FISHERY BULLETIN: VOL. 75, NO. 1 



STOCK SIZE 

 (Survival Density Dependent) 



ENVIRONMENTAL CONDITIONS 



(Survival Density Independent) 



YEAR-CLASS SUCCESS FACTORS 



Actual Survival Index (Ro/Rc) 



Predicted Survival Index 



FIGURE 5. — Schematic representation of logic used in the de- 

 velopment of the survival index predictive model. Location of 

 environmental parameters used in the model is indicated byXn, 

 description of parameters in Table 4. 



nificant spawning taking place farther offshore as 

 adults migrate southward in the fall. This should 

 result in increased significance of oceanic trans- 

 port factors from north to south in the determi- 

 nation of year-class strength. The hypothesis of 

 increasing importance of transport as spawning 

 activities move progressively farther offshore is 

 supported by the highly significant correlations 

 between the survival index and transport values 

 south of Cape Hatteras and similar correlations 

 which have a lower level of significance off Dela- 

 ware Bay. 



The selection of locations and time periods for 

 Ekman transport data was based on the availa- 

 bility of data for specific coordinates, desire for 

 representation of broad spawning areas, and 

 estimates of larval drift time and direction (Figure 

 5). Of the many possible environmental factors 

 which could influence survival during the oceanic 

 phase, three (transport, temperature, and river 

 discharge) were chosen because they appeared to 

 be factors of major importance and data series 

 were available for the same period in which vital 

 statistics of the Atlantic menhaden populations 

 have been taken. 



x 



UJ 



Q 

 Z 



-j 

 < 

 > 

 > 



19SS 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 



FIGURE 6. — Multiple regression of the survival index for Atlan- 

 tic menhaden on environmental factors, 1955-70. Predictive 

 equation and listing of environmental factors presented in text. 

 Correlation coefficients and model data presented in Tables 4 

 and 6. 



TABLE 6. — Data used in recruit-environment predictive model 

 for Atlantic menhaden. Location of factors identified in Figure 5, 

 individual factors identified in Table 4. 



The multiple-regression model developed to 

 relate recruitment to environmental variables 

 yields a correlation coefficient of 0.919, significant 

 at 0.003 with 9 df (Figure 6). Model data are given 

 in Table 6. The model accounts for over 84% of the 

 variance in the actual survival indices (Table 4). 

 Translated into recruits, the model indicates that 

 over 84% of the variation between actual re- 

 cruitment into the fishery and expected re- 

 cruitment during the 1955-70 period is accounted 

 for by environmental fluctuation. The model is 

 described by the equation: 



S.I. = 0.4148 + 0.0205XJ +0.00530Z 2 



- 0.00807X 3 + 0.00950X 4 + 0.23967X 5 



- 0.02679X 6 ± e 



where S.I. = survival index computed by dividing 

 observed recruits by expected re- 

 cruits 



34 



