SC/F14/J13

Time trends in the storage of energy in the Antarctic
minke whales during the JARPA and JARPA II research
periods
K ENJI K ONISHI1 AND L ARS W ALLØE 2
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
ABSTRACT
Yearly changes in the energy stores of sexually mature Antarctic minke whales were studied over the
24 years of the JARPA and JARPA II research programmes by examining five variables which are, or
could be, indices of storage of energy. These variables are the total fat weight in the whale body,
blubber thickness at two lateral measurement points and girth measured at two specified positions.
Three of these variables are available from almost all whales sampled, but girth at axilla wasmeasured over 20 years and fat weight was only measured over 17 years of the JARPA programme,
and only for the first whale sampled on each day. A number of covariates were also recorded. A large
number of linear mixed-effects statistical models were investigated for each of the dependent
variables, and the Bayesian Information Criterion (BIC) was used to select the best model. All models
examined had ‘year’ as a possible explanatory variable.
The results show that all five measures of energy storage declined substantially over time during the
JARPA period, with a more than 10% decline in total fat weight. For all five dependent variables thevalues for energy stores are higher for females than for males. The values increase during the feeding
season and are higher for higher body coverage of diatoms. This is assumed to be a measure of how
long the animal has spent in Antarctic waters. The results are similar when each sex is analysed
separately, but the decrease in energy stores was somewhat larger in females than in males. The
results from the JARPA II period are very different from the JARPA period. There is no clear trend
towards increase, or further decrease, in any of the four measures of energy storage. The results
suggest that fundamental changes have taken place in the eastern part of the Antarctic marine
ecosystem during the 1990’s. These changes have resulted in less optimal feeding conditions forminke whales.

KEY WORDS: ANTARCTIC, ANTARCTIC MINKE WHALE, ENERGETICS, TREND, FOOD/PREY

INTRODUCTION
At the JARPA Review meeting in 2006 the authors presented a paper which indicated that blubber thickness
measured at one lateral point in the middle of the body (directly below the centre of dorsal fin) had declined overthe 18 year JARPA period from 1987/88 to 2004/05 (Konishi, Tamura and Walløe, 2006), taking into accountother variables which could influence blubber thickness. An improved and extended manuscript was later
discussed at the IWC-SC meeting in 2007 and later published in Polar Biology (Konishi et al, 2008). In the
published paper the girth at the level of the umbilicus and the total fat weight in the whale body were used as
response variables which could be used as indices of energy storage in addition to the blubber thickness. Blubber
thickness and girth were available from nearly all whales taken, while fat weight was measured only from thefirst whale caught at each day in JAPRA period. Only sexually mature animals were included in the study to
avoid problems connected with the growth of immature animals. The method used in these studies was simple
multiple linear regression with either blubber thickness (cm), girth (cm) or fat weight (tons) as the dependent
variable, and with date (Dec 1st = 1), year (1987/88 = 1), longitude (!E), latitude (!S), the extent of diatom
adhesion on the skin (1 to 5), and body length (m) as independent variables. For some analyses body weight(tons), whale age (years) and foetus length (cm) were also used, but these variables were not available for all
whales.

Some analyses were carried out separately for each sex; other analyses were carried out with both sexes
combined and then with sex as an additional independent variable. In all regression runs the minimum BIC
PRGHOVLQFOXGHG³\HDU´³GDWH´³GLDWRP´DQG³VH[´VRPHDOVR³ORQJLWXGH´DQG³ODWLWXGH´³<HDU´ZDVDOZD\Vhighly significant different from zero with the regression coefficient ranging from -0.018 to -0.028 cm per year.
³)DWZHLJKW´ZDVIRXQGWRGHFUHDVHE\DSSUR[LPDWHO\NJSHU\HDUDQG³JLUWK´E\DSSUR[LPDWHO\FPSHU
year (Konishi et al. 2008).
In the IWC-SC meeting in 2011 William de la Mare presented a paper claiming that the particular multiple
regression model used by Konishi et al (2008) could have been inappropriate (de la Mare, 2011), and in the SC
meeting he suggested that mixed-effects models should be fitted to the data to account for various forms ofheterogeneity. During the meeting Hans J. Skaug fitted six such models which arose from the discussion,
including all mixed-effects models suggested by de la Mare. In all models except one the coefficients for year
were statistically significant and with values ranging from -0.017 to -0.026 cm/year. The model with the lowest
AIC value had coefficient for year ± 0.019 which was very close to the value in the best model published by
Konishi et al. (2008), but the SE was three times larger than the value published by Konishi et al. (an increase
from 0.0022 to 0.0068 cm/year), but the slope was still significantly different from zero at the 5% level. A jackknife analysis by Lars Walløe with one year as the sampling unit to subsume the consequences of lack of
independence in the data gave similar results (regression slope -0.0213 cm/year, SE 0.00836). The text of theWorking Paper by Skaug is attached as an appendix (Appendix 1). De la Mare was offered the data file under the
IWC Data Availability Agreement to explore other models himself, but he did not accept the conditions specified
in the agreement. In the IWC-SC meeting in 2012 de la Mare presented a paper which argued that the transect
sampling of JARPA and JARPA II precludes reliable and appropriate analysis of the data collected (de la Mare,2012). He argued that that the transects could in reality have been the basic sampling unit in the analyses by
Konishi et al (2008), not the individual whales, because whales taken on the same transect could have highly
correlated properties. The discussion continued at the SC in 2013 with a reanalysis by mixed effect models byHiroko Kato Solvang and Lars Walløe of the decrease in minke whale fat stores during the 17 JARPA years$SSHQGL[ 6LQFHRQO\RQHZKDOHZDVGLVVHFWHGHDFKGD\GHOD0DUH¶VDUJXPHQWDERXWFRUUHODWLRQEHWZHHQ
neighbouring whales in the data file should at least be less relevant, if relevant at all, for this statistical analysis.
The results were similar to the results obtained by Skaug (Appendix 1) on blubber thickness, a largely
unchanged and statistically significant decline compared to the results of the simple linear regression analysis of
Konishi et al (2008), but a higher SE (0.0041 compared to 0.0025). The SC did not conclude the issue, however,requested further analyses of the data, including:(1) determining whether the models fitted so far capture all the main features of the data,(2) determining whether the estimate of trend could be made more precise,(3) analysing the two sexes separately,(4) including the interaction of slopes by latitudinal band with year as a random effect, and(5) investigating independence issues by using mixed-effects models with track line as a random effect.
The SC encouraged additional analyses to be undertaken on both the blubber thickness and body fat data andnoted that papers should ideally be submitted to the forthcoming JARPA II review. This is part of the
background for the present paper.
M A T E R I A LS A N D M E T H O DS
The present investigation has been expanded in two ways compared to the analyses carried out by Konishi et al.
(2008) and the reanalyzes of these data carried out by Skaug (2011, Appendix 1) and Solvang and Walløe (2013,
Appendix 2): The set of dependent variables has been increased from the three used by Konishi et al. (2008) andnow also includes girth at level of the axilla and blubber thickness at a lateral point at the level of the umbilicus.
Three of these five dependent variables were measured on most whales during the JARPA period and themeasurement series were continued in the JARPA II period. Girth at level of the axilla was measured during 20
years of JARPA and JARPA II, Fat weight was only measured during 17 of the JARPA years and themeasurements were not continued in JARPA II. In the current analyses we have fitted a large number of linear
models to the data, both simple models with and without interaction terms and mixed models with random
effects. For all dependent variables we have first analyzed the JARPA data only to try to resolve thedisagreements expressed in the meetings of the IWC-SC from 2010 to 2013. We have then repeated the analyses
for only the data from first six years of the JARPA II period (2005/06-2010/11) and finally analyzed the total
JARPA + JARPA II period (1987/88-2010/11) for four of the dependent variables.

2

Samples and measurements
During all years from 1987/88 to 2010/11 blubber thickness at two lateral points under the dorsal fin (BT11) andlevel of umbilicus (BT7) were carefully measured to the nearest mm on a most whales on the left side of thebody, but in several cases they were made on the right side, mainly because of damage to the left side caused by
the harpoon. Measurements are missing from 16 whales LQ³%7´ and 4 whales LQ³%7´. The reasons forchoosing this particular lateral point for blubber thickness measurements were that skin surface and muscle
fascia are parallel in this area, and blubber thickness is close to constant in an area around themeasurement site. Dorsal blubber, such as anterior and posterior to the dorsal fin, is highly variable in thickness
along the axis of the body and has been shown difficult to measure consistently by different researchers.
Therefore measurements of blubber thickness at the lateral positions are the only measurement positions which
can be used to obtain reliable long time series of data. A small area of skin and blubber around the measurement
points was also dissected free from surrounding skin and blubber to avoid stretch or pressure from surrounding
areas before the measurements were obtained. 7KHUHVXOWLQJYDULDEOHVZHUHFDOOHG³%7´DQG³%7´LQWKH
equations and in the Results section below. The distance between the dorsal mid-line and the ventral mid-line
was measured to the nearest cm at two positions at umbilicus (³HalfGirth-u´) and axillary (³HalfGirth-a´) levels.
,QWKH¿rst animal caught each day, all the blubber including the ventral groove and visceral fat was also
removed from the body and weighed to the nearest kilogram during the last 17 years of the JARPA period. Since
the total weight of the whale body was also available, the difference between these two weights for each whale
KDVEHHQFDOOHG³OHDQERG\ZHLJKW´DQGKDVEHHQXVHGas a predictor variable in some of the statistical analyses.
These variables are only available for the JARPA period. Other predictor variables available for each whale
include position of catch (latitude, longitude), time (year, date and local time) and a track line identifier. Fetus
length was measured in the same way as adult body length. In addition to using continuous variables, some
YDULDEOHVZHUHVSOLWLQWRFDWHJRULHVDQGLQFOXGHGLQUHJUHVVLRQDQDO\VHV)RUVRPHRIWKHDQDO\VHV³ODWLWXGH´DQG
³ORQJLWXGH´ZHUHGLYLGHGLQWRHOHYHQFDWHJRULHV ³/DW&DW´ and ³/RQJ&DW´ DQG³\HDU´LQWRVHSDUDWH
categRULHVIRUHDFKVXUYH\\HDU ³<HDU&DW´ WRVHHLIWKHUHZHUHQRQ-continuous effects of any of these
explanatory variables. The study area includes the Ross Sea down to about 78ͼS. Since the research area covereda wide range of latitudes and longitudes, extending as far south as the Ross Sea, geographical variables separated
IRUORZHUDQGKLJKHUODWLWXGHDUHDVZLWK6DVWKHGLYLGLQJOLQH ³/DW´ DQGORQJLWXGLQDODUHDVDVWKHGLYLGLQJ
line 155°E ³/RQJ:(´ KDVDOVREHHQXVHGLQWKHVWDWLVWLFDODQDO\VHV
Statistical analysis
All statistical analyses were conducted in R environment version 3.0.2 (R Core Team 2013) using package³OPH´YHUVLRQ- %DWHVHWDO IRUPL[HGHIIHFWVPRGHOVDQG³VWDWV´ 5&RUH7HDP IRURWKHU
regression models.
In the R formulas tKHV\PEROµ¶LQGLFDWHVan interaction between parameters. In mixed effects models
lHIWVLGHRIYHUWLFDOEDUµ_¶LVIL[HGHIIHFWDQGULJKWVLGHJURXSLQJIDFWRUWRZKLFKWKHUDQGRPHIIHFWDSSOLHVThe
abbreviations µlm¶ means linear model and µlmer¶ means linear model with random effects.
There are different opinions among statisticians how to select the best model from a range of
SRVVLELOLWLHV7KHTXHVWLRQLVKRZWREDODQFHPRGHOILWZLWKFRPSOH[LW\$NDLNH¶VLQIRUPDWLon criterion (AIC) iscurrently much used. A related criterion, the Bayesian information criterion (BIC) usually selects the samemodel as AIC, but if there is a difference, BIC usually selects a simpler model. We have presented the values ofboth criteria in this paper, but generally we have a preference for BIC which was also the criterion used in
Konishi et al. (2008). As can be seen from the results section, the two criteria have in most cases selected thesame model, and when they have selected different models the coefficients for the change of blubber thickness
with time are usually about the same. This is usually also the case when some models have about the same value
for BIC. In both these situations it would have been possible to use the focused information criterion (FIC)(Claeskens and Hjort, 2008) and average the decline in blubber thickness over the best models with weights
dependent on the fit, since the discussion so far has mainly been focused on the time trend in blubber thickness.
It has so far not been necessary to use FIC, since models with close values of BIC have similar coefficients foryear. If new models are suggested during the discussion of our results during the review meeting or in the IWCSC, we may choose to use the FIC with averaging. The other four dependent variables can of course be dealt
with in a similar way.
R ESU L TS
The output from all model runs can be found as pdf-files in an electronic attachment to this paper. A large
number of different models have been explored, but the number is still small compared to the near infinite
number of possible models. To make it easier to refer to the different models in the attachment, the models havebeen numbered consecutively. As an example Table 1 shows the different models which have been used in the3analyses of the lateral blubber thickness at the level of the dorsal fin (called BT11) for both sexes combined. The
log likelihood, number of parameter, AIC and BIC values and the coefficients for year with its SEs and t-values
are also given. The models fall in four groups: simple linear models, linear models with categorical terms, linear
models with interaction terms and finally mixed-effects models with random effect terms. The best model ineach group according to the BIC criterion is shown in bold, and the best model of all are shown in bold italics.
The models include models with random effect of track lines.
T he J A RP A period:%OXEEHUWKLFNQHVV³%7´For all models investigated (except one) the results show a decline in blubber thickness over the 18 JARPA years
ranging from -0.0196 to -0.0299 cm/year (Table 1). The model with the lowest BIC value has a decline of-0.0203 cm/year (SE=0.0024). All the random-effects models have higher BIC values than the best linear model:lm(BT11 ~ YearNum + BL m^3 + DateNum + Diatom + LongCat11 + Sex +DateNum :LongNum) ..(#BT11jarpa17)
The best model with random effects was:lmer(BT11 ~ YearNum + BLm^3 + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex +DateNum :LongNum) + (DateNum | YearCat)) ..(#BT11jarpa18)
The total printouts of the results from the fitting of these two models are shown in Appendix 3 and 4 (and they
can of course also be found in the electronic attachment as models # BT11jarpa17 and # BT11jarpa18). The AIC
preferred a model with three additional random effect terms in addition to the last model above. The two random
effect models gave a decline in blubber thickness of -0.0189 and -0.0197 cm/ year, respectively. In addition to a
decline in blubber thickness BT11 over the 18 JARPA years, the blubber thickness increased from west to eastand from north to south. It also increased with the body length, diatom coverage and from December to March(Appendix 3 and 4). The scatterplot of residuals in BT11jarpa17 shows that the distribution of residuals is close
to a normal distribution (Figure 1).
When the two sexes were analyzed separately, the results were largely the same as when the sexes were analyzed
together. The decline over the JARPA period was somewhat larger for females than for males (-0.0297 cm/year
versus -0.0176 cm/year for the models (#BT11jarpa15females and #BT11jarpa15male) with the lowest BIC
values; see electronic attachment).
%OXEEHUWKLFNQHVV³%7´
The analyses of BT7 show a similar pattern, although the decline in blubber thickness is not quite as large as for
BT11 (Table 4a). All models except two KDYHQHJDWLYHFRHIILFLHQWIRU³<HDU1XP´DQGWKHPRGHOZLWKORZHVWBIC is a linear model (#BT7jarpa17):lm(BT7 ~ YearNum + BL m^3 + DateNum + Diatom + LatNum + Lat70 + Sex + YearNum :LongCat11 +DateNum :LongNum) which has slope -0.011cm/year. The BIC values in the all mixed effects modes are all larger

than in #BT7jarpa17.
*LUWK³+DOI*LUWK-X´
$OOPRGHOVH[FHSWRQHKDYHQHJDWLYHFRHIILFLHQWIRU³<HDU1XP´UDQJHGIURP -0.464 cm/year to -0.075cm/year,
and the model with lowest BIC is mixed-effects model with coefficient -0.34 cm/year (SE=0.12) (#HGirthUjarpa25)(Table 4b):lmer(UnbilicusGirth ~ YearNum + BL m + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex +DateNum :LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine)). In the regression trial

ZLWK³+DOI*LUWK-u´, linear effect RI³%/P´ZDVSUHIHUUHGboth by the variance of residuals and BIC.
*LUWK³+DOI*LUWK-D´The analyses of HalfGirth-a show a similar pattern to those of HalfGirth-u. The point estimates of coefficients
IRU³<HDU1XP´DUHDOVRVLPLODU, although the time series is a little shorter in HalfGirth-a since it is only available
from the 1991/92 survey season. Interestingly, the model with lowest BIC is a simple linear model withcoefficient for year -0.46 cm/year (SE=0.054) (#HGirth-Ajarpa6) (Table 4c):lm(AxillaryGirth ~ YearNum + BLm + DateNum + Diatom + Sex)

4)DWZHLJKW³)DW:HLJKW´$OOPRGHOVKDYHQHJDWLYHFRHIILFLHQWIRU³<HDU1XP´ ranged from -0.014 to -0.006 (tons/year), and the modelwith lowest BIC is linear model has coefficient -0.011 tons/year (SE=0.0012) (#FatWjarpa5)(Table 4d):lm(F atWeight ~ YearNum + BL m^3 + DateNum + Diatom + LatNum + LongNum + LongWE + Sex + LeanBW) In the
different regression runs, the large majority had coefficients for ³<HDU1XP´ very close to 0.011 tons/year.

T he J A RP A I I period:%OXEEHUWKLFNQHVV³%7´The analyses of BT11 did not show any clear decline of blubber thickness. None of the models explored hadcoefficients for ³<HDU1XP´which were statistically significant different from zero. In this group of regressions,complicated models tend to have lower BIC than simple models. 7KHFRHIILFLHQWIRU³<HDU1XP´LQWKHPRGHO
with lowest BIC (#BT11jarpaII17) was not statistically significant from zero at 5% level (-0.006, t-value 0.562)(Table 2).
%OXEEHUWKLFNQHVV³%7´
The analyses of BT7 show a similar pattern to those of BT11, and change of BIC between models are small. The
model with the lowest BIC value (#BT7jarpaII18) KDVDSRVLWLYHFRHIILFLHQWIRU³<HDU1XP´, significant at the
5% level (0.661 cm/year) (Table 5a).
lm(BT7 ~ YearNum + BL m^3 + Date.quad + Diatom + LatNum + LongNum + Sex + YearNum :LatNum +Date.quad:LongNum)*LUWK³+DOI*LUWK-X´All of the coefficients for ³YearNum´ have positive values and the model with the lowest BIC (#HGirthUjarpaII19) shows significant and large increase of the girth per year (2.036 cm/year) (Table 5b).

lm(UnbilicusGirth ~ YearNum + BL m + Diatom + LongCat11 + Sex + YearNum :LongCat11 + I(DateNum^2):LongNum)*LUWK³+DOI*LUWK-D´The analyses of HalfGirth-a show a similar pattern to those of HalfGirth-u, and all models except two havepositive coefficient for ³YearNum´. The coefficient for ³YearNum´ in the linear model (HGirth-AjarpaII 14)
with lowest BIC is 0.363 cm/year while the coefficient is not significant at 5% level(Table 5c).
T he J A RP A + J A RP A I I period:%OXEEHUWKLFNQHVV³%7´All models have negative coefficient for ³YearNum´ but the decline were smaller than those in the only JARPA
period ranged from -0.1063 to -0.0056. The mode with lowest BIC is mixed effects model #BT11jarpa&II18(Table 3):lmer(BT11 ~ YearNum + BL m^3 + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum :LongNum +(DateNum|YearCat))%OXEEHUWKLFNQHVV³%7´All models except one have negative coefficient for ³YearNum´ ranging from -0.073 cm/year to -0.006 cm/year,
and the model with lowest BIC is mixed-effects model (coefficient of ³YearNum´ -0.010 cm/year, t=-2.165)(#BT7jarpa&II22)(Table 6a):lmer(BT7 ~ YearNum + BLm + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum :LongNum +(DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))*LUWK³+DOI*LUWK-X´
All models except one have negative coefficient for ³YearNum´ ranged from -0.616 cm/year to -0.198 cm/year,
and the model with lowest BIC is mixed-effects model (coefficient of ³YearNum´ -0.258 cm/year, t=-2.900)(#HGirth-Ujarpa&II24)(Table 6b):lmer(U mbilicusG ~ YearNum + BL m + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex +DateNum :LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))*LUWK³+DOI*LUWK-D´The analyses of HalfGirth-a show a similar pattern to those of HalfGirth-u and all models have negative
coefficient for ³YearNum´ The model with lowest BIC is mixed-effects model (coefficient of ³YearNum´ 0.321 cm/year, t=-3.080)is #HGirth-Ajarpa&II23 (Table 6c)

5lmer(U mbilicusA ~ YearNum + BLm + DateNum + Diatom + LatNum + LongNum + LongCat11 + Sex +DateNum :LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))

D ISC USSI O N
The discussion in the IWC-SC during the last three years has mainly been about whether the decline during the
JARPA period of blubber thickness BT11has been demonstrated with sufficient statistical significance to justify
its acceptance, although the decline in girth at the level of umbilicus and the decline in total fat weight have also
been questioned (Konishi et al. 2008, de la Mare 2011, 2012). The results presented here clearly show that all
five measures of energy storage declined substantially during the JARPA years, and that the declines in all fivevariables are statistically significant at the 5% level, in four of them highly significant. The point estimates of thedecline of BT11 is the same as reported in Konishi et al 2008, and that is also the SE of the estimate (0.0024).
The jack-knife reanalysis by Walløe and the simple mixed model runs by Skaug (Appendix 1) both
overcompensated for the heterogeneity. Also for the decline of girth at the level of umbilicus and the decline intotal fat weight the point estimates in the best mixed models are about the same as in Konishi et al (2008). For
all five dependent variables the values are higher for females than for males, the values increase during thefeeding season and are higher for higher body coverage of diatoms which is assumed to be a measure of how
long time the animal has spent in Antarctic waters.
The results are about the same when each sex is analysed separately, but the decline is somewhat larger for
females than for males. The decline in blubber thickness for females does not change to any large degree when
foetal length is included as an additional independent variable.
De la Mare suggested in the IWC-SC meeting in 2013 that for each whale the distance to the ice edge should be
used as an independent variable in the analyses. The ice edge changes considerably from year to year andchanges also within each research season. It will therefore be an insurmountable task to assign these distances toall whales in the database. As a proxy for the distance to the ice edge we have analysed separately the whales
taken west of 155႖E. In this area the coast goes roughly at a constant latitude, and the ice edge could perhaps as afirst approximation also be regarded as being at a constant latitude, but possibly vary from year to year. We haveanalysed the blubber thickness at the level of umbilicus also for these whales with all the models with interaction
terms and including random effects of latitude category for year category (LatCat | YearCat). The results
remained the same as without these terms in the model with a strong and significant decline in blubber thickness.
The BIC and AIC were also higher in these models than for models without these terms.
In the IWC-SC de la Mare (2012) has argued that whales taken on the same transect most likely would havehighly correlated properties, and for this reason were far from independent of each other. To investigate thispossibility we included random-effects analyses with transects (track lines) as the sampling unit in the mixedeffects models. All of the five models with lowest BIC values for the JARPA period and all models including
random effects with track line as sampling unit still show a decline of coefficient of year similar to that inKonishi et al. (2008) and Sag (2011; Appendix 1). Our interpretation of these results is that the correlation
between whales on the same track line is small or is covered by including spatial explanatory variables as wehave done. Thus whales sampled on the same transect can be regarded as independent of each other. This finding
could be of importance also for other types of investigations.
The results from the JARPA II period are very different from the JARPA period. There is no clear tendency of
increase or decrease in any of the four measures of energy storage.
When the two periods are analysed together, the results are in general a significant decline of the four variables
we have used as proxies for energy storage, but the absolute value of the coefficients with time is smaller thanfor the JARPA period. This could of course be expected.
The decline of energy storage during the 18 years JARPA period is substantial, close to 10% for fat weight andfor the blubber thickness under the dorsal fin (BT11). Approximately at the end of the JARPA period the decline
came to an end, and there is no further decline during the JARPA II period, nor an increase. The interpretationmust be that there was a substantial decline in food availability during the JARPA period. This interpretation is
supported by the finding of a decrease in stomach contents weights during the JARPA and JARPA II periods
1990/91 to 2009/10 (Konishi et al 2013).

6

What could be the explanation of the large decline in food availability during the 1990-ies and the following few
years, followed by a constant food availability during the next years. One possibility is that the decline is causedby competition with rapidly growing humpback stocks during the JARPA period, and that this growth later has
slowed down to a level which did not cause further difficulties for minke whale foraging. Another possibility isthat some fundamental changes in the production of krill took place during these years, for instance caused byclimatic changes, with the production decreasing from one level and levelling off at another lower level
The increase in the five proxies for energy storage from west to east is in need of an explanation. It could be areflection of a better production of krill in the eastern JARPA area which is the one region of the Antarctic where
the ice krill E crystallorophus dominates E. superba . It could also be explained if the I-stock and P-stock ofminke whales had different feeding conditions north of the Antarctic feeding area. The gradient could then havebeen caused by the mixing of whales from the two stocks in the JARPA research area, as Kitakado et al (2013)
have shown take place.

Conclusions:
On the statistical methods: De la Mare was right when he pointed out that simple multiple linear regressions
could be dangerous when the multidimensional material could contain various forms of heterogeneity. However,when ordinary linear regressions are carried out on different subsets of the total material resulting inapproximately the same results, as in Konishi at al. (2008), although not all regression runs were published, thepoint estimates of the regression coefficients are likely to be correct. The most dangerous part of the results islikely to be the SE of the coefficients. A jack-knife analysis can often take care of that problem, but may
overcompensate for the heterogeneity, as has happened in the present example.
On the substance: In this paper and in a parallel paper (Konishi et al 2013) from the JARPA and the JARPA II
programmes we have shown that fundamental changes have taken place in the eastern part of the Antarctic
marine ecosystem during the 1990-ies resulting in worsened feeding conditions for minke whales.
A C K N O W L E D G E M E N TS
We  would  like  to  thank  all  the  captains  and  crews  who  were  involved  in  JARPA  and  JARPA  II  surveys.  Thanks  are  also  due  to  H.K. Solvang  for  advice  on  statistical  method,  to  T.  Tamura  for  checking  the  dataset  and  to  D.  
Butterworth,  K.  Liestøl  and  T.  Schweder  for  comments  on  the  manuscript.    

R E F E R E N C ES
Claeskens, G. and Hjort, N.L. (eds). 2008. Model Selection and Model Averaging (Cambridge Series in Statistical andProbabilistic Mathematics). Cambridge University Press, Cambridge.
Bates, D., Maechler, M. Bolker, B. and Walker, S. 2013. lme4: Linear mixed-effects models using Eigen and S4. R package
version 1.0-5. ; http://CRAN.R-project.org/package=lme4
de la Mare, W.K. 2011. Are reported trends in Antarctic minke whale body condition reliable? IWC-SC/63/O16, 1-25.
de la Mare, W.K. 2012. Lurking variables and the interpretation of statistical analyses of data collected under JARPA. IWCSC/64/EM3, 1-65.
Kitakado, T. Schweder, T. Kanda, N. Pastene, L.A. and Walløe, L. 2013. Dynamic population segregation by genetics andmorphometrics in Antarctic minke whales. SC/F14/J29.
Konishi, K., Tamura, T. and Walløe, L. 2006. Yearly trend of energy storage in the Antarctic minke whale Balaenoptersbonarensis in the JARPA research area. IWC-SC/D06/J19, 1-6.
Konishi, K., Tamura, T., Zenitani, R., Bando, T., Kato, H. and Walløe, L. 2008. Decline in energy storage in the Antarctic
minke whale ( Balaenopters bonarensis) in the Southern Ocean. 2008, Polar Biology 31(12):1509-1520.
Konishi, K., Hakamada, T., Kiwada, H., Kitakado, T. and Walløe, L. in press (accepted in 2013). Decrease in stomach
contents in the Antarctic minke whale ( Balaenoptera bonaerensis) in the Southern Ocean. Polar Biology, also SC/F14/J14.
R Core Team. 2013. R: A language and environment for statistical computing. R Foundationfor Statistical Computing,
Vienna, Austria; http://www.R-project.org/.2013.

7

LogLik-5196.793-5223.098-5223.709-5223.648-5200.599-5213.326-5213.790-5214.572-5206.531-5282.577-5222.711-5204.465-5234.472-5188.787-5228.864

BT11jarpa10
BT11jarpa11
BT11jarpa12
BT11jarpa13
BT11jarpa14
BT11jarpa15
BT11jarpa16

BT11jarpa17

BT11jarpa18
BT11jarpa19
BT11jarpa20
BT11jarpa21
BT11jarpa22
BT11jarpa23
BT11jarpa24-5267.378-5297.075-5267.073-5266.802-5264.549-5223.732-5220.485-5207.125-5220.293

0.5795507
0.5870889
0.579474
0.5794055

BT11jarpa1
BT11jarpa2
BT11jarpa3
BT11jarpa4

BT11jarpa5
BT11jarpa6
BT11jarpa7
BT11jarpa8
BT11jarpa9

Var. of resid.

Model No.

AIC

10552.76
10612.15
10552.15
10551.6

10613.43
10607.69
10609.63
10658.810626.11

23 10459.06 10607.020
23 10611.15 10759.11
23 10491.42 10639.38
26 10460.93 10628.19
29 10526.94
10713.5
32 10441.57 10647.43
29 10515.73 10702.28-0.0189-0.0203-0.0230-0.0188-0.0203-0.0197-0.0201

0.0296-0.0252-0.0299-0.0251-0.0198-0.0206-0.0205-0.0203-0.0198-0.0225-0.0231-0.0220-0.0231-0.0196-0.0211-0.0196-0.0196

BIC Year Effects

10610.65
10670.05
10610.04
10609.5

29 10451.59 10638.14
10486.2 10614.85
20
20 10487.42 10616.08
10487.3 10615.95
2010459.2 10645.75
29
20 10466.65 10595.31
19 10465.58 10587.81
18 10465.14 10580.94

10549.110
19 10485.46
20 10480.97
29 10472.25
22 10484.59

9
9
9
9

No. ofparameter

Table1 Model selection for the trend of BT11 in JARPA period (1987/88-2004/05) 18 years
t-value-2.853-8.165-7.212-2.850-3.062-3.139-3.0601.118-7.424-0.848-3.701-7.714-8.670-8.631-8.564-8.795-9.587-9.811-9.192-9.805-8.715-9.358-8.721-8.726

ModelsYearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat))YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine) + (DateNum|LatCat11))
YearNum + BLm +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))

YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LongCat11)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LatNum)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:DateNum)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongCat11)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongCat11 + Sex + DateNum:LongNum)
YearNum + BLm^3 +DateNum +Diatom + LongCat11 + Sex + DateNum:LongNum)

YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongWE + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Lat70 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + LatCat11 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Area4 + Sex)

YearNum + BLm +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm +Date^2 +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^2 +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + Sex)

LogLik-2840.053-2848.721-2838.729-2839.581-2836.100-2836.134-2833.198

BT11jarpaII17

BT11jarpaII18
BT11jarpaII19
BT11jarpaII20
BT11jarpaII21
BT11jarpaII22
BT11jarpaII23
BT11jarpaII24

23
23
23
26
29
32
29

19
10
10
10
19
10

10
19
10
16
12

9
9
9
9
9
9

No. ofparameter

AIC

5713.442
5717.848
5713.238
5745.261
5723.822

5726.105
5743.441
5723.457
5731.162
5730.199
5736.267
5724.397

5858.2215875.556
5855.572
5880.515896.779
5920.085890.977

0.0754-0.0031-0.03360.04400.01930.05500.07680.0000-0.0084
0.3267-0.03190.0090-0.0065-0.0030
0.0022-0.0024-0.0014-0.0008-0.0042-0.0027-0.0042-0.0042-0.0027-0.0027

BIC Year Effects

5745.1195707.391
5744.213
5743.455706.515705.754

5608.809 5717.947
5655.796 5713.237
5653.568 5711.009
5652.754 5710.196
5616.558 5725.697
5646.399 5703.841

5656.001
5608.709
5655.796
5653.355
5654.892

5693.422
5655.694
5692.516
5691.753
5654.813
5654.056

t-value

1.568-0.210-1.945
0.831
0.379
1.236
1.462

0.001
-0.5361.560-1.6360.638-0.586-0.2690.160-0.213-0.122-0.071-0.373-0.246-0.373-0.375-0.246-0.248

29
30
30
29
30
39
39
30

10
19
20
29
22

9
9
9
9

16184.97
16186.89
16182.76
16180.916180.33
16129.62
16129.62
16151.94

16359.3
16287.86
16289.86
16268.16
16290.73

16360.01
16392.46
16358.67
16357.5

No. ofAIC
parameter

16383.32
16392.08
16387.95
16379.26
16385.53
16396.37
16396.37
16357.14

16427.7
16417.82
16426.66
16466.52
16441.21

16421.57
16454.02
16420.22
16419.06

BIC-8044.414
23 16134.83 16292.14
BT11jarpa&II19-8178.390
23 16402.78 16560.10
BT11jarpa&II20-8073.202
2316192.4 16349.72
BT11jarpa&II21-8036.293
26 16124.59 16302.42
BT11jarpa&II22-8058.704
29 16175.41 16373.76
BT11jarpa&II23-8080.035
32 16224.07 16442.95
BT11jarpa&II24-8067.573
29 16193.15 16391.50
Bold Best three models, Italic the best model among each group

BT11jarpa&II18-8063.484-8063.444-8061.378-8061.451-8060.166-8025.809-8025.809-8045.970

BT11jarpa&II10
BT11jarpa&II11
BT11jarpa&II12
BT11jarpa&II13
BT11jarpa&II14
BT11jarpa&II15
BT11jarpa&II16
BT11jarpa&II17-8171.005-8187.228-8170.333-8169.750-8169.650-8124.932-8124.929-8105.081-8123.366

0.6245668
0.6275089
0.624445
0.6243397

Var. of resid. LogLik

BT11jarpa&II5
BT11jarpa&II6
BT11jarpa&II7
BT11jarpa&II8
BT11jarpa&II9

BT11jarpa&II1
BT11jarpa&II2
BT11jarpa&II3
BT11jarpa&II4

Model No.

-0.0078-0.0063-0.0111-0.0072-0.0091-0.0069-0.0056-0.0290-0.0285-0.0951-0.1057-0.1063-0.0538-0.0538-0.0782-0.0093-0.0091-0.0091-0.0074-0.0086-0.0092-0.0095-0.0092-0.0093-1.554-3.694-4.740-1.388-1.817-1.321-0.928-2.984-2.888-2.821-5.511-5.543-2.456-2.456-3.958-6.245-5.608-5.594-4.455-5.238-6.232-6.415-6.238-6.244

Year Effects t-value

Table3 Model selection for the trend of BT11 in JARPA and JARPA II period (1987/88-20010/11) 24 years-2785.404-2817.898-2816.784-2816.377-2789.279-2813.200

BT11jarpaII12
BT11jarpaII13
BT11jarpaII14
BT11jarpaII15
BT11jarpaII16-2837.711-2818.847-2837.258-2836.876-2818.407-2818.028-2818.001-2785.355-2817.898-2810.677-2815.446

0.6849413
0.673836
0.6846725
0.6844461
0.6735788
0.673358

Var. of resid.

BT11jarpaII7
BT11jarpaII8
BT11jarpaII9BT11jarpaII10
BT11jarpaII11

BT11jarpaII1
BT11jarpaII2
BT11jarpaII3
BT11jarpaII4
BT11jarpaII5
BT11jarpaII6

Model No.

Table2 Model selection for the trend of BT11 in JARPA II period (2005/06-20010/11) 6 years
ModelsYearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat))YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine) + (DateNum|LatCat11))
YearNum + BLm +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))

YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LongCat11)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum)
YearNum + BLm^3 +DateNum +Diatom + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum)
YearNum + BLm^3 +DateNum +Diatom + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum + YearNum:DateNum)
YearNum + BLm^3 +DateNum +Diatom + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum + DateNum:LongCat11)
YearNum + BLm^3 +Diatom + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum + DateNum:LongCat11)
YearNum + BLm^3 +DateNum +Diatom + LongNum + LongCat11 + Sex + YearNum:LongCat11 + YearNum:LatNum + DateNum:LongNum)

YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongWE + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Lat70 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + LatCat11 + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Area4 + Sex)

YearNum + BLm +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm +Date^2 +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^2 +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + Sex)

ModelsYearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat))YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine) + (DateNum|LatCat11))
YearNum + BLm +DateNum +Diatom + LatNum + LongNum + LongCat11 + Sex + DateNum:LongNum + (DateNum|YearCat) + (DateNum|LongCat11) + (DateNum|TrackLine))

YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + YearNum:LongCat11)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + YearNum:Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + YearNum:LatNum)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + YearNum:Date^2)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + Date^2:LongCat11)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex + Date^2:LongNum)

YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + LongWE + Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + LongCat11 + Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Lat70 + Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + LatCat11 + Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Area4 + Sex)

YearNum + BLm +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm +Date^2 +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^2 +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^3 +DateNum +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^2 +Date^2 +Diatom + LatNum + LongNum + Sex)
YearNum + BLm^3 +Date^2 +Diatom + LatNum + LongNum + Sex)

-4426.920-4426.893-4426.920-4426.896-4425.689-4406.409-4418.531-4419.658-4430.359-4517.981-4463.336-4427.865-4470.212-4428.872-4457.480

BT7jarpa10
BT7jarpa11
BT7jarpa12
BT7jarpa13
BT7jarpa14
BT7jarpa15
BT7jarpa16

BT7jarpa17

BT7jarpa18
BT7jarpa19
BT7jarpa20
BT7jarpa21
BT7jarpa22
BT7jarpa23
BT7jarpa24-17758.220-17786.440-17852.660
17814.890-17784.670-17827.150-17771.360

Hgirth-Ujarpa19
Hgirth-Ujarpa20
Hgirth-Ujarpa21
Hgirth-Ujarpa22
Hgirth-Ujarpa23
Hgirth-Ujarpa24

Hgirth-Ujarpa25-17819.370-17831.090-17832.770-17830.120-17811.120-17817.010

Hgirth-Ujarpa13
Hgirth-Ujarpa14
Hgirth-Ujarpa15
Hgirth-Ujarpa16
Hgirth-Ujarpa17
Hgirth-Ujarpa18-17879.050-17885.490-17883.090-17889.350-17891.290-17879.000-17834.770-17833.940-17823.480-17827.590-17834.810

142.04890
142.44810
142.29950
142.68840

Var. of resid. LogLik

Hgirth-Ujarpa6
Hgirth-Ujarpa7
Hgirth-Ujarpa8
Hgirth-Ujarpa9
Hgirth-Ujarpa10
Hgirth-Ujarpa11

Hgirth-Ujarpa1
Hgirth-Ujarpa2
Hgirth-Ujarpa3
Hgirth-Ujarpa4
Hgirth-Ujarpa5

Modelsb) Half Girth at the level of umbilicus (HalfGirth-u)-4491.517-4454.353-4486.970-4466.689-4483.777

BT7jarpa5
BT7jarpa6
BT7jarpa7BT7jarpa8
BT7jarpa9

29

23
23
23
26
29
32

28
19
19
19
29
20

10
19
20
29
22
18

No. ofparameter
9
9
9
9
8

23
23
23
26
29
32
29

20
21
20
21
21
30
21
20

10
19
10
19
12

35574.4435618.87
35751.32
35675.79
35621.33
35712.30
35606.71

35694.75
35700.19
35703.5435698.25
35680.25
35674.02

35778.01
35707.54
35707.88
35704.95
35699.17
35705.62

35776.0935788.97
35784.18
35796.70
35798.58

AIC

8906.729081.968972.678907.738998.43
8921.74
8972.968893.848895.798893.848895.798893.38
8872.828879.06
8879.329003.038946.718993.94
8971.38
8991.55

35760.94

35766.79
35899.24
35823.71
35788.5435898.80
35812.51

35874.8235822.38
35825.74
35820.44
35866.75
35802.64

35842.32
35829.73
35836.50
35891.46
35840.66
35821.38

35833.98
35846.85
35842.06
35854.58
35850.03

BIC

9054.749229.98
9120.699075.059185.06
9127.689159.599008.039022.55
9030.939022.55
9030.949028.539065.899014.219067.399068.98
9058.30
9093.659068.78-2.975-7.721-6.806-3.043-2.871-3.378-3.119-2.074-1.256-1.244-1.256-0.007-1.8912.003-2.558-8.235-8.857-8.552-8.276-8.698-0.340-0.328-0.420-0.445-0.306-0.312-0.337-0.286-0.5620.653-0.154-0.099-0.075-0.427-0.464-0.467-0.451-0.456-0.458-0.418-0.434-0.418-0.418-0.432-2.800-2.710-10.870-8.890-2.530-2.420-2.760-0.688-10.577
1.183-1.452-0.840-0.706-12.104-12.626-12.699-12.041-12.410-12.473-11.867-12.317-11.863-11.845-12.267

Year Effects t-value-0.018-0.016-0.018-0.019-0.019-0.016-0.019-0.011-0.008-0.008-0.0080.000-0.0140.033-0.017-0.016-0.018-0.016-0.016-0.017

Table 4 Regression results of four response variables for only JARPA perioda) Blubber thickness at the level of umbilicus (BT7)
No. ofModelsVar. of resid. LogLik
AIC
BIC
Year Effects t-value
parameter
BT7jarpa1
0.41182-4493.924
99005.859063.77-0.015-8.162
BT7jarpa2
0.41672-4521.180
99060.369118.28-0.017-8.786BT7jarpa3
0.41174-4493.477
99004.95
9062.87-0.015-8.170BT7jarpa4
0.41167-4493.066
99004.139062.05-0.015-8.177

LinearModel.5.I1
LinearModel.5.I2
LinearModel.5.I3
LinearModel.5.I4
LinearModel.5.I5
LinearModel.5.I6
LMER.6.I6.1
LMER.6.I6.2
LMER.6.I6.3
LMER.6.I6.4
LMER.6.I6.5
LMER.6.I6.6
LMER.6.I6.5.1

FatWjarpa10
FatWjarpa11
FatWjarpa12
FatWjarpa13
FatWjarpa14
FatWjarpa15
FatWjarpa16
FatWjarpa17
FatWjarpa18
FatWjarpa19
FatWjarpa20
FatWjarpa21
FatWjarpa22

LinearModel.6
LinearModel.7
LinearModel.8
LinearModel.9

LinearModel.5

FatWjarpa5
FatWjarpa6
FatWjarpa7
FatWjarpa8
FatWjarpa9

LinearModel.1
LinearModel.2
LinearModel.3
LinearModel.4

FatWjarpa1
FatWjarpa2
FatWjarpa3
FatWjarpa4

Models
0.023120.023120.02307
0.02303272.224246.047258.512272.559279.065240.504
283.057

337.098
329.096
329.083331.208
338.925330.655

334.038
330.001
337.113330.657

329.077

322.421322.391323.146
323.798

24
24
24
27
30
33
30

21
12
12
12
21
12

21
12
21
13

11

No. ofparameter
10
10
10
10

29
32
29

26

-14907.680-14920.730-14887.950-14917.320

23
23
23

17
8
8
17
8

8
17
8
16
10

7

No. ofparameter
9
9
9
9
8

-14917.820-14950.360-14927.080-14923.760-14939.880-14939.860-14928.090-14938.240-14939.290-14923.430-14939.550-14930.190-14938.800-14940.140-14939.260-14944.480-14944.750-14953.440-14939.740

Var. of resid. LogLik

LMER.6.I6.1
LMER.6.I6.2
LMER.6.I6.3
LMER.6.I6.4
LMER.6.I6.5
LMER.6.I6.6
LMER.6.I6.5.1

Hgirth-Ajarpa17
Hgirth-Ajarpa18
Hgirth-Ajarpa19
Hgirth-Ajarpa20
Hgirth-Ajarpa21
Hgirth-Ajarpa22
Hgirth-Ajarpa23

old nameLinearModel.1.2.I1
LinearModel.1.2.I2
LinearModel.1.2.I3
LinearModel.1.2.I4
LinearModel.1.2.I5

Hgirth-Ajarpa12
Hgirth-Ajarpa13
Hgirth-Ajarpa14
Hgirth-Ajarpa15
Hgirth-Ajarpa16d) Fat Weight (ton)LinearModel.5
LinearModel.6
LinearModel.7
LinearModel.8
LinearModel.9

Hgirth-Ajarpa7
Hgirth-Ajarpa8
Hgirth-Ajarpa9
Hgirth-Ajarpa10
Hgirth-Ajarpa11

170.09770
170.57240
170.59760
171.39000

Var. of resid. LogLik

LinearModel.1.2

LinearModel.1
LinearModel.2
LinearModel.3
LinearModel.4
LinearModel.1.1

old name

Hgirth-Ajarpa6

Hgirth-Ajarpa1
Hgirth-Ajarpa2
Hgirth-Ajarpa3
Hgirth-Ajarpa4
Hgirth-Ajarpa5

Modelsc) Half Girth at the level of axilla (HalfGirth-a)-496.45-444.09-469.02-491.12-498.13-415.01-506.11-632.20-634.19-634.17-638.42-635.85-637.31-626.08-636.00-632.23-635.31-636.15-624.84-624.78-626.29-627.60

AIC

29881.64
29946.72
29900.16
29886.64
29873.36
29905.4629833.91

29881.53
29895.75
29895.73
29890.19
29892.48

29894.58
29880.86
29895.10
29892.39
29897.60

29894.29AIC
29896.51
29906.96
29907.51
29924.87
29895.47-387.46-335.11-360.04-368.51-361.90-265.15-369.88-536.83-579.70-579.67-583.92-540.49-582.82-530.71-581.51-536.86-576.28-586.20-579.43-579.37-580.88-582.19

BIC

30024.9030089.98
30043.4230048.5930053.99
30104.78
30014.5429987.41
29945.58
29945.56
29996.0729942.31

29944.41
29986.75
29944.93
29992.05
29959.88

29937.89

BIC
29952.57
29963.0229963.57
29980.93
29945.30-2.600-7.270-6.870-2.520-2.620-2.650-2.560-2.660-0.745-4.408-8.819-8.726-8.239-8.111-8.472-8.297-8.117-8.592-8.457-8.403-8.505-8.539-8.405-0.010-0.012-0.011-0.010-0.010-0.009-0.010-0.014-0.011-0.009-0.006-0.012-0.011-0.012-0.011-0.011-0.011-0.011-0.011-0.011-0.011-0.011-4.021-9.201-8.018-4.277-4.231-3.484-4.201-3.580-5.920-0.501-1.875-8.994-8.858-9.160-9.116-8.832-9.129-9.067-9.027-9.275-9.049-9.070Year Effects t-value-0.389-0.436-0.483-0.391-0.410-0.432-0.405-0.297-0.235-0.547-0.490-0.472-0.451-0.463-0.459-0.458-0.447-0.464-0.462-0.459-0.465-0.468-0.457

Year Effects t-value

-8814.566-8814.565-8814.485-8813.393-8798.053-8807.017-8807.084-8831.733-8858.305-8841.682-8830.472-8829.475-8826.679-8813.655

HGirth-UjarpaII13
HGirth-UjarpaII14
HGirth-UjarpaII15
HGirth-UjarpaII16
HGirth-UjarpaII17
HGirth-UjarpaII18
HGirth-UjarpaII19

HGirth-UjarpaII20
HGirth-UjarpaII21
HGirth-UjarpaII22
HGirth-UjarpaII23
HGirth-UjarpaII24
HGirth-UjarpaII25
HGirth-UjarpaII26-8930.420-8923.608-8933.576-8937.833-8926.748-8930.969-8923.310-8857.565-8856.718-8841.066-8851.187-8858.807

151.47040
150.56520
151.89160
152.46150

Var. of resid. LogLik

HGirth-UjarpaII7
HGirth-UjarpaII8
HGirth-UjarpaII9
HGirth-UjarpaII10
HGirth-UjarpaII11
HGirth-UjarpaII12

HGirth-UjarpaII1
HGirth-UjarpaII2
HGirth-UjarpaII3
HGirth-UjarpaII4
HGirth-UjarpaII5
HGirth-UjarpaII6

Modelsb) Half Girth at the level of umbilicus (HalfGirth-u)

BT7jarpaII18
BT7jarpaII19
BT7jarpaII20
BT7jarpaII21
BT7jarpaII22
BT7jarpaII23
BT7jarpaII24

17866.62
17753.13
17753.44
17734.13
17746.37
17753.61

17878.84
17865.22
17885.15
17893.67
17871.50
17879.94

AIC

4884.624909.224881.694887.744885.33
4905.174876.7117923.91
17861.98
17868.01
17883.08
17872.41
17856.73

17930.40
17916.78
17936.71
17945.23
17923.06
17931.50

BIC

5016.735041.34
5013.815037.085051.915088.985043.294833.144875.524844.074837.494840.634882.30

23
23
23
26
29
32
29

17709.47
17762.61
17729.36
17712.94
17716.95
17717.36
17685.31

17841.23
17894.37
17861.13
17861.89
17883.09
17900.68
17851.45

27 17683.13 17837.81
28 17685.13 17845.54
28 17684.97 17845.38
28 17682.79 17843.19
37 17670.11 17882.07
28 17670.03 17830.44
27 17668.17 17822.85

9
18
19
25
21
17

No. ofparameter
9
9
9
9
9
9

23
23
23
26
29
32
29

4766.38
4786.634780.05
4777.444767.424769.95

0.631
0.466
0.097
0.745
0.693
0.721
0.690

2.036

0.480
0.486
0.315
0.028
0.557
2.209

0.444
0.516
0.559
0.699
0.561
0.498

0.421
0.432
0.418
0.414
0.429
0.426

Year Effects-0.028-0.021-0.051
0.010
0.005
0.011
0.006

0.661

-0.018-0.040
0.446
0.481
0.298

1.202
2.101
0.351
1.550
1.356
1.482
1.312

2.278

0.526
0.525
0.315
0.030
0.144
2.182

2.638
2.479
2.653
3.256
2.657
2.397

2.503
2.577
2.484
2.459
2.558
2.533

t-value-0.951-1.684-3.304
0.345
0.231
0.550
0.261

3.599

-2419.309-2431.611-2417.846-2417.868-2413.665-2420.586-2409.356

BT7jarpaII17

19
10
10
11
20
11

-1.204-3.081
2.575
2.766
1.373

-2364.191-2383.315-2380.023-2377.720-2363.708-2373.976-0.032-0.026-0.030-0.026-0.029BT7jarpaII12
BT7jarpaII13
BT7jarpaII14
BT7jarpaII15
BT7jarpaII16

4843.654873.434844.154878.974850.07-3.457-2.248-3.226-2.627-3.1444786.214764.294786.714787.06
4781.14-2383.103-2363.147-2383.356-2377.531-2378.572

BT7jarpaII7BT7jarpaII8
BT7jarpaII9BT7jarpaII10
BT7jarpaII11

10
19
10
16
12

-3.453-3.353-3.454-3.457-3.354-3.356t-value

Table 5 Regression results of three response variables for only JARPA II perioda) Blubber thickness at the level of umbilicus (BT7)
No. ofModelsVar. of resid. LogLik
AIC
BIC
Year Effects
parameter
BT7jarpaII1
0.47026-2403.760
94825.524877.22-0.032
BT7jarpaII2
0.46275-2385.182
94788.364840.06-0.031
BT7jarpaII3
0.46997-2403.030
94824.06
4875.76-0.032
BT7jarpaII4
0.46970-2402.389
94822.784874.48-0.032
BT7jarpaII5-2384.466
94786.934838.63-0.031
BT7jarpaII6-2383.828
94785.664837.35-0.031

HGirth-AjarpaII20
HGirth-AjarpaII21
HGirth-AjarpaII22
HGirth-AjarpaII23
HGirth-AjarpaII24
HGirth-AjarpaII25
HGirth-AjarpaII26

HGirth-AjarpaII15
HGirth-AjarpaII16
HGirth-AjarpaII17
HGirth-AjarpaII18
HGirth-AjarpaII19

HGirth-AjarpaII14

HGirth-AjarpaII13

HGirth-AjarpaII7
HGirth-AjarpaII8
HGirth-AjarpaII9
HGirth-AjarpaII10
HGirth-AjarpaII11
HGirth-AjarpaII12

HGirth-AjarpaII1
HGirth-AjarpaII2
HGirth-AjarpaII3
HGirth-AjarpaII4
HGirth-AjarpaII5
HGirth-AjarpaII6

ModelsAxillaryLMER.6.I6.1
AxillaryLMER.6.I6.2
AxillaryLMER.6.I6.3
AxillaryLMER.6.I6.4
AxillaryLMER.6.I6.5
AxillaryLMER.6.I6.6
AxillaryLMER.6.I6.5.1

LinearModel.6.1.I1.2
LinearModel.6.1.I1.3
LinearModel.6.1.I1.4
LinearModel.6.1.I1.5
LinearModel.6.1.I1.6

170.01230
169.29180
170.83360
172.01210
170.10770
171.27680

Var. of resid.

LinearModel.6.1.I1.1

LinearModel.6.1.I1

LinearModel.5
LinearModel.6
LinearModel.7
LinearModel.8
LinearModel.9
LinearModel.6.1

LinearModel.1
LinearModel.2
LinearModel.3
LinearModel.4
LinearModel.2.1
LinearModel.2.2

old namec) Half Girth at the level of axilla (HalfGirth-a)-8968.984-8980.465-8970.076-8968.611-8965.314-8965.892-8945.467-8962.914-8961.627-8963.191-8954.665-8963.443-8952.585-8964.480-8995.672-8961.914-8961.362-8945.307-8955.813-8963.023-9001.861-8997.066-9007.302-9015.064-9002.494-9010.227

LogLik

23
23
23
26
29
32
29

18
18
18
27
18

27

17

10
19
20
26
22
18

No. ofparameter
9
9
9
9
9
9
AIC

BIC

18068.57
18070.55
18077.17
18091.39
18081.51
18065.05

18073.22
18063.63
18084.10
18099.63
18074.49
18089.95

17983.97
18006.93
17986.15
17989.22
17988.63
17995.78
17948.93

18115.58
18138.54
18117.76
18138.00
18154.57
18178.90
18114.88

17959.17 18113.67
17962.97 18060.25
17961.83 18064.83
17959.25 18062.25
17962.38 18065.38
17963.33 18117.83
17962.89 18065.89

18011.34
17961.83
17962.72
17942.61
17955.63
17962.05

18021.72
18012.13
18032.60
18048.13
18022.99
18038.45

0.029
0.298
0.357
0.118
0.089
-0.1430.107

0.040-0.507
0.815
0.247
0.413

0.122

0.363

0.300
0.400
0.438
0.625
0.449
0.422

0.267
0.273
0.262
0.256
0.268
0.261

Year Effects

0.033
1.264
1.202
0.128
0.109
-0.1910.127

0.142-1.204
2.318
0.952
1.938

0.122

1.726

1.677
1.796
1.940
2.715
1.984
1.894

1.494
1.531
1.461
1.421
1.498
1.458

t-value

-6818.411-26677.940-26825.730-26714.600-26721.770-26653.200-26762.900-26623.460

HGirth-Ujarpa&II18
HGirth-Ujarpa&II19
HGirth-Ujarpa&II20
HGirth-Ujarpa&II21
HGirth-Ujarpa&II22
HGirth-Ujarpa&II23

HGirth-Ujarpa&II24-26743.000-26742.130-26740.870-26742.030-26703.710-26724.950

HGirth-Ujarpa&II12
HGirth-Ujarpa&II13
HGirth-Ujarpa&II14
HGirth-Ujarpa&II15
HGirth-Ujarpa&II16
HGirth-Ujarpa&II17-26878.740-26882.120-26886.370-26897.310-26879.390-26877.200-26820.670-26819.750-26801.660-26796.980-26797.270

148.04160
148.18740
148.37150
148.84530

Var. of resid. LogLik

HGirth-Ujarpa&II6
HGirth-Ujarpa&II7
HGirth-Ujarpa&II8
HGirth-Ujarpa&II9
HGirth-Ujarpa&II10
HGirth-Ujarpa&II11

HGirth-Ujarpa&II1
HGirth-Ujarpa&II2
HGirth-Ujarpa&II3
HGirth-Ujarpa&II4
HGirth-Ujarpa&II5

Modelsb) Half Girth at the level of umbilicus (HalfGirth-u)

BT7jarpa&II22-6847.282-6974.155-6881.731-6833.623-6832.767-6912.868

BT7jarpa&II16
BT7jarpa&II17
BT7jarpa&II18
BT7jarpa&II19
BT7jarpa&II20
BT7jarpa&II21

23
23
23
26
29
32
29

30
31
31
31
40
31

9
18
19
28
21
20

No. ofparameter
9
9
9
9
8

29

23
23
23
26
29
32

20
21
21
21
30
21

53304.91

53401.88
53697.47
53475.20
53495.53
53364.40
53589.80

53546.00
53546.25
53543.74
53546.0753487.41
53511.89

53772.40
53677.34
53677.51
53659.32
53635.9653634.5453775.48
53782.2353790.75
53812.63
53774.79

AIC

13694.82

13740.56
13994.31
13809.46
13719.25
13723.53
13889.74

13793.56
13795.44
13789.02
13788.14
13746.10
13773.66

53503.0953559.05
53854.64
53632.37
53673.21
53562.58
53808.48

53751.01
53758.09
53755.58
53757.91
53760.76
53723.73

53833.9053800.35
53807.34
53850.66
53779.46
53771.2153836.98
53843.73
53852.25
53874.13
53829.46

BIC

13893.23

13897.92
14151.67
13966.82
13897.13
13921.94
14108.67

13930.39
13939.11
13932.69
13931.82
13951.35
13917.34-0.258-0.229-0.262-0.350-0.198-0.265-0.228-0.582-0.6160.179-0.522-0.586-0.369-0.335-0.336-0.340-0.317-0.309-0.307-0.334-0.336-0.334-0.335-0.339Year Effects-0.010-0.008-0.006-0.009-0.009-0.008-0.008-0.016-0.015-0.073-0.0230.011-0.017-6876.779-6876.720-6873.510-6873.071-6843.052-6865.831

BT7jarpa&II10
BT7jarpa&II11
BT7jarpa&II12
BT7jarpa&II13
BT7jarpa&II14
BT7jarpa&II15

13983.32
13993.1413980.63
14018.02
13997.82-0.007-0.007-0.008-0.006-0.00813914.91
13863.15
13912.21
13888.03
13915.72-6947.453-6912.576-6946.106-6925.016-6945.859

BT7jarpa&II5
BT7jarpa&II6
BT7jarpa&II7
BT7jarpa&II8
BT7jarpa&II9

10
19
10
19
12

-0.007-0.008-0.007-0.007

Year Effects

Table 6 Regression results of three response variables for JARPA and JARPA II perioda) Blubber thickness at the level of umbilicus (BT7)
No. ofModelsVar. of resid. LogLik
AIC
BIC
parameter
BT7jarpa&II1
0.43692 -6949.657
913917.31
13978.89
BT7jarpa&II2
0.43854 -6962.446
913942.89
14004.47
BT7jarpa&II3
0.43679 -6948.590
913915.18
13976.75
BT7jarpa&II4
0.43667-6947.626
913913.25
13974.83-2.900-2.490-9.990-9.360-2.010-3.050-2.200-3.846-4.0130.448-3.314-2.643-2.375-14.863-13.725-13.793-12.457-12.255-12.231-14.576-14.686-14.598-14.613-15.110t-value-2.165-1.585-3.943-4.500-1.967-1.776-1.727-5.256-4.468-3.224-5.7351.704-5.650-6.029-5.420-6.181-5.042-6.077-6.013-6.177-6.020-6.028t-value

old name

AxillaryLMER.6.I6.1
AxillaryLMER.6.I6.2
AxillaryLMER.6.I6.3
AxillaryLMER.6.I6.4
AxillaryLMER.6.I6.5
AxillaryLMER.6.I6.6

LinearModel.5.I1
LinearModel.5.I2
LinearModel.5.I3
LinearModel.5.I3.1
LinearModel.5.I3.2
LinearModel.5.I3.3
LinearModel.5.I3.3.1

LinearModel.5
LinearModel.6
LinearModel.7
LinearModel.8
LinearModel.9

LinearModel.1
LinearModel.2
LinearModel.3
LinearModel.4

HGirth-Ajarpa&II23 AxillaryLMER.6.I6.5.1

HGirth-Ajarpa&II17
HGirth-Ajarpa&II18
HGirth-Ajarpa&II19
HGirth-Ajarpa&II20
HGirth-Ajarpa&II21
HGirth-Ajarpa&II22

HGirth-Ajarpa&II10
HGirth-Ajarpa&II11
HGirth-Ajarpa&II12
HGirth-Ajarpa&II13
HGirth-Ajarpa&II14
HGirth-Ajarpa&II15
HGirth-Ajarpa&II16

HGirth-Ajarpa&II5
HGirth-Ajarpa&II6
HGirth-Ajarpa&II7
HGirth-Ajarpa&II8
HGirth-Ajarpa&II9

HGirth-Ajarpa&II1
HGirth-Ajarpa&II2
HGirth-Ajarpa&II3
HGirth-Ajarpa&II4

Modelsc) Half Girth at the level of axilla (HalfGirth-a)

LogLik-23926.130-23992.800-23933.580-23925.480-23902.230-23921.570-23867.890-23915.370-23915.320-23910.060-23909.850-23891.480-23903.290-23903.290-23974.180-23942.450-23972.580-23959.570-23965.620

172.34170 -23981.540
172.43630 -23983.180
172.99800 -23992.950
173.97510 -24009.860

Var. of resid.

23
23
23
26
29
32
29

20
21
21
22
31
22
21

10
20
11
19
12

No. ofparameter
9
9
9
9
AIC

47793.7847898.26
48031.60
47913.17
47902.95
47862.46
47907.1447870.74
47872.63
47862.13
47863.70
47844.97
47850.5847848.5947968.36
47924.90
47967.16
47957.15
47955.25

47981.0747984.37
48003.9048037.72

BIC

47988.09

48052.37
48185.70
48067.28
48077.16
48056.77
48121.55

48004.75
48013.34
48002.83
48011.11
48052.68
47997.99
47989.29

48035.37
48058.91
48040.86
48084.46
48035.6548041.38
48044.6748064.20
48098.02-0.321-0.341-0.329-0.382-0.331-0.324-0.077-0.388-0.375-2.294-2.144-2.586-2.472-2.477-0.363-0.355-0.360-0.331-0.332-0.366-0.360-0.370-0.373

Year Effects-3.080-3.260-9.450-8.260-3.110-3.110-0.430-5.534-4.669-3.889-3.385-3.947-4.181-4.214-11.457-10.530-11.350-9.985-10.201-11.551-11.346-11.635-11.712t-value

13

APPENDIX 1

14

15

APPENDIX 2

16

17

18

APPENDIX 3.
Model: BT11jarpa17
Residuals:
Min

1Q Median

3QMax-2.5225 -0.5120 -0.0536 0.4419 3.4671
Coefficients:
Estimate Std. Error t value Pr(>|t|)(Intercept)

2.651e+00 1.253e-01 21.160 < 2e-16 ***YearNum-2.027e-02 2.367e-03 -8.564 < 2e-16 ***I(BLm^3)

5.390e-04 1.339e-04 4.025 5.80e-05 ***DateNum

8.737e-03 1.435e-03 6.088 1.24e-09 ***Diatom2.339e-01 9.328e-03 25.073 < 2e-16 ***LongCat11[T.2] 3.072e-02 9.247e-02 0.332 0.73978
LongCat11[T.3] -6.727e-02 8.668e-02 -0.776 0.43780
LongCat11[T.4] -2.165e-01 8.490e-02 -2.550 0.01081 *LongCat11[T.5] -2.616e-01 8.553e-02 -3.058 0.00224 **LongCat11[T.6] -2.223e-01 8.659e-02 -2.568 0.01027 *LongCat11[T.7] -1.351e-01 8.914e-02 -1.515 0.12979
LongCat11[T.8] 2.843e-02 9.096e-02 0.313 0.75466
LongCat11[T.9] -1.543e-01 9.265e-02 -1.665 0.09600 .
LongCat11[T.10] -1.527e-01 9.852e-02 -1.550 0.12123
LongCat11[T.11] -6.713e-03 9.792e-02 -0.069 0.94535
Sex[T.M]-3.455e-01 2.806e-02 -12.311 < 2e-16 ***DateNum:LongNum 5.088e-05 1.011e-05 5.034 4.98e-07 ***--Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7539 on 4579 degrees of freedom(22 observations deleted due to missingness)
Multiple R-squared: 0.4007, Adjusted R-squared: 0.3986
F-statistic: 191.3 on 16 and 4579 DF, p-value: < 2.2e-16

19

APPENDIX 4
Model: BT11jarpa18
Random effects:
GroupsName

Variance

YearCat(Intercept) 5.274e-02

Std.Dev.

Corr

0.229661

DateNum 1.661e-05 0.004075
Residual

5.421e-01-0.83

0.736268

Number of obs: 4596, groups: YearCat, 18

Fixed effects:
Estimate Std. Error t value(Intercept)

1.710e+00 3.765e-01 4.542

YearNum-1.885e-02 6.608e-03 -2.853

I(BLm^3)

5.680e-04 1.314e-04 4.323

DateNum

1.016e-02 2.692e-03 3.774

Diatom2.298e-01 9.290e-03 24.737

LatNum1.297e-02 4.749e-03 2.731

LongNum

2.723e-03 2.714e-03 1.003

LongCat11[T.2] -7.730e-02 1.045e-01 -0.740
LongCat11[T.3] -2.512e-01 1.292e-01 -1.943
LongCat11[T.4] -4.295e-01 1.587e-01 -2.707
LongCat11[T.5] -5.414e-01 1.971e-01 -2.747
LongCat11[T.6] -5.238e-01 2.327e-01 -2.251
LongCat11[T.7] -4.832e-01 2.727e-01 -1.772
LongCat11[T.8] -3.361e-01 3.035e-01 -1.107
LongCat11[T.9] -6.055e-01 3.476e-01 -1.742
LongCat11[T.10] -6.193e-01 3.815e-01 -1.624
LongCat11[T.11] -5.428e-01 4.260e-01 -1.274
Sex[T.M]-3.306e-01 3.035e-02 -10.895

DateNum:LongNum 3.905e-05 1.924e-05 2.030

20

Correlation of Fixed Effects:(Intr) YearNm I(BL^3 DateNm Diatom LatNum LongNm LC11[T.2 LC11[T.3 LC11[T.4 LC11[T.5 LC11[T.6 LC11[T.7 LC11[T.8 LC11[T.9 LC11[T.10 LC11[T.11 S[T.M]

YearNum-0.136I(BLm^3)-0.289 -0.023

DateNum-0.322 -0.052 -0.020

Diatom

0.056 -0.012 0.023 -0.024

LatNum-0.827 -0.026 0.051 0.085 -0.109

LongNum-0.351 -0.039 0.020 0.291 0.034 -0.020

LngC11[T.2] 0.041 0.024 -0.017 -0.154 -0.027 -0.015 -0.461
LngC11[T.3] 0.103 0.087 -0.019 -0.265 -0.038 0.018 -0.695 0.760
LngC11[T.4] 0.105 0.066 -0.022 -0.180 -0.045 0.082 -0.804 0.721

0.921

LngC11[T.5] 0.136 0.068 -0.021 -0.121 -0.045 0.080 -0.859 0.681

0.882

0.944

LngC11[T.6] 0.158 0.046 -0.031 -0.101 -0.035 0.083 -0.888 0.649

0.857

0.935

0.962

LngC11[T.7] 0.171 0.036 -0.029 -0.106 -0.047 0.079 -0.898 0.617

0.824

0.909

0.943 0.964

LngC11[T.8] 0.179 0.032 -0.022 -0.078 -0.048 0.075 -0.909 0.601

0.810

0.903

0.943 0.966

0.981

LngC11[T.9] 0.233 0.026 -0.020 -0.044 -0.040 0.016 -0.915 0.581

0.789

0.889

0.938 0.963

0.976

0.984

LnC11[T.10] 0.245 0.020 -0.021 -0.033 -0.039 0.008 -0.918 0.568

0.776

0.880

0.932 0.958

0.971

0.982

0.992

LnC11[T.11] 0.234 0.007 -0.013 -0.062 -0.037 0.037 -0.929 0.557

0.766

0.873

0.924 0.950

0.960

0.972

0.982

Sex[T.M]

0.984-0.465 -0.007 0.514 0.005 -0.144 0.372 0.016 -0.027 -0.017 -0.011 -0.009 -0.010 -0.011 -0.012 -0.025 -0.029

DatNm:LngNm 0.373 0.066 0.012 -0.909 0.015 -0.189 -0.304 0.150

0.237

21

0.147

0.089

0.071

0.078

0.052

0.023 0.014-0.0190.051-0.021