SC/F14/J11

A statistical model for quantifying age-reading errors
and its application to the Antarctic minke whales
TOSHIHIDE KITAKADO1, CHRISTINA LOCKYER2 AND ANDRÉ E. PUNT3
Contact email: kitakado@kaiyodai.ac.jp
ABSTRACTA statistical method for quantifying age-reading error, i.e. the extent of bias and inter-reader
variability among readers, is introduced. The method assumes the availability of an
independent control reader who produces reference ages for ageing structures which are also
read by the subject readers. This reader is assumed to provide unbiased age estimates. Linear
structures in bias and variance are incorporated in a conditional probability matrix
representing the stochastic nature of age-determination for each reader. A joint likelihood
function for the parameters related to ageing bias, variance and nuisance parameters isdefined based on observed ageing outcomes from both the control and subject readers. The
method is applied to data for Antarctic minke whales taken during Japanese commercial(1971/72-1985/86) and scientific (1986/87-2004/05) whaling. 250 earplugs selectedaccording to a predetermined protocol were used in the analyses to estimate the inter-reader
variation for four Japanese readers. One of the authors acted the control reader. The Japanesereaders and the control reader differed in terms of both the expected age given the true age,and variance in age-estimates. The expected age and random uncertainty in age-estimatesdiffered among the Japanese readers, although the two readers in charge of age-reading forsamples taken during Japanese scientific whaling (JARPA I and JARPA II) provided quite
similar ageing outcomes. These results contribute to analyses using catch-at-age data for thisspecies. It should also be noted that the model and approach in this paper can be applied topopulations other than the Antarctic minke whales, if a control reader is available, evenretrospectively.

KEYWORDS: ANTARCTIC MINKE WHALES; AGE-READING ERROR; EARPLUGS;INTRODUCTION
The primary source of information on the abundance of many cetacean populations is estimates ofabundance from sightings surveys (e.g. Branch, 2007) and from mark-recapture studies (e.g. Larsen andHammond, 2006). This information allows an evaluation of recent (up to the last 20-30 years) trends inabundance when a time-series of comparable estimates is available. However, inferences regarding the statusof populations relative to management reference points are more precise if estimates of abundance andinformation from other data sources are used to fit population dynamics models. Although a variety of typesof population models has been applied to cetacean populations, most of those presented to the IWC
Scientific Committee have been age- and sex-structured.
Population dynamics models have been proposed as one way to test the hypothesis that the abundanceof Antarctic minke whales (Balaenoptera bonaerensis) increased in abundance prior to the start of directed
harvesting during the early 1970s, perhaps due to the ‘krill surplus’ which has been postulated to have arisen
because of the substantial declines of species such as blue, fin and sei whales (e.g. Mori and Butterworth,1Tokyo University of Marine Science and Technology, 5-7, Konan 4, Minato-ku, Tokyo 108-8477, Japan.
The North Atlantic Marine Mammal Commission, P.O. Box 6453 Tromsø, N-9294, Norway.
3
School of Aquatic and Fisheries Sciences, University of Washington, Seattle, WA 98195-5020.
2

2006). The output from these models can also provide the information needed to assess the impact ofenvironmental factors on, for example, reproductive success, as is common in fisheries assessments (e.g.
Maunder and Watters, 2003, but see Haltuch and Punt, 2011).
Age-structured assessment models can be divided into two major ‘classes’: Virtual Population Analysis(VPA), and ‘integrated’ methods. VPA methods assume that the catch age-composition is measured withnegligible error compared to that associated with the remaining data sources such as estimates of abundancefrom sightings surveys, while ‘integrated’ methods allow for sampling and other sources of error with theage-composition data, albeit at the expense of greater complexity. Both of these classes of model have been
applied to data for Antarctic minke whales (e.g. Mori et al., 2007; Mori and Butterworth, 2008; Punt andPolacheck (2005, 2006, 2007, 2008)), and both suggest an increase in abundance from ~1930 to ~1970.
However, Punt and Polacheck (2005) found that there were substantial differences between growth curves
estimated internally to the ‘integrated’ model based on the length and age data collected from the commercial
catches or externally using JARPA data. Several possible explanations for this result have been explored,
including time-varying growth and time-varying fishery selectivity. However, one key possible reason for thisdiscrepancy is age-reading error.
Age-reading error can be divided into age-reading bias (i.e. the expected age assigned to ageing structures,in this case, ear plugs, for animals of a given age, differ from the actual age) and random age-reading error (i.e.
variation about the expected age for a given ageing structure). Both of these types of error can be consequential
for assessments based on population models. For example, Reeves (2003) found that random age-reading error
led to ‘smoothing’ of recruitment estimates (i.e. large year-classes ‘smoothed’ to adjacent, less abundant,
year-classes). More, importantly perhaps, a ‘drift’ of ageing methods could have led population models toestimate spurious trends in recruitment for the Antarctic minke whales (Butterworth and Punt, 2009).
The impact of age-reading error can be included in assessments by specifying a matrix which defines
the conditional probability of an animal of true age a being aged to be that age or some other age, a ' ,P(a ' | a) . The model-predictions upon which the likelihood component in the assessment for the agecomposition data is based are then a function of the model-estimate for the observed catch of animals of age
a after accounting for age-reading error. Given P(a ' | a) , this prediction would be:

Ca '   P(a ' | a)Ca(1)awhere Ca is the model-estimate of the catch of animals of age a, and Ca ' is the model-estimate of the catchof animals of (perceived) age a ' after accounting for age-reading error. Therefore, it is crucial for the
analyses which use catch-at-age data to have information on P(a ' | a) for each age reader.
This paper introduces a method for quantifying age-reading errors. It was applied to data from an agereading experiment conducted for the Antarctic minke whales. The experiment involved one reader(Lockyer) reading 250 ear plugs using a protocol designed by the Scientific Committee of the IWC(Butterworth and Punt, 2009) and comparing the resulting age-estimates with values obtained from past andcurrent age readings by Japanese scientists.
METHODS
The age-reading experiment2

The experiment involved reading 250 ear plugs from female minke whales caught in Antarctic Area IV(Table 1). The plugs were chosen from five groups of years (50 from each group), corresponding to periods
near the start and the end of commercial whaling, and the start, middle and end of JARPA sampling (1974/51976/7, 1982/3-1984/5, 1989/90-1991/2, 1997/8-1999/2000 and 2003/4-2005/6; referred to as Periods I-V
respectively). For this random selection, all the female plugs for the period concerned were allocated asequential number starting at 1 and culminating at N. A random number was then drawn randomly from [1,N] and that plug selected, unless it was seen to be damaged or to have deteriorated in quality, in which caseanother random draw was made. The length of the whale, previous age readings, and the names of theoriginal age readers (Kato, Masaki or Zenitani) were recorded for the selected whale. In addition to thesethree readers, a new reader (Bando) who aged all of the samples taken during JARPAII so far (2005/062010/11) also read 100 recent samples three times so that his reading outcomes could be standardized
against the others.
One of us (Lockyer) read all of the plugs twice, with randomized sample order both initially and after
each complete set of readings. Fifty of the plugs (10 from each of the five periods), again selected at random,
were read a third time. Another two readers (Zenitani and Bando) also read each plug three times. All
readings were blind, i.e. the reader had no knowledge of other data pertaining to the whale from which theplug was taken.
Lockyer was unable to obtain an age for all of the plugs (Table 2). Age estimates could be obtained formore than 86% of the plugs for each trial, although the proportion of plugs which could be read decreased
between the first and second trials. All the records of ages from the Japanese readers were "valid" except for
1% of values by Bando, which were recorded as "minimum". The bulk of the analyses is based on the“valid” readings only, although sensitivity tests consider the use of the data from the other categories inTable 2 (see below).
Statistical Analysis
Conditional probability for age-reading errors
Suppose that two groups of readers independently obtain age-estimates using a common set of n samples(here n =250). Group 1 consists of only one reader (Lockyer), who conducted ageing at most three times for
all the n samples. Group 2 consists of four readers (Masaki, Kato, Zenitani and Bando). Masaki, Kato and
Zenitani read different plugs from different time periods, whereas Bando read the 100 samples from Periods
IV and V, which Zenitani also read. The sample sizes for Masaki and Kato were respectively nM =50 and nK=78 (Table 1), and Zenitani and Bando read plugs three times for their samples of nZ =122 and nB =100,
respectively.
Let a1 jk ( j  1,2,..., n; k  1,..., r j ) be the observed ages by Group 1 (assuming that it is a “valid” count)of the j-th sample during the k-th of r j trials ( r j =2 or 3). Similarly, for Group 2, let a2 j ( j  1, 2,..., nM ) anda2 j ( j  nM  1,2,..., nM  nK ) respectively denote the observed ages by Masaki and Kato anda2 jk ( j  nM  nK  1, 2,..., n; k  1,2,3) denote the observed counts for the j-th sample during the k-th trial byZenitani. Also, let a2 jk ( j  151,..., n; k  1, 2,3) be the readings by Bando. As noted above, Lockyer did not
assign “valid” ages to all of the samples during all of the trials (Table 2). In such cases, the notation changes(1)( 2)
accordingly. For example, the data for the “either” or “interval” categories can be denoted a1 jk and a 2 jk
(1)
(2)
respectively (for “either” the age is either a1 jk or a1 jk , while for “interval” the age-estimate is betweena1(1jk) and a1(2)jk ). The "minimum" counts by Lockyer and Bando were treated in a similar manner.

3

Now, consider the joint probability distribution of the observations. Let bi (a; ) and  i (a; ) ,respectively, denote the expected age and standard deviation for the age-estimates for the i-th Group for an
animal of true age a, where  is a vector of unknown parameters. The variability in ageing is expressed as amatrix form {Pi (a ' | a; )}a ,a ' L,..., H , where: (a ' bi (a;  )) 2 
Pi (a ' | a;  )  exp  2 i2 (a;  ) (2)is the conditional probability that the i-th group draws ageing outcomes a ' given that the true age of theHanimal is a, and  Pi (a' | a;  )  1 for all a (Punt et al. 2008), where H and L are respectively maximuma ' Land minimum possible ages.

The expected age for Reader 1 is assumed to be proportional to the true age:b1 (a)  (1  x)a(3)

On the other hand, the expected age for the readers in Group 2 is a linear function of true age a:b2 (a;  )  bL  (bH  bL )

aL
.
H L

(4)

This is a 2-parameter model from Punt et al. (2008). The parameters of equation (4) should relate to eachreader when considering hypotheses related to reader effects. The values of L and H are pre-specified (L =0and H=70) and are not estimated.
The functional form of the ageing error standard deviation for the two Groups is also assumed to be a
linear function of true age: i (a; )   iL  ( iH   iL )

aL
H L

(i  1, 2)(5)

As for the expectation, the parameters in the equation (5) are specific to the reader concerned.
Likelihood function
Let   ( L ,,  H ) be the true age composition of sampled animals, which is unknown. The contributionof j-th sample by Reader 1 to the likelihood given the true age (say a ) is:rj

P1 (a1 j | a; 1 )   P1 (a1 jk | a; 1 )

(6)

k 1

where a1 j  (a1 j1 ,..., a1 jr ) and 1 is the vector of parameters of interest. By considering the distribution forjGroup 2 in a similar way, the joint probability distribution of ageing outcomes by the two groups is provided
by a mixture form as:
H

Pr(a1 j , a2 j ; ,  )    a P1 (a1 j | a;1 ) P2 (a2 j | a;2 )aL

4( j  1, 2,...,150)

(7)

H

Pr(a1 j , a2 j , a2 j ; ,  )    a P1 (a1 j | a; 1 ) P2 (a2 j | a; 2 )P2 (a2 j | a; 2 )( j  151,..., 250)

(8)

aL

where 2 is the parameter vector for Group 2 and   (1 , 2 ) . Finally, the full likelihood function for theparameters is :
150

n

j 1

j 151

Like( ,  )   Pr(a1 j , a2 j ;  ,  )  Pr(a1 j , a2 j , a2 j ;  ,  ) .

(9)The likelihood contribution for the data that are not in the “valid” category can be expressed as follows;(1)( 2)
for example, when a data type is “interval” as [a1 jk , a1 jk ] , the distribution is:a1( 2jk)

P1 ([a , a ] | a; )   P1 (a '| a; ) .
(1)
1 jk

( 2)
1 jk

(10)

a ' a1(1jk)

The parameters in the expectation and variance structures are of interest in this model, whereas L ,,  H are nuisance parameters. To make the estimation easier and to reduce the number of nuisanceparameters, a functional constraint is incorporated on the parameters for the true age composition of thesample  a (a  A) as  a   A exp( Z (a  A)) , where A is the largest number which satisfies:#{ j  1,..., n | a1 j1  A}
n

q,

(11)

and Z is a mortality parameter. The threshold value q is, of course, ad hoc, but the constraint is neverthelessuseful in cases such as this experiment. We use a value q = 0.20 as a base case assumption.
Scenarios
Table 3 lists the scenarios considered in this paper. Lockyer is taken to be the control reader for Cases 1, 2, 3
and 5, and Zenitani for Case 4. Case 5 examines the sensitivity of the results to using all of the data not only
the “valid” data, but also the "either", "interval" and "minimum" data. Several alternative models are
considered based on the covariates included in the models for the mean and variance structures for agereading Group 2 (see Table 4).
RESULTS
Lockyer’s age-reading
A sample of 100 specially selected ear plugs, independent of the experimental sample, was made available to
Lockyer, who had expressed a wish to undertake a “trial” reading of minke whale ear plugs in general during
1-2 December 2009. Lockyer read 50 ear plugs from this sample to become re-familiarised with the Growth
Layer Group (GLG) counting methods for this species. Although the specimens bore their true ID
numbering, they were read “blind”. The results of this trial, although not part of the experimental design,
helped to refine the design of a proposed age recording form.
The first reading began on 2 December in the afternoon, and continued each day until completion, withreadings on 3, 4, 6 and 7 December 2009, with approximately 50 ear plugs read each day or a maximum of
70 on any one day, with breaks every two hours to rest the eyes. A Nikon binocular microscope was used to
examine all ear plugs with an eye objective 10xB22 and zoom magnification x0.8-x8 facility. Even at
maximum magnification, it was only just possible to read all GLGs at the plug base of some older animals.

5

Five ear plugs were placed in water in separate petri dishes with individual labelling for examination at any
one time. These were then replaced in sample jars before the next set of five.
The second readings began after a 2-day break on 10 December and continued on 11, 12, and 15
December. A break was then taken 16 December, before the third reading of a sub-set of 50 ear plugs took
place. These readings were completed on t17 December.
An excel data book (Appendix 1) was updated regularly (usually after reading 10 plugs) throughout theexperimental readings compiling all information written on the working form. This also helped to makeconvenient breaks between each microscope use, and avoid monotony. Reading efficiency depends greatly
on the degree of alertness, and the day’s reading session was terminated on two occasions because of onsetof tiredness.
The colour of the ear plugs varied from pale ivory through tan to dark brown. The ear plugs for young
animals were usually pale cream while most ear plugs for older animals appeared dark. However, this was
not always consistent. The pale colouration frequently made it difficult to discern any GLG differentiation,and plugs for apparently very young animals were often very difficult to age. In addition, accessory laminae
were sometimes present and led to difficulties with age determination. For this reason, occasionally two
possible alternative readings were provided because the reader could not be certain which to choose.
Normally, not in an experimental setting, one might refer to biological data to help resolve such issues.
Statistical analysis
Histograms and scatter plots of the “valid” age-reading outcomes from Lockyer do not suggest evidence forbetween-trial bias (Figure 1). Similarly, there is no evidence for between-trial bias for Zenitani (Figure 2)
and Bando (Figure 3). Consequently, trial was not considered as a covariate in the analyses. The ageing
outcomes of the two primary readers for JARPA (Zenitani) and JARPA II (Bando) appeared similar (seeFigure 4).
Figure 5 plots the ageing outcomes for each of the Japanese readers (“best” estimates for Masaki andKato, and the medians of the three estimates for Zenitani and Bando) against the age-estimates by Lockyer.
These plots indicate a consistent discrepancy between the age-estimates obtained by Lockyer and thoseobtained by the Japanese scientists. In fact, under Case 1, where Lockyer’s bias is assumed to be zero, theestimated ages by the four Japanese readers appear negatively biased (solid lines in Figure 5). Figure 6
shows the difference in absolute and relative biases among the Japanese readers against the control reader.
The standard errors and coefficient of variation for the control and Japanese readers also differ (see Figure 7).
Table 5 summarizes the results of the parameter estimation and model selection for the different models
under Case 1. Incorporating a reader effect into the mean component tended to improve the goodness of fit
substantially (in terms of model selection criteria) compared to incorporating these effects into the variancestructure (i.e. the extent of random age-reading error). Model 3, in which the reader effects wereincorporated into both the mean and variance structures, led to the most parsimonious fit to the data. The
adequateness of the fits for Model 3 in Case 1 is also confirmed by Figure 5.
Table 6 provides estimates of parameters which could be used to compute ageing error matrices. It
should be noted that the differences in parameter estimates between Cases 1 (base case) and 5 (which use
data for indexes 0-3 in Table 2) are almost negligible.

6Ageing-error matrices based on Model 3 could be incorporated into assessments of the impact of agedetermination error on the outputs from age-structured models for Antarctic minke whales (e.g. Punt, 2010,
Punt et al., 2013). It should be noted that the analyses of this paper are predicated on Lockyer’s ageestimates. It cannot necessarily be assumed that Lockyer provides unbiased estimates of age. Overall, theresults suggest that the age-reading errors for Lockyer and the four Japanese readers differ.
DISCUSSION
We have introduced a statistical method for quantifying age-reading error and the extent of inter-reader
variability between the subject readers and applied it to a data set for the Antarctic minke whales.
Availability of the independent control reader played an important role in standardizing outcomes by the
subject readers. It is not possible to evaluate possible biases in the control reader using this experiment, andtherefore we conducted sensitivity analyses to determine how the estimates of the parameters of the modelchange.
The results suggested that the expected age and random uncertainty in age-estimates differed among theJapanese readers, although the two readers in charge of age-reading for JARPA and JARPA II provided
quite similar ageing outcomes. This is likely because the new reader Bando had a training period to develop
his reading skill using JARPA samples which had previously been aged by Zenitani (these samples were, ofcourse, not chosen from the 250 samples on which this study is based).
The analyses of this paper assumed that the age-composition of the catch was the same over more than
30 years to reduce the number of nuisance parameters. However, the assessment of age-reading errors is
subject to confounding if the catch age-composition changes over time. The impact of possible violation ofthis assumption was examined by assuming different age-compositions between Periods I-III and Periods IV
and V. The fit of the model to data was better than for the base-case, but Model 3 remained the best model.
The values of parameters which determine age-reading erros were also quite similar (see Figure 8)
suggesting that how the nuisance parameters are treated only has a small impact on the final results.
The original motivation of the experiment and analysis was to provide quantitative information on agereading error for use in the statistical catch-at-age analysis. Results by Punt et al. (2013) confirm that theresults of this analysis are sensitive to whether age-reading error is accounted for.
It should also be noted that the model and approach shown in this paper are applicable to populations
other than the Antarctic minke whales provided that a control reader is available, even retrospectively as was
the case in this study.
ACKNOWLEDGEMENTS
The authors are also grateful to Hidehiro Kato, Ryoko Zenitani, Takeharu Bando, Toshiya Kishiro, Hikari
Maeda and Yui Zennyoji for their preparation of Lockyer’s age-reading experiment according to the protocol.
Hidehiro Kato, Ryoko Zenitani and Takeharu Bando are especially thanked for their dedicated coordinationof the experiment and giving the authors helpful information on past Japanese age-reading experiments. The
IWC provided support to Lockyer under contract.
REFERENCES
Branch, T.A. 2007. Abundance of Antarctic blue whales south of 60°S from three complete circumpolar setsof surveys. J. Cetacean Res. Manage. 9:253-62.

7

Butterworth, D.S. and Punt, A.E. 2009. Proposed further work to aid resolution of questions concerning
ageing of Antarctic minke whales. Appendix 4 to the Report of the Sub-Committee on In-Depth
Assessment. J. Cetacean Res. Manage. (Suppl. 1) 11:209.
Haltuch, M.A. and Punt, A.E. 2011. The promises and pitfalls of including decadal-scale climate forcing ofrecruitment in groundfish stock assessment. Can. J. Fish. Aquat. Sci. 68: 912-26.
Larsen, F. and Hammond, P.S. 2006. Distribution and abundance of West Greenland humpback whales(Megaptera novaeangliae). J. Zoology 263: 343-58.
Maunder, M.N. and Watters, G.M. 2003. A general framework for integrating environmental time series into
stock assessment models: Model description, simulation testing, and example. Fish. Bull. 101: 89-99.
Mori, M. and Butterworth, D.S. 2006. A first step towards modelling the krill-predator dynamics of the
Antarctic ecosystem. CCAMLR Science, 13:217-277
Mori, M., Butterworth, D.S. and Kitakado, T. 2007. Further progress on application of ADAPT-VPA to
Antarctic minke whales. Paper SC/59/IA13 presented to the IWC Scientific Committee, May 2007
(unpublished). 32pp.
Mori, M. and Butterworth, D.S. 2008. Some modifications to the current ADAPT-VPA model for Antarctic
minke whales Paper SC/60/IA13 presented to the IWC Scientific Committee, June 2008 (unpublished).
5pp.
Polacheck, T. and A.E. Punt. 2006. Minke whale growth models for use in statistical catch-at-age models.
Paper SC/58/IA3 presented to the IWC Scientific Committee, May 2006 (unpublished). 36pp.
Punt, A.E. 2010. A note on the impact of accounting for age-determination error on the outcome of thestatistical catch-at-age analysis for Antarctic minke whales. Paper SC/60/IA6 presented to the IWC
Scientific Committee, June 2008 (unpublished). 6pp.
Punt, A.E., Bando, T., Hakamada, T. and Kishiro, T. 2013. Assessment of Southern Hemisphere Minke
Whales using Statistical Catch-at-age Analysis. Paper SC/65a/IA1 presented to the IWC ScientificCommittee, June 2013(unpublished).
Punt, A.E. and Polacheck, T. 2005. Application of statistical catch-at-age analysis for Southern Hemisphereminke whales in Antarctic Areas IV and V. paper SC/57/IA9 presented to the IWC ScientificCommittee, June 2005 (unpublished). 40pp.
Punt, A.E. and Polacheck, T. 2006. Further statistical catch-at-age analyses for Southern Hemisphere minke
whales. Paper SC/58/IA2 presented to the IWC Scientific Committee, May 2006. (unpublished). 40pp.
Punt, A.E. and Polacheck, T. 2007. Further development of statistical catch-at-age models for southernhemisphere minke whales. Paper SC/59/IA4 presented to the IWC Scientific Committee, May 2007
(unpublished). 42pp.
Punt, A.E. and Polacheck, T. 2008. Further analyses related to the application of statistical catch-at-age
analysis to Southern Hemisphere minke whales. Paper SC/60/IA2 presented to the IWC ScientificCommittee, June 2008 (unpublished). 46pp.
Punt, A.E., Smith, D.C., Tuck, G.N. and Methot, R.D. 2006. Including discard data in fisheries stock
assessments: Two case studies from South-eastern Australia. Fish. Res. 79:239–50.
Reeves, S.A. 2003. A simulation study of the implications of age-reading errors for stock assessment andmanagement advice. ICES J. Mar. Sci. 60: 314–328.

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Table 1. The number of samples employed in this experimentGroup 1
Group 2
Lockyer*
Masaki
Kato
Zenitani
Period I
74/75-76/77
50 (10)50
00Period II
82/83-84/85
50 (10)050
0Period III
89/90-91/92
50 (10)028
22Period IV
97/98-99/00
50 (10)0050Period V
03/04-05/06
50 (10)0050* The numbers in brackets indicate how many plugs were read three times by Lockyer.
Period

Bando
0
0
0
50
50

Table 2. Types of data provided by Lockyer
Index

Category$

Data type

1st trial

2nd trial

3rd trial

0

Valid

Age

228 (91.2%)

216 (86.4%)

43 (86%)1

EitherAge1 or Age 2

2 (0.8%)4 (1.6%)02Minimum

Age >=

11 (4.4%)

10 (4.0%)

3 (6.0%)3Interval(Age1, Age2)

1 (0.4%)00

4

may be missingAge

1 (0.4%)0

0

10

UncertainAge

2 (0.8%)12 (4.8%)

3 (6.0%)100

unreadableNA

5 (2.0%)8 (3.2%)1 (2.0%)$“valid”: a single age was recorded; “either”: two possible ages were offered; “minimum”: only a minimum
age was counted; “interval”: a range of possible ages was given; “missing”: part of the plug was missing;“uncertain”: the reader was not confident in the age estimate. The numbers in brackets are percentages foreach trial.

Table 3. The scenarios considered in the analyses.
Bias in control
reader

Data

Case 1 (Base)

Lockyer; 0%"valid" only

Case 2

Lockyer; 10%"valid" only

Case 3Lockyer; -10%"valid" only

Case 4

Zenitani; 0%"valid" only

Case 5

Lockyer; 0%

Index=0,1,2,3

9

Table 4. List of assumptions regarding the covariate effects and parameters. In all the models,constraints  iH   iH for all the readers are incorporated.

Model

Assumption0

No reader effects

1

Reader effects in Group 2 only in the mean structure

2

Reader effects in Group 2 only in the variance structure

3

Reader effects in Group 2 both in the mean and variance structures

4

Reader effects both in the mean and variance structures, but the expected ages by the recent
two readers, Zenitani and Bando, are same

Table 5. Results of the analysis (Upper value=estimate; Lower value= SE) for the Case 1, where ageing by
the control reader (Lockyer) is assumed to be unbiased. Note that the column “#parameters” does not include
the number of nuisance parameters for the age composition.

Model

Loglike #parameters D-AIC

D-AICcReader 1 (Lockyer)
bL1

bH1

0

-3004.0

6

106.18104.54070

1-2958.6

12

27.38

26.50

0

70

2

-2978.1

12

66.40

65.52

0

70

3

-2938.9

18

0.00

0.00

0

70

4

-2964.7

16

47.60

47.29

Model
0

1

2

3

4

0

70

Reader 2-1 (Masaki)

Reader 2-2 (Kato)

bL21

bL22

1.39

bH21

bH22

Reader 2-3 (Zenitani)
bL23

bH23

Reader 2-4 (Bando)
bL24

bH24

61.17

0.10

0.51

2.65

60.51

2.33

56.21

1.03

62.92

1.58

63.93

0.44

2.06

0.38

1.27

0.10

0.55

0.10

0.57

1.68

61.86

0.28

0.76

3.08

58.79

2.45

56.01

1.03

62.85

1.64

63.64

0.53

1.91

1.36

4.10

0.09

0.54

0.11

0.61

3.10

58.74

2.63

55.49

1.24

63.07

0.53

1.90

0.60

2.00

0.08

0.52

Reader 1 (Lockyer)

Reader 2-1 (Masaki)

Reader 2-2 (Kato)

Reader 2-3 (Zenitani)

Reader 2-4 (Bando)

sigL1

sigH1

sigL21

sigH21

sigL22

sigH22

sigL23

sigH23

sigL24

sigH24

1.62

3.43

0.56

4.17

0.18

0.66

0.06

0.34

1.64

3.36

0.52

3.98

0.17

0.60

0.06

0.28

1.46

3.38

1.66

1.66

0.08

9.53

0.57

3.39

0.84

3.22

0.15

0.50

0.27

0.27

0.35

1.56

0.08

0.41

0.12

0.44

1.55

3.14

1.55

1.55

0.54

7.37

0.46

3.66

0.66

3.41

0.17

0.51

0.24

0.24

1.64

4.40

0.06

0.38

0.09

0.40

1.50

3.21

1.57

1.57

0.75

6.85

0.42

3.83

0.91

3.07

0.15

0.49

0.24

0.24

0.44

1.39

0.06

0.38

0.11

0.42

10

Table 6. Results of the analysis (Upper value=estimate; Lower value= SE) for the Cases 1-5 under the bestmodel (Model 3). The values in italics are pre-specified.
Reader 1 (Lockyer)

Reader 2-1 (Masaki)

Reader 2-2 (Kato)

bL21

bL22

Reader 2-3 (Zenitani)

Reader 2-4 (Bando)

Model 3
Case 1

bL1

bH1

0.00

70.00

(Lockyer: unbaised)

Case 2

bH21

bH22

bL23

bH23

bL24

bH24

3.08

58.79

2.45

56.01

1.03

62.85

1.64

63.64

0.53

1.91

1.36

4.10

0.09

0.54

0.11

0.61

3.10

64.27

2.67

60.66

1.09

69.04

1.70

69.85

0.52

2.11

0.56

2.16

0.10

0.64

0.12

0.70

3.08

53.22

2.62

50.27

1.14

56.35

1.74

57.15

0.00

77.00

0.00

64.00

0.53

1.66

0.65

1.85

0.09

0.49

0.11

0.54

Case 4

0.00

75.52

3.00

63.51

2.68

59.58

0.00

70.00

0.71

70.26

(Zenitani: unbaised)

0.00

0.62

0.52

2.11

0.55

2.10

0.12

0.62

Case 5

0.00

70.00

3.01

59.03

2.36

55.99

1.02

62.65

1.63

63.41

0.51

1.87

0.47

1.78

0.09

0.57

0.11

0.63

(Lockyer: 10% bias)

Case 3(Lockyer: -10% bias)(Case 1 with Index=0~3)

Reader 1 (Lockyer)

Reader 2-1 (Masaki)

Reader 2-2 (Kato)

Reader 2-3 (Zenitani)

Reader 2-4 (Bando)

sigL1

sigH1

sigL21

sigH21

sigL22

sigH22

sigL23

sigH23

sigL24

sigH24

1.55

3.14

1.55

1.55

0.54

7.37

0.46

3.66

0.66

3.41

0.17

0.51

0.24

0.24

1.64

4.40

0.06

0.38

0.09

0.40

1.47

3.44

1.56

1.56

0.75

7.46

0.45

4.10

0.69

3.63

0.16

0.58

0.24

0.24

0.40

1.50

0.06

0.43

0.09

0.46

1.49

3.02

1.56

1.56

0.73

6.25

0.48

3.33

0.63

3.22

0.15

0.45

0.24

0.24

0.51

1.35

0.06

0.36

0.09

0.35

1.87

2.65

1.48

1.48

0.70

7.44

0.41

3.97

0.64

3.62

0.16

0.51

0.25

0.25

0.38

1.45

0.06

0.41

0.10

0.44

1.60

3.05

1.49

1.49

0.45

7.40

0.47

3.58

0.65

3.51

0.15

0.48

0.24

0.24

0.41

1.47

0.06

0.37

0.09

0.42

11

Figure 1. Scatter plots and histograms for Lockyer’s ageing data for her three trials.

Figure 2. Scatter plots and histograms for Zenitani’s ageing data for her three trials.

12Figure 3. Scatter plots and histograms for Bando’s ageing data for his three trials.

Figure 4. Scatter plot of the best estimates for the two primary readers in JARPA and JARPA II (Zenitani
and Bando).

13

Figure 5. Scatter plots of the “best” age-estimates from the four Japanese readers against Lockyer’s 1 st, 2nd
and 3rd trials (“valid” data only). The dashed lines show the 1-1 lines. Lockyer’s age-estimation is assumed
to be unbiased (Case 1).

14

Figure 6. Absolute (left) and relative (right) biases for the Japanese readers relative to the control reader(Lockyer), who is assumed to be unbiased (Case 1).

Figure 7. Standard errors (left) and coefficient of variations (right) for the control and Japanese readers if thecontrol reader (Lockyer) is assumed to be unbiased (Case 1).

15

Figure 8. Sensitivity of the relationship between expected age and true age for the base-case analysis (solid
black lines) and for the sensitivity test in which the catch age-composition is assumed to change over time
(shaded black lines).

16

Appendix 1
Format used by Lockyer to summarize age readings

SpecimenID no

Age readings
Trialcounts given insequence

Agreed countfrom trials
based onweightedmean (CHL)

Comments
Best countaccording toJapanese
method ofaverage ofcountsPlugcomplete?
Yes or No;
comment

Neonatal line
present? Yesor No

Central cut?
Yes or No

Generalappearance

Readability Excellent;
Good:
Poor;
Unreadable

Other

Specimen ID no
This refers to the experimental number provided for this reading stage of the experiment.
Age readings
In general following descriptors were used. When there is uncertainty about age, the age is prefixed by ca – e.g. ca N. When part of theplug is missing, + is suffixed on the age. However, + can also be applied in young animals (range up to 6 GLGs) where a new GLG is forming at the edge but
maybe incomplete. Other ways of giving this are e.g. N - N+1 – in other words a range. Sometimes two possible ages are offered because of difficulties in reading.
Here the ages will be e.g. N or P. Where only a minimum age is counted in difficult to read plugs, the age will be given as e.g. >N. Sometimes this notation is also
used for incomplete plugs.
Trial counts - given in sequenceThis gives the numbers of GLGs counted in sequence. The minimum number of trials is three, but may be many more depending on the confidence of the reader inwhat is being seen. It should be noted that before recording counts, the ear plug has been scanned several times to get a feel for the GLG patterns with rough counts
made. The written counts reflect when the reader is more confident in the counting.
Agreed count from trials based on weighted mean (CHL)
In cases where there is no consistency of count, the mean may be weighted to the most recent count depending on the relative confidence in the reading.

17

Best count according to Japanese method of average of counts
The mean here is a simple mean and treats all readings equally.
Plug complete? Yes or No; comment
Yes denotes that all parts of the core were found, even if in two or more pieces. A comment will usually describe how many pieces or what is missing.
Neonatal line present? Yes or No
Yes means that at least part of the neonatal Line has been identified.
Central cut? Yes or No
Yes means that the core is adequately exposed at the centre line.
General appearance
Information on colouration, relative size, etc. is given here. However, this has not been consistently provided, but has often been added if there has been a problem
with reading. If the plug or part of it is attached to the glove finger, this is noted.
Readability - Excellent; Good: Poor; Unreadable
E – Excellent means very clear GLGs and little error likely in reading.
G – Good means generally quite readable with mostly clear GLGs. However, there may be some error.
P – Poor means parts of the plug are difficult to read because GLGs are obscure or irregular. A large margin of error is likely in GLGs.
U – Unreadable means that the clarity of GLGs is so poor and/or confusing, that any GLG count provided is likely to be erroneous orincomplete.
Combinations of categories e.g. G/P mean partly good and partly poor – often which part will be specified e.g. P(top)/G (base).
Other
Here expanded information on readability may be given; also possible transition phase age if determined.

18