NUMERICAL INTEGRATION OF DAILY GROWTH INCREMENTS: 



AN EFFICIENT MEANS OF AGEING TROPICAL FISHES 



FOR STOCK ASSESSMENT 



Stephen Ralston' and Happy A. Williams^ 



ABSTRACT 



For an objective, cost-effective ageing methodologi,' applicable to tropical species, a new approach to 

 estimating parameters of the von Bertalanffy growth equation through the study of otolith microstruc- 

 ture was developed and applied to Pristipomoides zonatus. a deepwater snapper widely distributed 

 throughout the Indo-Pacific region. The average width of sagittal daily growth increments was used to 

 measure otolith growth rate, which was then related to the size of the otolith. The data were numerically 

 integrated, providing estimates of age (in years) at regular 500 |jm increments to otolith length, which 

 was then used to predict fork length (FL mm) at age with regression analysis. The data were fitted to 

 the von Bertalanffy growth model, resulting in FL = 442 (1 - exp(- 0.234 (Age + 0.892))). 



The method was critically examined and validated through the study of 1) annual hyaline and opaque 

 markings that appear in the otoliths, 2) Monte Carlo simulation. 3) length-frequency analysis. 4) ex- 

 amination of spawning seasonality relative to back-calculated birth date taken from the time of first 

 annulus formation, and 5) empirical comparisons with the literature concerning snapper growth. 



Developing stock-assessment models tailored to the 

 characteristics and needs of tropical fisheries is an 

 area of active and productive research. In particular, 

 significant progress has been made over the last 

 several years in the area of length-based methods 

 (Schnute and Fournier 1980; Jones 1981; Pauly 

 1982, 1987b; Fournier and Breen 1983; Fournier 

 and Doonan 1987; Schnute 1987). With these ad- 

 vances, a powerful array of biologically realistic 

 models is now available for analyzing length-fre- 

 quency data. 



Although tremendous strides have been made in 

 developing these new length-based methods, the im- 

 portance of acquiring other information besides 

 length-frequency data and total catch statistics is 

 all the more evident. Ancillary information usually 

 helps to stabilize and improve the estimation of 

 model parameters (Schnute and Fournier 1980; 

 Fournier and Doonan 1987). Foremost is develop- 

 ing an independent knowledge of growth dynamics 

 (Gulland 1987; Morgan 1987). It is now generally 

 accepted that the analysis of length-frequency data, 



'Southwest Fisheries Center Honolulu Laboratory, National 

 Marine Fisheries Service, NOAA, 2570 Dole Street, Honolulu, HI 

 96822-2396; present address: Southwest Fisheries Center Tiburon 

 Laboratory, National Marine Fisheries Service, NOAA, 3150 Para- 

 dise Drive, Tiburon, CA 94920. 



^Southwest Fisheries Center Honolulu Laboratory, National 

 Marine Fisheries Service. NOAA, 2570 Dole Street, Honolulu, HI 

 96822-2396. 



Manuscript accepted September 1988. 

 Fishery Bulletin. U.S. 87:1-16. 



in conjunction with age estimates derived from the 

 study of hard parts, represents the most promising 

 avenue for future assessment work on exploited 

 tropical species (Pauly 1987a). 



Nonetheless, estimating growth rates of tropical 

 species by using otoliths has been a difficult and per- 

 sistent problem. Investigators have often failed in 

 their efforts, either because of an absence of con- 

 ventional hyaline and opaque markings, as is true 

 of most tropical species, or because of an aversion 

 to direct enumeration of daily otolith increments. 

 The latter can be an extremely difficult, time con- 

 suming, and tedious process. 



Since Pannella (1971) first discovered the exis- 

 tence of daily otolith increments, a large body of 

 work has developed on the subject. While many 

 investigators have touted the potential benefits of 

 ageing tropical species by using otolith microstruc- 

 ture, few have attempted to develop growth curves 

 with assessment goals specifically in mind. Instead, 

 most work to date has dealt with ageing larval 

 forms (Jones 1986) and elucidating endogenous and 

 environmental effects on increment formation (Cam- 

 pana and Neilson 1985). Although much useful in- 

 formation has been gained, daily increments have 

 yet to fulfill their promise with respect to applica- 

 tions in the area of juvenile and adult population 

 dynamics. 



The purpose of this study was to develop a gen- 

 eral method of ageing tropical fishes by using daily 



1 



