, 436-439, DOI: 10.1577/1548-8659(1963)92[436:PRAEOO]2.0.CO;2
To link to this article: http://dx.doi.org/10.1577/1548-8659(1963)92[436:PRAEOO]2.0.CO;2
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436 SHORT PAPERS AND NOTES
(Cochran, 1953). For bluegill, v(p)=0.000674 and v'(p) = 0.00219, while for redear sunfish v(p) = 0.00101 and v'(p) = 0.00394.
In both cases formula (3) estimated vari- ances greater than those expected by binomial theory. Therefore the sex ratios are distrib- uted with greater patchiness than expected by the binomial theory, and the binomial formula for the variance of a proportion would under- estimate the variance. Thus it appears that bluegill and redear sunfish segregate them- selves by sex to a certain degree; however, there are factors other than segregation by sex that could cause the sex ratio to vary from sample to sample; e.g., the sampling technique could be selective for sex, and this selectivity could vary from area to area. However, I believe this unlikely with these data.
I am indebted to the many employees of the Louisiana Wild Life and Fisheries Commission who assisted in the collection and analysis of the data. This report is a contribution of Louisiana Federal Aid in Fish Restoration Project F-10-R.
COCHRAn, W.G. 1953. Sampling techniques. John Wiley & Sons, Inc., New York, xiv - 330 pp.
1954. Some methods for strengthening the common x tests. Biometrics, 10: 417451.
LAMBOU, VCTOR W. 1962. Distribution of fishes in Lake Bistineau, Louisiana. Jour. Wildl. Mgt., 26(2): 193-203.
VICTOR W. LAMBOU Louisiana Wild Li/e and Fisheries Commission Baton Rouge, Louisiana
Parent-Progeny Relation and Estimation of Optimum Yield
for American Shad in the Connecticut River
In a recent paper entitled "Natural Mor- tality of American Shad," I wrote that, "In the Connecticut River over 80 percent of the fluctuations in size of runs can be attributed
to changes in the size of the escapement from the fishery (Fredin, 1954). Therefore, the number of progeny is dependent on the size of the spawning stock" (Walburg, 1961). Ricker (1962) concluded from these state- ments that "... more than 80 percent of the variation in size of these shad runs was as-
sociated with the size of their parental spawn- ing stocks." Ricker correctly pointed out that, "... this would be a remarkably close rela- tionship if it were true, but it is not." He further pointed out that no parent-progeny relationship was demonstrated in Fredin's study.
It was not my intention that the reader con- strue my remarks as Ricker has done. It must be acknowledged, however, that my statement was misleading. Ricker objected to the in- ference that "... number of progeny is depen- dent on the size of the spawning stock . . ." was a conclusion from Fredin (1954). As indicated by Fredin, the size of run in any year was mostly affected by the size of the previous year's escapement from the fishery (fraternal relationship). The statement on parent-progeny relation in my 1961 note should have been more fully explained since it concerned unpublished information on the American shad (Alosa sapidissima) in the Connecticut River.
Comparison of the sizes of spawning stocks with the sizes of resultant year classes would reveal the degree of parent-progeny relation. Unfortunately, adequate data on year-class abundance are not available, and inferences regarding the relation between escapements and recruits must be made using indirect methods.
Catch and effort statistics on the Connecti-
cut River shad fishery have been collected by the Connecticut State Board of Fisheries and
Game each year since 1935. With these data and the results of tagging studies conducted in 1951 (Fredin, 1954) and 1957, fishery biologists of the Bureau of Commercial Fish- eries have estimated the size of the shad run
and the spawning escapement for each year (Table 1).
The Connecticut River shad run consists
of fish that are spawning for the first time (initial spawners) and fish that are spawning for the second or more times (repeat spawn- ers). Fish spawning for the first time are 3
x Unpublished data, U.S. Bureau of Commercial Fisheries, Biological Laboratory, Beaufort, North Carolina.
SHORT PAPERS AND NOTES 437
TABLE 1.--Estimated abundance o] the Connecticut River shad runs and the escapements during 1935- 61
[Nuinbers are thousands of fish]
Size of ffpawning Size of Spawning Year rnn escapenlent Year rnn escapement
1935 306 182 1949 188 57 1936 277 171 1950 131 54 1937 270 155 1951 178 77 1938 272 147 1952 249 114 1939 255 144 1953 230 115 1940 277 184 1954 191 113 1941 370 249 1955 173 112 1942 336 221 1956 223 170 1943 356 196 1957 313 232 1944 378 166 1958 372 246 1945 309 92 1959 348 240 1946 366 66 1960 340 224 1947 270 51 1961 317 193 1948 241 64
Data for 1935-51 are from Fredin (1954); those for 1952-61 are from files of the U.S. Bureau of Com- mercial Fisheries.
to 7 years old, with the majority 4 and 5 years old (Table 2). These fish are termed catchable recruits. Fish spawning for the first time at 3 years of age (precocious males) are gen- erally too small to be captured by the com- mercial fishery, and are first liable to capture when they return as 4-year-olds. Therefore some fish spawning for the second time are also catchable recruits. Fish in age groups 6 and 7 were too few to be considered.
The number of catchable recruits in any year is associated primarily with the spawn- ing stocks 4 and 5 years previously. Thus fish escaping the fishery (spawning stock) 4 and 5 years preceding the year of return of catchable recruits are the parental stocks I used to calculate the parent-progeny relation.
To estimate the numbers of catchable re-
cruits in each year's run (the dependent vari- able in the parent-progeny relation), it is necessary to assume a fixed between-season survival rate for the spawners of the preceding year. The escapement in the preceding year is multiplied by the assumed survival rate, and the product (number of survivors or repeat spawners) is subtracted from the total run.
TABLE 2.--Numbers o! initial spawners by age group in the commercial shad fishery of the Connecticut River, 1956-59
Number of Age group Year initial spawners
sampled III IV V VI VII
1956 396 3 251 124 18 0 1957 312 7 58 233 14 0 1958 380 9 175 154 42 0 1959 394 I 107 266 19 I
TABLE &--Estimated numbers o! catchable recruits (Y), escapements ]rom the fishery 5 years earlier (X) and 4 years earlier (X.o), and average escape- ments during the 5th and 4th years (X) in the Connecticut River shad fishery, 1940-61
[Numbers arc thousands of fish]
Year Y X Xa X
1940 216 182 171 176 1941 293 171 155 163 1942 232 155 147 151 1943 263 147 144 146 1944 296 144 184 164 1945 239 184 249 216 1946 327 249 221 235 1947 242 221 196 208 1948 220 196 166 181 1949 161 166 92 129 1950 107 92 66 79 1951 155 66 51 58 1952 217 51 64 58 1953 182 64 57 60 1954 143 57 54 56 1955 126 54 77 66 1956 176 77 114 96 1957 242 114 115 114 1958 274 115 113 114 1959 245 113 112 112 1960 239 112 170 141 1961 223 170 232 201
The remainder is an estimate of the number of catchable recruits in the total run.
Walburg (1961) estimated that the average annual survival rate of adult Connecticut River
shad during 1956-59 was 42 percent. Using this survival rate, the number of catchable recruits for each year's run from 1940 through 1961 was estimated (Table 3).
A multiple regression equation calculated from the data in Table 3 indicated a positive relationship between parent stocks and prog- eny (Y = 128.48 q- 0.2136X1 q- 0.4651X). Analysis of variance indicated that the re- duction in variation in numbers of recruits
owing to regression on numbers of spawners 4 and 5 years previously was highly significant (F = 8.25; d.f. 2, 19; p < 0.01). Curviline- arity in the regression was examined by squar- ing the independent variables. Departure from linearity was not significant (F -- 2.05; d.f. 2, 17; p0.18). These results suggest that, over the range of data available, numbers of catchable recruits increase linearly in relation to the abundance of parental stocks.
The coefficient of determination calculated
from the multiple regression analysis (r e= 0.4648), when adjusted for degrees of free- dom, indicates that the fraction of the total variance of y1 accounted for by regression is
1-(1-0.4648) (22-1) = 41 percent. = i22-3)
438 SHORT PAPERS AND NOTES
m / eo
catcha]e ecuts and aeae escapement om the Connecticut ve shad fishe vious]7, umea]s indicate the eas n which the ecaRs ecame catchable.
These results suggest that 41 percent of the variability in numbers of catchable recruits can be ascribed to changes in abundance of spawning stocks. It is concluded that size of spawning stocks significantly influences abun- dance of progeny at the population levels found during the period of study.
Since the relation between size of spawning
stocks and resultant progeny was highly sig- nificant, these data were used to calculate a reproduction curve for Connecticut River shad. This was accomplished by averaging the size of spawning stocks 4 and 5 years previously and comparing this mean with the estimated number of resultant progeny or catchable recruits (Table 3). A simple re- gression analysis calculated from these data again indicated a positive relation between parent stocks and progeny (r = 0.68; 20 d.f.; p < 0.01). A curved regression line (repro- duction curve) was also calculated from these data to obtain the best estimate of the relation
between average size of spawning stocks and number of catchable recruits (Figure 1). Al- though departure of the regression from line- arity was not significant (p ~ 0.30), curvature of the regression relationship is probable on biological grounds. The curvilinear regression equation is:
Y1 = 82.06 + 1.4818X - 0.0029X e.
From the reproduction curve, yields of catchable recruits were estimated for various
parent stock sizes (Table 4). Maximum dis- tance between the replacement line and the reproduction curve was 102,000 fish. This is the theoretical maximum yield (Ricker, 1958), and it is associated with an escapement of about 75,000 fish in both the 4th and 5th preceding years. Thus an escapement of 75,000 fish annually might be considered optimum. Because a substantial fraction of the spawners survive to reenter the fishery the following year, the optimum escapement is that which provides the maximum number of catchable recruits and repeat spawners.
Assuming a 42-percent survival rate for
Tarx.z 4.---Estimates o/ optimum escapement and theoretical yield for the Connecticut River shad fishery [Numbers are thousands of fish]
Number of Potential Number of Average catchable catch of repeat Size Theoretical
escapement recruits recruits spa*vners of run yield (X) (Y-) (Y--X) (0.42X) (Y- + 0.42X) (Y-q-O.42X-X) 50 149 99 21 170 120 75 177 102 x 32 209 134
100 201 101 42 243 143 125 222 97 52 274 149 a 150 239 89 63 302 152 a 175 a 253 78 74 327 152a
200 262 62 84 346 146 225 269 44 94 363 138 250 271 21 105 376 126
First estimate of optimum escapement and theoretical yield. Adjusted estimate of range of optimum escapement and theoretical yield.
SHORT PAPERS AND NOTES 439
fish which escape the fishery, the size of run including catchable recruits and repeat spawn- ers combined was estimated (Table 4). Sub- tractlug the escapements from the sizes of the runs gave the theoretical yields which are possible at the various population sizes. Op- timum escapement is estimated to be some- where between 125,000 and 175,000 spawners annually. Escapements in this range suggest a theoretical maximum sustainable yield of approximately 150,000 fish, catchable recruits and repeat spawners combined. Analysis of the parent-progeny data using a 65-percent survival rate for adult fish which escape the fishery (Fredin, 1954) gave results similar to those using the 42-percent rate. The effect of changes in population density on fish growth was not considered here.
It is realized that the reproduction curve calculated in this study is probably not pre- cise, especially because of the need to obtain a single estimate for size of parent stock in each year. Thus the results pres...