HUNTSMAN ETAL.: YIELD PER RECRUIT MODELS 



Parameters t and K are derived from the von Ber- 

 talanffy (1938) growth equation, and W„ is estimated 

 as the weight corresponding to the asymptotic length 

 (L,„) based on a length-weight regression. Growth was 

 assumed to be isometric. 



The Beverton and Holt model implies instan- 

 taneous or "knife edge" recruitment with respect to 

 age. Knife edge recruitment is not an apparent 

 attribute of the hook-and-line fishery for at least two 

 reasons. First, relatively large variation in size offish 

 of a single nominal age (resulting in part from long 

 spawning seasons, e.g., vermilion snapper, Grimes 

 and Huntsman 1980) makes it difficult to specify the 

 initial age of capture. Second, the probability of a fish 

 being taken by hook appears to increase somewhat 

 more gradually with size than do probabilities 

 associated with other gears. 



Specifying an age at first recruitment is critical to 

 determining the yield being taken from a stock We 

 believe that the mean age of recruitment provides a 

 practical estimate of recruitment age for species 

 which enter fisheries gradually. 



Determination of Mean Age at 

 Recruitment 



Computation of mean age at recruitment occurs in 

 three steps: 



1) A minimum size at which fish first become 

 vulnerable to the gear is determined from in- 

 spection of catch length frequencies. We 

 designated the lower limit of the first class 

 interval containing substantial numbers 

 (usually five or more) of observations as the 

 minimum size of vulnerability. This designa- 



tion was usually unambiguous, but for species 

 where it was not we evaluated more than one 

 size. 



2) The probability that a fish of a given age will 

 equal or exceed the minimum size of vulnera- 

 bility is determined on the assumption of a nor- 

 mal distribution of lengths about the mean 

 length at age. 



3) The probability for each age is multiplied by 

 the numerical age value (e.g., 0.5 X 3). The pro- 

 ducts and probabilities are summed over all 

 ages and the sum of the products is divided by 

 the sum of the probabilities. The success of 

 this treatment depends on exclusion from the 

 calculations of ages beyond the first age at 

 which all (P > 0.99) fish are vulnerable. 



The estimation described here should be successful 

 if the specified minimum size at vulnerability is 

 accurate and if the relationship between size and re- 

 cruitment is strong. 



RESULTS 



Regardless of the estimate of M, all models had a 

 strikingly similar response to F (Table 2, Figs. 1-18). 

 For median recruitment ages there was a rapid 

 increase in yield as F increased, then an abrupt 

 change as the rate of increase in yield declined at 

 about F = 0.3, and finally a broad plateau of yield 

 near the maximum. In general the absolute maximum 

 yield per recruit was attained at a very high F relative 

 to that needed to achieve 80 to 909r of the maximum 

 yield. At the lowest estimate of M for all species 

 examined, about 87%, on the average, of the max- 

 imum yield could be taken with an F = 0.3, which is 



Table 2. — Summary of yield per recruit (Y/R) models for South Atlantic reef fish. M= instantaneous rate of natural mortality; F= instan- 

 taneous rate of fishing mortality; t r = age at recruitment to the gear. 



683 



