Growth rates of four Hawaiian deep slope

fishes: a comparison of methods for estimating

age and growth from otolith microincrement

widths

Happy A. Williams and M. Kimberly Lowe

Abstract: Two methods were used to estimate the age and growth of four Hawaiian deep slope fishes. Otolith daily incrementwidth estimates from radial sections of sagittal otoliths were integrated over the otolith radius to approximate age by(i) dividing interval length (micrometres) by mean increment width (micrometres per day) and summing this quotient forconsecutive 500-µm radial intervals (S. Ralston and H.A. Williams. 1989. Fish. Bull. 87: 1–16) and (ii) fitting incrementwidth (y) versus otolith radius (x) to a Gompertz rate curve and calculating the inverse integral of this curve (M.K. Smith andE. Kostlan. 1991. Fish. Bull. 89: 461–472). The methods also differ in the way the age–length key is generated. Ralston andWilliams’ method uses integrated age versus a regression-based estimate of fish length at 500-µm otolith radial intervals;Smith and Kostlan’s method uses estimated age versus actual fish length. Neither method of integration produced significantlydifferent age estimates; however, the use of regression-based fish length estimates instead of sampled fish lengths resulted insignificant differences between estimated growth curves. The minimum number of daily increment width estimates requiredas a function of otolith radius was calculated, on the basis of observed microincrement width variation.

Résumé: Deux méthodes ont été utilisées pour estimer l’âge et la croissance de quatre espèces de poisson de la partieprofonde du talus continental d’Hawaï. Des valeurs estimées de la longueur d’accroissement quotidien des otolithes à partir decoupes radiales d’otolithes sagittaux ont été intégrées sur le rayon des otolithes pour déterminer l’âge approximatifen (i) divisant la longueur de l’intervalle (micromètres) par la longueur d’accroissement moyen (micromètres par jour) et enfaisant la somme de ce quotient pour des intervalles de rayons consécutifs de 500 µm (S. Ralston et H.A. Williams. 1989.Fish. Bull. 87 : 1–16) et (ii) en ajustant la longueur d’accroissement (y) en fonction du rayon de l’otolithe (x) à une courbe decroissance de Gompertz et en calculant l’intégrale inverse de cette courbe (M.K. Smith et E. Kostlan. 1991. Fish. Bull.89 : 461–472). Les méthodes diffèrent également par la façon dont la relation âge–longueur est établie. La méthode de Ralstonet Williams fait appel à l’âge intégré en fonction d’une valeur estimée, fondée sur une régression, de la longueur du poisson àdes intervalles radiaux d’otolithe de 500 µm, tandis que la méthode de Smith et Kostlan repose sur l’âge estimé en fonction dela longueur réelle du poisson. Les valeurs estimées de l’âge ne différaient pas de manière statistiquement significative entreces deux méthodes d’intégration; cependant, l’utilisation de valeurs estimées de la longueur des poissons fondées sur larégression plutôt que sur des longueurs de poissons échantillonnés a entraîné des différences significatives pour ce qui est descourbes de croissance estimée. Le nombre minimal de valeurs estimées de la longueur d’accroissement quotidien nécessairecomme fonction du rayon de l’otolithe a été calculé, d’après la variation observée de la longueur de microaccroissement.[Traduit par la Rédaction]

Introduction

Deep slope hook and line fishing (bottom fishing) at depths of140–330 m is one of the most important commercial fisheriesin the state of Hawaii. The catch is comprised primarily ofeteline snappers, groupers, sharks, and large carangids. The

high commercial value of this fishery alone signals the impor-tance of developing an understanding of the age, growth, andlife history of the fishes caught, but recent concern that keyspecies may be overexploited in the main Hawaiian Islands(Western Pacific Regional Fisheries Management Council1994) indicates a more urgent need for information that can beused to design appropriate management. The parameters of thevon Bertalanffy growth equation (von Bertalanffy 1957) areused in modelling the effects of different harvest strategies onfish populations (Beverton and Holt 1957; Gulland 1987; Mor-gan 1987; Pauly 1987). Therefore, a quick and reliable methodof estimating a growth curve for Hawaiian bottom fishes couldbe a useful tool to improve management of this fishery.

Relatively little is known about age and growth of Hawaiianbottom fishes. Although growth estimates based on length fre-quency have been obtained for bottom fishes elsewhere in thePacific (Brouard and Grandperrin 1985; Wrobel 1985; Ralston

Can. J. Fish. Aquat. Sci. 54: 126–136 (1997)

Received June 10, 1994. Accepted June 14, 1996.J12414

H.A. Williams. 1 Southwest Fisheries Science Center, HonoluluLaboratory, National Marine Fisheries Service, 2570 DoleStreet, Honolulu, HI 96822-2396, U.S.A.M.K. Lowe. Division of Aquatic Resources, Department ofLand and Natural Resources, 1151 Punchbowl Street, Room330, Honolulu, HI 96813, U.S.A.

1 Author to whom all correspondence should be addressed.e-mail: Happy.Williams@noaa.gov

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and Williams 1988; Carlot and Nguyen 1989), few studieshave examined their growth by enumeration of otolith dailyincrements (Brouard et al. 1983; Radtke 1987; Ralston andWilliams 1989; Smith and Kostlan 1991). Ralston andKawamoto (1987, 1988) estimated growth of onaga (Eteliscoruscans), and hapu’upu’u (Epinephelus quernus), usinglength frequency data from fish caught throughout the Hawai-ian Archipelago. The same authors estimated L∞ for butaguchi(Pseudocaranx dentex) from the northwestern Hawaiian Is-lands, but were unable to estimate K for that species.

Otoliths can provide an additional source of information.Counts of the microincrements (terminology of Secor et al.1995), resulting from periodic shifts in otolith crystalline mi-crostructure (Gauldie and Nelson 1988, 1990), are commonlyused to estimate age and growth in fishes (Pannella 1971,1974; Campana and Neilson 1985; Beamish and McFarlane1987; Gauldie 1988). Although not confirmed for all species(Beamish and McFarlane 1983; Campana and Neilson 1985),the rate of microincrement deposition appears to be diurnal infishes from diverse taxa and habitats (Jones 1986). The use ofdaily increments is particularly useful in ageing tropical spe-cies, since the rate of deposition of seasonal bands can becomplex and difficult to quantify (Ralston 1985; Radtke 1987).However, the amount of work required to section and countdaily increments from adult otoliths often precludes examininga sufficiently large number to make a precise growth estimatefor a given population.

During the 1980s, a labor-efficient method of age andgrowth estimation was developed in Hawaii (Ralston 1985;Ralston and Miyamoto 1981, 1983; Ralston and Williams1989). Ralston and colleagues estimated fish age by integrat-ing estimates of microincrement width versus otolith radiusacross the otolith radius. Ralston and Miyamoto (1981) esti-mated age of pink snapper (Pristipomoides filamentosus) byintegrating the function relating daily increment width (mi-crometres per day) to otolith radius (micrometres from primor-dium). They fit a curve by log linear regression to pooledincrement width data for many individuals, producing a singleotolith growth rate curve for the sample population, thensolved the resulting nonlinear combination of variables (usingthe mean values of the first few terms of a Taylor series) toestimate age at any otolith radius. Ralston and Williams (1989)simplified the calculations. Finding that the rate of change inmicroincrement width was roughly constant over 500-µm in-tervals of otolith radius for gindai (Pristipomoides zonatus),they estimated the number of days to grow through subsequent500-µm radial intervals by dividing the interval length (500µm) by its mean microincrement width and summing thesequotients. They developed an otolith growth rate curve frompooled microincrement width estimates for the population,then estimated individual fish lengths at consecutive 500-µmintervals from a regression curve relating sampled fish lengthsand otolith radius.

Smith and Kostlan (1991) applied Ralston and Williams’(1989) method and a revised method of their own to a limiteddata set available for Etelis carbunculus. They fit a modifiedGompertz rate curve (Gompertz 1825) to microincrementwidth data and estimated the inverse integral of this curve.They also used pooled data to develop individual age esti-mates, but fit the von Bertalanffy growth curve to estimatedages versus actual fish length (instead of using regression-

based fish length estimates). Because they worked from lim-ited data, Smith and Kostlan suggested that there should be asubsequent comparison of growth estimates obtained, usingRalston and Williams’ (1989) method and their own on a largerdata set.

The present study evaluates age and growth of four Hawai-ian bottom fishes (the onaga, hapu’upu’u, butaguchi, and ka-lekale (Pristipomoides sieboldii)) using samples collectedthroughout the Hawaiian Archipelago. Each species represents3–16% annually by weight and value of Hawaiian bottom-fishcatches (Ralston and Kawamoto 1988). Intensive sampling ofa large number of fish and otoliths made it possible to (i) com-pare results using Ralston and Williams’ (1989) versus Smithand Kostlan’s (1991) methods, (ii) examine underlying vari-ation in microincrement width along the otolith radius, and(iii) consider the differences in results obtained from pooledversus individual data.

Materials and methods

Fish were caught with hook and line at depths of 50–180 fathoms(1 fathom = 1.829 m). Weight and fork length were recorded for allspecies except the hapu’upu’u, for which total length was measured.From 1986 through 1990, samples were collected from local fishmarkets and research cruises aboard the research vessel TownsendCromwell. An effort was made to collect the widest possible sizerange during research cruises. Additional samples were sought fromthe market to augment and fill in gaps in the size range. For thesereasons, it took several years to obtain a sufficient sample.

Ralston and Williams (1989) described the methods used to pre-pare otolith sections and estimate microincrement width (∆l/∆t), bycounting the number of (presumed daily) increments within a minus-cule radial segment of the otolith (t is time in days and l is length ofthe segment in micrometres). This provides an index of the rate ofaccretion of the otolith (otolith growth rate in micrometres per day),which is integrated over the length of the otolith radius (primordiumto postrostral margin) to estimate age. A single central primordium,believed to be the central origin of growth, was seen in otolith sectionsfrom all four bottom-fish species (terminology of Summerfelt andHall 1987).

Video-relayed images of otolith preparations were observedthrough a Nikon light microscope at a magnification of 800×, usingBiosonics (1987) Optical Pattern Recognition System software tocalibrate measurements and record the number of microincrements.Although the frequency of microincrement deposition was not vali-dated for these fishes, daily deposition is considered likely, on thebasis of validation for Pristipomoides filamentosus, another etelinesnapper found at similar depths and locations throughout Hawaii(Ralston 1981; Demartini et al. 1994). The radial distance (microme-tres) at which each microincrement width estimate was made wasmeasured from the otolith primordium to the middle of the segment.Estimates were made from as close to the primordium to as near theperimeter as possible. In most cases, this was to within 85–90% of thetotal postrostral radius.

Fish age was estimated by integrating the function relating mi-croincrement width and otolith radius, either by Ralston and Wil-liams’ (1989) or Smith and Kostlan’s method (1991). Using Ralstonand Williams’ (1989) method, age as a function of otolith radius wasestimated from mean microincrement widths in consecutive 500-µmradial intervals. Expected fish length at the end of each 500-µm radialinterval was estimated from a curve fit by double logarithmic regres-sion to sampled fish length versus otolith radius. Resulting length atage data were fit to a von Bertalanffy growth curve.

With Smith and Kostlan’s (1991) method, nonlinear regressionwas used to fit a modified Gompertz rate curve,

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(1) y = axe–bx + c

to sampled microincrement widths (y is otolith growth rate, microme-tres per day) versus otolith radius (x is radial distance in micrometresfrom the primordium). No constraints were placed on the value of theconstant (c), an estimated parameter representing the otolith’s asymp-totic growth rate. The integral of the reciprocal of this function wassolved as described by Smith and Kostlan (1991), providing an esti-mate of fish age in days. Estimated age versus sampled fish lengthswere then fit to a von Bertalanffy growth curve.

Separate calculations were made for a few individuals of eachspecies, solely on the basis of the microincrement series within theindividual’s own otoliths (individual data). This was done directly bySmith and Kostlan’s (S&K) method, fitting a modified Gompertzcurve to individual data and integrating the curve to the otolith radius

measured for each fish. Since total otolith radius was not evenly di-visible by 500 for any individual, making an even multiple of the500-µm integral inappropriate, two approximations of the Ralstonand Williams’ (R&W) integral were made for comparison, as follows.

R&W approximation IThe R&W numerical integral was summed to the nearest even multi-ple of 500 µm below the total otolith radius, then the number of daysin the remaining (shorter) radial interval (from the last multiple of 500µm to the perimeter) was estimated by dividing its length by the meanof the remaining microincrement widths.

R&W approximation IIThe R&W integration was summed only to the nearest even multiple

Fish length (cm)Number of

MIWE(pooled data)

Number of samples Range sampled MaximumrecordedCommon name Fish Otoliths Min. Max.

Etelis coruscans Onaga 28 34 26.5 94.4 94.4 3 472Pristipomoides sieboldii Kalekale 36 59 23.7 43.5 43.5 16 686Pseudocaranx dentex Butaguchi 37 57 34.0 96.0 131.4 13 592Epinephelus quernus Hapu’upu’u 50 82 30.7 77.5 110.6 11 429

Note: Fish length represents the fork length for all species except Epinephelus quernus, for which total length was measured. Number of MIWE represents thetotal number of microincrement width estimates made for all otoliths sampled for the species (pooled sample).

Table 1.Summary of fish and otolith samples and microincrement width estimates.

Subsamplespecifications N a b c

Multipleregression

coefficient (r2)

Etelis coruscans (onaga) Pooled sample 3 472 0.074 0.0018 1.843 0.82Fish No. 11 366 0.095 0.0019 1.775 0.81Fish No. 219 172 0.072 0.0019 1.852 0.74

Pristipomoides sieboldii (kalekale) Pooled sample 18 528 0.117 0.0020 2.818 0.81Fish No. 4 1 573 0.149 0.0022 3.076 0.80Fish No. 71 2 292 0.139 0.0020 2.434 0.86Fish No. 75 1 087 0.109 0.0019 3.067 0.77Fish No. 86 1 234 0.120 0.0023 2.807 0.81Fish No. 87 442 0.109 0.0020 3.413 0.81Fish No. 115 1 735 0.120 0.0021 2.797 0.82Fish No. 134 1 479 0.134 0.0024 2.870 0.82

Pseudocaranx dentex (butaguchi) Pooled sample 13 592 0.065 0.0023 2.789 0.79Fish No. 3 504 0.054 0.0022 2.494 0.76Fish No. 10 751 0.118 0.0029 2.369 0.79Fish No. 11 189 0.054 0.0020 2.779 0.79Fish No. 29 545 0.100 0.0025 2.901 0.81Fish No. 35 266 0.112 0.0028 2.301 0.81Fish No. 43 709 0.085 0.0025 2.570 0.83Fish No. 56 559 0.102 0.0032 2.980 0.78Fish No. 204 665 0.110 0.0026 2.104 0.84Fish No. 235 623 0.120 0.0025 1.796 0.77

Epinephelus quernus (hapu’upu’u) Pooled sample 11 429 0.043 0.0016 3.565 0.79Fish No. 2 342 0.052 0.0019 3.757 0.84Fish No. 27 408 0.104 0.0024 3.079 0.80Fish No. 62 735 0.047 0.0017 3.697 0.80

Note: Fish No., the fish identification number for individual data; pooled sample, curve fit using all microincrement width estimates fora given species; N, number of microincrement width estimates made for the specified subsample. Otolith growth rate equation: y =axe–bx + c.

Table 2.Estimated otolith growth rate parameters for four Hawaiian bottom fishes using Smith and Kostlan’s (1991)method.

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of 500 µm below the total radius and compared with an S&K estimatefor that radius, using individual data.

All data analyses were conducted using SAS Institute, Inc. (1985)software, except the S&K age integration, which was estimated usinga Fortran program (Smith and Kostlan 1991).

Results

Fish lengths sampled (Table 1) ranged to within 70–100% ofmaximum length records and asymptotic length estimates (L∞)from the literature (Uchida and Uchiyama 1986; Ralston andKawamoto 1988). The table shows maximum recorded lengthfor all four species, rather than asymptotic length, since theformer values were always greater. All maximum length re-cords were taken from Uchida and Uchiyama (1986), exceptthe one for Etelis coruscans, for which the reference is thepresent study. The widest possible length range was obtainedfor each species, but small fish (less than 20 cm fork length)were rarely caught.

Figure 1 illustrates the range and number of microincre-ment width estimates as a function of otolith radius. The gen-eral shape of these curves was similar for all species.Scatterplots all displayed a left skewed tendency, and microin-crement widths approached (but never reached) zero with in-creasing otolith radius. Table 2 summarizes the S&Kparameters (variables a and b and constant c from eq. 1) forindividual and pooled data, fit to the modified Gompertz ratecurve by nonlinear regression. This function was consideredappropriate, on the basis of the shape of the scatterplots

(Fig. 1), acceptable multiple regression values (r2 ≥ 0.79 forpooled samples), and the fact that microincrement widths didnot reach zero at any radial distance sampled. The inverseintegral of the S&K curves for individual and pooled data(Table 2) produced the S&K age estimates shown in Table 3.

To illustrate the relationship between regression curves fitto individual versus pooled data, Fig. 2 shows the four S&Kcurves derived for Epinephelus quernus (parameters listed inTable 2). The differences between the curve for fish No. 27and the other three (including pooled and individual curves)can be seen. It has a much higher amplitude, peaks at lowerotolith radius, and displays a lower asymptotic growth rate (cvalue). Although the curves for fish No. 2, fish No. 62, andpooled data look quite similar, a Kolmogorov–Smirnov test forgoodness of fit (Sokal and Rohlf 1969) showed that all fourcurves were significantly different (α < 0.01). Thus, signifi-cant differences were seen between curves derived frompooled versus individual data and between individual curves.The fact that the curve for pooled data more closely resemblesthose for fishes Nos. 2 and 62 than the individual estimate forfish No. 27 indicates qualitatively that sampling error is theprimary cause of the observed differences in regression curvesfit to the various data sets.

Although significant differences were seen in the regres-sion-derived curves, because a shift in one of the regressionparameters (a, b, or c) may be compensated for by changes inthe other two, it is difficult to assess the net effect of thesechanges except by comparing the integrated age estimates

Fig. 1. Microincrement width (presumed daily increment width) versus otolith radius. n, number of microincrement width estimates.

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themselves. Table 3 shows age estimates derived from individualand pooled data, using the S&K integral versus approximationI (see Methods) of the R&W integral. Individual fish (identi-fied in the table by an arbitrary sample number) were selectedbecause a relatively large number of microincrement widthestimates had been made for them over a wide range of otolithradii. The difference between pooled and individual age esti-mates ranged from 3 to 427 days (mean = 113 days) for R&Wnumerical integrals and from 4 to 366 days (mean = 135 days)for S&K estimates.

A series of pairwise t tests were performed to evaluate dif-ferences between age estimates in each column of Table 3(Ho = zero difference between age estimates in any two col-umns, N = 21 for all tests). These tests showed that there wasless difference between integrated age estimates derived usingeither method with the same data subset than between resultsobtained using the same method with different data subsets.There was no significant difference between R&W versusS&K age estimates when both were made with pooled data(p = 0.677) or when both were made with individual data(p = 0.325); between age estimates using the S&K on individ-ual data versus the R&W on pooled data (p = 0.144); or be-tween S&K individual versus S&K pooled (p = 0.067) ageestimates, although the latter difference was almost statisti-cally significant. R&W age integrals made with individual ver-sus pooled data were significantly different (p = 0.003), aswere R&W individual integrals versus S&K pooled estimates(p = 0.004). Thus, although the method of integration affected

the outcome, the choice of data set was more important indetermining the result.

A rank test was also performed using age estimates fromall four columns of Table 3, to evaluate whether there wereany significant trends towards a higher or lower age estimateas a function of method or subsample. To eliminate value-spe-cific range differences, the four estimates were ranked (onethrough four) and a Tukey’s studentized range test (Tukey1952, 1953) was performed on the 21 sets of rank variables.The results showed that age estimates from individual datausing either method of integration tended to be higher thanestimates from pooled data. However, only the R&W esti-mates from individual data were significantly higher thanthose obtained using the other three method – data set combi-nations (α = 0.05).

Integrated age estimates were also compared using approxi-mation II of the R&W integral (see Methods). Since it becameclear that all otoliths had not been sampled through the entireradius (data were collected with the intent of utilizing a pooledsample), age estimates were calculated only to the maximum500-µm radial interval for which continuous growth data wereavailable from the primordium. With this restriction, a pair-wise t test showed that S&K and R&W integrated age esti-mates were not significantly different (p > 0.05). Althoughestimated ages by R&W approximation II differed somewhatfrom S&K estimates, ranked comparisons showed no signifi-cant trend towards one estimate being greater or less than theother.

Fig. 2. Modified Gompertz rate curve estimates from individual and pooled data for hapu’upu’u (Epinephelus quernus).

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Table 4 summarizes parameter estimates for the doublelogarithmic regression curve relating fish length to otolith ra-dius, and Fig. 3 shows von Bertalanffy growth curves, derivedusing the R&W method (on pooled microincrement widthdata). The number of fish length to otolith radius pairs used toestimate the double logarithmic regression (N in Table 4) dif-fers from the number of fish and otoliths given in Table 1,because (i) when possible, both sagittal otoliths were meas-ured for each fish, and (ii) in a few instances either otolithradius or fish length data were accidentally omitted. The pointsshown in Fig. 3 represent predicted age and estimated forklength at subsequent 500-µm otolith radial intervals. Thenumber of points on the curve is equal to the number of 500-µmintervals at which age–length estimates were made (NR&W).

Table 5 and Fig. 4 show von Bertalanffy growth curvesderived by the S&K method. Each point used to fit the curve(open circles) represents an integrated age estimate and sam-pled fork length (total length for hapu’upu’u). The number ofopen circles is equal to the number of fish sampled (Table 1),referred to as NS&K in Fig. 4 to distinguish it from the numberof points used to fit the von Bertalanffy curve using the R&Wmethod (NR&W). Each plot also includes a few points (solidtriangles), showing sampled lengths and corresponding ageestimates using the R&W integral (approximation I). Regres-sion curves for Pristipomoides seiboldii (kalekale) andPseudocaranx dentex (butaguchi) fit easily without con-straints. Nonlinear fitting for Etelis coruscans (onaga) andEpinephelus quernus (hapu’upu’u) had to be constrained to anasymptotic length (L∞). The curve that fit best for these speciesis shown in Fig. 4, using an L∞ based on the maximum length

record as 95% of L∞. Any limitations in the range and distri-bution of fish lengths sampled are apparent in these plots, asis the fact that some fish had very small or very large otolithsfor their length (unusually fast or slow growing fish). Thisinformation is masked by the R&W method, which creates auniform length at age sample regardless of the distribution offish lengths sampled.

A data set as large as the one compiled for the present studyaffords the opportunity to evaluate the variability of microin-crement width estimates as a function of otolith radius andbetter understand how much data is needed to arrive at a preciseage estimate. The number of microincrement width estimatesused to fit the modified Gompertz curves presented in thispaper ranged from 3472 to 16 686 per species (see Fig. 1).Table 2 shows that some individual Gompertz curves were fit

Estimated log–logregression (y = axb)

a b N r2

Etelis coruscans (onaga) 0.003 1.38 17 0.90Pristipomoides sieboldii (kalekale) 0.013 1.10 39 0.85Pseudocaranx dentex (butaguchi) 0.009 1.32 53 0.66Epinephelus quernus (hapu’upu’u) 0.004 1.32 67 0.70

Note: Curves were used to estimate fish length at subsequent 500-µmotolith radial intervals via Ralston and Williams’ (1989) method. y, fishlength (mm); x, otolith radius (µm); n, number of fish length to otolithradius pairs used in regression (more than one otolith used for some fish).

Table 4.Log–log regression curves relating sampled fish forklengths (mm) and total otolith radius (µm).

Individualotolith

radius (µm)

Estimated age (days)

Fish length(mm)

S&K method R&W method

Fish No. Individual data Pooled data Individual data Pooled data

Etelis coruscans (onaga) 11 548 6630 2300 2307 2255 2103219 671 7169 2666 2599 2776 2429

Pristipomoides sieboldii (kalekale) 4 409 7575 1815 1943 2127 208771 435 8254 2424 2184 2516 243975 273 5134 934 1078 921 101586 382 6217 1558 1462 1579 146987 388 7152 1523 1793 1850 1897

115 416 7663 2007 1975 2196 2131134 392 7169 1872 1799 1885 1905

Pseudocaranx dentex (butaguchi) 3 307 3237 707 651 676 59210 659 4537 1330 1110 1317 113011 575 4094 900 952 941 91529 476 4017 856 924 829 88635 765 4974 1528 1266 1393 136643 596 4219 1055 996 1053 97056 477 3857 940 868 913 822

204 515 4288 1265 1021 1204 999235 621 4582 1492 1126 1148 1151

Epinephelus quernus (hapu’upu’u) 2 486 7687 1637 1648 1731 162727 608 8227 2164 1799 2284 185762 376 6134 1209 1213 1252 1134

Note: Fork length given for all species, except Epinephelus quernus, for which total length is used. Smith and Kostlan (S&K) age estimates were made usingotolith growth equation parameters specified in Table 2; Ralston and Williams (R&W) age estimates were made using R&W approximation I (see Methods).

Table 3.Individual age estimates using either Smith and Kostlan’s (1991) or Ralston and Williams’ (1989) method to integratemicroincrement width versus otolith radius for individual versus pooled data.

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to as few as 172 microincrement width versus otolith radiusmeasurements. This suggests that an adequate representationof the otolith growth rate curve can be obtained with a rela-tively small number of microincrement width estimates, offeringa means of reducing the amount of work in this labor-intensivestep of research.

The number of microincrement width estimates needed andtheir distribution as a function of otolith radius depend on themethod used to integrate the data. For example, a samplingscheme for data to be integrated by the R&W method shouldprovide a precise estimate of mean microincrement widthwithin each 500-µm radial interval. The observed variance ofmicroincrement width in each interval provides an index of thenecessary sample size. Table 5 summarizes the estimatedminimum number of microincrement width estimates neededfor each species per 500-µm interval, on the basis of a 95%confidence interval around the true mean otolith growth rate(mean microincrement width) in each interval and an arbitrarytolerance of 5% between the estimated and actual number ofdays lapsed within each radial interval. A hypothetical t valuefor large samples (t0.025 ≈ 1.96) was used for the confidenceinterval, and the following equation was solved for N:

0.05(500/x_) ≤ 500 / (x

_+ 1.96(s/(N)½))

where 500/x_

is the time transpired (in days) during each R&Winterval (500 µm divided by the mean microincrement width),x_

is the mean microincrement width, s is the standard deviationof this mean, and N is the number of microincrement widthestimates.

Given the large number of microincrement width estimates

obtained for the present study, the sampled microincrementwidth was assumed to be a close approximation of the truemean. It should be noted from this example that the number ofmicroincrement width estimates required increases as a func-tion of increasing otolith growth rate within 2000–3000 µm ofthe primordium. The necessary sample size also increasessomewhat towards the otolith perimeter, owing to the largenumber of days required to grow through these intervals (slowgrowth rate). Small differences in microincrement width vari-ability towards the otolith perimeter have a relatively largeeffect on sample size.

On the basis of this estimate, the necessary number of mi-croincrement width estimates per 500-µm interval was consid-erably less than the number obtained for most intervals in thepresent study. Recommended sample size ranged from 44 to901 microincrement width estimates per interval, averagingabout 224 per interval for all four species. The average numberof microincrement width estimates needed per 500-µm inter-val was 180, 226, 227, and 229 for onaga, kalekale, butaguchi,and hapu’upu’u, respectively. This crude estimate provides anindex of regions of the otolith where more sampling effortshould be invested and a model upon which to base estimatesof sample size versus otolith radius in future studies.

Discussion

This study provides an estimate of the growth rates of fourimportant Hawaiian bottom fishes. It is our hope that this in-formation will contribute to the general understanding of ageand growth trends for these species, allowing improvements to

Fig. 3. Estimated von Bertalanffy growth curves (Lt = L∞(1 – e−K(t−to))) derived using Ralston and Williams’ (1989) method. NR&W, number of

age–length estimates (one age–length estimate per 500-µm otolith radial interval).

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be made in their management. The in-depth evaluation oftrends in the variance of microincrement widths as a functionof otolith radius should also contribute to the development ofa clearer perspective on how to optimize future returns for theinvestment of time and effort in otolith preparation for growthestimation.

The von Bertalanffy growth parameter estimates obtainedin the present study, by either method, generally seem reason-able. However, there are important differences. Most notableis that estimated K values produced using the S&K methodwere always higher than those obtained using the R&Wmethod. S&K estimates of to were also higher and seem un-reasonable in most cases. The problems encountered in fittingthe low (to) end of the von Bertalanffy curve using the S&Kmethod were to be expected, since there were no extremelysmall fish in the data set. The R&W method generates a morecomplete distribution of estimated length at estimated age,prior to fitting the von Bertalanffy curve, whereas the S&Kmethod uses only sampled fish lengths and corresponding ageestimates. Thus, deficiencies in the S&K estimates of to reflectactual deficiencies in the sample.

There is no clear reason for observed differences in esti-mated K values. However, since the value of K helps to definethe overall shape of the von Bertalanffy curve between itsintercept and asymptote, K values are also influenced by thescarcity of extremely small specimens. Estimated K values byeither method were within the range of those in the literaturefor three of the four species in Hawaii (Ralston and Kawamoto1988) and for other tropical snappers and groupers (summa-rized by Ralston 1987). Estimates of L∞ for kalekale and

hapu’upu’u were close to expected values from the literature,whereas the L∞ estimate for onaga was somewhat higher andfor butaguchi considerably lower than expected. For the twocases where S&K von Bertalanffy regressions converged with-out imposing constraints on this parameter, L∞ estimates wereclose to the available maximum length records and asymptoticlength estimates.

Two of the S&K regressions shown in Fig. 4 (for onaga andhapu’upu’u) had to be constrained to an asymptotic length (L∞)derived from information obtained from the literature. Becausethe fishery in the northwestern Hawaiian islands was largelyunexploited prior to 1970, maximum length records registeredduring the first exploratory cruises (Uchida and Uchiyama1986) are considered to be near actual maximum lengths inthis region for most species. The need to constrain L∞ forhapu’upu’u was not surprising, since the maximum lengthsampled for this species was only 70% of its maximum re-corded length. This was unexpected for onaga, but Fig. 4shows that the poor fit may have been due to the presence ofa few outlying age–length pairs from fish that had relativelylarge or small otoliths for their size, compared with the rest ofthe sample.

Multiple regression coefficients (r2) for von Bertalanffycurves fit to data generated by the S&K method were less than85% for all species, because of observed variability in otolithradius for similar fish lengths (i.e., variation in individual fishgrowth rates). The multiple r2 for kalekale was highest andthere was no need to place any constraints on L∞. The lengthrange of kalekale sampled was limited, but this species is muchsmaller than the others, placing the maximum length sampled

Endpointotolith radialinterval

Etelis coruscans

(Onaga)Pristipomoides sieboldii

(Kalekale)Pseudocaranx dentex

(Butaguchi)Epinephelus quernus

(Hapu’upu’u)

x s ne na x s ne na x s ne na x s ne na

500 10.8 4.0 236 107 18.1 6.3 203 477 12.1 5.6 371 893 11.5 4.8 291 4961 000 16.9 4.5 121 176 22.6 7.2 176 421 11.0 6.1 526 1 185 11.9 6.0 431 4801 500 10.5 3.8 227 164 15.2 8.7 558 684 6.8 3.4 432 1 773 12.1 6.1 433 5002 000 6.7 2.3 202 328 6.9 5.0 901 938 5.5 2.0 231 1 815 7.2 4.0 526 6672 500 4.5 1.4 153 308 4.8 2.4 412 1 416 4.2 1.3 164 1 811 5.4 2.4 348 8633 000 3.4 1.0 130 349 4.7 1.9 281 1 608 3.4 0.9 107 1 721 5.6 1.8 179 8313 500 2.8 0.7 103 225 4.2 1.6 253 2 184 2.8 0.7 100 1 432 5.1 1.2 102 9304 000 2.6 0.5 71 267 3.6 1.5 283 1 847 2.7 0.8 158 1 544 4.8 1.4 148 7764 500 2.2 0.6 120 294 3.1 1.2 243 2 131 2.1 0.7 169 928 4.4 1.4 176 8985 000 2.1 0.4 81 300 2.8 0.8 147 1 843 1.9 0.6 200 349 4.3 1.1 110 8785 500 2.1 0.6 133 168 2.5 0.7 134 1 716 1.2 0.4 222 129 3.9 1.1 141 9076 000 2.2 0.5 86 83 2.4 0.6 123 1 386 0.9 0.1 44 12 3.3 0.9 123 8986 500 1.8 0.5 110 151 2.3 0.8 214 969 3.2 1.1 189 3687 000 1.6 0.3 59 180 2.2 0.6 151 666 3.2 1.4 324 3477 500 1.3 0.7 533 129 2.2 0.5 94 157 3.3 1.0 155 3298 000 1.1 0.4 289 142 2.0 0.4 90 85 2.5 0.7 143 3908 500 0.6 0.2 156 46 2.3 0.7 170 2389 000 0.9 0.4 424 55 2.2 0.7 158 1579 500 1.7 0.6 198 153

10 000 1.4 0.4 146 10910 500 1.0 0.4 324 11211 000 1.0 0.4 226 102Totals 3234 3472 4263 16 686 2724 13 592 5041 11 429

Note: x, mean microincrement width observed per 500-µm otolith radial interval; s, sample standard deviation; ne, estimated minimum number ofmicroincrement width estimates needed in this interval; na, actual number of microincrement width estimates obtained for the present study.

Table 5.Estimated sample size needed based on observed variance within each 500-µm otolith radial interval.

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closer to its maximum attainable size. The smallest sample sizewas for onaga, but the length range covered was the greatestof the four species, and the resulting von Bertalanffy multipleregression coefficient was still relatively high (r2 = 80–83%).A relatively small number of butaguchi were also sampled,with a wide length range, and this von Bertalanffy regressionwas also successful without constraining L∞ (r2 = 78%). Theseresults suggest that sampling the widest possible length rangemay be more important than having a large number of fish.

Advantages of Ralston and Williams’ (1989) method ofestimating fish growth rates include its speed and ease of ap-plication. Another advantage is that it readily adjusts to differ-ences in the shape of the otolith growth rate curve without aneed to change the method of calculating the numerical inte-gral. Presuming that a radial interval length can be selectedalong which the mean growth rate remains constant, the tech-nique can be used with confidence. Its tendency to smoothirregularities in sample size and structure can be offset by com-plete and systematic sampling. During the step in which a uni-form length at age key is developed, the method produces aseemingly perfect sample regardless of any deficiencies in theoriginal sample. This makes it extremely important to ensurethat the data collected represent the full length range and vari-ation in the population.

One advantage of the S&K method is that the nonlinearregression of microincrement width versus otolith radius pro-vides a direct estimate of the fit of a given data set to the

modified Gompertz curve. Another advantage is that inte-grated age estimates can easily be calculated for otoliths of anysize. The latter is true for any other method that continuouslyestimates the age integral (i.e., Ralston and Miyamoto 1981).The disadvantages of the S&K method lie primarily in thedegree of fit (or lack of it) of observed microincrement widthsto the modified Gompertz rate curve. If the data are not wellrepresented by a Gompertz curve, the method is invalid. How-ever, any curve that provides a better fit can be employed andintegrated appropriately. The preliminary choice of a curvecan be made through visual examination of plotted data, thenrefined on the basis of achieving a reduction of the multiplecorrelation coefficient (r2). The potentially large effect of sub-tle variation in estimated Gompertz parameters a and b onresulting age estimates is another disadvantage of the S&Kmethod, which can be offset by efforts to ensure that a repre-sentative and complete sample of microincrement widths isobtained along the entire otolith radius.

On the basis of the foregoing results, significant differencesin age and growth estimates are more likely to arise from dif-ferences in the sampling regime (size range and distribution offish lengths, distribution of microincrement width estimatesalong the otolith radius, or the use of individual versus pooleddata) than from differences in the method of integration. Inte-grated age estimates based on the same data were not signifi-cantly different, using either the S&K or R&W method.Regardless of the method of integration, age estimates in species

Fig. 4. Estimated von Bertalanffy (VB) growth curves (Lt = L∞(1 – e−K(t−to))) derived using Smith and Kostlan’s (1991) method. NS&K, number

of fish-otolith pairs sampled (one age estimate and corresponding length per fish, delimited by open circles) A few individual growth estimatesare also shown (solid triangles), based on approximation I of the Ralston and Williams integral (see Methods). Asymptotic length (L∞) of VBcurves for Etelis coruscans (onaga) and Epinephelus quernus (hapu’upu’u) constrained, on the basis of L∞ as 95% of maximum recordedlength (see Table 1).

Can. J. Fish. Aquat. Sci. Vol. 54, 1997134

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(like Epinephelus quernus) for which microincrement widthsare highly variable at the modal (larval to juvenile) end of thecurve are more susceptible to sampling error than in species(or environments) where juvenile growth is less variable. Forthis reason, a preliminary examination of the variability ofmicroincrement width estimates as a function of otolith radiusis an important first step in selecting a curve or method ofintegration.

This study provides a means of estimating the required sam-ple size for ageing otoliths from individual fish or entire popu-lations using microincrement width data. It shows that aconsiderably smaller sample than was obtained for most of thefish described herein may be sufficient. Ralston (1985) andRalston and Williams (1989) showed that otolith growth ratesin other species were also less variable towards the otolithperimeter. A representative sampling scheme can be devisedat an early stage by estimating the variance in microincrementwidth as a function of radial distance.

An indirect result of using a single otolith growth rate curveto estimate age for all fish in the population (pooled data) isthat fish with wider otoliths are always assumed to be older.This was not always found to be the case when the age estimatefor each fish was based solely on its own microincrement data(see samples Nos. 86 and 87, Table 3, for Pristipomoides sie-boldii). It is possible that a more accurate age estimate forindividuals could be made by taking a limited number of mi-croincrement width estimates along the full otolith radius foreach fish and ageing each one only from its own data. Thisstudy indicates that a relatively small number of well- distrib-uted microincrement width estimates may provide an adequateage estimate for individual fish; however, the time investmentmight not be justified by the level of increased accuracy whena large number of fish must be examined. Errors may resultfrom pooling data for otoliths with dissimilar rates of growthto estimate a single growth curve for a population. Althoughit is more correct to estimate otolith growth rate for individuals,time and sampling constraints may sometimes make it imprac-tical. It must be left to the discretion of the researcher to de-termine where and how the sampling design can be optimized.

The observation that estimated microincrement widths reg-istered in this study never reached zero might prompt the ar-gument that the asymptotic growth rate (c) represents theoptical limitations of the light microscope and the human eye.The three-dimensional complexity of otolith microstructureand the physical constraints of flat sections mean that otolithpreparations often contain a few illegible radial segments(Radtke 1987; Gauldie and Nelson 1988, 1990). The problemwas minimized in the present study by the experience of thesenior author in sectioning otoliths from diverse taxa. A betterunderstanding of the three-dimensional aspects of crystallinegrowth in otoliths is needed and may develop more rapidly asnew technologies make it possible to section otoliths preciselyand quantitatively along various planes. In the meantime,questions such as what causes illegible segments to occur andwhether growth within these areas is comparable to that reg-istered in adjacent portions of the otolith cannot be fully ad-dressed.

With the advent of computerized video optics, the task ofcounting microincrements in otoliths has been greatly simpli-fied. However, otolith preparation is still very time consuming.Therefore, methods that maximize returns for this effort must

continue to be developed. The procedures described hereinshould help to optimize data collection, reduce sample size,and ensure the reliability of fish age and growth estimatesusing otolith microincrement width data.

Acknowledgements

We thank Kurt Kawamoto, Paul Shiota, and the crew of theNational Marine Fisheries Service research vessel TownsendCromwell for their assistance in obtaining fish samples. We arealso indebted to the United Fishing Agency and the vendors ofHonolulu’s open markets for helping us acquire samples; toBert Kikkawa for technical assistance; and to Steve Ralston,Robert Gauldie, Bob Humphreys, Richard Radtke, JamesUchiyama, Jeff Polovina, and Ed DeMartini for critical reviewof the manuscript.

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