Variation in the relationship between otolith weight ...

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Variation in the relationship between otolith weight and age: implications for the estimation of age of two tropical damself ish (Pomacentrus moluccensis and wardi) 8.6. Wsrthington, P.J. Dsherty, and A.9. Fowler

Abstract: The weight of otoliths may provide an objective and economic method of ageing fish. To investigate this potential, populations of two species of fish (Psmacentrus mo&uccensisand P. wardi) were sampled from the lagoons of seven coral reefs within the Great Barrier Reef, Australia. The weight of otoliths increased with age throughout the life of both species. Two factors appeared to have the potential to undermine the use of otolith weight to estimate the age of individuals. First, overlap in the range of otolith weight among fish of different ages caused normally distributed errors in the subsequent estimation of age by otolith weight. Second, variation among reefs in the relationship between otolith weight and age biased subsequent age determinations. Both these types of error also affected the estimation s f the age structure of the populations. Random errors in age determination resulted in the smoothing of the age structure whilst bias either shifted or compressed the age structure. While smoothing of an age structure will not eomprornise the results of several types of analysis, bias will be detrimental to most. Consequently, randomization methods were used to estimate the power of tests to detect variation in the relationship between otolith weight and age. Our results show that by frequently recalibrating the relationship between otolith weight and age, it can be used as an objective and economic method of age determination with the potential to be as reliable as counting annuli in sectioned otoliths.

RCsnmC : Nous rnontrons que la mesure du poids d'un otoBithe peut constiduer une niCthode objective et 6conomique pour determiner l'lge des poissons, et peut $tre aussi fiable que le dtnornbrement des anneaux de croissance sur les sections d90tolithes. Le poids des otslithes augrnente tout au long de la vie chez deux poissons de rtcifs coralliens (Pomacentrus mobscccensis et P. wardi) trouvts dans des lagons de la Geande Barrikre, en Australie. Deux facteurs ont toutefois limit6 B'ernploi du poids des otolithes pour estimer l'lge : He chevauchement de la fourchette de poids des otolithes entre des poissons d'sges diffkrents causait des erreurs suivant une distribution norrnale dans l'estirnation subsiquente de 1'Bge et la variation de la relation d'un recif B l'autre biaisait les determinations subskquentes des lges. Les estimations de la structure d'iige Ctaient aplanies par les erreurs distribukes normalement chez les individus dont on dkterminait l'Bge, tandis que %ebiais dkcalait ou cornprimait la structure d'lge. Le Bissage d'une structure d9i3gene cornpromet pas les rksultats de divers types d'analyses, rnais Be biais rCduit Ba validit6 de la plupart des analyses. En consequence, nous avons eu recours i la randomisation afin d'estimer la puissance des tests de detecter la variation dans Ba relation entre le poids de l'otolithe et l'lge. Cela permet de penser qu'un rbetalonnage de Ba relation est possible si l'on dCtermine l'&ge d'un petit wombre de poissons B 19aide de methodes diffkrentes. [Traduit gar la R a a c t i s n ]

Received November 1 1, 1993. Accepted July 7, 1994. 512169

D.G. ort thing ton,' B.J. Dolmerty9and A.J. Fowler. Australian Institute of Marine Science, BMB 3, Townsville MC, QLB, 48 18, Australia.

' Author to whom correspondence should be addressed at: NSW Fisheries Research Institute, P . 8 . Box 21, Cronulla, NSW 2230, Australia.

Can. J. Fish. Aquat. Sci. 52: 233-242 (1995). Printed in Canada 1 IinprirnC au Canada


Can. J. Fish. Aquat. Sci. Vol. 52, 1995

introduction Methods of stock assessment that require information on the age structure of populations form the basis of fisheries management (see review by Megrey 1989). Age structures have traditionally been estimated by interpreting annual marks in the scales or otoliths of fish (e.g., Francis et al. 1992). Differences in the interpretation of annuli by the same reader and among readers can affect the apparent age of individual fish and, as a result, the estimated age structure of a population (Boehlert and Yoklavich 1984). Similarly, the time-consuming procedures required to section and prepare otoliths may restrict the size of the sample that can be aged and, hence, affect the precision of the estimated age structure. Consequently, more reliable estimates of age structure could be produced by a more objective and economic method of determining the age of individual fish. One alternative method of ageing that has the potential to be both objective and economic uses the weight of otsliths to assign an age to a fish (Boehlert 1985; Pawson 1990; Fletcher 1991). This method first requires a knowledge of the relationship between the age of a fish and the weight of its otolith. As otoliths may increase in weight throughout the life of a fish (Fowler and Doherty 1992) and appear not to be greatly resorbed (Mugiya and Watabe 1977), there may be a direct relationship between otolith weight and age. If the relationship between otolith weight and age can be estimated, a calibration curve (Snedecor and Cochran 1989) can be established, and subsequently used to estimate the age of a larger sample of fish. In common with traditional methods of ageing, the use of otolith weight may result in both random errors and bias in age determination. In contrast, because of the reduced processing time (see Boehlert 1985), the use of otolith weight may allow larger samples to be aged, thus reducing Sampling error. Errors in age determination can have considerable influence on subsequent stock assessment models (Eai and Gunderson 1987; Tyler et al. 1989; Bradford 1991). Consequently, variability in the determination of age by annuli has been well investigated for many species (e.g., Boehlert and Yoklavich 1984; Kimura and Lyons 199I), and several techniques have been developed to compare this variability among different methods (Kimura et al. 1979; Beamish and Fournier 1981; Chang 1982) and compensate for any systematic errors (Hoenig and Heisey 1987; Richards et al. 1992). In contrast, no study has yet used these techniques to investigate variability in age determination using otolith weight, or compared such variability to that when age is determined by annuli (see also Boehlert 1985). This comparison is particularly relevant in tropical regions where the less seasonal environment can increase the ambiguity of structures in the otolith. Populations of damselfish have been extensively studied on the Great Barrier Reef (GBR), Australia (see review by Doherty and Williams 1988). Damselfish are small ( 0.05; Fig. 2b), although it is clear that the peaks and troughs evident in the true-age structure have been smoothed by the use of otolith weight (Fig. 2b). When the relationship from One Tree Reef was used to estimate the age of I? w a r d individuals from that reef, 36% of the individuals were estimated to be the same age as determined by annuli. Of those incorrectly aged, 90% were within 2 years of the age determined by annuli, although one 1%-year-oldfish was estimated to be 6 years old based on the weight of its otolith. The CV for each age-class was consistently greater than the Wistari example (compare Tables 3 and 4) and the average CV across all age-classes was 10.5%. Similar to the example from Wistari Reef, there was no significant difference between the estimated and true age structures for One Tree Reef (Kolmogorov-Smirnov test; P > 0.05). Once again, it is clear that the peaks and troughs evident in the true age structure have been smoothed by the use of otolith weight (Fig. 2b). In particular, the proportion of fish in the troughs of 4, 6- and 9-year-old fish were increased, and the peaks of 2-, 3- and 8-year-old fish were reduced (Fig. 2b). As well as the above examples, age structures were estimated for both species on each reef using the appropriate relationship between otolith weight and age (Fig. 2)-


Can. J. Fish. Aqua%.Sci. Val. 52, 1995

Fig. 2. Age structures of (a) rnslueeensi and ($9 P. w a d i from all reefs sampled. Bars show true age structure determined from annuli in sectioned otoliths and lines show estimated age structure from the relationship between otolith weight and age for each reef. b.

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In general, it is apparent that the use of otolith weight smooths the true age structure. This is shown most clearly by the strength of all relatively abundant age-classes (e.g., 10-year-sIds of R moluccensis from One Tree and Wistari reefs; Fig. 2a) being underestimated by otolith weight. Conversely, the strength of most weak age-classes is overestimated by otolith weight. Despite this, there was no significant difference among the true and estimated age structures for any reef (Ko1,mogorov-Smirnov tests, P 9 0.05). It also appears that the differences in age structure among reefs were maintained when otolith weight was used to estimate age (Fig. 2). Using an inappropriate relationship When the relationship from One Tree Reef was used to estimate the age of individuals fmm Heron Reef, 28% of the individuals were estimated to be the same age as determined by annuli. Sixty percent sf the individuals were estimated to be younger than the true age. This negative bias in estimation increased with age (Table 5 ) , because the relationship used to estimate age had a lower slope than the appropriate relationship. The average CV across all age-classes was 15.7%. There was a significant difference

Wistari Reef

between the true age structure of Heron Reef and that estimated using the calibration relationship from One Tree Reef (Fig. 3; Kolmogorov-Srnirnov test, P < 0.01). Despite this, the age structures are of the same general shape, although the peaks evident in the true age structure have been smoothed by the use of otolith weight, and there has been a reduction in the average age s f individuals. Ability to detect differences in the relationship between otolith weight and a W e n trying to detect a difference in the slope of two relationships as great as that between One Tree and Heron reefs for B. w a d i (Table 2), only small numbers of fish (e.g., 10-20) would need to be aged from the new sample to allow a powerful test (i.e., power sf 85-9596) against the previously used standard relationship (Fig. 4). In contrast, to detect differences in the slope of two relationships as small as those between One Tree and Fitzrsy reefs for I? ward (Table 2), a much lager number (e.g., 80-108) of fish would need to be aged from the new sample to allow a powerful test (Fig. 4). Consequently, the size of the subsample sf fish aged to achieve a given power is dependent on the difference in slopes that it is desired to


Wosthington et al.

Table 4. Comparison of age determinations from annuli and otolith weight for dP. war& on One Tree Reef. Otolith weight was used to estimate age with the relationship derived from fish on One Tree Reef.

True age

Count

Range of estimates

Percent agreement

CV (%)

Bias (years)

detect and, in turn, that will be dependent on the desired degree of accuracy and precision in the subsequent age determination and age structure. Improvements in power could be achieved by taking a size-structured sample of fish for ageing (i.e., a selection of luge and presumably old fish, and a selection of small and presumably young fish). If this were done, it would result in a more reliable estimate of the relationship between otolith weight and age for a given number of fish sampled.

Discussion Relationship between otolith weight and age The average weight of otoliths increased with age throughout the life of both P. moluccensis and P. wardi. This implies that otolith weight may provide a rapid and economic method of ageing, as suggested in many previous studies (e.g ., Templeman and Squires 1956; Boehlert 1985; Reznik et al. 1989; Pawson 1990; Fletcher 1991). Several of these authors have emphasised that the average weight of otoliths in old fish continues to increase unlike other variables (e.g., standard length, weight, otolith length, etc.). Indeed, growth of otoliths appears to be somewhat decoupled from other somatic growth rates, and may simply be more closely related to time and age (Reznik et al. 1989). Consequently, otolith weight provides a more accurate estimate of age than these other parameters (e.g., Fletcher 1991) and, in some circumstances, may provide a more reliable estimate of age than annuli in sectioned otoliths (e.g., when interpretation of annuli is ambiguous). Many previous studies have investigated the relationship between otolith weight and age, and cited its strength and apparent potential for age determination. Reported coefficients of determination range from otolith weight

Table 5. Comparison of age determinations from annuli and otolith weight for I? Wardi on Heron Reef. Otolith weight was used to estimate age with the relationship derived from fish on One Tree Reef.

Age (from annuli) Count

Range of Percent CV Bias estimates agreement (9%) (years)

explaining 95% of the variation in age of splitnose rockfish (&bastes diplopma) (Boehlert 1985) to 51% of the variation in age of Pacific hake (Merluccius productus) (Beamish 1979). Most studies report otolith weight explaining 80-95% of the variation in sage (e.g., Radtke et al. 19 et al. 1991; Wilson et al. 1991; Fletcher 1991). In this study, otolith weight explained 84-96% of the variation in age of P. neol~ccemsisand P. wardi. That is, values spanned the range commonly reported for the relationship between otolith weight and age. Unfortunately, the coefficient of determination is not the best index on which to assess the utility of otolith weight to estimate age, as it does not directly incorporate information on the slope of the relationship. This is important as more reliable estimates of age will be possible when there is little variation in otolith weight within age-classes and large variation among ageclasses. That is, there is a tight fit of observations to a relationship with a high slope. Consequently, the ratio of the mean squares due to the regression and the residual, which is traditionally used to assess the significance of a regression relationship, is a more appropriate index of the potential of otolith weight to estimate age.

Estimation of age by otolith weight Overlap in the range of otolith weights for fish from adjacent age-classes contributed to the errors in ageing. Bverlap was approximately symmetrical among adjacent ageclasses, and consequently mainly resulted in normally distributed errors in the estimation of age. Nonetheless, variability in otolith weight did increase with age, causing an increase in the overlap of otolith weights of fish from older age-classes. This resulted in decreased sion of ages estimated for older fish, a result similar to that reported for the use of annuli (Kimura and Lyons 1991). Within the age structure, such ageing errors led to the loss of incorrectly aged individuals from an age-class


Can. J. Fish. Aquat. Sci. Vsl. 52, 1995 Fig. 3. Age structures of F! w a d i Rom Heron Reef. Bars show true age structure determined from annuli in sectioned oltoliths and lines show estimated age structure from the relationship between otolith weight and age from One Tree Reef. 4"

i

O

Fig. 4. Results of simulations to estimate the power to detect a significant difference between the slopes of two relationships between otolith weight and age of F! w a d i . Values are given for differences in slope as large as those between One Tree and Heron reefs (open cirdes) and One Tree and Fitzrsy reefs (filled circles). One Tree v Heron

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Age Rears)

and the addition of incorrectly aged individuals from adjacent age-classes. The frequency of incorrectly aged individuals lost and gained by an age-class in this way is dependent on both the size of the error and the abundance of each age-class. For example, Kimura and Lyons (1991) noted "if two adjacent year-classes have absolute strengths of 10 m d 108 fish, a 10% imprecision of k1 year will add 5 fish from the strong year-class to the weak one (a 50% change) but only one-half a fish from the weak year-class to the sarong (a 0.5% change)". That is, the true peaks and troughs in an age structure can be smoothed by normally distributed ageing errors (see also Richards et al. 1992). Overlap in otolith weight among age-classes will be the most common cause of such errors when using otolith weight to estimate age. In contrast with overlap in otolith weight among ageclasses, spatial variation in the relationship between otolith weight and age biased subsequent estimates of age. For example, if a relationship with a lower elevation than the true relationship is used, the ages of all fish will be underestimated, resulting in the shifting of the age structure. A calibration line with a lower slope than the true relationship will underestimate the age of old fish more than young fish, resulting in the compression and (or) shifting of the age structure (e.g., Table 5). Once again, biases similar to these are frequently reported when using annuli to estimate age (Boehlert and Yoklavich 1984). Regardless, any biases in ageing can seriously modify age structures, with resultant implications for subsequent analyses (Lai and Gunderson 198'7; Bradford 199 1). Consequently, it is important to use an appropriate calibration relationship to estimate age from otolith weight. Whilst errors in the determination of age will occur when using otolith weight, a great deal of the subjectivity of age determination can be removed. This is obviously desirable when it can be stated that traditional techniques of age determination are "as much an art as a science" (Williams and Bedford 19'74). Determining age by annuli involves the counting of marks in otoliths, the interpretation of which may change among replicate readings, as a reader becomes more experienced or among different readers. Once an appropriate relationship between otolith weight and age has been determined, subjective

0

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errors can only be introduced during the estimation of the weight of an otolith. This process will obviously be less subjective than interpretation of annuli for most species. As a consequence, there will be little if any variation among replicate estimates of age for the same otolith. Errors in the determination of age by otolith weight will be dominated by objective errors simply caused by the relationship between otolith weight and age. Perhaps most importantly. such objective ageing errors will be more easily quantified and corrected (see Richards et al. 1992) than errors in interpretation of annuli that differ among readers and through time. Throughout this paper we have assumed that the initial annuli counts represented the true age of each individual. This is almost certainly untrue. Errors in the interpretation of annuli in otoliths are frequent and there can be substantial variability both among and within readers of the same otolith (e.g., Boehlert and Yoklavich 1984). Similarly, there can be spatial or temporal variation in the interpretability of a species9 otoliths (Fowler and Doherty 1992). Errors caused by such factors may complicate the use of otolith weight to estimate age, as the method is eonstrained by the reliability of the initial age estimates used for calibration. That is, if imprecise or biased estimates of age are used for calibration, the use sf otolith weight to estimate age will be similarly affected. As a consequence, the use of known-age fish for calibration may greatly increase the reliability of subsequent age determinations using otolith weight. Alternatively, in any sample of fish to be used for calibration, extra effort can be used to ensure some consensus of opinion among separate readers of the annuli. The CV has been previously used as an index of the precision of a set of age determinations (e.g., Chang 1982; Campana and Moksness 199 1; Kimura and Lyons 1991). For example, Kimura and Lyons (1991) compared the precision of age determination using annuli for several species. CVs ranged from 3% for the relatively short-lived Pacific hake to 13% for sablefish (Anopk~pomsfirnbrka), which


Wssthingtsn et al.

was dificult to age due to "unresolved" marks in its otoliths (Kimura and Lyons 1991). In the central GBR, similar estimates for I? molkgccensis are approximately $76, but can vary greatly with latitude (Fowler 1990; Fowler and Doherty 1992). CVs comparing ages determined by otolith weight to the true age in this study ranged from 5 to 16%. It must be remembered that the examples that produced these values were chosen to represent the best and worst cases, and in practice, CVs between these limits might be expected. Nonetheless, these data indicate the potential of otolith weight to be as reliable in the determination of the age of P molncccensis and P. ward6 as the use of annuli in sectioned otoliths.

Potential uses of otolith weight The utility of otolith weight as an estimator of age will be dependent on how the age data will be used. Some types of analysis will be particularly sensitive to any ageing errors. For example, hind-casting rates of recruitment from age structures, by methods such as sequential population analysis, may be particularly sensitive to any type of ageing error (Bradford 1991). Other types of analysis will be more sensitive to particular types of ageing error. For example, underageing bias has potentially great effects on estimates of growth and yield-per-recruit (kai and Gunderson 1987). In contrast, some methods of analysis will be reasonably robust to different types of ageing error. Estimation of rates of mortality from catch curves should be affected little by the smoothing of normally distributed ageing errors (Brander 1974, but see Barlow 1984). In all these respects, errors in ageing by otolith weight are no different from errors in ageing by annuli in otoliths. Perhaps one of the most obvious uses for the relationship between otolith weight and age would be for monitoring the age structure of populations. Provided there were not large random errors or bias in the determination of age, such a monitoring program could provide estimates of spatial and temporal variation in parameters such as longevity and mortality, and estimate levels of recent recruitment. One way to ensure that age determinations were not biased by using an inappropriate relationship between otolith weight and age would be to age a subsample of any new collection of fish. This would enable a test between a previously used standard relationship and that from the new collection. Bur preliminary results suggest that large differences in the slope of two relationships can be detected with a small number of fish. The procedures for optimising the subsampling of fish from new collections will be very similar to those for the use of age-length keys (Kimura 1977; Lai 1987). Providing significant biases can be eliminated by recalibration of the relationship between otolith weight and age, it appears that otolith weight may provide a reliable estimate of age for many fish species. For some species and (or) places, otolith weight may even provide an estimate of age as reliable as annuli in sectioned otoliths. This is particularly true for species that are difficult to age using annuli, provided an initial calibration equation can be determined. In addition, the ability to age larger samples of fish using otolith weight can provide a more precise estimate of the true age structure of a population than a smaller

sample with fewer ageing errors (Worthington et al. 1995). That is, the sampling error encountered by ageing small numbers of fish may outweight the advantages of a more reliable ageing method, particularly in species with many age-classes. At worst, otolith weight can be used as a check on ages determined by annuli, especially in old fish or species with otoliths that are difficult to interpret. Essential to the use of otolith weight (or any ageing technique) is a knowledge of the potential variability and bias in the determination of true age (see Richards et al. 1992). If this were possible, otolith weight could provide a rapid, easy, and economic method of objective age determination.

Acknowledgments Many people helped with the sampling involved in this study. We thank them all. Doug Ferrell, Dave Williams, and Nokome Bentley provided comments on the manuscript. This is contribution 728 from the Australian Institute of Marine Science.

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