Modeling Otolith Weight Using Fish Age and Length: Applications to Age Determination

Transactions of the American Fisheries Society

ISSN: 0002-8487 (Print) 1548-8659 (Online) Journal homepage: http://www.tandfonline.com/loi/utaf20

Modeling Otolith Weight using Fish Age and Length: Applications to Age Determination

S. Dale Hanson & Craig P. Stafford

To cite this article: S. Dale Hanson & Craig P. Stafford (2017) Modeling Otolith Weight using Fish Age and Length: Applications to Age Determination, Transactions of the American Fisheries Society, 146:4, 778-790, DOI: 10.1080/00028487.2017.1310138 To link to this article: http://dx.doi.org/10.1080/00028487.2017.1310138

Accepted author version posted online: 03 Apr 2017. Published online: 03 Apr 2017.

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Download by: [US Fish & Wildlife Service] Date: 31 May 2017, At: 07:47 Transactions of the American Fisheries Society 146:778–790, 2017 © American Fisheries Society 2017 ISSN: 0002-8487 print / 1548-8659 online DOI: 10.1080/00028487.2017.1310138

ARTICLE

Modeling Otolith Weight using Fish Age and Length: Applications to Age Determination

S. Dale Hanson* U.S. Fish and Wildlife Service, Green Bay Fish and Wildlife Conservation Ofﬁce, 2661 Scott Tower Drive, New Franken, Wisconsin 54229, USA Craig P. Stafford College of Forestry and Conservation, University of Montana, 32 Campus Drive, Missoula, Montana 59812, USA

Abstract Relationships among otolith weight and age have been explored widely as cost-effective means to predict age. However, otolith weight is influenced by both fish age and somatic growth, making it necessary to partition these confounding effects to best use otolith weight to predict age. We used several hatchery strains of Lake Trout Salvelinus namaycush that varied in capture season, year, location, and mean size at stocking to develop a maximum likelihood model of otolith weight as complementary but independent functions of age (mg/year) and fi fi

sh length (mg/mm). Once these relationships were established, we determined age probabilities for each sh based on their measurements. Our best model included age and somatic growth components, with cumulative mean temperature as a variable to scale for seasonal differences in otolith accretion. For fish between 3 and 19 years of age, otolith weight increased by 1.16 mg/year, with an additional somatic growth component of 0.62 × exp(fish length × 0.0038) mg/mm. We correctly assigned age to 60% of the age-3 fish, but this decreased to about 10% among the oldest age-classes; however, predicted age residuals approximated normal distributions within each age- class. The model was robust to seasonal and annual variation, but somatic growth differences among some strain and stocking-size groupings resulted in modal aging biases of ±1 year. Given the stability in otolith weight components arising from fish age and somatic growth, we suggest that modeling otolith weight using reader age estimates offers a new quality assurance/quality control tool to assess whether reader ages support the widely documented properties of otolith growth. When otolith weight and fish length are more informative of age, our model may also be useful in estimating age composition data similar to an age–length key.

Mismanaged fisheries may be a consequence of inaccurate common problem that is best addressed with rigorous reader fish age determinations that misconstrue estimates of spawner training and quality assurance/quality control (QA/QC) mea- biomass, mortality, growth, recruitment, and age at maturity sures. Campana (2001) recommended allocating a small pro- (Beamish and McFarlane 1995; Yule et al. 2008). Error in portion of annual aging effort to a reference sample of known these population attributes will often affect mid- to long-term age—or at least consensus-based age—to measure aging con- population forecasting (Reeves 2003; Koenigs et al. 2013; sistency over time and between readers. However, Morison Hamel et al. 2016). Aging inaccuracies arise from structural et al. (2005) reported that one-third of aging laboratories do errors (e.g., not all annuli are discernable on the calcified not employ reference sets while the remainder use them more structure) or reader interpretational errors. Structural error is for reader training than routine QA/QC, apparently because minimized through the use of validated aging methods these QA/QC efforts reduce the number of new fish that can (Beamish and McFarlane 1983). Interpretational error is a be aged. More commonly, laboratories report reader precision

*Corresponding author: [email protected] Received December 19, 2016; accepted March 20, 2017

778 MODELING OTOLITH WEIGHT 779 for age structures based on a limited number of multiple this effort, Pawson (1990) ultimately used an otolith mass– readings (Chang 1982). Age estimates are typically accepted fish length slope that was constant for all age-classes—an when readers attain some minimum coefficient of variation assumption that we felt warranted further investigation. benchmark, although this does not imply that the ages are Many methods have been proposed for making age predic- accurate. Finally, others use ad hoc methods to corroborate tions from otolith weight and fish length measurements, but reader ages, such as comparisons of mean size at age, inspec- the most statistically comprehensive method is the maximum tion of scatterplots of age versus otolith weight or fish length, likelihood-based mixture analysis by Francis and Campana and following strong year-classes over successive years. (2004). Their approach employed a reference sample and an Inter-relationships of age, otolith weight, and fish length are unaged sample consisting of only fish measurements. For both appealing to use for identification of potential age misclassifi- samples, they simultaneously estimated distributions for mean cations because fish measurements, unlike reader annulus otolith weight and length at age, their correlation, and the counts, have objective properties that are regulated by biolo- proportions of fish within each age-class. Regrettably, the gical processes. This is particularly true for the physiologically Francis and Campana (2004) method is difficult to implement complex process of otolith growth, which (unlike somatic due to its statistical complexity and the potentially large num- growth) continues throughout a fish’s life. Otolith growth is ber of parameters that must be estimated (up to four per controlled by metabolic rate (Mosegaard et al. 1988; Gauldie age-class). Furthermore, the method has yet to be validated and Nelson 1990) but is also influenced by temperature, water by others. chemistry, photoperiod, and diet (see reviews by Campana In the current investigation, we developed an explicit model 1999; Morales-Nin 2000). Specific mechanisms of otolith consistent with TSR principles to predict otolith weight from fish growth are complex, but two consistent properties—collec- age and length, and then we used the modeled otolith weights as a tively known as Templeman–Squires relationships (TSRs)— basis for age assignment. We first explored a maximum likelihood have been recognized and widely corroborated: (1) larger fish approach to fit simple linear and curvilinear functions for model- within a year-class generally have heavier otoliths; and (2) ing otolith weight as the sum of independent contributions arising older, slower-growing fish generally have heavier otoliths than from fish age (mg/year) and fish length (mg/mm). Once these younger, faster-growing fish of the same size (Templeman and relationships and the underlying error distribution were estab- Squires 1956; Secor and Dean 1989). Accordingly, accretion lished, we predicted age probabilities based on otolith weight in otolith mass has been conceptualized as the sum of the and fish length measurements in accordance with Francis and independent processes that are correlated with somatic growth Campana (2004). We illustrate our model of otolith accretion by and age (Secor and Dean 1989). Therefore, it is necessary to using a reference sample of known-age Lake Trout Salvelinus partition these confounding effects of somatic growth and age namaycush captured in Lake Michigan. Our specificobjectives to best use otolith weight for predicting age. were to (1) explore candidate models to characterize relationships The TSR principles have provided the foundation for sev- among otolith weight, age, fish length, and various error structures; eral methods of estimating age from otolith weight and fish (2) use the best model to predict the most likely age for each fish in length measurements. An early approach suggested using the the reference sample based on fish measurements; and (3) employ residuals of otolith weight versus fish length in multiple data-mining techniques to assess whether residuals of known age regression models of age (Reznick et al. 1989). Although versus predicted age differed across capture season and year, this use of residuals may seem consistent with the second stocking location, and capture location as well as among biological TSR principle, several aspects are problematic. When age- factors including sex, genetic strain, and mean size at stocking. We groups do not overlap in length, the otolith weight residuals suggest that our approach offers a standardized method to interpret reflect variance within an age-class that cannot be applied to TSR principles and thus may be used to infer a “biological valida- the second TSR principle. Further, it is unlikely that a given tion” of reader age estimates and, in some cases, could provide an otolith mass residual expresses a consistent basis for adjusting age-subsampling method similar to an age–length key (ALK); in ages over varied growth rates, age-classes, and resulting body this paper, we focus on the former. sizes. A subtle but important aspect of these concerns is that individual age-groups have a lower slope in their otolith weight–fish length relationships than the age-pooled sample METHODS (Pawson 1990: their Figure 4). Accordingly, the otolith weight Known-age Lake Trout data set.—Several genetic strains residuals from the age-pooled sample are infl uenced by fish of Lake Trout have been stocked annually into Lake lengths within each year-class and thus are biased by growth. Michigan since the early 1960s as part of the rehabilitation Pawson (1990) recognized the general issue associated with efforts to restore self-sustaining populations (Holey et al. pooling and thus calculated age-class-specific regressions of 1995). Stocked fish were reared for 14–16 months at one of otolith weight versus fish length. He then adjusted otolith three national fish hatcheries (NFHs), and a percentage of weight to the modal fish length for each age-class that fish from the 1988–2004 year-classes were marked with an improved discrimination among age-groups. However, for adipose finclippairedwithacodedwiretag(CWT)that 780 HANSON AND STAFFORD was implanted into the fish’s snout. Uniquely numbered divided by the Fulton’s condition factor (as determined by CWTs were used to differentiate groups of stocked fish by the hatcheries). year-class, genetic strain, NFH origin, and management Recoveries of coded-wire-tagged Lake Trout were obtained unit. Several Lake Trout strains were stocked over the from gill-net surveys conducted in April–June (spring) and mid- years prior to our reference sample collections, but most October–mid-November (fall) 2006–2008. Fall surveys targeted of the stocking in these management units involved three mature fish on spawning reefs, whereas spring surveys targeted strains: Green Lake (GL), Lewis Lake (LL), and Seneca both subadults and adults. Recoveries were obtained from four Lake (SL). The GL and SL strains were stocked in the general locations, including the three Lake Michigan management offshore Southern Refuge, and GL and LL strains were units (IL, WM3, and WM5) and the offshore Southern Refuge, stocked in nearshore waters of three Lake Michigan which is mostly contained within WM5. Recaptured fish were management units (Wisconsin Management Units 3 and 5 sexed and measured for TL (mm); the sagittal otoliths were [WM3, WM5] and Illinois waters [IL]; Figure 1). Beginning extracted, and the snout (containing the CWT) was removed. in 1995, the target stocking mass for Lake Trout was Strain, year-class, rearing hatchery, stocking location, and mean increased from roughly 44 fish/kgtoabout24fish/kg in size at stocking for each fish were determined from CWT stocking an effort to increase postrelease survival. An approximate records. All otoliths were allowed to air dry for a minimum of 30 d measure of mean size at stocking for each CWT group was and were weighed on a microbalance with precision ≤ 0.1 mg. calculated from estimates of the total weight of fish stocked Weight was recorded for both the left and right otoliths when both were available. In the Great Lakes, the incidence of otolith defor- mities is high, with 66–86% of stocked Lake Trout containing vaterite in one or both otoliths (Bowen et al. 1999). For this study, we discarded broken otoliths; however, vateritic and otherwise deformed otoliths were retained to prevent subjective discarding of data. As vateritic otoliths are lighter (~15% on average) than normal aragonitic otoliths (Tomas and Geffen 2003), we used the weight of the heavier otolith to help reduce this issue. Fish age was represented as an integer age and as a decimal age (decimal age = [capture date – January 1]/365). Given that meta-

bolism and, hence, otolith accretion are dependent on water temperature, we evaluated the use of Lake Michigan mean daily surface temperature data from the period 1992–2014 as a surrogate of metabolic activity; this was used as an alternative to decimal age when scaling the amount of age-related otolith accretion that occurs during the year of recovery. Readers may access this temperature data from the National Oceanic and Atmospheric Administration at http://coastwatch.glerl.noaa.gov/statistic/dat. We calculated an annual cumulative proportion of temperature (T) for each day of the year as the daily mean temperature divided by the sum of all daily mean temperatures. Values of T for the first day of each month (January–December) were 0.00, 0.03, 0.04, 0.06, 0.09, 0.14, 0.25, 0.42, 0.61, 0.77, 0.88, and 0.96 in chron- ological order. Therefore, a fish captured on July 1 would be expected to have gained 25% of its annual otolith accretion if scaled with cumulative temperature data compared to 50% if scaled to decimal age. We only used T when estimating the age component of otolith mass. The somatic growth component of otolith accretion in our model is independent of time, and thus T is unnecessary, although it is worth noting that temperature is impli- citly scaled within the somatic growth component because somatic growth rate is positively correlated with metabolism until fish reach asymptotic size. FIGURE 1. Map showing the four Lake Michigan management units where Model of otolith weight.—Fish beyond the early life stages hatchery Lake Trout were stocked and recovered: Wisconsin Management Units 3 and 5 (WM3, WM5), Illinois waters (IL), and the Southern Refuge. generally exhibit an approximately linear relationship between Squares denote locations of gill-net sampling. Coded-wire-tagged fish were otolith weight and age, whereas otolith weight is generally an stocked in IL, WM3, the Southern Refuge, and the Northern Refuge. allometric or exponential function of fish length (Boehlert 1985; MODELING OTOLITH WEIGHT 781

Fletcher 1991; Araya et al. 2001; Pilling et al. 2003). A key Maximum likelihood estimates for ƟA,L given the observed element of using fish age and length to predict otolith weight is data were derived by finding the values that minimized the that the chosen model generates predictions that fitthe negative log likelihood (NegLL): underlying relationship between otolith weight and fish length within each age-class. Each fish in our reference sample was X ¼ ½ ; μ ; σ : described by a vector X containing measurements of otolith NegLL ilog g OWi A;L A;L (6) weight (OW), fish length (L), and age (A). For fish of a given age and length, we assumed that OW was lognormally We compared several candidate models of otolith accretion distributed and described by the density function g(OW; ϴA,L) that increase in complexity. Our base model assumed that relating accretion in otolith weight to some unknown vector of otolith weight is solely attributable to the age and decimal age ϴ σ fi parameters A,L.Modelerror( A,L) was speci ed with linear, component; we used this as a base model because previous power, or exponential functions of otolith weight. Following the studies have often employed otolith weight as a univariate maximum likelihood framework outlined by Francis and predictor of age (Worthington et al. 1995). We then considered Campana (2004), we modeled otolith weight as the sum of a candidate model with cumulative proportional temperature independent functions of fish length and age as follows: (instead of decimal age) to scale seasonal otolith accretion. We also examined models of otolith weight as the sum of Somatic growth componentðiÞ ¼ a exp Fish lengthðÞi b ; (1) somatic growth and age components, and finally we examined models that fit error with constant, power, or exponential functions. Akaike’s information criterion corrected for small sample

Age componentðiÞ ¼½integer ageðiÞ c½þ c decimal ageðiÞ size (AICc) was used to select the most plausible model þ ðÞy-intercept ; (Burnham and Anderson 2002). Parameter estimates were obtained with optimization routines using AD Model Builder or version 11.2-0 (http://admb-project.org/). Age predictions from the model of otolith weight.—After Age componentðiÞ ¼½integer ageðiÞ c½þ c TðiÞþðÞy-intercept ; parameter estimates and their associated error estimates were (2) obtained for the somatic growth and age components, we then predicted ﬁsh age from measurements of otolith weight, ﬁsh

σA;L ¼ d exp½OWðiÞ f ; (3) length, and capture date. We applied this approach by predicting the most likely age for each fish in the reference where i represents fish1,..., n in the reference sample; a and b sample, although in practice this would be applied to a parameters describe the exponential rate at which otolith weight different sample. For example, the model would typically be increases relative to fish length (mg/mm); c and y-intercept para- applied to a data set based on reader age estimates for QA/QC meters describe the age component in otolith accretion rate checks or a random unaged sample representative of the (mg/year); T is the annual cumulative proportion of temperature reference sample if used as an age-subsampling method. For fi for the capture date associated with fish i;andd and f are para- each sh, we used the length measurement to calculate the meters for the exponential or other relationship used to describe amount of otolith weight arising from the somatic growth the SD of log(OW). Our overall model of otolith weight is component; we then added the age component of otolith weight that would be predicted over the range of potential ages (a + decimal age, . . ., A + decimal age). Thus, for each OWA;L ¼ Somatic growth component þ Age component fish i, we have a vector of expected OW(a + decimal age, . . ., A + þ σ ; : A L decimal age). Using equation (5), the most likely age is the age (4) that maximizes the density function. The resulting vector of density function values from a + decimal age, . . ., A + decimal Otolith weight for fish of a given age and length is described age can subsequently be transformed into probabilities (P), by the density function g(OW; ϴA,L) for some unknown vector where the probability that each fish is age a is of parameters ϴA,L: X a 8 hi9 ¼ ; μ ; σ ; = ; μ ; σ ; : 2 Pa ga OW A;L A L A g OW A;L A L <> ðÞμ => 1 loge OW A;L g OW; μ ; σ ; ¼ pffiffiffiffiffi exp ; A;L A L > σ2 > Evaluation of age predictions.—The magnitude of σ OW 2πσA;L : 2 A;L ; A,L influences the probability distribution for age determinations; (5) for example, as error increases, the probabilities are spread out across a greater number of age-classes. We illustrated this by where μA,L = loge(OWA,L). predicting the age probabilities for simulated data 782 HANSON AND STAFFORD representative of our reference sample. Accordingly, we Marquette (SM). Older fish (age ≥ 14 years) were primarily generated mean length-at-age data from a von Bertalanffy LO strain (67.4%). Mean size at stocking, reported as an function fitted to the reference data set, and with the average value for fish recovered from each age-class, parameters from our best predictive model, we generated an increased by about 40 mm for more recently stocked Lake expected otolith weight for fish of an average size over a select Trout (early 2000s) compared to those stocked in the late range of age-classes (ages = 3, 7, 12, and 19, although we 1980s. These data, along with the number of recoveries (by added 0.5 year to each age-class, which represents a July 1 age-class) for each capture location, strain, and capture sea- capture date). We evaluated the density function g son, are reported in Table 1. ; μ ; σ (OW A;L A;L) over a range of potential ages between 0.5 and 25.5 years, and we plotted the spread among age Otolith Weight Empirical Findings assignment probabilities for our previously modeled There was no significant difference in the weight of left and magnitude of σA,L. Finally, for our predicted ages of each right otoliths (paired t-test, t = 0.87, df = 1,906, p = 0.38), and the fish in the reference sample, we generated histogram plots of average absolute difference between left and right otoliths was the age residuals (known age minus predicted age) to assess 8.2% (SD = 7.7%) of the lightest otolith. By age-class, correla- overall bias. We evaluated our model error estimates by tions between otolith weight and fish length were relatively high comparing the proportion of reference sample fish that were (r ≥ 0.71) among fish younger than age 7, but correlations aged correctly to the age assignment probabilities of the generally dropped below 0.5 by age 11. Otolith weight was simulated average-sized fish within each age-class. approximately linear with respect to age and was exponentially Assessment of temporal, spatial, or other biological biases related to fish length. Accordingly, we used the linear and expo- of age predictions.—Fish within our reference sample differed nential regression coefficients as starting values to find the best temporally (season and capture year), spatially (capture and parameter estimates for modeling otolith weight as a combina- stocking locations and NFH origin), and biologically (strain, tion of the somatic growth component and age components. sex, and mean size at stocking). These sources of variation may influence otolith accretion and cause bias within predicted ages Model of Accretion in Otolith Weight relative to these factors. Knowledge of these biases would be Model 1 (our base model) assumed that accretion in otolith useful in defining appropriate temporal and spatial scales for weight was solely a function of age, that otolith growth occurred at modeling otolith accretion. We assessed factor bias using a constant rate throughout the year, and that error was constant regression trees with the age residuals as the dependent over all observed values of otolith weight. Model 2 was similar variable. Regression trees use recursive partitioning to split the except that we used the cumulative proportional temperature T that data into nodes (minimum group size ≥ 10) based on the ability of diminished age-related otolith accretion when water temperatures factors to account for variation in the dependent variable. We were low (e.g., fish sampled in the spring); this decreased AICc by generated 1,000 regression trees and pruned the final tree by 113.1 units relative to the base model, and thus T was used for the using tenfold cross validation of the data. The number of splits remaining models. The third candidate model (model 3) estimated retained by the best tree was the number that minimized cross- both age and somatic growth components, resulting in a decrease validation prediction error (Brieman et al. 1984). Regression in AICc by 807.0 units. The last two candidate models (models 4 trees were fitted by using R version 3.2.5 (R Core Team 2015) and 5) assumed that error increased with otolith weight and was and the “rpart” package (Therneau and Atkinson 2010). best fitted with an exponential function (model 5), further reducing AICc by 15.9 units relative to model 3. In model 2, otolith accretion was solely a function of age, and the annual age-related RESULTS accretion rate (i.e., the c parameter) was 2.07 mg/year compared Fish Capture and Hatchery Information with 1.16 mg/year in model 5, where about 50% of the otolith Spring and fall survey effort varied among years and weight in younger fish was explained by the somatic growth among locations, and the number of recoveries was influ- component; as fish approached asymptotic size, otolith weight enced by both survey effort and numbers of coded-wire- continued to increase due to the age-related component tagged Lake Trout stocked in each location. In total, 2,081 (Table 2). Importantly, the increase in otolith weight from somatic known-age Lake Trout representing age-classes between 3 growth in model 5 was in accordance with the patterns within age- and 19 were recaptured during 2006–2008, with 65% of all classes, albeit at lower magnitudes due to the separation of the age recoveries involving fish that were stocked at and recovered effects that contributed about 50% to total predictions of otolith from the same location. The number of fish recovered each weight. Age inferences from pooled ages, akin to Pawson (1990), year was 855 in 2006; 611 in 2007; and 655 in 2008. The projected a steeper rate of increase (Figure 2). Bias was particu- primary strains (GL, LL, and SL) accounted for 89% of all larly evident among older age-classes; for example, all fish with recoveries, while 9% were Lake Ontario (LO) strain and less otolith weights above the pooled curve in Figure 2 would be than 2% were Jenny Lake (JD) strain or the following Lake interpreted as slower growing, but the age-specific curves clearly Superior strains: Apostle Islands (SA), Isle Royale (SI), and show that some of these fish are fast for their age (larger than MODELING OTOLITH WEIGHT 783

TABLE 1. Characteristics of the Lake Trout reference sample data by age-class, including the total number of recoveries (n) and the average calculated mean fish TL at stocking. Numbers of recoveries for each survey season, hatchery strain (see Methods for definition of strain abbreviations), and recovery location (see Figure 1 for locations; SR = Southern Refuge) are also presented.

Survey season Strain Recovery location Age-class n Mean TL at stocking (mm) Fall Spring GL LL SL Other IL SR WM3 WM5 3 10 180 0 10 10 0 0 0 9 1 0 0 4 60 176 24 36 48 1 7 4 37 18 5 0 5 244 175 92 152 201 0 39 4 112 95 11 26 6 334 173 148 186 257 21 46 10 176 107 21 30 7 377 170 237 140 249 64 61 3 144 73 59 101 8 254 171 200 54 157 46 50 1 113 33 47 61 9 175 169 137 38 94 31 50 0 71 38 27 39 10 112 165 85 27 25 42 44 1 35 31 43 3 11 84 161 76 8 14 37 33 0 25 19 37 3 12 85 159 71 14 14 22 48 1 26 29 22 8 13 67 159 60 7 12 11 43 1 29 27 10 1 14 55 154 36 19 9 0 13 33 23 24 0 8 15 65 144 54 11 10 9 0 46 30 28 1 6 16 87 144 81 6 3 19 0 65 41 32 0 14 17 53 141 50 3 0 9 0 44 25 18 2 8 18 12 139 11 1 0309550 2 19 7 142 6 1 0 0 0 7 4 3 0 0 Total 2,081 1,368 713 1,103 315 434 229 905 581 285 310

average body length), whereas others are comparatively slow for was minimized at an older age (additional years of age-related their age (smaller than average body length). otolith accretion in the predicted value). Slight curvilinear trends were apparent in the otolith weight residuals from Age Assignment model 2, where predictions for the lightest and heaviest Predicted and observed values of otolith weight for model 2 otoliths generally were biased low, and consequently the pre- (age component only) and model 5 (age and growth compo- dicted ages tended to be overestimated. In contrast, the addi- nents) are shown in Figure 3. Model underestimation of otolith tion of temperature and length data in model 5 produced weight resulted in a predicted age that was biased high when evenly distributed residuals of otolith weight that were closer ; μ ; σ 2 evaluating the density function g(OW A;L A;L) over the to the observed otolith weight values (r = 0.88 in model 5 range of potential ages. This occurred because the most likely versus 0.83 in model 2). However, even in model 5, the age was generally the age that minimized the difference predicted values of otolith weight were imprecise, especially between predicted and observed otolith weights; therefore, a for otoliths larger than 20 mg, where the mean absolute positive otolith weight residual (observed minus predicted) residual was nearly 3 mg.

TABLE 2. Description of otolith weight models for Lake Trout, summarizing whether age or length data were used, inclusion of the cumulative temperature term T, model error specification, negative log likelihood (NegLL), values of Akaike’s information criterion corrected for small sample size (AICc; ΔAICc = difference in AICc value relative to that of the best-performing model), and modeled parameters (a and b = exponential function parameters for the somatic growth component of otolith accretion; c and y = linear parameters for the age component; d and f = parameters used to estimate error arising from either constant error or error fitted with power and exponential functions of otolith weight).

Model Model data used T used? Error specification NegLL AICc ΔAICc abcydf 1 Age only No Constant 5,098.8 10,203.6 0.0 na na 2.11 –0.50 0.16 na 2 Age only Yes Constant 5,042.2 10,090.5 –113.1 na na 2.07 0.04 0.15 na 3 Age and fish length Yes Constant 4,636.7 9,283.5 –807.0 0.616 0.0038 1.19 –0.51 0.13 na 4 Age and fish length Yes Power 4,631.0 9,274.0 –9.5 0.585 0.0038 1.17 –0.36 0.08 0.140 5 Age and fish length Yes Exponential 4,627.8 9,267.6 –6.4 0.616 0.0038 1.16 –0.39 0.11 0.009 784 HANSON AND STAFFORD

seemingly low rate of correct age assignment resulted from Pooled ages the substantive age-class overlap in otolith weight at a given Model−predicted OW at a given length fish length (evident in Figure 2 even among age-classes sepa- Age 4 rated by 4-year intervals) and was reflected by the relatively Age 8 σ Age 12 high values of estimated in model 5. This underlying error Age 16 distribution defines the shape of the probability curves when predicting age from otolith weight and fish length measurements. For a simulated fish representing an average size at age from the reference sample, the ϴA,L from model 5 returned a 70% probability of correctly assigning age for a fish 3.5 years

Otolith weight (mg) Otolith weight of age; however, by age 19.5, this probability dropped to 10%, with similar probabilities assigned to adjacent year-classes (Figure 5). Returning to our reference-sample age predictions, the proportion of ﬁsh within each year-class that were correctly aged (60% for age-3 ﬁsh; roughly 10% among the

0 102030405060 oldest age-classes) was in close agreement with the probabilities we generated for the simulated average-sized ﬁsh 400 500 600 700 800 900 (Figure 5). Fish length (mm)

FIGURE 2. Exponential relationship between otolith weight (OW) and fish Temporal, Spatial, and Other Biological Biases in Age TL for pooled ages of Lake Trout, lines fitting the exponential relationship Predictions between OW and TL for selected age-classes, and the somatic growth com- Minimized cross-validation errors indicated that one split ponent of OW as a function of fish TL from model 5. was optimal for 5.8% of all regression trees, two splits were optimal for 86.7% of trees, and four or more splits were Predicted ages for each fish in the reference sample based fi ϴ optimal for 7.5% of trees. We pruned the nal tree to two on the A,L from model 5 resulted in age residuals that were splits that, in total, explained 4.5% of the variation, thereby fairly symmetrical about zero, with an overall correct assign- fi indicating that random or other unknown sources of variability ment rate of 23.4% (486 of 2,081 sh; Figure 4). Our were the primary underlying cause for the lack of precision in age predictions from model 5. The first split explained 3.2% of Model 2 the variation in age residuals by separating the age residuals 60 into two strain groupings: the first group contained the JL, LL, 50 LO, SA, and SL strains (hereafter, “SL strain grouping”), with 40 a mean age residual of –0.69 year; and the second group 30 included the GL, SI, and SM strains, with a mean age residual of 0.14 year (Figure 6). The next split explained an additional 20 1.2% of the variation by segregating the GL, SI, and SM strain 10 ≥ OW = 0.94 * Predicted OW + 1.29, R^2 = 0.83 grouping based on a mean stocking size of 170 mm (i.e., 0 average age residual was –0.03 year for fish stocked at a larger Model 5 size versus 0.84 year for fish stocked at a smaller size); here- 60 after, these groupings are referred to as GL-large and GL- 50 small groups. For the three groupings identified within the 40 regression tree, otolith weight residuals were normally distributed for the GL-large group but were positive for the SL strain

Observed otolith weight (mg) 30 grouping and negative for ﬁsh larger than about 750 mm in the 20 GL-small group (Figure 7). Most of the other factors were 10 involved in surrogate splits, such as factors that were retained 0 OW = 1.02 * Predicted OW − 0.01, R^2 = 0.88 in the best model but did not result in additional splits where 0102030405060cross-validation error was minimized. Variable importance Predicted otolith weight (mg) values (scaled to sum to 100) for the best tree were 33 for strain, 32 for mean size at stocking, 14 for stocking location, 9 FIGURE 3. Observed versus predicted otolith weights (OWs) for Lake Trout for NFH, 8 for recovery location, and 5 for season, whereas based on model 2 (in which otolith accretion was solely a function of age) ﬁ compared to model 5 (best model; in which accretion was dependent on age recovery year and sex were not used in the nal tree. Although and somatic growth). The black line represents the observed OW regressed on stocking and recovery locations contributed to variable impor- predicted values; the gray line represents a slope of 1.0 through the origin. tance, the only location with median age residuals that differed MODELING OTOLITH WEIGHT 785

All age−classes Age−class = 3 Age−class = 4 Age−class = 5 Age−class = 6 Age−class = 7 500 6 100 100 25 80 400 5 80 20 80 4 60 300 60 60 3 15 200 40 40 40 2 10 100 1 5 20 20 20 0 0 0 0 0 0

−10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10

Age−class = 8 Age−class = 9 Age−class = 10 Age−class = 11 Age−class = 12 Age−class = 13 15 40 20 12 8 30 10 30 15 10 8 6 20 20 10 6 4 5 4 10 2 10 5 2

Frequency 0 0 0 0 0 0

−10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10

Age−class = 14 Age−class = 15 Age−class = 16 Age−class = 17 Age−class = 18 Age−class = 19 10 10 14 7 2.0 2.0 8 8 12 6 10 5 1.5 1.5 6 6 8 4 1.0 1.0 4 4 6 3 4 2 0.5 0.5 2 2 2 1 0 0 0 0 0.0 0.0

−10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10 −10 0 10 Age residual in years

FIGURE 4. Frequency histograms of age residuals (known age minus predicted age) for all Lake Trout in the reference set and for each known age-class.

from zero was WM3 (median = –1.0 year for both factors). been modest given the magnitude of random and/or unex- Because only LL-strain fish were stocked in WM3 and the LL plained error. Our age estimates employed length-based cor- strain comprised 79% of the recoveries from that location, the rections to otolith weight without constraining length to the retention of stocking and recovery location factors in the final observed age-specific patterns. A technical weakness of this tree was likely due to the unbalanced nature of stocking and indirect approach is that age estimates may be inconsistent fish recoveries across locations. Terminal nodes were not with the empirical length-at-age distributions. For example, associated with stocking or recovery locations, as the variation among the age-5 fish in our study, a small proportion were explained by these factors was already identified by the strain estimated to be younger than age 3 (i.e., age residuals of 2–3 grouping split. There were no differences between recoveries years; Figure 4), but the lengths of 3- and 5-year-old fish in stocked by Iron River NFH (Iron River, Wisconsin) or Jordan our empirical data did not overlap (Figure 8, top panel). River NFH (Elmira, Michigan), but fish stocked by Pendills Creek NFH (Brimley, Michigan) exhibited positive age residuals (median = 2.0 years), although these fish comprised DISCUSSION 0.005% of the reference sample and all were SM strain recov- Brander (1974) speculated that better age-predictive relation- ered as old fish (1990 and 1991 year-classes). Season was low ships could be attained with dual measurements of otolith weight in terms of variable importance; however, variation in age and fish length. However, until now, there has not been an explicit residuals was higher among fall-caught fish due to their model that incorporates length measurements within an age-spe- older average age. cific context. Our otolith accretion model does so by simulta- Length-at-age, otolith weight-at-length, and otolith weight- neously estimating the mean increase in otolith weight relative to at-age data for the three groupings are shown in Figure 8. both fish length and age, and this method produced evenly dis- Group differences can be identified from otolith weight versus tributed age residuals for our aggregate data set. Correlations fish length without knowledge of age. If we had restricted our between otolith weight and fish length are generally strong, at analyses to group(s) with similar growth patterns, we could least among younger age-classes (Secor and Dean 1989;Pawson have obtained more precise estimates of ϴ and age, although 1990); therefore, our model uses the TSR principles associated we acknowledge that for our data, any such gain would have with fish length to obtain more accurate predictions of otolith 786 HANSON AND STAFFORD

Proportion of reference sample correctly aged −0.24 A = 3.5, L = 385 A = 7.5, L = 659 n=2081 A = 12.5, L = 778 A = 19.5, L = 820 Strain = JL,LL,LO,SA,SL

Strain = GL,SI,SM 0.14 n=1125

Size_at_stocking >= 170

Size_at_stocking < 170

−0.69 −0.032 0.84 Probability of fish age given measures of OW and L measures of OW Probability of fish age given 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 n=956 n=906 n=219 0 5 10 15 20 25

Range of fish ages evaluated in g(X,θ(A,L))

FIGURE 5. Vector of probability assignments for expected otolith weight (OW) from select young and old age-classes of Lake Trout (A = age, years; L = TL, mm). Probabilities represent g(OW; ϴA,L) (described in Methods) evaluated across potential age-classes of 0–25 years. The proportions of correctly aged reference sample ﬁsh in each age-class are denoted by black circles. weight compared to the univariate linear calibration method. More importantly, ages that are predicted from otolith weight alone are Age residual likely to be biased, as there is no mechanism to account for the effect of varied somatic growth on otolith accretion (Casselman

1990). This may help explain the previously reported biases −10 −5 0 5 10 encountered when using univariate otolith weight versus age rela- fi tionships in tropical damselfishes Pomacentrus spp. (Worthington FIGURE 6. Regression tree tted to age residuals for Lake Trout, with explanatory factors scaled to relative importance value (sum = 100): strain et al. 1995), the Argentine Straptail (Patagonian Grenadier) (importance = 33; see Methods for definition of strain abbreviations); mean Macruronus magellanicus (Pino et al. 2004), and the Leopard size (TL, mm) at stocking (importance = 32); and model-retained, nonsplitting Coralgrouper Plectropomus leopardus (Lou et al. 2005). factors of stocking location (importance = 14), national fish hatchery (impor- For Lake Trout in our study, substantive overlap in otolith tance = 9), recovery location (importance = 8), and season (importance = 5). weight and fish length measurements—exacerbated by the vateritic Box plots of the age residuals are shown for each terminal node. Box dimen- — sions represent interquartile ranges, the thick black line in each box represents nature of the otoliths and our heterogeneous sample further lim- the median, whiskers represent 1.5× the interquartile range, and open circles ited the age-predictive power of our approach. Our highest age- indicate outliers. prediction accuracy was observed for the youngest year-classes, as has been reported by others using otolith weight. Dub et al. (2013) reported 95% accuracy for Yellow Perch Perca flavescens up to effective alternative to otolith aging. Lepak et al. (2012)employed age 2, and an accuracy rate of 97% was obtained for yearling random forest methods, where otolith weight and fish length Haddock Melanogrammus aeglefinus (Cardinale and Arrenhius enabled correct age predictions in 90% of kokanee 2004), but the accuracy of age predictions rapidly declined with Oncorhynchus nerka between age 1 and age 4. This approach age in both of those studies. Low precision among older ages is was also used for long-lived deepwater snappers (Lutjanidae), apparently common, as substantive overlap was also reported for with otolith weight and otolith thickness (but not fish length) tropical damselfishes (Worthington et al. 1995), the Hollowsnout identified as the most important variables. Snapper age composi- Grenadier Coelorinchus caelorhincus (Labropoulou and tions and estimates of fishing mortality were not different than Papaconstantinou 2000), and the Sky Emperor Lethrinus mahsena those derived from sectioned otoliths (Williams et al. 2015). (Pilling et al. 2003). However, more recent works have success- Furthermore, similar mortality rates were also obtained for the fully used otolith weight with a suite of other variables as a cost- Sand Whiting Sillago ciliata and Yellowfin Bream MODELING OTOLITH WEIGHT 787

of fish length was greater among fish in the SL strain grouping. When multiple strains are present, they are often uniden- tified and thus grouped in standard stock assessments. In such cases, it would not be practical to model otolith accretion separately for each strain. Therefore, variation associated with the strain variable led to elevated model error (σ) in our study. However, in other species or populations, variability in otolith growth characteristics may arise from other sources of variation (e.g., sex or sampling location); in such cases, it may be preferable to model otolith accretion separately within each group to obtain the most precise age-predictive relationship. Recognizably, these data-restrictive approaches entail additional aging of reference samples for each age-predictive SL,LL,LO strain relationship. Observed − predicted otolith weight (mg) Observed − predicted otolith weight GL,SI, SM strain >= 170 mm length−at−stocking Age-predictive relationships are less precise when they GL, SI, SM strain < 170 mm length−at−stocking are applied to fish sampled throughout the year due to −15 −10 −5 0 5 10 15 continued growth during the sampling interval (Doering- 300 400 500 600 700 800 900 1000 Arjes et al. 2008). Therefore, standard practice when using fi Fish length (mm) sh measurements for age predictions is to pool data across monthly or seasonal capture dates in ALKs (Fridriksson FIGURE 7. Otolith weight residuals (observed minus predicted) from model 1934) and modal analyses (Fletcher 1995; Araya et al. 5 for each of the three Lake Trout groups identified in the regression tree 2001). Our model is not limited by this restriction because fi (Figure 6; see Methods for de nition of strain abbreviations). the somatic growth component of otolith accretion is independent of time and because the age-predictive relationship Acanthopagrus australis with ages either obtained from ALKs or is applied to the actual capture date of each fish. However, estimated from generalized linear models with fish length, location, otolith accretion is regulated through metabolic processes, otolith weight, and sex as predictor variables (Ochwada et al. and therefore it may be advantageous to address the rela-

2008). Clearly, the degree to which otolith weight and length tionship between temperature and otolith growth. Fey (2006) measurements are informative of fish age varies widely across used multiple regression models to predict otolith mass from species, and it will be necessary to employ a cost–benefitanalysis age, temperature, and average somatic growth rate in to assess whether an age-predictive relationship can sufficiently Atlantic Herring Clupea harengus and European Smelt address management objectives (Francis and Campana 2004). Osmerus eperlanus. He reported that elevated temperatures A separation index can be used as a cursory method to elicited a species-specific response. For European Smelt, age evaluate the expected precision of predicted ages derived from and somatic growth were equally important predictors of our otolith accretion model. This index describes how well otolith weight, whereas temperature, though significant, otolith weight and length measurements predict age by discrimi- was negligible in comparison. In contrast, the temperature nating normal distributions—each representing a cohort of fish— effect was much more pronounced in Atlantic Herring, as from the overall size–frequency distribution (Bhattacharya 1967); elevated temperatures weakened the otolith weight–fish see Francis and Campana (2004) for details on extending this to length relationship, presumably because higher metabolism the use of bivariate predictors. Separation values less than 2 led to greater otolith growth rates that were outside the indicate substantial overlap between age-classes and imply a temperature limits for optimal somatic growth (Mosegaard low degree of precision within the estimated ages (Sparre et al. et al. 1988). In waters that exhibit thermal stratification, we 1989). For our Lake Trout, separation indices were less than 1.4 anticipate temperature effects on otolith growth to be mod- among all adjacent age-classes of fall-caught fish(S.D.Hanson, erated, given the affinity for fish to seek preferred thermal unpublished data), but our otolith accretion model should enable habitat. Our use of mean cumulative proportional surface more precise age estimates in a species such as Atlantic Cod temperature over a 22-year period to scale the temperature Gadus morhua, for which bivariate separation indices exceeded effects on the age-related component of accretion appears 3.6 for adjacent age-classes (Francis and Campana 2004). reasonable, as capture season had a minor influence on The precision of age estimates within our otolith accretion predicted age residuals; however, a better approximation model is dependent on the information contained within fish would be based on temperatures within the fish’s environ- measurements but also on the degree of population-level var- ment (e.g., thermal tagging data). iation in otolith growth characteristics. For the Lake Trout data For many species, including the hatchery Lake Trout in the in our study, otolith weight plotted against fish length clearly present study, there may be too much overlap in otolith weight showed that the mean increase in otolith weight per millimeter and fish length among age-classes to derive precise estimates 788 HANSON AND STAFFORD

of individual fish age by using only these metrics. Nevertheless, we assert that our model may lend a QA/QC biological validation to reader age estimates without the need for multiple readings, but it is predicated on first fitting a model of otolith accretion to a high-quality reference sample for the population(s) of interest. Otolith accretion can then be modeled from the reader age estimates for new samples from the population of interest, with three possible outcomes: (1) the model cannot be fitted to the reader age estimates; (2) the model estimates otolith accretion as positive components of age and somatic growth, and the results are consistent with the reference sample model results; or (3) the model estimates accretion as in outcome 2, but the results are inconsistent with the reference sample results. Biological validation of reader ages is inferred when model results are consistent with those of the reference sample. Alternatively, we place lower con- fidence in reader ages that do not support the existence of TSR properties or generate substantially different model parameters from the reference sample. In such cases, low precision among reader ages will likely increase model error (σ), while systematic aging bias will primarily be evident from deviations in the y-intercept term or in the slope of the age-related accretion rate (c); alternatively, the reader ages may be accurate, but the fish measurements do not exhibit TSR properties. Because TSR properties are especially informative among younger age-classes, use of the model as an independent corroborator of reader age estimates can be particularly well suited to

identify likely age misclassifications associated with false annuli, which are prominent among juvenile life stages of many species. We advocate this as a QA/QC procedure that is complementary to other published methods. We foresee this is as a plausible use of our model in the near term, at least until (1) relationships among otolith weight, fish length, and age are reported in a standardized manner; and (2) the resulting age inferences are evaluated within a cost–benefit analysis to assess the model’s potential as an age-subsampling method. Several age-subsampling methods, including regression (Boehlert 1985), linear calibration (Worthington et al. 1995), discriminant analysis (Fletcher and Blight 1996), and random forest (Lepak et al. 2012), have all incorporated otolith weight measurements to estimate ages for individual fish. However, stock assessments require age composition data. Subsequent conversion of individual age estimates into age compositions is known to be biased (McLachen and Basford 1988). This bias, termed “discriminant bias” by Francis and Campana (2004), is due to the necessity of a “cutting rule” to assign an age from measurements that overlap one or more age-classes. Like the mixture analysis proposed by Francis and Campana (2004), our otolith accretion model can be used to estimate age compositions directly without assigning an age to each individual fish. Our FIGURE 8. Measurements for the three Lake Trout groupings identified by model uses a two-step procedure wherein we (1) estimate the the regression tree (Figure 6; see Methods for definition of strain abbrevia- age–fish measurement relationship (ϴ) from only the reference tions). The top panel shows TL at age, the middle panel presents otolith sample to ensure that otolith weight versus fish length estimates weight versus fish TL, and the bottom panel depicts otolith weight at age. are fitted for each age-class; and (2) calculate the density function MODELING OTOLITH WEIGHT 789 and age-specific probabilities for the fish measurements in the have been documented in dozens of freshwater and marine fishes. unaged sample. Similar to an ALK, we could readily obtain age Accordingly, we assert that our general modeling approach is compositions by summing the rows (fish) of age probabilities widely applicable for relating otolith accretion to fish length and within each column (age) and dividing by the sum of all prob- age and that the resulting predictions can be used in age assign- abilities. Under this approach, age composition estimates should ment/composition or QA/QC procedures. The strength of the TSR not be affected by discriminant bias. relationships will largely dictate the utility of these efforts. Lastly, Francis and Campana (2004) reviewed other forms of bias we note that a small proportion of our predicted ages were incon- affecting previously published aging methods that incorporated sistent with observed length-at-age data. This issue could be otolith weight. Methods that ignore age-class-specificvariation addressed by adapting our approach to include a separate like- in the age–fish measurement relationship contain a “heterosce- lihood function relating fish length to age. Predicted age could then dastic” bias. Our model is subject to this heteroscedastic bias to be derived from the joint likelihood; however, the trade-off is that the extent that σ differs among age-classes—for example, if fish the model is then subject to the standard spatial and temporal in a particular age-class exhibit otolith weights with a much assumptions of length-at-age data (Westrheim and Ricker 1978). higher or much lower correlation with fish length. Smoothing bias arises when there are differing proportions describing the age-classes within the sample. Due to overlap within the fish ACKNOWLEDGMENTS measurements, estimated age compositions will be under-repre- We thank Pat McKee and Steve Robillard for contributing sented for strong year-classes and vice versa for weak year- Lake Trout otoliths to this study; Jean Adams and Ted Treska classes. However, smoothing bias can be eliminated or reduced for statistical advice; and Chris Francis, Steven Campana, and when the reference sample is randomly created from the unaged Mark Fowler for helpful discussions and code to implement sample; in this manner, the reference sample proportions are their mixture analysis and bivariate separation indices. informative of the proportions in the unaged sample (see Comments by Chris Francis and three anonymous reviewers Francis and Campana 2004). In our model, smoothing bias is substantially improved the content of this paper. The findings ; μ ; σ minimized by taking the product of ga OW A;L A;L times and conclusions in this article are those of the authors and do the proportion of reference sample fish in age-class a.For not necessarily represent the views of the U.S. Fish and example, the age–fish measurement relationship for our data Wildlife Service. would have assigned some proportion of fish to age-classes greater than 20 years, but these older age-classes would not be represented since the oldest fish in our data set were age 19. REFERENCES It remains to be seen whether our model would provide Araya, M., L. A. Cubillos, M. Guzmán, J. Peñailillo, and A. Sepúlveda. 2001. unbiased estimates of age composition, but for our Lake Trout Evidence of a relationship between age and otolith weight in the Chilean σ Jack Mackerel, Trachurus symmetricus murphyi (Nichols). Fisheries data, the exponential increase in wouldtendtoover-represent Research 51:17–26. young age-classes since the age assignment probabilities for Beamish, R., and G. A. McFarlane. 1983. The forgotten requirement for age small otoliths will be spread among fewer potential age-classes validation in fisheries biology. Transactions of the American Fisheries than larger otoliths. The larger issue we encountered was that Society 112:735–743. the age–fish measurement relationships were relatively uninfor- Beamish, R., and G. A. McFarlane. 1995. A discussion of the importance of fi aging errors, and an application to Walleye Pollock: the world’s largest mative of age, especially for older sh in our data set; therefore, fishery. Pages 545–565 in D. H. Secor, J. M. Dean, and S. E. Campana, the age composition estimates would essentially be driven by editors. Recent developments in fish otolith research. University of South the proportions in the representative reference sample. Hence, Carolina Press, Columbia. the value of our model in estimating age compositions requires Bhattacharya, C. G. 1967. A simple method of resolution of a distribution into further exploration in situations where fish measurements are Gaussian components. Biometrics 23:115–135. Boehlert, G. W. 1985. Using objective criteria and multiple regression models more informative of age. for age determination in fishes. U.S. National Marine Fisheries Service In summary, relatively few aging laboratories presently use Fishery Bulletin 83:103–117. otolith weights for QA, for age assignment, or to assist readers in Bowen, C. A., C. R. Bronte, R. L. Argyle, J. V. Adams, and J. E. Johnson. making age determinations. We have addressed several concerns 1999. Vateritic sagitta in wild and stocked Lake Trout: applicability to that may help to broaden these applications. Specifically, we (1) stock origin. Transactions of the American Fisheries Society 128:929–938. Brander, K. 1974. The effects of age-reading errors on the statistical reliability provided a relatively rare account of the temporal, spatial, and of marine fishery modelling. Pages 181–191 in T. B. Bagenal, editor. The biological variation within otolith weight, fish length, and age ageing of fish. Unwin Brothers, Surrey, UK. relationships for fish beyond early juvenile life stages; (2) devel- Breiman, L., J. Friedman, R. Olshen, and C. Stone. 1984. Classification and oped an explicit model to segregate the confounding age and regression trees. Wadsworth, Belmont, California. somatic growth properties that influence otolith weight; and (3) Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference, 2nd edition. Springer, New York. applied a statistical approach to deal with the ambiguity of age Campana, S. E. 1999. Chemistry and composition of fish otoliths: pathways, assignments when otolith weight measurements overlap for two or mechanisms and applications. Marine Ecology Progress Series more age-classes. Templeman–Squires relationship properties 188:263–297. 790 HANSON AND STAFFORD

Campana, S. E. 2001. Accuracy, precision and quality control in age determi- Morales-Nin, B. 2000. Review of the growth regulation processes of otolith nation, including a review of the use and abuse of age validation methods. daily increment formation. Fisheries Research 46:53–67. Journal of Fish Biology 59:197–242. Morison, A. K., J. Burnett, W. J. McCurdy, and E. Moksness. 2005. Quality Cardinale, M., and F. Arrhenius. 2004. Using otolith weight to estimate the issues in the use of otoliths for fish age estimation. Marine and Freshwater age of Haddock (Melanogrammus aeglefinus): a tree model application. Research 56:773–782. Journal of Applied Ichthyology 20:470–475. Mosegaard, H., H. Svedäng, and K. Taberman. 1988. Uncoupling of somatic Casselman, J. M. 1990. Growth and relative size of calcified structures of fish. and otolith growth rates in Arctic Char (Salvelinus alpinus) as an effect of Transactions of the American Fisheries Society 119:673–688. differences in temperature response. Canadian Journal of Fisheries and Chang, W. Y. 1982. A statistical method for evaluating the reproducibility of Aquatic Sciences 45:1514–1524. age determination. Canadian Journal of Fisheries and Aquatic Sciences Ochwada, F. A., J. P. Scandol, and C. A. Gray. 2008. Predicting the age of fish 39:1208–1210. using general and generalized linear models of biometric data: a case Doering-Arjes, P., M. Cardinale, and H. Mosegaard. 2008. Estimating popula- study of two estuarine finfish from New South Wales, Australia. tion age structure using otolith morphometrics: a test with known-age Fisheries Research 90:187–197. Atlantic Cod (Gadus morhua) individuals. Canadian Journal of Fisheries Pawson, M. G. 1990. Using otolith weight to age fish. Journal of Fish Biology and Aquatic Sciences 65:2342–2350. 36:521–531. Dub, J. D., R. A. Redman, D. H. Wahl, and S. J. Czesny. 2013. Utilizing Pilling, G. M., E. M. Grandcourt, and G. P. Kirkwood. 2003. The utility of random forest analysis with otolith mass and total fish length to obtain otolith weight as a predictor of age in the Emperor Lethrinus mahsena and rapid and objective estimates of fish age. Canadian Journal of Fisheries other tropical fish species. Fisheries Research 60:493–506. and Aquatic Sciences 70:1396–1401. Pino, C. A., L. A. Cubillos, M. Araya, and A. Sepúlveda. 2004. Otolith weight Fey, D. P. 2006. The effect of temperature and somatic growth on otolith as an estimator of age in the Patagonian Grenadier, Macruronus magella- growth: the discrepancy between two clupeid species from a similar nicus, in central-south Chile. Fisheries Research 66:145–156. environment. Journal of Fish Biology 69:794–806. R Core Team. 2015. R: a language and environment for statistical computing. Fletcher, W. J. 1991. A test of the relationship between otolith weight and age R Foundation for Statistical Computing, Vienna. Available: https://www. for the Pilchard Sardinops neopilchardus. Canadian Journal of Fisheries R-project.org/. (May 2017). and Aquatic Sciences 48:35–38. Reeves, S. A. 2003. A simulation study of the implications of age-reading Fletcher, W. J. 1995. Application of the otolith weight–age relationship for the errors for stock assessment and management advice. ICES Journal of Pilchard, Sardinops sagax neopilchardus. Canadian Journal of Fisheries Marine Science 60:314–328. and Aquatic Sciences 52:657–664. Reznick, D., E. Lindbeck, and H. Bryga. 1989. Slower growth results in larger Fletcher, W. J., and S. J. Blight. 1996. Validity of using translucent zones of otoliths: an experimental test with Guppies (Poecilia reticulata). Canadian otoliths to age the Pilchard Sardinops sagax neopilchardus from Albany, Journal of Fisheries and Aquatic Sciences 46:108–112. western Australia. Marine and Freshwater Research 47:617–624. Secor, D. H., and J. M. Dean. 1989. Somatic growth effects on the otolith–fish Francis, R. I. C. C., and S. E. Campana. 2004. Inferring age from otolith size relationship in young pond-reared Striped Bass, Morone saxatilis. –

measurements: a review and a new approach. Canadian Journal of Canadian Journal of Fisheries and Aquatic Sciences 46:113 121. Fisheries and Aquatic Sciences 61:1269–1284. Sparre, P., A. Ursin, and S. C. Venema. 1989. Introduction to tropical fish Fridriksson, A. 1934. On the calculation of age-distribution within a stock of stock assessment, part 1: manual. FAO (Food and Agriculture cod by means of relatively few age-determinations as a key to measure- Organization of the United Nations) Fisheries Technical Paper 306. ments on a large scale. Rapports et Procès-Verbaux des Réunions Conseil Templeman, W., and H. J. Squires. 1956. Relationship of otolith lengths Permanent International pour l’Exploration de la Mer 86:1–14. and weights in the Haddock Melanogrammus aeglefinus (L.) to the rate Gauldie, R. W., and D. G. A. Nelson. 1990. Otolith growth in fishes. of growth of the fish. Journal of the Fisheries Board of Canada Comparative Biochemistry and Physiology Part A: Physiology 13:467–487. 97:119–135. Therneau, T. M., and B. Atkinson. 2010. rpart: Recursive partitioning. R Hamel, M. J., J. J. Spurgeon, C. J. Chizinski, K. D. Steffensen, and M. A. package version 3.1-46. R Foundation for Statistical Computing, Vienna. Pegg. 2016. Variability in age estimation results in ambiguity and false Available: http://www.r-project.org/. (April 2017). understanding of population persistence. North American Journal of Tomas, J., and A. J. Geffen. 2003. Morphometry and composition of aragonite Fisheries Management 36:514–522. and vaterite otoliths of deformed laboratory reared juvenile herring from Holey, M. E., R. W. Rybicki, G. W. Eck, E. H. Brown, J. E. Marsden, D. S. two populations. Journal of Fish Biology 63:1383–1401. Lavis, M. L. Toneys, T. N. Trudeau, and R. M. Horrall. 1995. Progress Westrheim, S. J., and W. E. Ricker. 1978. Bias in using an age–length key to toward Lake Trout restoration in Lake Michigan. Journal of Great Lakes estimate age-frequency distributions. Journal of the Fisheries Research Research 21(Supplement 1):128–151. Board of Canada 35:184–189. Koenigs, R. P., R. M. Bruch, and K. K. Kamke. 2013. Impacts of aging error Williams, A. J., S. J. Newman, C. B. Wakefield, M. Bunel, T. Halafihi, J. on Walleye management in the Winnebago system. North American Kaltavara, and S. J. Nicol. 2015. Evaluating the performance of otolith Journal of Fisheries Management 33:900–908. morphometrics in deriving age compositions and mortality rates for Labropoulou, M., and C. Papaconstantinou. 2000. Comparison of otolith assessment of data-poor tropical fisheries. ICES Journal of Marine growth and somatic growth in two macrourid fishes. Fisheries Research Science 72:2098–2109. 46:177–188. Worthington, D. G., A. J. Fowler, and P. J. Doherty. 1995. Variation in Lepak, J. M., C. N. Cathcart, and M. B. Hooten. 2012. Otolith mass as a the relationship between otolith weight and age: implications for the predictor of age in kokanee salmon (Oncorhynchus nerka) from four estimation of two tropical damselfish (Pomacentrus moluccesis and Colorado reservoirs. Canadian Journal of Fisheries and Aquatic Sciences P. wardi). Canadian Journal of Fisheries and Aquatic Sciences 69:1569–1575. 52:233–242. Lou, D. C., B. D. Mapstone, G. R. Russ, C. R. Davies, and G. A. Begg. 2005. Using Yule, D. L., J. D. Stockwell, J. A. Black, K. I. Cullis, G. A. Cholwek, and J. T. otolith weight–age relationships to predict age-based metrics of coral reef fish Myers. 2008. How systematic age underestimation can impede under- populations at different spatial scales. Fisheries Research 71:279–294. standing of fish population dynamics: lessons learned from a Lake McLachlan, G. J., and K. E. Basford. 1988. Mixture models: inference and Superior Cisco stock. Transactions of the American Fisheries Society applications to clustering. Marcel Dekker, New York. 137:481–495.