Abstract . - The projection of re- 

 source production and the effect of 

 removals on fisheries populations are 

 based on abundance estimates, partic- 

 ularly estimates of the most current 

 abundance. Monte Carlo methods 

 were used to investigate a size-based 

 method of estimating abundance for 

 instances where the age of caught 

 fish cannot be established, but where 

 size samples and a growth schedule 

 exist. Neither process variabUity (re- 

 cruitment dates, growth rates, and 

 unobserved change rates) nor sam- 

 pling error (catch estimation, growth 

 rate estimation, and relative abun- 

 dance sampling) adversely affected 

 estimation, although low sampling 

 intensities often decreased precision. 

 Abundances of recently recruited 

 fish too small to occur in relative 

 abundance samples more than once 

 were estimated with large uncertain- 

 ty. Inappropriately wide size-class 

 widths caused uncertain abundance 

 estimates of larger size-classes. How- 

 ever, if size-classes were of suitable 

 width, the abundance of fish large 

 enough to occur in abundance sam- 

 ples more than once were accurate- 

 ly and precisely estimated even in 

 cases of high process variability and 

 small sample sizes. Sampling gear 

 efficiency (catchability) coefficients 

 were often estimated without large 

 bias but imprecisely. The exponent 

 of the unobserved change rate (in- 

 cluding natural mortality) was esti- 

 mated precisely, but estimates were 

 often biased. High correlations be- 

 tween estimates of the unobserved 

 change rate and sampling gear effi- 

 ciencies were not often observed. 

 Estimation characteristics were un- 

 like those based on virtual population 

 analysis calculations. Maximum-like- 

 lihood estimates of the most recent 

 abundances were accurate and pre- 

 cise, yet calculations of historical 

 abundances were biased and extreme- 

 ly imprecise. 



Estimating stocic abundance 

 from size data 



Michael L. Parrack 



Miami Laboratory, Southeast Fisheries Science Center 



National Marine Fisheries Service, NOAA 



75 Virginia Beach Drive, Miami, Florida 33149-1099 



Manuscript accepted 9 March 1992. 

 Fishery Bulletin, U.S. 90:302-325 (1992). 



Most often, the objective of fisheries 

 regulations is to insure that stock 

 abundance does not decrease or, if 

 abundance is low, to increase it. The 

 welfare of the entire stock may be of 

 concern, or only a part of it such as 

 the adult portion (spawning stock). 

 These objectives are obtained by 

 limiting yields (weight caught) to 

 stock growth or, in instances were 

 abundance is low, to less than stock 

 growth. Abundance estimates are the 

 bases for this regulation strategy. An 

 opinion as to whether stock abun- 

 dance is currently depressed or not 

 is based on a comparison of an esti- 

 mate of current abundance with esti- 

 mates of previous abundances. Stock 

 production (growth) in the immediate 

 future is projected from the estimate 

 of current abundance. Since the pro- 

 duction projection is the basis for the 

 yield limit, the estimate of current 

 abundance determines the yield limit. 

 Because it is a critical element of 

 regulatory responsibility, abundance 

 estimation methodology is of major 

 interest. 



Most estimation methods are based 

 on age data. These methods specify 

 that the population is entirely com- 

 posed of unique groups of fish of 

 equal age (cohorts) and that all mem- 

 bers of a cohort grow into the first 

 exploitable size (recruit) instanta- 

 neously before fishing begins once 

 each year. These two requirements 

 rarely, if ever, occur. Most popula- 

 tions spawTi during several months, 

 or sometimes throughout the entire 

 year, so that annual or even monthly 

 cohorts do not really exist. The 

 growth of the young fish to sizes 



large enough to be caught is a con- 

 tinuous process so that recruitment 

 is typically an ongoing phenomena. 

 These biological realities are often ig- 

 nored, and age-based analysis meth- 

 ods are used anyway. 



Since the primary data element of 

 age-based methods is the number of 

 caught fish of each age, the ages of 

 caught fish must be determined. 

 Sometimes this requirement is dif- 

 ficult to satisfy. Major circuli from 

 differing bone densities or the chem- 

 ical composition of skeletal structures 

 (scales, fin spines, or otoliths) have 

 been validated as age marks in only 

 3.4% of age determination studies 

 (Beamish and McFarlane 1983). Even 

 in cases where indirect evidence of 

 validation seems ample (Kreuz et al. 

 1982), direct measurement of growth 

 from mark and recapture data can 

 document a very different reality 

 (Pikitch and Demory 1988). Collect- 

 ing and processing samples can be so 

 difficult and time consuming that 

 large data voids occur. Frequent 

 molting and the absence of bony 

 tissue preclude the possibility of 

 using hardpart ageing methods for 

 many invertebrates, and the technol- 

 ogy to determine age from somatic 

 tissue does not currently exist. 



These problems can be avoided by 

 methods that model populations in 

 terms of size and time rather than 

 age and years (or months). Size-based 

 methods need not require that the 

 population be composed of age-spe- 

 cific cohorts nor that recruitment be 

 an instantaneous, one-time event. 

 The first size-based methods, how- 

 ever, are not so constructed. 



302 



