NELSON ET AL.: LARVAL TRANSPORT OFBREVOORTIA TYRANNUS 



X x = sum of monthly average zonal 

 (westward) Ekman transport rates 

 for January-March of the year-class 

 year at lat. 35°N long. 75°W 



X 2 = sum of monthly average zonal 

 (westward) Ekman transport rates 

 for January-March of the year-class 

 year at lat. 33°N, long. 78°W 



X 3 = sum of monthly average zonal 

 (westward) Ekman transport rates 

 for November-December of the year 

 prior to the year class and January- 

 February of the year-class year at 

 lat. 39°N, long. 72°W 



X 4 = sum of monthly average zonal 

 (westward) Ekman transport rates 

 for November-December of the year 

 prior to the year class and January- 

 February of the year-class year at 

 lat. 39°N, long. 75°W 



X 5 = minimum mean sea surface temper- 

 ature at the mouth of Delaware Bay 

 in the year-class year 



X 6 = sum of monthly average discharge 

 rates from Susquehanna, Potomac, 

 and James rivers in July-September 

 of the year preceding the year-class 

 year 

 e= error term. 



The predicted number of recruits for each year is 

 given by: 



R p - R CI 



x S.I. 



where R p = 



Rr, = 



predicted number of recruits 

 number of recruits calculated from 

 the Ricker curve at spawning stock 

 size in the ith year. 



A correlation between the observed number of 

 recruits (R ) and the predicted recruits (R p ) for 

 each year yields a coefficient of 0.943 and a slope of 

 0.914 with no systematic bias around the regres- 

 sion line. Further evidence of the validity of the 

 model is the failure of adjustments to increase the 

 percent of variance accounted for by the en- 

 vironmental factors. The initial model, based on 

 judgments of the proper time and location of 

 environmental parameters, yielded a higher 

 correlation coefficient than any subsequent mod- 

 els in which any of the parameters or time-spans 

 were varied away from those which were consid- 



ered the most significant from a biological stand- 

 point. The parameters were not selected by a 

 screening process from a large number of vari- 

 ables, but were selected because of their probable 

 impact on survival. 



The four largest year classes ( 1955, 1956, 1958, 

 and 1969) during the 16-yr period are accurately 

 described by the model. The average error of 

 prediction for these years is 4.3% and the 

 maximum error is 6.3%. Smaller year classes are 

 not described with the same degree of accuracy, 

 although the mean error for the 16-yr period is 

 reduced from 1.5 billion fish using only the Ricker 

 curve to 610 million individuals per year by the 

 model, and the standard error of the mean is re- 

 duced from 501 to 155 million fish. 



The multiple-regression model has a high 

 correlation coefficient and therefore describes the 

 data well. Its value for prediction is somewhat 

 more tenuous and requires testing on a sub- 

 sequent set of data to determine its accuracy. The 

 model was not broken into separate time-series 

 units for testing because of the brevity of the 16-yr 

 data base. 



The model is a first-cut approximation for the 

 evaluation of transport and other factors. The 

 number of variables included tends to increase the 

 R 2 value, even though some parameters do not 

 show individual significance levels when corre- 

 lated with the survival index. However, only the 

 Chesapeake Bay discharge has a /3 value of which 

 ±2 standard errors encompasses 0, indicating that 

 the factor is probably not significant. The other 

 parameters are associated with the same major air 

 mass movements, and are therefore interrelated. 

 A more sophisticated model should be based on 

 either principal components regression or Ridge 

 regression techniques to correct for the inter- 

 dependence of some of the parameters and to 

 improve the predictive capability. A reduction in 

 the number of variables used is desirable from a 

 statistical standpoint because of the short time 

 span of the data base. Regression of the survival 

 indices on the three transport values off of Cape 

 Hatteras (lat. 35°N, long. 75°W) and Delaware 

 Bay (lat. 39°N, long. 72°W; lat. 39°N, long. 75°W) 

 yields an R 2 of 0.741 (12 df, P<0.001). The ab- 

 breviated model accounts for a significant portion 

 of the variance around the spawner-recruit curve. 

 It describes the data for high and low survival 

 years nearly as well as the full model and probably 

 has a similar predictive capability. Determination 

 of the actual influence of the other factors (dis- 



35 



