SC/65b/EM02

Detailed responses to some of the conclusions andrecommendations from the Review Panel regarding Body
condition trend in the Antarctic minke whale
KENJI KONISHI AND L ARS WALLØE 2

SC/65b/J13Rev

1

Institute of Cetacean Research, 4-5 Toyomi-cho, Chuo-ku, Tokyo 104-0055, Japan2

Department of Physiology, Institute of Basic Medical Sciences, University of Oslo, P.O. Box 1103 Blindern,
N-0317 Oslo, Norway

The review Panel writes on the statistical modelling:‘Following the selection of which factors to consider in the modelling, the following steps should be undertaken:(1) identify whether any of the covariates are highly correlated and either (a) exclude a subset of the covariates
so that the remaining covariates are uncorrelated or (b) develop new covariates which represent independent
aspects of the current covariates (using for example PCA);(2) select a ‘full model’ (this may be difficult if the data set is unbalanced) and base selection of which factors
and their interactions to treat as random effects - the models should be fitted using REML and a model
selection approach such AIC, BIC or standard hypothesis testing approach applied; and(3) select the fixed effects structure given the random effects structure selected at step (2), where the models arefitted using maximum likelihood;(4) use REML to fit the best model identified in (3) above.’
Comment on (1): The potential correlations between the independent correlates have been extensively discussed inmeetings of the Scientific Committee. The variables age, body length and body weight are highly correlated, whichis the reason why the authors preferred to use only length (values of the two other variables were not available for allwhales) as independent variable in the models. The correlation matrix for the independent variables is provided inAppendix 1. The matrix shows that all the other correlations between the independent variables have values less thanabout 0.1 (except the correlation between longitude and latitude caused by the catches in the Ross Sea). For thisreason the authors have not considered it necessary either to exclude any of the other variables (except age and bodyweight) or to develop new independent variables by the use of principal component analysis (PCA). In the publishedlinear regression paper (Konishi et al. 2008) correlations between independent variables were taken into account by
the use of Abraham Wald’s forwards stepping procedure.
Comments on (2) to (4):a) There is no objective ‘full model’. The choice of the ‘full model’ is dependent on what one regards asrelevant and plausible assumptions. In the following the authors comment only on the modelling ofstorage of energy during the JARPA period, since this is the period which has been discussed repeatedlyin the SC.
b) The authors’ understanding from reading the report from the Review Panel and listening to the Paneldiscussions is that the linear models lm 1 to lm 6.18 are explored in a useful way, but that they havemissed out an important model when they tried out interaction models with random effects. The random
term should first have been explored as an interaction term. An example of this is the model

1 This version incorporates the recommendation by the chair of EM that the title should be more
inofrmative. In addition, some calculations which had no shown year coefficients in the Appendix 2
because of equation error were fixed and recalculated.

lm(BT11 ~ YearNum + BLm^3 + DateNum + Diatom +LatNum +LongNum + LongCat11 + Sex +DateNum :LongNum) + (DateNum : YearCat))
which should have been explored before random effects model BT11jarpa 18 was explored:lmer(BT11 ~ YearNum + BLm^3 + DateNum + Diatom +LatNum +LongNum + LongCat11 + Sex +DateNum:LongNum) + (DateNum | YearCat)).
The authors have now performed these calculations for the interaction terms which were suggested by the SC in2013and an interaction term which they found useful based on de la Mare et al.’s models from their paper O6. Themodels and the results from ‘BT11’ and ‘FatWeight’ are presented in Appendix 2. This adjustment did not result inany change in model selection (based on lowest BIC value) in any of the cases we have explored.

The Review Panel writes on the presentation of results:‘SC/F14/J13 and SC/F14/J14 do not report many fit diagnostics. The Panel recommends that any revised papers
provide at least plots of the residuals versus the predictor variables (including year and stratum), histograms ofresiduals and random effects, plots of residuals spatially, and Q-Q plots for the ‘best model’.’Response: The authors have now developed the plots recommended for the four of the best models (three sets ofplots for ‘BT11’ and one for ‘FatWeight’ (Appendix 3).

The review Panel further writes:‘The Panel also recommends that future analyses of the data on the condition of Antarctic minke whales include (a)consideration of a model in which year is a categorical variable and is treated as a random effect if a plot of residuals
against year show there are residual patterns by year,’
As can be seen clearly from Appendix 3 the plots of residuals against year show no pattern for any of the models
explored. For this reason the authors see no reason to consider a model in which year is a categorical variable and istreated as a random effect.

Appendix 1
Correlations among independent variables

The correlation matrix for the independent variables
BLm
DateNum Diatom
LatNum LongNum LtimeNum YearNum
BLm
1.000
0.105
-0.087-0.117-0.0820.000
0.052
DateNum
0.105
1.000
0.111
-0.3640.105-0.065-0.047
Diatom-0.0870.111
1.000-0.0800.039
0.005-0.030
LatNum-0.117-0.364-0.0801.000-0.4740.062-0.097LongNum-0.0820.105
0.039-0.4741.000-0.051
0.052
LtimeNum
0.000-0.0650.005
0.062-0.0511.000-0.042YearNum
0.052-0.047-0.030-0.0970.052-0.042
1.000

Appendix 2 The models and the results of models for ‘BT11’ and ‘FatWeight’

Results of linear and linear mixed-effects models with the BT11 as the response variable
Covariates ofNo.
BIC Year effctSEtmodel
random effects
Date-LonSect
1 10822.3-0.0026
0.01 -0.35 M11ModKW_BT11.1 <- lm(BT11 ~ DateNum*Sex + DiatomNum + YearNum + BLm + (DateNum:LonSect:Year))-0.01540.01 -2.24 M11ModKW_BT11.2 <- lmer(BT11 ~ DateNum*Sex + DiatomNum + YearNum + BLm + (DateNum|LonSect:Year)) # Original from J13 modified m112 10649.6
10764.3-0.01890.00-8.50 M11ModKW_BT11.3 <- lm(BT11 ~ DateNum*Sex + DiatomNum + YearNum + BLm + DateNum:LonSect)
310824.84-0.0195
0.00 -8.24 M11ModKW_BT11.5 <- lmer(BT11 ~ DateNum*Sex + DiatomNum + YearNum + BLm + DateNum|LonSect)
10828.9-0.0034
0.04-0.10 BT11jarpa12 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LatNum)
YearNum-LatNum
110818.4-0.0200
0.04-0.55 BT11jarpa12F <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum)
210965.03-0.0196
0.00 -7.78 BT11jarpa12F.2 <- lmer(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum|LatNum)
10811.2-0.02080.04-0.58 BT11jarpa12F.5 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum) # - LongNum
410804.0-0.0537
0.02-2.54 BT11jarpa12F.6 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum) # - LongNum, - Latnum
510798.2-0.0195
0.00-8.39 BT11jarpa12F.7 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum) # - LongNum, - Latnum, - YearNum:LatNum
610818.0-0.02110.00-6.78 BT11jarpa12F.10 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice)
YearNum-Ice110972.7
2-0.0175
0.01 -2.79 BT11jarpa12F.12 <- lmer(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum|Ice)10810.8-0.02100.00-6.76 BT11jarpa12F.15 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice) # - LongNum
310804.4-0.0223
0.00-7.46 BT11jarpa12F.16 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice) # - LongNum, -LatNum
410798.2-0.0195
0.00-8.39 BT11jarpa12F.17 <- lm(formula = BT11 ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum) # - LongNum, -LatNum, -YearNum:Ice
5
Same as BT11jarpa12F.7

Results of linear and linear mixed-effects models with the FatWeight as the response variable
Covariates ofNo.
BICYear effectSEtmodelrandom effects-168.60.0005
DateNum and LonSect
10.00
0.11 FatWeightModKW.1 <- lm(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm + (DateNum:LonSect:Year))-277.3-0.0095
20.00 -4.10 FatWeightModKW.2 <- lmer(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm + (DateNum|LonSect:Year)) # Original from J13 modified m11
3 -299.7 -0.0087
0.00 -5.96 FatWeightModKW.3 <- lm(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm + DateNum:LonSect)-250.2-0.0093
0.00-6.25 FatWeightModKW.5 <- lmer(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm + (DateNum|LonSec))4-304.3-0.0088
0.00-6.02 FatWeightModKW.3.1 <- lm(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm + DateNum:LonSect - DateNum:Sex) #FatWeightModKW.3 - DateNum:Sex
56 -330.1 -0.0084
0.00 -5.90 FatWeightModKW.3.2 <- lm(FatWeight ~ DateNum*Sex + DiatomNum + YearNum + BLm - DateNum:Sex) #- DateNum:Sex, - DateNum:LonSect-276.9-0.0052
YearNum-LatNum
10.02 -0.22 FatWeightjarpa12F <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum) # + DateNum:LongNum-101.9 -0.0090
20.00 -5.89 FatWeightjarpa12F.2 <- lmer(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (YearNum|LatNum)) # + YearNum|LatNum-283.4-0.0049
30.02 -0.21 FatWeightjarpa12F.5 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum) # - LongNum-290.0-0.0057
40.01 -0.42 FatWeightjarpa12F.6 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum + YearNum:LatNum) # - LongNum, - LatNum-296.6-0.0089
50.00 -6.06 FatWeightjarpa12F.7 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum ) # - LongNum, - LatNum, - YearNum:LatNum
6 -300.7 -0.0087
0.00 -5.92 FatWeightjarpa12F.8 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + Diatom + LongCat11 + Sex + DateNum:LongNum ) # - LongNum, - LatNum, - YearNum:LatNum, - DateNum-277.6-0.0098
YearNum-Ice
10.00 -5.43 FatWeightjarpa12F.10 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice)-100.6 -0.0089
20.00 -6.02 FatWeightjarpa12F.12 <- lmer(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (YearNum|Ice))-284.1-0.0098
30.00 -5.44 FatWeightjarpa12F.15 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LatNum + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice) # - LongNum-290.4-0.009640.00 -5.46 FatWeightjarpa12F.16 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum + YearNum:Ice) # - LongNum, - LatNum-296.6-0.0089
50.00 -6.06 FatWeightjarpa12F.7 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum ) # - LongNum, - LatNum, - YearNum:LatNum
Same as BT11jarpa12F.7
6 -300.7 -0.0087
0.00 -5.92 FatWeightjarpa12F.17 <- lm(formula = FatWeight ~ YearNum + I(BLm^3) + DateNum + Diatom + LongCat11 + Sex + DateNum:LongNum) # - LongNum, - LatNum, -YearNum:Ice
Same as BT11jarpa12F.8

Results of M11ModKW_BT11.2
BT11 ~ DateNum * Sex + DiatomNum + YearNum + BLm + (DateNum | LonSect:Year)
Random effects:
GroupsName
Variance
LonSect:Year (Intercept) 1.34e-01
DateNum
4.62e-05
Residual
5.26e-01

Std.Dev.
Corr
0.366046
0.006797 -0.87
0.725291

Number of obs: 4719, groups: LonSect:Year, 44
Fixed effects:
Estimate(Intercept)
2.0269530
DateNum
0.0121695
Sex[T.M]-0.7193948
DiatomNum
0.2313461
YearNum-0.0153637BLm
0.1107355
DateNum:Sex[T.M] 0.0057632

Std. Error
0.2587477
0.0014020
0.0633247
0.0090855
0.0068451
0.0265370
0.0009243

t value
7.834
8.680-11.360
25.463-2.244
4.173
6.235

Result of the model FatWeightModKW.3.2
FatWeight ~ DateNum * Sex + DiatomNum + YearNum + BLm - DateNum:Sex)
Residuals:
Min
1Q Median
3Q Max-0.63386 -0.13028 -0.01238 0.11409 0.65558
Coefficients:
Estimate
Std. Errort value Pr(>|t|)(Intercept)-2.218507
0.151496-14.644 < 2e-16 ***DateNum
0.003238
0.000251
12.902 < 2e-16 ***Sex[T.M]-0.132435
0.017378-7.621 7.83e-14 ***DiatomNum 0.041396
0.005895
7.022 5.00e-12 ***YearNum-0.008443
0.001432-5.895 5.72e-09 ***BLm
0.426379
0.016834
25.328 < 2e-16 ***Appendix 3 Diagnosis plots for the modelsa) Model lm 6.18 for ‘BT11’b) Model lmer 6.16.1 for ‘BT11’c) Model m11 modified KW for ‘BT11’d) Diagnosis plots for the best model for FatWeight