566 



Fishery Bulletin 93(3), 1995 



Discussion 



Virtual population analysis assumes that there is 

 complete recruitment for a set of age classes and that 

 availability remains constant for all recruited age 

 classes. The existence of sharp initial and ending 

 seasonal catchability peaks is probably due to un- 

 derestimation of abundance at the beginning and end 

 of the season from the VPA method. This indicates 

 that VPA can be biased when availability fluctuates. 

 Virtual population analysis measures the "virtual" 

 abundance, that which appears to the fishery to be 

 there, rather than absolute abundance. Early in the 

 season, when the menhaden are migrating into the 

 fishing area from their wintering grounds, only part 

 of the stock is available for exploitation. Changes in 

 availability, or accessibility, can affect the catchability 

 coefficient (Cushing, 1968). Marr (1951) showed that 

 catchability is directly related to availability. How- 

 ever, because VPA assumes that there is full avail- 

 ability, abundance is underestimated. If the abun- 

 dance is underestimated, then the catchability coef- 

 ficient will be overestimated (Shardlow and Hilborn, 

 1985). 



Theoretically, this first peak should extend to in- 

 finity prior to the start of the season when VPA is 

 used to estimate abundance, because availability at 

 this point in time is zero. If abundance had been 

 measured with a method independent of the fishery 

 catch statistics, such as mark-recapture, catchability 

 estimates would have been based on absolute rather 

 than on virtual abundance and there would not have 

 been an early season peak. The rise from zero or near- 

 zero catchability which occurs in many of the plots, 

 particularly with older age groups, may be due to an 

 earlier or faster migration of these age groups into 

 the fishing area or to more complete recruitment of 

 the age group at the start of the season. Younger age 

 groups are not completely recruited into the fishery, 

 but by age 2, the menhaden are fully recruited into 

 the Atlantic coast purse-seine fishery (Atlantic Men- 

 haden Management Board, 1981). If availability is 

 at or near maximum by the time of the first catch, 

 VPA will not underestimate abundance, and conse- 

 quently catchability will not be overestimated. One 

 advantage of examining within-season fluctuations 

 of catchability, therefore, may be to assess when the 

 stock becomes available to the fishery. 



After the initial peak, a gradual rise in catchability 

 can be seen as the season progresses, most likely due 

 to a decrease in abundance during a period of full 

 availability. This observation is consistent with 

 Schaaf (1975), who reported a logarithmic inverse 

 relation between annual values of catchability and 

 abundance of menhaden. An increase in this rate 



might result if stock abundance during the season 

 were decreasing faster than normal, and it would 

 then be an indicator of overfishing. 



The pattern of catchability for age-0 menhaden 

 differs from that of the other age groups in that there 

 is no initial peak and landings begin much later in 

 the season (Fig. 1). Age-0 menhaden are fished ex- 

 tensively in the North Carolina fall fishery which is 

 largely directed toward these fish. Paloheimo and 

 Dickie ( 1964) stated that when fishermen selectively 

 apply their effort toward some schools, the result is 

 variance in the catchability coefficient depending on 

 age, species, and relative abundance. This effect is 

 apparent in the plot of average weekly catchability 

 coefficient for age-0 menhaden. When the age-0 men- 

 haden, commonly referred to as "peanuts," migrate 

 out of Virginia and North Carolina estuaries, they 

 become readily available close to shore where they 

 dominate the landings, usually in December and 

 January. 



Acknowledgments 



This manuscript is based on a thesis submitted by 

 Steven Atran to the School of Marine Science of the 

 College of William and Mary in partial fulfillment of 

 the requirements for an MA. degree. Herbert Aus- 

 tin, David Evans, George Grant, and Robert Huggett 

 of the School of Marine Science, and Douglas 

 Vaughan of the NMFS Beaufort Laboratory reviewed 

 an earlier draft of the manuscript and made many 

 helpful comments and suggestions. John Merriner 

 and Douglas Vaughan provided access to the NMFS 

 Atlantic menhaden catch and effort database. 



Literature cited 



Abramson, N. J. 



1971. Computer programs for fish stock assessment. FAO 

 Fisheries Technical Paper 101, var. pages. 

 Atlantic Menhaden Management Board. 



1981. Fishery management plan for Atlantic men- 

 haden. Atlantic States Marine Fisheries Commission, 

 Fish. Manage. Rep. 2, 134 p. 

 Clark, F. N., and J. C. Marr. 



1956. Population dynamics of the Pacific sardine. Calif. 

 Coop. Oceanic Fish. Invest. Progress Rep., p. 11-48. 

 Cushing, D. H. 



1968. Fisheries biology. Univ. Wisconsin Press, Madison, 

 WI, 200 p. 

 Hollander, R. L., and D. A. Wolfe. 



1973. Nonparametric statistical analysis. John Wiley and 

 Sons, New York, NY, 503 p. 

 Marr, J. C. 



1951. On the use of the terms abundance, availability and ap- 

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