Journal of Mammalogy, 101(3):742–754, 2020
DOI:10.1093/jmammal/gyaa028
Published online April 15, 2020
Growth and development of North Pacific gray whales (Eschrichtius
robustus)
Selina Agbayani,*, Sarah M. E. Fortune, and Andrew W. Trites
* Correspondent: selina.agbayani@alumni.ubc.ca
Understanding variability in growth patterns of marine mammals provides insights into the health of individuals
and status of populations. Body growth of gray whales (Eschrichtius robustus) has been described for particular
life stages, but has not been quantified across all ages. We derived a comprehensive growth equation for gray
whales by fitting a two-phased growth model to age-specific length data of eastern North Pacific gray whales that
were captured, stranded, or harvested between 1926 and 1997. To predict mass-at-age, we used the allometric
relationship between mass and length. We found that on average (± SD), calves were 4.6 ± 0.043 m and 972 ±
26 kg at birth, and reached 8.5 ± 0.095 m and 6,019 ± 196 kg by the end of their first year of life (n = 118). Thus,
calves almost double (2×) in length and octuple (8×) in mass while nursing, and are effectively about two-thirds
of their asymptotic adult length and one-third of their maximum mass when weaned. The large sample of aged
individuals (n = 730) indicates that gray whales live up to ~48 years and have a life expectancy of < 30 years.
Adult females attain a mean (± SD) asymptotic size of 13.1 ± 0.048 m and 20,758 ± 222 kg, while the smaller
males average 12.6 ± 0.048 m and 19,938 ± 222 kg at ~40 years of age. Females are thereby ~4% longer and
heavier than males. These age-specific estimates of body size can be used to estimate food requirements and
assess nutritional status of individuals.
Key words:
dimorphism
eastern gray whale, growth curves, length, life expectancy, longevity, mass, morphometrics, Putter model, sexual
measurements have been used to construct separate growth
models per life stage, they never have been compiled to derive
a comprehensive growth model.
Models describing the growth of marine mammals have been
used to determine and understand variability in sizes among individuals and populations (Stevick 1999; Winship et al. 2001;
Fortune et al. 2013). They also have been important tools to
assess the health of individuals and derive the age structure of
populations (Shotwell et al. 2010). However, age-specific estimates of body size are not available for all marine mammals
(Stevick 1999) and are incomplete for gray whales.
The objective of our study was to quantitatively determine
how gray whale growth varies across all age-classes. We therefore mathematically describe the growth of eastern North
Body growth of gray whales (Eschrichtius robustus) has been
extensively studied, but there are no comprehensive models that
describe growth over their entire life span. A number of studies
have quantified growth for different life stages, such as fetal
growth (Rice 1983; Sumich et al. 2013), postnatal growth patterns of calves and juveniles (Rice and Wolman 1971; Blokhin
and Tiupeleyev 1987; Sumich et al. 2013), and sexually mature
adults (Zimushko 1970; Rice and Wolman 1971; Zimushko
and Ivashin 1980). In addition, there is detailed information
on the growth rates of two captive gray whale calves (named
Gigi and JJ) during their first year before release (Sumich 1986;
Sumich et al. 2001, 2013). Unfortunately, additional information on growth rates of calves and juvenile gray whales less
than 5 years old is sparse. While existing data sets on body-size
© The Author(s) 2020. Published by Oxford University Press on behalf of the American Society of Mammalogists.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License
(http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction
in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com
742
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Institute for Resources, Environment and Sustainability, University of British Columbia, Vancouver, British Columbia V6T 1Z4,
Canada (SA, AWT)
Marine Mammal Research Unit, Institute for the Oceans and Fisheries, University of British Columbia, Vancouver, British
Columbia V6T 1Z4, Canada (SA, SMEF, AWT)
Present address of SA: Fisheries and Oceans Canada, Institute of Ocean Sciences, Sidney, British Columbia V8L 5T5, Canada
743
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
Pacific gray whales using all available age-associated observations of body lengths. We also derive a length–mass relationship to describe changes in body mass with age using the
few available sets of mass and length measurements. The comprehensive growth model and mass estimates we derive can be
used to model energetics, estimate food requirements, and estimate drug dosages where gray whales may need rehabilitation,
veterinary care, or humane euthanasia (e.g., Wahrenbrock et al.
1974; Sumich et al. 2001; Gulland et al. 2005).
We conducted a review of published literature on eastern North
Pacific gray whale lengths and compiled all reported measurements from 1926 to 1997 (n = 999) into a single data set.
The data set was compiled from a collection of US scientific
surveys and studies (Gilmore 1960, 1961; Rice and Wolman
1971; Norris and Gentry 1974; Wahrenbrock et al. 1974; White
and Griese 1978; Rice 1983; Sumich 1986; Sumich et al. 2001,
2013; Perryman and Lynn 2002). The data set also included
data from the Norwegian Whalers Association (Risting 1928),
and Russian research reports to the International Whaling
Commission (IWC) on the Chukotkan Indigenous fishery
(Zenkovich 1937; Zimushko 1970; Zimushko and Ivashin
1980; Blokhin 1982, 1984, 1985, 1986, 1987; Yablokov and
Bogoslovskaya 1984). Reported body lengths were standard
lengths measured as a straight-line distance from the tip of the
rostrum to the fluke notch (Lockyer 1976).
We estimated age from published data on: (1) counts of adjacent light and dark ear plug layers, known as growth layer
groups (GLGs), each representing 1 year of life (Rice and
Wolman 1971; Blokhin and Tiupeleyev 1987); and (2) counts
of corpora albicantia and corpora lutea found in the ovaries
of female gray whales (Rice and Wolman 1971). Two studies
describe methods of estimating ages of gray whales: Rice and
Wolman (1971) and Blokhin and Tiupeleyev (1987). Rice and
Wolman (1971) assumed that the first year was represented by
two GLGs based on their observation that the smallest whales
in their data set had a minimum of 2 GLGs. Using this method,
the estimated age at sexual maturation is ~8 years based on a
count of 9 GLGs. This was later challenged by Blokhin and
Tiupeleyev (1987) who observed fewer than 2 GLGs during
the first year of growth. Blokhin and Tiupeleyev (1987) also
presented additional data showing the average age of sexual
maturation occurs slightly earlier, at ~7 years of age. We chose
to use the method described by Blokhin and Tiupeleyev (1987)
to estimate age from GLG counts and age at sexual maturation.
We further assumed that gray whales reproduce once every
2 years on average as concluded by others (Rice and Wolman
1971; Blokhin and Tiupeleyev 1987).
Where corpora counts were available, we used the estimate of age at sexual maturation from Blokhin and Tiupeleyev
(1987) to calculate age estimates for late pregnant or postpartum females. We did so by multiplying the number of corpora (albicantia and lutea) in the ovaries (n) by 2 years to
account for the reproductive cycle and added 7 years to account
for age at sexual maturation. As this method applies only to
Table 1.—Growth models fit to size (S) at age (t) data. Size is measured as standard length (in meters), and age is measured in decimal
years. A represents asymptotic size, t0 is time at which size is zero,
c is a constant of integration, and k is a fitted parameter indicative
of growth rate. Each parameter, while generally comparable across
models, does not necessarily represent the same property in each
model.
Model
Equation
Sources
)
(1)
3
(2)
Putter
St = A(1 − e
von Bertalanffy
St = A(1 − e−k(t−t0 ) )
Gompertz
Logistic
−k(t−t0 )
−kt
St = Ae−ce
St =
A
1+e−k(t−t0 )
(3)
(4)
(von Bertalanffy 1938;
Ricker 1979)
(von Bertalanffy 1938;
Ricker 1979)
(Gompertz 1825;
Zach et al. 1984)
(Ricker 1979)
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Materials and Methods
sexually mature females, all male gray whales in the data set
were aged using the GLG method.
We fit four commonly used mathematical growth functions
to the gray whale length-at-age data (Table 1). We then used the
Akaike Information Criterion (AIC) to determine which model
best described gray whale growth (Winship et al. 2001; Fortune
et al. 2012). Only observations that had both length and age
data (n = 730) were used to fit the length-at-age growth models
(Risting 1928; Zimushko 1970; Rice and Wolman 1971;
Zimushko and Ivashin 1980; Blokhin 1982, 1984, 1985, 1986,
1987; Rice 1983; Rice et al. 1984; Yablokov and Bogoslovskaya
1984; Sumich 1986; Sumich et al. 2001, 2013; Perryman and
Lynn 2002). Repeated measures from captive gray whale calves
Gigi and JJ (Sumich et al. 2001, 2013) were not included in
the analysis. Instead, only one length measurement from each
whale (i.e., Gigi and JJ) was included in the analysis (i.e., their
lengths at 1 year, just before they were returned to their natural
habitat and presumably at their healthiest while in captivity).
We fit each of the growth models to the length-at-age data using
nonlinear least squares regression from the nls2 package of the
statistical program R (Grothendieck 2013; R Core Team 2018),
and compared the relative fits of each model using AIC. The
model with lowest AIC value was selected as the “best model”
(Akaike 1974; Burnham and Anderson 2002).
Once the best model was selected, a visual assessment of
the fit revealed that a single growth curve did not adequately
describe the data. The single model overestimated body lengths
of nursing calves, and underestimated body lengths of weaned
juveniles and adults. We therefore used a two-phased approach
to fit the length-at-age data, similar to the method used for
other cetacean species (Perrin et al. 1976; Danil and Chivers
2007; Larese and Chivers 2009; Fortune et al. 2012). Phase 1
represented the early growth stages of calves before weaning
(occuring ≥ 6–7 months—Sumich 1986); Phase 2 represented
the decelerated growth phase after weaning. We identified the
transition point between the two phases as the point where the
difference between predicted lengths of Phase 1 and Phase 2
was zero (Fortune et al. 2012). We incorporated uncertainty
into the growth model by running 10,000 Monte Carlo simulations and calculating the 95% confidence interval around the
model fit.
744
JOURNAL OF MAMMALOGY
W = aLb
(5)
which was linearized in logarithmic form:
log10 W = log10 a + b · log10 L
(6)
where W represents mass in kg, L represents length in meters,
a is a constant factor, and b is an exponential constant. We fit
a regression to length and mass data (n = 15) to solve for the a
and b parameters and calculated gray whale body mass at each
age using lengths-at-age predicted by the two-phased growth
model (Gilmore 1961; Rice and Wolman 1971; Wahrenbrock
et al. 1974; White and Griese 1978; Blokhin 1986; Sumich
1986; Sumich et al. 2013; details in Supplementary Data SD1).
To incorporate uncertainty into our mass estimates, we bootstrapped the data by running 10,000 Monte Carlo simulations.
Before fitting the model, we examined the data for potential
outliers (i.e., biologically improbable measurements). We excluded one animal from our analysis because the reported mass
measurement (3,500 kg) was considerably less than what was
reasonable for its reported length (9.1 m). It was reported to
have died of probable starvation (Sumich 1986), and was therefore considered to be nonrepresentative of a typical individual
at that size. Pregnant females also were poorly represented,
with only three observations for animals of unknown ages: (1)
12.7 m and 16,360 kg; (2) 13.55 m and 33,846 kg (Rice and
Wolman 1971); (3) 13.35 m and 31,466 kg (Zenkovich 1937;
Rice and Wolman 1971).
Results
The gray whale data set spans the period 1926–1997 and consists of 999 observations. Of these, 730 were associated with
age estimates and used to describe average changes in body
lengths. The age-sex frequency distribution of the age-length
data set (n = 730) shows an imbalanced sex ratio, with a notably high number of females (n = 73) between the ages 10
and 15 years (Fig. 1). The majority of the data obtained for
calves and juveniles up to 4 years of age were of unknown sex
(n = 195). There also were notably fewer observations for female calves in the data set. Individuals < 30 years old accounted
for ~91% of the data set. The oldest individual in the data set
was female, estimated to be 77 years of age from counts of corpora albicantia (Rice and Wolman 1971), and the mean age of
sampled animals was 11.7 years.
Body lengths.—Mean body lengths of gray whale calves
at birth and at 1 year of age were consistent with estimates
from prior studies (Table 2; Fig. 2; Sumich et al. 2013). There
was no evidence of sexual dimorphism between male and female calves and juveniles within the data set. However, the
statistical power for the t-test was very low (power = 0.1 for
calves at birth; 0.05 for juveniles), which may have affected
our ability to detect a significant difference. We did find evidence of sexual dimorphism when comparing the mean (± SD)
lengths of sexually mature females (12.7 ± 0.611 m) and males
(12.1 ± 0.705 m) (t250 = 8.94, P < 0.001) assuming that sexual
maturation occurs at ~7 years of age on average (Blokhin and
Tiupeleyev 1987).
Overall, we found that the two-phased Putter growth model
was the best model to describe growth of gray whales (equation
1, Table 1) as it yielded the lowest AIC scores, highest likelihood, and greatest weight of evidence in favor of the model
(Table 2; Figs. 3 and 4). The point of inflection between the
two growth phases (i.e., the point where the difference between
predicted lengths of Phase 1 and 2 was zero) was at 0.8 years
(~9.6 months) of age.
Gray whale calves reach up to two-thirds of their adult asymptotic lengths in the first year, growing on average ~1.05 cm
per day. Estimated asymptotic lengths ( X̄ ± SD) were 13.11
± 0.048 m for adult females and 12.59 ± 0.048 m for adult
males, which they reach at ~40 years of age (Rice and Wolman
1971). On average, observed lengths of female calves during
Phase 1 growth (< 0.8 years) were 1.13% (0.05 m) longer
than the lengths predicted by the two-phased Putter model,
while male calves were 0.17% (0.01 m) shorter than predicted
(Supplementary Data SD2). Similarly, observed lengths of females during Phase 2 growth (> 0.8 years) were 1.91% (0.25
m) longer than predicted, while males were 2.11% (0.26 m)
shorter than predicted (Supplementary Data SD2). Due to the
paucity of data on differences in body size between female and
male gray whales during Phase 1 growth, we applied the adult
sex-specific correction factors across all ages to generate comprehensive sex-specific growth curves (Fig. 4).
Body mass.—Parameter values for the allometric relationship between body length and mass (equation 6) were log10
a = 1.0354 ± 0.1590 (a ± SE), b = 2.9509 ± 0.1963 (b ± SE),
R2 = 0.96, P < 0.01 (Fig. 5). Applying this relationship to
the length-at-age estimates from the fitted two-phased Putter
growth model (Fig. 6) showed that calves attained up to onethird of maximum predicted mass ( X̄ ± SD) in the first year of
growth (females = 6,134 ± 196 kg; males = 5,892 ± 196 kg).
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
The number of observations for length data at each age was
insufficient to determine the exact age at which sexual dimorphism in size becomes significant. However, we calculated the
difference in length of males and females for each age cohort:
(1) at birth; (2) as calves (0–1 years); (3) as weaned juveniles (>
1–7 years); and (4) as sexually mature adults (7+ years). We calculated statistical significance for sexual differences in length
using a Welch two-sample t-test (an adaptation of Student’s
t-test) from the R stats package (R Core Team 2018), and
power analyses using the pwr R package (Champely 2018) to
determine whether the sample sizes for each age were sufficient
to detect sexual dimorphism if it did exist. Where evidence for
sexual dimorphism was found, we generated sex-specific size
correction factors by calculating mean differences between observed lengths and model-predicted lengths (values are shown
in Supplementary Data SD2). We then multiplied these values
with the predicted lengths from the two-phased Putter growth
curves to estimate sex-specific length estimates.
Body mass was estimated using an allometric length–mass
relationship (Schultz 1938):
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
745
It also showed that upon reaching maximum predicted lengths
at ~40 years of age, females have a predicted mass of 20,758 ±
222 kg, and males reach a maximum predicted mass of 19,938
± 222 kg (Fig. 6).
Discussion
Gray whales have two distinct phases of growth. The first is
characterized by a rapid growth rate from birth to weaning,
while the second represents decelerated growth rate after
weaning. The two-phased growth model fit to the body lengths
of all known-aged gray whales measured from 1926 to 1997
shows that the average gray whale attains about two-thirds of
its maximum body length by the time it weans. Applying the
allometric relationship between mass and length further shows
that calves attain one-third of their body weight during the first
few months while they nurse. Overall, adult males are about
4.2% shorter and 4.3% lighter than adult females.
Confidence in our model predictions are tempered by difficulties apparent in the data set in identifying the sex of younger
animals. Similar shortcomings in model confidence are associated with limitations in methods of aging gray whales and measuring whales that were captured, stranded, or harvested. These
issues on data error and model uncertainty are addressed below.
Data error and model uncertainty.—Historical data sets of
morphometric measures of marine mammals, such as the ones
we used for gray whales, typically come from harvested or
stranded animals that have recognized errors and uncertainties (Lockyer 1981a; Fortune et al. 2012; Rechsteiner et al.
2013). A large portion of the measurements in our data set were
from Russian aboriginal harvests and US strandings, neither of
which can be assumed to be a random sample of the population
(Stevick 1999). Historical commercial harvest was known to
target specific size classes of whales—usually larger whales—
depending on the IWC regulations for each species (Stevick
1999), but it is uncertain whether more recent subsistence harvests targeted smaller, more easily handled whales. Some of
the stranded animals may have had compromised growth due
to poor health and could be a source of error. New noninvasive
methods using aerial images to measure living baleen whales
have been developed in recent years (Perryman and Lynn 2002;
Miller et al. 2012; Christiansen et al. 2016). However, aerial
photographs fail to capture age, and need to be linked to a database of birth dates for each photographed animal to describe
changes in body size.
Measurement errors also can be attributed to the way in
which animals are handled, and the way in which they are
measured. In contrast to multiple measurements that can be
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Fig. 1.—Age-frequency distribution of measured gray whales (Eschrichtius robustus) by sex (captured or stranded individuals). A portion of the
data obtained for calves and juveniles (up to 4 years of age) were of unknown sex (195 individuals). Lighter shaded bars on the left represent male
gray whales (n = 211) and darker shaded bars on the right represent females (n = 324).
18
1.00
−0.960
< 0.001
250
8.94
57
−0.13
0.611
0.705
12.70
12.07
36
39
53
1.200
0.725
0.633
10.40
10.40
8.97
2
3
80
0.382
0.000
0.650
8.87
9.14
7.75
260
139
0.05
0.90
0.0292
Sample sizes too low to compare mean lengths
18,462
507
0.10
−0.176
0.52
48
0.65
26
30
62
0.379
0.305
0.336
4.66
4.60
4.59
Statistical power
Effect size
P
d.f.
t
n
SD
Mean Length (m)
Age cohort
taken from aerial images to decrease uncertainty, measurements
taken during necropsies tend to only be done once (Fortune
et al. 2012). Accurately measuring the straight-line distance
from the tip of the nose to tip of the tail for large animals can
also be logistically challenging depending on the environment
and size of the animal. Measurements taken with the measuring tape stretched along the ground alongside a whale would
likely differ from measurements taken with the measuring tape
stretched above the whale, because of potential sagging in the
measuring tape (Stevick 1999). In addition, lengths of harvested
animals when pulled up on shore can be overestimated due to
stretching—which can potentially increase the body length of
an animal by up to 1 m (J. L. Sumich, Oregon State University,
pers. comm.), which is ~7% of an adult’s length. This is similar to the 9% increase in lengths reported for stretched bowhead whales (George et al. 2004). This should not be an issue
for stranded gray whales on shore that are measured in place.
Unfortunately, we were unable to assess measurement error for
the data we used because it was unclear from published reports
which measurements were from hauled animals.
A second source of possible error in our data set is the accuracy with which the gray whales were aged. The two methods
most commonly used for aging gray whales are counting the
number of adjacent pairs of light and dark layers, known as
GLGs, from ear plugs, and estimating age from counts of
corpora albicantia and corpora lutea in sexually mature females (Zimushko 1970; Rice and Wolman 1971; Blokhin and
Tiupeleyev 1987). The majority of age estimates of gray whales
in our data set were from GLG counts. Age estimates based on
GLG counts depend on the rate of accumulation of age layers,
but there are discrepancies regarding whether one or two layers
are accrued in the first year (Zimushko 1970; Rice and Wolman
1971; Blokhin and Tiupeleyev 1987). Where GLG counts were
available, we assumed that one GLG layer (i.e., a pair of adjacent light and dark bands) was accrued for each year of growth
(Blokhin and Tiupeleyev 1987). Corpora counts are considered
to provide a more reliable estimate of age for sexually reproductive female gray whales than GLG counts, where ovulation
is assumed to occur once every 2 years, and sexual maturation is
assumed to occur after 7 years of age (Blokhin and Tiupeleyev
1987). However, corpora counts were only available for a small
fraction (~16%) of the individual gray whales in our analysis.
The gray whales included in our analysis were between 0
and 77 years old and had an average age of 11.7 years. This age
range covers the period of significant growth. Our model shows
cessation of growth at about 40 years. However, longevity is
unknown. Although the oldest gray whale was estimated to be
77 years old based on corpora counts (Rice and Wolman 1971),
it was an unusually old whale compared to other whales in the
data set. It is possible that this whale is a good representative of
maximum life span given that individuals of other whale species have been known to reach this age or older (Lockyer 2001).
However, based on the age distribution of this particular data
set, this age does not reflect average longevity.
A rigorous means to estimate longevity is to use the 99th
percentile of the age distribution of a sample of aged animals
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
At birth
Female
Male
Unknown
Calf (up to 1 year)
Female
Male
Unknown
Juvenile (1–7 years)
Female
Male
Unknown
Adult (7+ years)
Female
Male
Min n for power of 0.8
JOURNAL OF MAMMALOGY
Table 2.—Mean lengths of gray whales (Eschrichtius robustus) for each age cohort. Ages at birth are zero, calves are ≤ 1 year, juveniles are 1–7 years, and adults are sexually mature
individuals > 7 years. Data for calves between 0 and 1 year were insufficient to determine sexual dimorphism within that age cohort. SD = standard deviation; n = sample size; t = t-value;
d.f. = degrees of freedom; P = P-value; Effect size = Cohen d measure of effect size; Min n for power of 0.8 = minimum sample size to obtain statistical power of 0.8.
746
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
747
(i.e., the age at which only 1% of the sample is older—Barlow
and Boveng 1991; Trites and Pauly 1998). Thus, we estimate
the longevity of gray whales is on average ~48 years, and their
life expectancy is < 30 years, based on > 90% of the samples
being < 30 years old. These estimates represent average longevity and life expectancy for the population from 1926 to
1997, when our data were collected. The gray whale population has been increasing since the data were collected, but experienced unusual mortality events (UMEs) in 1999–2000 and
2019 (Le Boeuf et al. 2000; NOAA Fisheries 2020). Emaciated
adults and subadults during these events could reflect the population overshooting carrying capacity. However, it is unknown
whether carrying capacity has been relatively constant or is artificially depressed due to changing climatic conditions (Reilly
1992; Le Boeuf et al. 2000; Moore et al. 2001). Whether or not
average longevity has changed from before whales were harvested to the time after harvesting ceased and the population
began to recover, is unknown in the absence of more data.
Populations may experience decreased growth rates as they
approach carrying capacity due to increased competition for
food (Scheffer 1955; Eberhardt 1977; Fowler 1987; Trites
1990). Climate change (Cheung et al. 2013; Baudron et al.
2014; Pauly and Cheung 2018) and high levels of exploitation
(Allendorf and Hard 2009; McLenahan 2009; Therkildsen et al.
2019) can also reduce body size. However, testing whether
decadal changes had occurred in the body lengths of mature
gray whales as the population approached carrying capacity revealed no change in mean sizes (± SD) of adult gray whales
between the 1970s (12.5 ± 0.727 m) and 1980s (12.5 ± 0.648
m) (t133 = −0.65, P = 0.52). Unfortunately, we were unable to
assess whether body size has decreased since the 1920s, or remained constant in recent decades, due to limited sample sizes.
In addition to changes in body size, populations at carrying capacity may also experience delayed maturity, resulting
in an increase in age at sexual maturation (Eberhardt 1977;
Fowler 1987). Inter-calving intervals have increased from
2.1 ± 0.40 years (± SD) for the period 1977–1982 to 2.39 ±
0.58 years (± SD) for the period 2005–2017 (Swartz and Jones
1983; Swartz et al. 2018). This suggests that age estimations
using corpora counts (assuming that age at sexual maturation
has remained the same, and that one corpora is produced every
2 years) may result in underestimating ages of whales in the
current population.
The length estimates we calculated from the growth model
were derived from a large sample size of body measurements
that yielded a good model fit. However, there was a lack of
weight measurements available to model changes in body mass
due to the logistical difficulties associated with weighing large
whales (Lockyer 1976). We therefore calculated mass at age by
applying the allometric relationship between mass and length to
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Fig. 2.—Individual measurements (unfilled circles) and distributions (boxplots) of body lengths of gray whales (Eschrichtius robustus) by sex and
cohort including neonates and newborns (at birth), calves (ages up to 1 year), juveniles (1–7 years old), and adults (sexually mature, 7+ years).
The majority of the observations for calves are of unknown sex. Mean values for each cohort are reported in Table 3.
748
JOURNAL OF MAMMALOGY
Table 3.—Parameter estimates for four different two-phased models (Putter, von Bertalanffy, Gompertz, and logistic; equations 1–4) describing
the growth of gray whales (Eschrichtius robustus). A = asymptotic size; k = growth rate; c = constant of integration; t0 = time at which size is
zero. Standard lengths are in meters, and time (age) is in decimal years. We selected the best model using the Akaike Information Criterion (AIC).
Also reported are the differences in AIC values (ΔAIC) between the model with the lowest AIC value (i.e., Putter; equation 1) and the other fitted
models, the likelihoods of each model, and the weight of evidence in favor of each model. The model with the lowest AIC value, greatest likelihood, and greatest AIC weight was considered the “best” model.
Model
9.47 ± 0.19
9.32 ± 0.16
9.13 ± 0.07
9.21 ± 0.14
12.82 ± 0.06
12.85 ± 0.05
12.84 ± 0.05
12.82 ± 0.05
c
0.68 ± 0.01
0.49 ± 0.01
k
t0
ΔAIC
Likelihoods
AIC weights
1.85 ± 0.15
2.24 ± 0.15
2.56 ± 0.11
2.64 ± 0.15
−0.36 ± 0.02
−0.70 ± 0.04
0.00
0.59
85.00
1.22
1.00
0.74
0.00
0.54
0.44
0.33
0.00
0.24
0.18 ± 0.01
0.19 ± 0.01
0.20 ± 0.01
0.07 ± 0.00
−5.09 ± 0.40
−9.81 ± 0.60
0.00
1.75
2.74
6.03
1.00
0.42
0.25
0.05
0.58
0.24
0.15
0.03
Fig. 3.—The two-phased growth model describing the first 2 years of
life for gray whales (Eschrichtius robustus; males, females, and individuals of unknown sex have been combined). Phase 1 spans from 0
to 0.8 years and Phase 2 spans from 0.8 years onwards. Length-at-age
(meters) can be calculated by inserting age (decimal years) into the
following equations: (i) St = 9.47(1 − e−1.85(t + 0.36)) for Phase 1, and (ii)
St = 12.82(1 − e−0.18(t + 5.09)) for Phase 2. 95% CIs (dashed lines) were
derived from 10,000 Monte Carlo simulations.
the growth modeled estimates of length at age. Unfortunately,
our confidence in our predictions of mass at age are limited by
the small sample size of weighed and measured gray whales
(n = 15) we used to derive the allometric relationship (the biggest animal reported among the 15 individuals was 12.4 m and
~15 years old). This bias toward smaller whales is presumably
due to the relative ease in measuring and weighing smaller animals. This, combined with the small sample size, resulted in
increased uncertainty in body mass predictions, particularly for
older animals (Fig. 6). Additional mass-at-age measurements,
combined with information on fetal growth such as those from
Rice (1983) and Sumich et al. (2013), are needed to predict the
mass of pregnant gray whales.
We have greater confidence in our estimates of body length
than in the estimates of body mass. Although this limitation
−0.51 ± 0.02
−2.28 ± 0.25
in confidence in estimated body masses should be considered
when using our models, our mass-at-age estimates are an improvement over prior estimates because of the improvement in
length estimates.
Sexual dimorphism.—As with prior studies, we found sexual
dimorphism in length among adults, but not for calves and juveniles (Rice and Wolman 1971; Sumich 1986). However,
our data also show that observed lengths for female calves
are longer on average than predicted, while observed lengths
for male calves are shorter than predicted at a given age. It is
therefore possible that sexual dimorphism starts at birth (and
even before), such that young females should be ~4% longer
and heavier than males—similar to the difference in body size
observed among adult males and females. Other dimorphic
species such as northern fur seals (Callorhinus ursinus) with
large sample sizes exhibit sexual dimorphism starting at the
fetal stage (e.g., Trites 1991; Trites and Bigg 1996). Rice and
Wolman (1971) found no significant difference in the lengths of
as many as 30 male and 25 female near-term fetuses, but they
did find statistically significant differences for other factors in
postnatal individuals (e.g., as many as 167 males had longer
flippers and shorter tails compared to 147 females). Our sample
sizes for the younger age-classes of gray whales were relatively
small and the variability between the sizes of individual whales
of any given age was too large to detect such a relatively small
difference in sizes of young males and females.
There were notably few measurements of young females, and
many measurements from individuals of unknown sex (Fig. 1).
One possible explanation for the bias in reported sexes could
be the relative ease in definitively identifying males versus females. Sighting a penis clearly indicates that an animal is male,
whereas not sighting a penis does not necessarily indicate that
the animal is female, because the penis may be hidden or contracted. In the case of observations from gray whales of unknown sex, it is unclear whether the sex of the individuals was
not identified, or if the associated sex information simply was
not reported.
Even if all 195 gray whales of unknown sex (aged 0–4 years)
in our study had been identified as male or female, it is unlikely
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Phase 1 (0–0.8 years)
Putter
von Bertalanffy
Gompertz
Logistic
Phase 2 (> 0.8 years)
Putter
von Bertalanffy
Gompertz
Logistic
A
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
749
that the sample size would have been sufficient to detect sexual
dimorphism. Results from a power analysis (Table 4) indicates
that > 500 young whales would be needed to detect sexual dimorphism at birth, and over 18,000 whales would be required
to detect sexual dimorphism in juveniles. Thus, it is not possible to conclusively demonstrate sexual dimorphism in gray
whale calves and juveniles with these sample sizes. However,
our data show patterns indicating that sexual dimorphism observed in adults may indeed start at conception. We therefore
generated comprehensive growth curves under the assumption
that sexual dimorphism begins at birth in addition to the general
growth curves presented here.
Gray whale growth models.—Among the four models we
tested, the one that best fit the data was the Putter equation
(equation 1). As expected, gray whales grow extremely rapidly
in their first year, but their growth rates decrease considerably
following weaning until they are ~40 years old. This is consistent with observed growth patterns of other cetaceans, such
as North Atlantic right whales (Eubalaena glacialis—Fortune
et al. 2012), humpback whales (Megaptera novaeangliae—
Stevick 1999), whitebelly spinner dolphins (Stenella
longirostris—Larese and Chivers 2009), short-beaked common
dolphins (Delphinus delphis—Danil and Chivers 2007), and
the spotted dolphin (Stenella attenuata—Perrin et al. 1976).
Calves attain about two-thirds of their asymptotic adult length
and one-third of their maximum mass within the first year of
growth. This is slower than the reported growth rates of North
Atlantic right whales, which attain up to three-quarters of their
asymptotic adult mass in the first year (Fortune et al. 2012).
Large aquatic mammals are known to rely on size for energy and thermoregulation (Rice and Wolman 1971). Calves
that grow large and fat earlier in life have the thermoregulatory
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Fig. 4.—Comprehensive two-phased growth model (panel A) for gray whales (Eschrichtius robustus), showing Phase 1 (0–0.8 years) and Phase
2 (> 0.8–30 years). 95% CIs (dashed lines) were derived from 10,000 Monte Carlo simulations. Length-at-age (meters) can be calculated by
inserting age (decimal years) into the following equations: (i) St = 9.47(1 − e−1.85(t + 0.36)) for Phase 1, and (ii) St = 12.82(1 − e−0.18(t + 5.09)) for Phase
2. Length-at-age estimates (panel B) after sex-specific correction factors (females: +1.91%; males: −2.11%) were applied to the estimates from
the two-phased Putter growth model. The dashed line represents female gray whales, and the solid line represents males.
750
JOURNAL OF MAMMALOGY
Fig. 6.—Estimated mass-at-age (kg) for gray whales (Eschrichtius robustus) calculated using length-at-age estimates from the two-phased Putter
growth model (equation 1, Phase 1 and 2), sex-specific correction factors (females: +1.91%; males: −2.11%), and a length–mass allometric relationship (equation 6). Panel (A) shows mass estimates from the general two-phased Putter model (dashed lines = 95% CI calculated from 10,000
Monte Carlo simulations). Panel (B) shows sex-specific mass estimates (females = dashed line; males = solid line).
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Fig. 5.—Length–mass allometric regression for gray whales
(Eschrichtius robustus) where log10 Mass (kg) = 2.9509·log10 Length
(m) + 1.0354, R2 = 0.96, P < 0.01. Dashed lines represent the 95% CI.
Data are contained in Supplementary Data SD1.
benefit of a lower surface area to volume ratio (Christiansen
et al. 2018) with larger blubber reserves adding insulation and
an energetic buffer while they learn to forage independently
(Lockyer 2007). In addition, rapid growth rates may help prepare calves for transitioning between nursing and consuming
solid food in the Chukchi and Bering Seas. Juvenile baleen
whales allocate resources toward rapid growth and expansion
of the head and jaw regions (Lockyer 1981b), and calves with
bigger jaws or thicker baleen may have the advantage of an
increased filtering surface area for foraging. As a result, larger
gray whale calves likely have lower risks of starvation and predation from killer whales (Orcinus orca), and ultimately better
chances of surviving during migration (Rice and Wolman 1971;
Fortune et al. 2012).
Our model shows a decrease in the rate of growth at
~9.6 months (0.8 years), which is 2–3 months later than the
~7 months age at weaning reported by others (Rice and Wolman
1971; Sumich 1986). This could mean that while weaning may
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
Table 4.—Predicted length-at-age for gray whales (Eschrichtius
robustus) in meters ( X̄ ± SD) generated from the two-phased
Putter growth curves (Phase 1: 0–0.8 years; Phase 2: > 0.8–40 years),
and mass-at-age estimates in kilograms ( X̄ ± SD) generated from a
length–mass allometric relationship (equation 6). These values are
average sizes of males and females. Sex-specific correction factors
(females: +1.91%; males: −2.11%) can be applied to these values to
derive average lengths-at-age for males and females. SD values listed
are the standard deviations of 10,000 Monte Carlo bootstrap estimates
of mean lengths and mass for each age.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
25
30
35
40
Length (m)
Mass (kg)
4.59 ± 0.043
5.41 ± 0.046
6.09 ± 0.057
6.66 ± 0.062
7.13 ± 0.060
7.52 ± 0.056
7.85 ± 0.052
8.12 ± 0.048
8.34 ± 0.048
8.43 ± 0.099
8.51 ± 0.095
9.22 ± 0.066
9.81 ± 0.053
10.31 ± 0.049
10.72 ± 0.050
11.07 ± 0.051
11.36 ± 0.051
11.60 ± 0.049
11.81 ± 0.047
11.98 ± 0.044
12.12 ± 0.041
12.24 ± 0.038
12.34 ± 0.035
12.43 ± 0.033
12.50 ± 0.032
12.56 ± 0.032
12.61 ± 0.031
12.65 ± 0.032
12.69 ± 0.033
12.71 ± 0.034
12.80 ± 0.040
12.84 ± 0.044
12.86 ± 0.047
12.86 ± 0.048
972 ± 26
1,583 ± 39
2,248 ± 61
2,924 ± 80
3,577 ± 88
4,187 ± 92
4,743 ± 91
5,240 ± 90
5,679 ± 96
5,858 ± 200
6,019 ± 196
7,618 ± 158
9,155 ± 143
10,590 ± 148
11,901 ± 162
13,077 ± 176
14,119 ± 184
15,033 ± 186
15,828 ± 184
16,515 ± 177
17,105 ± 168
17,611 ± 160
18,042 ± 151
18,408 ± 144
18,719 ± 140
18,982 ± 138
19,205 ± 140
19,393 ± 143
19,551 ± 147
19,685 ± 153
20,094 ± 183
20,266 ± 204
20,338 ± 216
20,368 ± 222
begin at ~7 months, calf nutrition likely is supplemented with
energy rich milk for another 2 months. The decrease in growth
rate at 9.6 months may therefore be the combined effect of
weaning and decreased prey availability in the late summer or
early fall (Highsmith and Coyle 1990). The 7-month estimate
for age of weaning was based on stomach contents of calves
(Rice and Wolman 1971). However, calves have been observed
mimicking adult feeding behavior—diving and filtering mud
and sand through their baleen while still nursing (Swartz 1986).
Stomach contents of calves may therefore contain benthic invertebrate prey before weaning is complete.
Ultimately, our model agrees with the general premise that
calves are weaned by the end of their first year, and our descriptions of calf and neonate growth are consistent with prior estimates derived with the Gompertz model (Sumich 1986; Sumich
et al. 2001, 2013). Our descriptions of growth after weaning
also are consistent with prior estimates from von Bertalanffy
models (Rice and Wolman 1971; Zimushko and Ivashin 1980;
Blokhin and Tiupeleyev 1987). Overall, we generated robust
predictions of length-at-age by combining morphometric data
for gray whales obtained off the coasts of Chukotka and Alaska,
and further south to Mexico. This consolidated comprehensive
data set for the eastern North Pacific population provides better
descriptions of gray whale growth patterns than has been previously available. Our growth model can be applied to western
North Pacific gray whales as well, assuming that the two populations are indeed morphometrically similar (Yablokov and
Bogoslovskaya 1984).
Improvements to our model estimates likely will come as
sample sizes are increased. Most valuable would be obtaining
more weight measurements from whales > 12 m to refine the
allometric relationship between mass and length. Another improvement would be to estimate the body mass of pregnant females by including fetal growth (from Sumich et al. 2013), and
including mass of tissue growth during pregnancy. Similarly,
increasing sample sizes of young animals would substantiate
our assumption that sexual dimorphism begins at birth.
Prior efforts in modeling mass at age determined that adding
girth to allometric models allows for differences between lean
and fat body conditions to be accounted for, and can yield
better model fits (Lockyer and Waters 1986; Vikingsson et al.
1988; Sumich et al. 2013). Girth therefore significantly improves mass estimates for individual whales (pregnant females
in particular), but does not improve mass estimates across age
and length classes. Length also has been found to have a greater
effect than girth on mass estimates for gray whales, fin whales,
and sei whales (Sumich et al. 2013). To effectively incorporate the variability in girth for every age and size class, there
would ideally be girth measurements from multiple individuals
for every length and age-class measured. In light of this and
the paucity of published age-associated girth measurements
(n = 9), we only used length and mass measurements to derive
the allometric relationship.
The growth curves we derived describe length-at-age and
mass-at-age for male and nonpregnant female gray whales over
their entire age spectrum. Our resulting estimates can be used
to estimate food requirements, assess health and body condition, and model bioenergetic requirements for gray whales
throughout the North Pacific.
Acknowledgments
We are grateful to Dr. John Ford and Dr. James Sumich for
their advice in the early stages of this project. We also extend
our thanks to Dr. Sergey Blokhin and Dr. Vitaliy Samonov
(TINRO) for sharing their knowledge about the gray whale
morphometric data. This work was funded by an NSERC
Discovery Grant awarded to AWT.
Supplementary Data
Supplementary data are available at Journal of Mammalogy
online.
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Age (years)
751
752
JOURNAL OF MAMMALOGY
Literature Cited
Akaike, H. 1974. A new look at the statistical model identification.
IEEE Transactions on Automatic Control 19:716–723.
Allendorf, F. W., and J. J. Hard. 2009. Human-induced evolution
caused by unnatural selection through harvest of wild animals.
Proceedings of the National Academy of Sciences 106(Supplement
1):9987–9994.
Barlow, J., and P. Boveng. 1991. Modeling age‐specific mortality for marine mammal populations. Marine Mammal Science
7:50–65.
Baudron, A. R., C. L. Needle, A. D. Rijnsdorp, and
C. T. Marshall. 2014. Warming temperatures and smaller body
sizes: synchronous changes in growth of North Sea fishes. Global
Change Biology 20:1023–1031.
Blokhin, S. A. 1982. Investigations on gray whales taken off
Chukotka in 1980. Report of the International Whaling Commission
32:375–380.
Blokhin, S. A. 1984. Investigations of gray whales taken in the
Chukchi coastal waters, U.S.S.R. Pp. 487–509 in The gray
whale: Eschrichtius robustus (M. L. Jones, S. L. Swartz, and
S. Leatherwood, eds.). Academic Press. New York.
Blokhin, S. A. 1985. Investigations of gray whales taken off
Chukotka in 1983. Report of the International Whaling Commission
35:371–374.
Blokhin, S. A. 1986. Investigations of gray whales taken off
Chukotka in 1984. Report of the International Whaling Commission
36:287–290.
Blokhin, S. A. 1987. Investigations of gray whales taken off
Chukotka in 1985. Report of the International Whaling Commission
37:337–339.
Blokhin, S. A., and P. A. Tiupeleyev. 1987. Morphological study
of the earplugs of gray whales and the possibility of their use in age
determination. Report of the International Whaling Commission
37:341–345.
Burnham, K. P., and D. R. Anderson. 2002. Model selection and
multimodel inference: a practical information-theoretic approach.
2nd ed. Springer-Verlag. New York.
Champely, S. 2018. pwr: basic functions for power analysis. R
package. http://cran.r-project.org/package=pwr. Accessed 3 June
2019.
Cheung, W. W. L. et al. 2013. Shrinking of fishes exacerbates
impacts of global ocean changes on marine ecosystems. Nature
Climate Change 3:254–258.
Christiansen, F., et al. 2018. Maternal body size and condition determine calf growth rates in southern right whales. Marine Ecology
Progress Series 592:267–282.
Christiansen, F., A. M. Dujon, K. R. Sprogis, J. P. Y. Arnould,
and L. Bejder. 2016. Noninvasive unmanned aerial vehicle provides estimates of the energetic cost of reproduction in humpback
whales. Ecosphere 7:1–18.
Danil, K., and S. J. Chivers. 2007. Growth and reproduction of
female short-beaked common dolphins, Delphinus delphis, in the
eastern tropical Pacific. Canadian Journal of Zoology 85:108–121.
Eberhardt, L. 1977. Optimal policies for conservation of large mammals, with special reference to marine ecosystems. Environmental
Conservation 4:205–212.
Fortune, S., A. Trites, C. Mayo, D. Rosen, and P. Hamilton.
2013. Energetic requirements of North Atlantic right whales and
the implications for species recovery. Marine Ecology Progress
Series 478:253–272.
Fortune, S. M. E., A. W. Trites, W. L. Perryman, M. J. Moore,
H. M. Pettis, and M. S. Lynn. 2012. Growth and rapid early development of North Atlantic right whales (Eubalaena glacialis).
Journal of Mammalogy 93:1342–1354.
Fowler, C. W. 1987. A review of density dependence in populations
of large mammals. Pp. 401–441 in Current mammalogy, volume 1
(H. H. Genoways, ed.). Springer. New York.
George, J. C., J. Zeh, R. Suydam, and C. Clark. 2004. Abundance
and population trend (1978–2001) of western Arctic bowhead
whales surveyed near Barrow, Alaska. Marine Mammal Science
20:755–773.
Gilmore, R. M. 1960. A census of the California gray whale. Special
Scientific Report—Fisheries No. 342. U.S. Department of Interior,
Fish and Wildlife Service. Washington, D.C.
Gilmore, R. M. 1961. The story of the gray whale. 2nd ed. Privately
Published. San Diego, California.
Gompertz, B. 1825. On the nature of the function expressive of
the law of human mortality, and on a new mode of determining
the value of life contingencies. Philosophical Transactions of the
Royal Society of London 115:513–583.
Grothendieck, G. 2013. nls2: non-linear regression with brute
force. R package. http://cran.r-project.org/package=nls2. Accessed
3 June 2019.
Gulland, F., et al. 2005. Eastern North Pacific gray whale
(Eschrichtius robustus) unusual mortality event, 1999–2000.
NOAA Technical Memorandum. NMFS-AFSC-150:33 pp. U.S.
Department of Commerce. Springfield, Virginia.
Highsmith, R. C., and K. O. Coyle. 1990. High productivity of
northern Bering Sea benthic amphipods. Nature 344:862–864.
Larese, J. P., and S. J. Chivers. 2009. Growth and reproduction of
female eastern and whitebelly spinner dolphins incidentally killed
in the eastern tropical Pacific tuna purse-seine fishery. Canadian
Journal of Zoology 87:537–552.
Le Boeuf, B. J., H. Perez-Cortes M., J. Urban R., B. R. Mate,
and F. Ollervides U. 2000. High gray whale mortality and low recruitment in 1999: potential causes and implications (Eschrichtius
robustus). Journal of Cetacean Research and Management 2:85–99.
Lockyer, C. 1976. Body weights of some species of large whales.
ICES Journal of Marine Science 36:259–273.
Lockyer, C. 1981a. Estimates of growth and energy budget for the
sperm whale, Physeter catodon. Pp. 489–504 in Mammals in the
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Supplementary Data SD1.—Gray whale (Eschrichtius
robustus) length and mass data used in the allometric model.
We excluded pregnant individuals and one individual of length
9.1 m and mass of 3,500 kg from the analysis because the reported mass measurement was considerably less than expected
for its reported size. This individual was noted to have died of
probable starvation (Sumich 1986), and was not likely representative of a typical individual at that size.
Supplementary Data SD2.—Mean percent differences between observed and predicted lengths for female and male gray
whales (Eschrichtius robustus) in Phase 1 (0–0.8 years) and
Phase 2 (> 0.8–30 years). The observations available from individuals in Phase 1 were insufficient to calculate phase- and sexspecific correction factors. We therefore applied Phase 2 sex
correction factors (percent differences) to both growth phases
of the fitted Putter growth model to generate comprehensive
sex-specific growth curves (Fig. 4).
AGBAYANI ET AL.—GRAY WHALE GROWTH AND DEVELOPMENT
Rice, D. W. 1983. Gestation period and fetal growth of the gray whale.
Reports of the International Whaling Commission 33:539–544.
Rice, D. W., and A. A. Wolman. 1971. Life history and ecology
of the gray whale (Eschrichtius robustus). American Society of
Mammalogists, Special Publication No. 3. Stillwater, Oklahoma.
Rice, D. W., A. A. Wolman, and H. W. Braham. 1984. The gray
whale, Eschrichtius robustus. Marine Fisheries Review 46:7–14.
Ricker, W. E. 1979. Growth rates and models. Pp. 677–743 in Fish
physiology III, bioenergetics and growth (W. S. Hoar, D. J. Randall,
and J. R. Brett, eds.). Academic Press. New York.
Risting, S. 1928. Whales and whale foetuses: statistics of catch and
measurements collected from the Norwegian Whalers Association
1922–1925. Conseil Permanent International pour l’Exploration de
la Mer. Rapports et Procès–Verbaux de Réunions, v. 1. Andr. Fred.
Høst & Fils. Copenhagen, Denmark.
Scheffer, V. B. 1955. Body size with relation to population density
in mammals. Journal of Mammalogy 36:493–515.
Schultz, L. P. 1938. Can the weight of whales and large fish be calculated? Journal of Mammalogy 19:480–487.
Shotwell, M., W. McFee, and E. H. Slate. 2010. Estimating
Gompertz growth curves from marine mammal strandings in the
presence of missing data. International Journal of Ecological
Economics and Statistics 19:32–46.
Stevick, P. T. 1999. Age-length relationships in humpback whales: a
comparison of strandings in the western North Atlantic with commercial catches. Marine Mammal Science 15:725–737.
Sumich, J. L. 1986. Growth in young gray whales. Marine Mammal
Science 2:145–152.
Sumich, J. L., S. A. Blokhin, and P. A. Tiupeleyev. 2013.
Revised estimates of foetal and post-natal growth in young gray
whales (Eschrichtius robustus). Journal of Cetacean Research and
Management 13:89–96.
Sumich, J. L., T. Goff, and W. L. Perryman. 2001. Growth of two
captive gray whale calves. Aquatic Mammals 27:231–233.
Swartz, S. L. 1986. Gray whale migratory, social and breeding behavior. Report of the International Whaling Commission Special
Issue 8:207–229.
Swartz, S. L., and M. L. Jones. 1983. Gray whale (Eschrichtius
robustus) calf production and mortality in the winter range. Report
International Whale Commission 1981:503–507.
Swartz, S. L., J. Urbán R., S. Martínez A., L. V. Gómora, and
A. Gómez-Gallardo. 2018. 2018 research report for Laguna
San Ignacio and Bahía Magdalena, Baja California Sur, Mexico.
Laguna San Ignacio Ecosystem Science Program. San Ignacio,
Mexico.
Therkildsen, N. O., A. P. Wilder, D. O. Conover, S. B. Munch,
H. Baumann, and S. R. Palumbi. 2019. Contrasting genomic
shifts underlie parallel phenotypic evolution in response to fishing.
Science 365:487–490.
Trites, A. W. 1990. The northern fur seal: biological relationships,
ecological patterns and population management. Ph.D. dissertation, The University of British Columbia. Vancouver, British
Columbia, Canada.
Trites, A. W. 1991. Fetal growth of northern fur seals: life-history
strategy and sources of variation. Canadian Journal of Zoology
69:2608–2617.
Trites, A. W., and M. A. Bigg. 1996. Physical growth of northern
fur seals (Callorhinus ursinus): seasonal fluctuations and migratory influences. Journal of Zoology (London) 238:459–482.
Trites, A. W., and D. Pauly. 1998. Estimating mean body masses of
marine mammals from maximum body lengths. Canadian Journal
of Zoology 76:886–896.
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
seas. Vol. 3. General papers. Large cetaceans. Selected papers of
the Scientific Consultation on the conservation and management
of marine mammals and their environment. FAO Fisheries Series.
Food and Agriculture Organization of the United Nations and the
United Nations Environment Programme. Rome, Italy.
Lockyer, C. 1981b. Growth and energy budgets of large baleen
whales from the Southern Hemisphere. Pp. 379–487 in Mammals
in the seas. Vol. 3. General papers. Large cetaceans. Selected papers of the Scientific Consultation on the conservation and management of marine mammals and their environment. FAO Fisheries
Series. Food and Agriculture Organization of the United Nations
and the United Nations Environment Programme. Rome, Italy.
Lockyer, C. 2001. Ecological aspects of reproduction of marine
mammals. Pp. 93–131 in Marine mammals: biology and conservation (P. G. H. Evans and J. A. Raga, eds.). Springer. New York.
Lockyer, C. 2007. All creatures great and smaller: a study in cetacean life history energetics. Journal of the Marine Biological
Association of the United Kingdom 87:1035–1045.
Lockyer, C., and T. Waters. 1986. Weights and anatomical measurements of northeastern Atlantic fin (Balaenoptera physalus,
Linnaeus) and sei (B. borealis, Lesson) whales. Marine Mammal
Science 2:169–185.
McLenahan, L. 2009. Documenting loss of large trophy fish from
the Florida Keys with historical photographs. Conservation
Biology 23:636–643.
Miller, C. A., P. B. Best, W. L. Perryman, M. F. Baumgartner,
and M. J. Moore. 2012. Body shape changes associated with reproductive status, nutritive condition and growth in right whales
Eubalaena glacialis and E. australis. Marine Ecology Progress
Series 459:135–156.
Moore, S. E., et al. 2001. Are gray whales hitting “K” hard? Marine
Mammal Science 17:954–958.
NOAA [National Oceanic and Atmospheric Administration]
Fisheries. 2020. 2019 gray whale unusual mortality event along
the West Coast. Marine Life in Distress. http://fisheries.noaa.
gov/national/marine-life-in-distress/2019-gray-whale-unusualmortality-event-along-west-coast. Accessed 3 February 2020.
Norris, K. S., and R. L. Gentry. 1974. Capture and harnessing
of young California gray whales, Eschrichtius robustus. Marine
Fisheries Review 36:58–64.
Pauly, D., and W. W. L. Cheung. 2018. Sound physiological knowledge and principles in modeling shrinking of fishes under climate
change. Global Change Biology 24:e15–e26.
Perrin, W. F., J. M. Coe, and J. R. Zweifel. 1976. Growth and
reproduction of the spotted porpoise, Stenella attenuata, in the offshore eastern tropical Pacific. Fishery Bulletin 74:229–269.
Perryman, W. L., and M. S. Lynn. 2002. Evaluation of nutritive condition and reproductive status of migrating gray whales
(Eschrichtius robustus) based on analysis of photogrammetric data. Journal of Cetacean Research and Management
4:155–164.
R Core Team. 2018. R: a language and environment for statistical
computing. Foundation for Statistical Computing. Vienna, Austria.
http://www.r-project.org/. Accessed 3 June 2019.
Rechsteiner, E. U., D. a. S. Rosen, and A. W. Trites. 2013. Energy
requirements of Pacific white-sided dolphins (Lagenorhynchus
obliquidens) as predicted by a bioenergetic model. Journal of
Mammalogy 94:820–832.
Reilly, S. B. 1992. Population biology and status of eastern Pacific
gray whales: recent developments. Pp. 1062–1074 in Wildlife
2001: populations (D. R. McCullough and R. H. Barrett, eds.).
Elsevier. New York.
753
754
JOURNAL OF MAMMALOGY
(M. L. Jones, S. L. Swartz, and S. Leatherwood, eds.). Academic
Press. New York.
Zach, R., Y. Liner, G. L. Rigby, and K. R. Mayoh. 1984. Growth
curve analysis of birds: the Richards model and procedural problems. Canadian Journal of Zoology 62:2429–2435.
Zenkovich, B. A. 1937. More on the gray California whale
(Rhachianectes glaucus, Cope 1864). Bulletin of the Far East
Branch of the Academy of Science USSR 23:9–103 [in Russian].
Zimushko, V. V. 1970. Age determination of the gray whale (Eschrichtius
robustus). Translated from Izvestya (TINRO) 71:295–300.
Zimushko, V. V., and M. V. Ivashin. 1980. Some results of the
U.S.S.R. investigations and whaling of gray whales (Eschrichtius
robustus, Lilljeborg 1861). Report to the International Whaling
Commission 30:237–246.
Submitted 20 March 2019. Accepted 6 March 2020.
Associate Editor was Aleta Hohn.
Downloaded from https://academic.oup.com/jmammal/article-abstract/101/3/742/5820166 by guest on 24 July 2020
Vikingsson, G., J. Sigurjonsson, and T. Gunnlaugsson. 1988.
On the relationship between weight, length and girth dimensions in
fin and sei whales caught off Iceland. Reports to the International
Whaling Commission 38:323–326.
von Bertalanffy, L. 1938. A quantitative theory of organic growth
(inquiries on growth laws II). Human Biology 10:181–213.
Wahrenbrock, E. A., G. F. Maruschak, R. Elsner, and
D. W. Kenney. 1974. Respiration and metabolism in two baleen
whale calves. Marine Fisheries Review 36:3–8.
White, S. B., and H. J. Griese. 1978. Notes on lengths, weights,
and mortality of gray whale calves. Journal of Mammalogy
59:440–441.
Winship, A. J., A. W. Trites, and D. G. Calkins. 2001. Growth in
body size of the Steller sea lion (Eumetopias jubatus). Journal of
Mammalogy 82:500–519.
Yablokov, A. V., and L. S. Bogoslovskaya. 1984. A review of
Russian research on the biology and commercial whaling of the
gray whale. Pp. 465–485 in The gray whale: Eschrichtius robustus