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MARINE ECOLOGY PROGRESS SERIES
Mar Ecol Prog Ser
Vol. 575: 195–206, 2017
https://doi.org/10.3354/meps12211 Published July 20
INTRODUCTION
The exponential growth of populations when there
are enough resources and the environment remains
unchanged is one of the oldest and more pervasive
concepts of ecology (Turchin 2003, Kolasa 2011).
Although the instantaneous growth rate parameter
(r) has different meanings according to the subdisci-
plines of ecology (Fagan et al. 2010), it measures the
per capita population growth rate during an infini -
© Inter-Research 2017 · www.int-res.com*Corresponding author: leowedekin@gmail.com
Running fast in the slow lane: rapid population
growth of humpback whales after exploitation
L. L. Wedekin1,2,*, M. H. Engel1, A. Andriolo3, P. I. Prado2, A. N. Zerbini4,5, 6,
M. M. C. Marcondes1, P. G. Kinas7, P. C. Simões-Lopes8
1Instituto Baleia Jubarte, Caravelas, BA, 45900-000, Brazil
2LAGE do Departamento de Ecologia, Instituto de Biociências, Universidade de São Paulo, São Paulo, SP, 05508-090, Brazil
3Departamento de Zoologia, Instituto de Ciências Agrárias, Universidade Federal de Juiz de Fora, Juiz de Fora, MG,
36036-900, Brazil
4Cascadia Research Collective, Olympia, WA 98501, USA
5Marine Mammal Laboratory, Alaska Fisheries Science Center, NOAA Fisheries, Seattle, WA 98115, USA
6Instituto Aqualie, Juiz de Fora, MG, 36033-030, Brazil
7Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, Rio Grande, RS, 74690-900, Brazil
8Laboratório de Mamíferos Aquáticos, Departamento de Ecologia e Zoologia, CCB, Universidade Federal de Santa Catarina,
Florianópolis, SC, 88040-970, Brazil
ABSTRACT: Humpback whales were hunted almost to extinction in the 20th century, providing
an opportunity to measure their post-exploitation population growth rates. Variation in growth
rates may be related to many factors, and little work has been done to understand the differences
among populations. First, we provided an estimate of the growth rate for the Brazilian breeding
stock of humpback whales using models that consider imperfect detection applied to a long-term
and broad-scale dataset collected through systematic aerial surveys. Then, a review of the litera-
ture on the population growth rates of this species worldwide and a meta-analysis were conducted
to explore the differences in growth rates and their determinants. A finite growth rate of 12% yr−1
(95% CI = 8−16%; CV = 17 %) for the population wintering in Brazil was estimated from aerial sur-
veys conducted from 2002 to 2011 and may be regarded as an empirical estimate of its intrinsic
growth rate. The meta-analysis shows that there are geographical differences in growth rates,
with substantial heterogeneity among studies. Growth rates of populations in the Northern Hemi-
sphere are predicted to be lower than those in the Southern Hemisphere. The geographical differ-
ences in population parameters may be explained by spatial variability in productivity and prey
availability, human impact and distinct hunting histories. Moreover, the differences in population
growth rates are linked to genetic variability, with populations with higher haplotype diversity
growing at faster rates. Long-term studies on dynamics of baleen whale populations reduced by
whaling are invaluable to investigate the population growth and regulation of these cetaceans.
KEY WORDS: Megaptera novaeangliae · Population dynamics · Population growth rate ·
Exponential growth · Distance sampling · Meta-analysis
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Mar Ecol Prog Ser 575: 195–206, 2017
tesimally small period of time. The growth rate is a
‘unifying variable linking the various facets of popu-
lation eco logy’ (Sibly & Hone 2002). Ultimately, the
population growth rate is linked to the fate of popula-
tions and is vital for a variety of models with different
purposes in ecology (e.g. Morris & Doak 2002).
Most populations have a growth rate that fluctuates
around a mean of zero (Fryxell et al. 2014). Thus, op -
portunities for estimating the maximum rate of popu-
lation growth or the intrinsic growth rate (rmax) in the
wild are rare. Such opportunities arise when popula-
tions are reduced well below their carrying capacity
or when a species is introduced to an environment
with abundant resources and no natural enemies,
such as islands (Hone et al. 2010). Due to this limita-
tion, a common alternative to obtaining the intrinsic
growth rate is to use population models that require
other parameters that are easier to obtain, such as
body mass and the age of females at first reproduc-
tion (Caughley & Krebs 1983, Hone et al. 2010).
When applied to cetaceans, such models have shown
great variation in life histories (Taylor et al. 2007),
which is most likely linked to the great variation in
body sizes within the group. At one extreme, many
species live in the ‘fast lane’ (see Read & Hohn 1995),
which includes groups such as small porpoises, some
delphinids and river dolphins, which mature rela-
tively early and have rapid reproduction. At the other
extreme of life history variation within ceta ceans are
the baleen whales, the largest animals that have ever
lived on Earth, with slow reproduction, a longer life-
span and later maturity. Accordingly, the intrinsic
rate of population growth tends to decrease with
larger body sizes (Caughley & Krebs 1983).
Commercial whaling targeted the largest species,
with more than 2 million whales from at least 8 spe-
cies being severely hunted and many populations
being depleted almost to extinction (Clapham &
Baker 2009). Whaling in the 20th century was the
greatest wildlife exploitation event in human history
(Clapham et al. 2008). The decline in the whaling
industry and the worldwide embargo issued by the
International Whaling Commission (IWC) in 1966
allowed many populations to recover and provided a
unique opportunity to measure their post-exploita-
tion population growth rates (Best 1993). Despite its
associated controversy, commercial whaling in the
first half of the past century may be regarded as a
huge ecological uncontrolled ‘experiment’ (Laws
1977, Witting 2013). Of course, this large-scale hu -
man intervention cannot be called an experiment in
the strictest statistical sense, but it surely offers the
chance to better understand the dynamics of the
Southern Ocean ecosystem. The removal of whales,
for example, may have resulted in a surplus of prey
and an increase in the abundance of other krill con-
sumers, such as penguins and seals (Laws 1977).
In the present study, we focus on the post-exploita-
tion growth rate of humpback whales Megaptera no-
vaeangliae. There is a consensus among resear chers
that most or all populations of this species of the mar-
ine megafauna have been growing worldwide (e.g.
Zerbini et al. 2010). Although many studies on the
population growth rates of humpback whales exist,
with much variability in the growth rates observed
among them, the possible causes of such differences
have been poorly investigated. First, we used a long-
term dataset from this recovery period to study the
dynamics of the humpback whale population that
winters in Brazil. Our first question was: What is the
growth rate for this humpback whale population?
The instantaneous rate of population growth was es-
timated for this population using statistical methods
that account for imperfect detection (King 2014). The
second question was: How do the growth rates vary
among populations and what variables may explain
such variation? To answer this, available estimates on
the annual growth rate of different populations of this
species around the globe were reviewed and explor ed
using a meta-analysis approach (Côté & Jennions 2013).
MATERIALS AND METHODS
Humpback whale populations
Humpback whales typically migrate between sum-
mer feeding grounds at high latitudes, and winter
breeding and calving sites in the tropical seas of both
hemispheres (Kellogg 1929). Fidelity to distinct breed-
ing and feeding grounds promotes the worldwide
population structure, and the subpopulations are con-
sidered to be independent demographic units (Baker
et al. 1993). There is limited genetic exchange between
ocean basins, leading to the definition of 3 popula-
tions or subspecies (Baker et al. 1993, Jackson et al.
2014): North Atlantic, North Pacific and Southern
Hemisphere. Furthermore, 7 breeding stocks are rec-
ognized in the Southern Hemisphere (IWC 2011);
whales from these stocks are known to be genetically
differentiated (Olavarría et al. 2007, Rosenbaum et
al. 2009). Additionally, a non-migratory population is
found in the Arabian Sea (Mikhalev 1997). Whales
wintering off Brazil congregate in shallow and warm
habitats on the continental shelf (Andriolo et al. 2010)
and correspond to breeding stock A (IWC 2011).
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Wedekin et al.: Population growth rates of humpback whales
Aerial surveys
Aerial surveys covered the main area of concentra-
tion of humpback whales on the Brazilian coast (from
12° 10’ to 20° 42’ S) during 7 breeding seasons, from
2001 to 2005 and 2008 and 2011 (for more details see
Andriolo et al. 2006, 2010). The sampling was strati-
fied into 5 geographical regions that had differences
in whale density, including waters from the coastline
to the 500 m isobath (Supplement 1 in the supple-
mentary material at www. int-res. com/ articles/ suppl/
m575 p195 _ supp. pdf). The surveys were conducted
during the peak of the breeding season, from mid-
August to mid-September. The study area was flown
systematically from north to south.
The first aerial survey of our time series (2001) was
excluded from the estimation of the population growth
rate to minimize a possible bias in terms of the in -
creased efficiency of the observers over time, which
could have caused an overestimation of the growth
rate. The aerial surveys employed a 2-engine high-
wing aircraft (‘Aerocommander’) equip ped with bub-
ble windows. The survey altitude was 152.4 m, except
in 2008, when the survey altitude was 304.8 m. When-
ever a group of whales was detected, the declination
angle was measured with a hand-held clinometer to
estimate the perpendicular distance. Observers re -
corded groups of whales at unlimited distance from
the transect lines.
Distance sampling analyses
Density and abundance were estimated using mul-
tiple covariate distance sampling (Marques & Buck-
land 2003, 2004). A key feature of this method is fit-
ting a detection function to the data, which describes
how different covariates affect the rate at which the
probability of detecting a group decreases with dis-
tance. Hazard-rate and half-normal parametric func-
tions were considered as detection functions because
of their desirable properties and shapes (Buckland et
al. 2001). Additional adjustment terms (cosine, simple
polynomial or Hermite polynomial) were also consid-
ered to improve model fitting when necessary. The
covariates were included in the detection function
through a scale term (Marques & Buckland 2003).
For the estimation of density and abundance, year-
specific detection functions were fitted to the data
(Supplement 2). The year-specific detection func-
tions were estimated to account for interannual dif-
ferences in survey altitudes, teams of observers and
environmental conditions. The following covariates
were considered each year: individual observer, sun
glare (%), cloud cover (%), sea state on the Beaufort
scale (as a factor or numerical), sighting conditions
(poor, regular, good or excellent), cluster size, sight-
ing cue (body, aerial behavior or blow) and geo-
graphical region.
The stepwise approach was used to build detection
probability models for the distance data considering
different covariates (Marques & Buckland 2003; see
details in our Supplement 3). Model selection con -
sidered Akaike’s information criterion differences
(ΔAIC), which represents the difference between the
AIC of the best model (ΔAIC = 0) and the AIC of the
model being considered (Burnham & Anderson 2002).
Models with ΔAIC < 2 have a substantial level of
empirical support and were considered for inference
(Burnham & Anderson 2002).
Global density estimates were calculated as the
mean density of each stratum weighted by the stra-
tum area. A global detection function (as opposed to
a region-specific one) was fitted to the data for each
year, and maximum likelihood estimates (MLE) were
obtained using the software Distance, version 6.2
(Tho mas et al. 2010). Abundance was calculated
through a Horvitz−Thompson-like estimator (Bor -
chers & Burnham 2004, Marques & Buckland 2004).
Whales were detected in clusters, and total abun-
dance was estimated as number of groups multiplied
by mean cluster size within the program Distance.
The annual finite population growth rate (λ) and
the instantaneous growth rate (r) were derived from
a continuous exponential growth model fitted to the
abundance estimates. The instantaneous growth rate
(r) corresponds to the slope (β1) of a linear regression
model with the abundance estimates transformed by
the natural logarithm: ln(N
ˆ)= β0+ β1× (year), where
N
ˆis the abundance estimate and β0is the intercept of
the model. This log-linear model is equivalent to the
density-independent exponential population dynam-
ics model (Nt= N0ert , where Ntis the abundance in
time t, N0is the abundance in time zero or initial
abundance, ris the intrinsic population growth rate
and e is the Euler’s number, the base of the natural
logarithm) and is therefore adequate to estimate the
instantaneous population growth rate. Weighted lin-
ear regression was used to account for the variable
precision through the coefficient of variation (CV) of
the abundance estimates (weight = 1 / CV(Nt)2). The
relationship between the finite growth rate and the
instantaneous growth rate was given by λ= er. We
will refer to λsimply as the ‘population growth rate’
throughout the article. The growth rate may also be
referred to as ‘rate of increase’ in the literature.
197
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Mar Ecol Prog Ser 575: 195–206, 2017
Meta-analysis
Peer-reviewed articles and unpublished technical
documents reporting the growth rates of humpback
whales were scanned from the literature (see Supple-
ment 5). We chose an arbitrary cutoff precision level
for the parameter estimates and eliminated growth
rates with CVs that were higher than 30% from the
analysis. Studies that did not include any information
on the precision of estimates were also excluded from
the analysis (see Supplement 5 for details).
The standard error (SE) was used as a measure of
precision for the studies considered here. Because
many of these studies only reported the CIs of the
parameter estimates as error measures, we calcu-
lated an approximate normal standard error estimate
using the 95% CIs with the following equation: SE =
(upper CI − lower CI) / 3.92. The validity of this ap -
proach was confirmed by comparing the SE com-
puted from the 95% CIs with the estimated SE from
studies for which both SE and 95% CIs were
available.
A meta-regression was then used to investigate the
causes of variation in the estimates of the annual
population growth rates reported in the literature
(Chen & Peace 2013) using the R package ‘metafor’
(Viechtbauer 2010). Meta-regression is similar to a
multiple regression approach, where it is possible to
assess whether one or more explanatory variables
have an influence on the size of the effect of different
studies. Using random effects models, it was possible
to consider the variation within and between studies
(heterogeneity) and the contribution of the covariates
in explaining the heterogeneity found in the dataset.
The SEs were used as weights in the meta-regression
model.
The following covariates were considered sepa-
rately in the model selection procedure (for more de-
tails and rationale see Supplement 6): (1) length of the
study in years; (2) study method
(capture−recapture, naïve count-
based or count-based with distance
sampling); (3) study platform (air-
plane, vessel or shore-based); (4)
hemisphere; (5) ocean; (6) breed-
ing stock; (7) time lag from the year
when 90% of the whales were cap-
tured; (8) time length in years that
the population was hunted; (9)
total whales captured by whaling
activities; (10) haplotype diversity.
A set of models was considered
as plausible hypo theses explain-
ing the variability found in the data set, and model
selection was carried out using AIC. The total
amount of heterogeneity accoun ted for by the ex -
planatory variables (heterogeneity ex plained) in -
cluded in each model was also calculated as a rough
measure of the explanatory power of the model. The
heterogeneity explained (pseudo-R2sta tis tic) by each
model was calculated from the τ2in dex (=the vari-
ance of the true effect sizes as seen in the random-
effects model) (Raudenbush 2009), which may be re -
garded as a mea sure of among- study variance (Chen
& Peace 2013).
RESULTS
Trends in abundance from aerial surveys
In total, 1638 groups of humpback whales over a
distance of more than 21000 km were observed dur-
ing the aerial surveys conducted from 2002 to 2011
(Table 1). While the mean group size varied slightly
among years, the sighting rates increased steadily
over the years.
The half-normal function with no adjustment
terms was selected by AIC for all of the years as the
most supported detection probability model and
generally had fewer problems with convergence
than the hazard-rate function. The covariates that
influenced the shape of the detection function var-
ied among years. Cue was the most common covari-
ate affecting the detection probability, with aerial
behaviors and blows being detected at greater dis-
tances than the bodies of whales either near the sur-
face or submerged. In some years, the different
observers also had an effect on the detection func-
tion. Finally, sea conditions (as measured by the
Beaufort scale) had an influence on detection in
2004.
198
Year Line Effort Groups Mean Group Sighting Sighting
tran- (km) detec- group size rate (groups rate
sects ted size (% CV) km−1) (% CV)
2002 76 3730.9 178 1.53 3.45 0.015 68.68
2003 76 3928.4 207 1.79 3.79 0.053 10.65
2004 77 4011.2 267 1.57 3.00 0.067 9.09
2005 77 4004.1 304 1.61 3.22 0.076 8.23
2008 42 2373.7 268 1.58 3.59 0.113 12.19
2011 54 3122.4 414 1.54 2.50 0.246 9.16
TOTAL 402 21170.7 1638 − − − −
Table 1. Effort and sightings of humpback whales during aerial surveys from
2002 to 2011
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Wedekin et al.: Population growth rates of humpback whales
Except for the first 2 years (2002 and 2003), which
had similar abundance estimates, the uncorrected
abundance estimates for the humpback whales on
the Brazilian coast increased monotonically from
2003 to 2011. The precision of the uncorrected esti-
mates was reasonably high, with the CV ranging
from 9 to 18% (Table 2). The linear regression model
with the log-transformed abundance estimates from
2002 to 2011 yielded an instantaneous growth rate (r)
of 0.1135 (SE = 0.0130) (Fig. 1). The trend was
sig nificantly different from zero (F= 76.59; df = 1,4;
p < 0.001), and the model fit the data well (adjusted
R2= 0.938). A finite growth rate of 12.02% yr−1 (95%
CI = 8.06−16.13%; CV = 17%) was derived from
the in stantaneous growth rate. A linear model of
population growth also fit our data well (adjusted
R2= 0.8821).
Meta-analysis
The bibliographic review resulted in 28 documents
reporting growth rates of humpback whale popula-
tions worldwide (Supplement 5). A total of 14 docu-
199
Year Covariates Trunca- N N pp
tion (m) (% CV) (% CV)
2002 Observer (obs) >2500 3026 13.2 0.44 7.0
2003 Cue >2500 2999 13.1 0.52 5.0
2004 Beaufort >2500 3763 17.9 0.52 14.0
(factor)
2005 Cue >2500 4113 9.0 0.55 5.0
2008 Cue + obs >4000 5399 13.6 0.40 6.0
2011 Cue + obs >2500 8832 14.1 0.43 4.0
Table 2. Uncorrected abundance estimates for the hump-
back whale population from 2002 to 2011, and covariates in-
cluded in the best model of detection. Truncation refers to
elimination of data on shortest or longest distances from the
transect line to improve fit. N = uncorrected abundance
estimate; p= probability of group detection
Fig. 1. Abundance estimates (natural log scale) from aerial
surveys for humpback whales on the Brazilian coast from
2002 to 2011. The log-linear regression fit to the data is indi-
cated by the black dashed line (gray area corresponds to the
95% confidence bands). Error bars are SE
Fig. 2. Annual growth rates of the
global humpback whale populations
reported by the studies included
in the meta-analysis (n = 14). Black
boxes correspond to growth rate
estimates, and their sizes are pro -
portional to the weights (precision)
considered in the meta-regression
model. Gray diamonds indicate the
predicted growth rates from a meta-
regression model with breeding stock
as an explanatory variable. BSS =
Southern Hemisphere breeding stock.
Error bars are SE
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Mar Ecol Prog Ser 575: 195–206, 2017
ments that satisfied our criteria for inclusion in the
meta-analysis, including that of precision, were con-
sidered (Figs. 2 & 3). If we consider a meta-regression
with random effects and no moderator, the typical
annual growth rate for the humpback whales would
be 10.46% (95% CI = 8.55−12.37 %). The hetero-
geneity was high among studies, with an estimated
I2= 90.9% (see Higgins et al. 2003). I2refers to the
index of heterogeneity and represents the ratio of
excess dispersion to total dispersion
The meta-regression models were constructed
considering 10 explanatory variables (Table 3). The
most parsimonious meta-regression model according
to AIC included the breeding stock as an explanatory
variable but accounted for only 12.3% of the among-
study heterogeneity. The second-most parsimonious
model included ocean as an explanatory variable,
predicting the lowest growth rates in the North
Pacific and North Atlantic oceans, respectively
(Fig. 4). The model that included the haplotype diver-
200
Fig. 3. Locations of the studies reporting annual growth rates of humpback whale populations that were included in the meta-
analysis (n = 14). Size of the red triangles is proportional to the growth rate reported by each study. Polygons showing different
types of habitats are approximations of the true distributions
Model description % Het AIC ΔAIC Akaike
weight
Breeding stock 12.3 57.4 0 0.782
Ocean 20.1 60.1 2.7 0.203
Haplotype diversity 38.8 67.4 10.0 0.005
Hemisphere 34.2 68.4 11.0 0.003
Research method 5.7 68.6 11.2 0.003
Research platform 0.0 69.6 12.2 0.002
Total whales hunted 14.5 70.9 13.5 0.001
Period whaling 0.0 73.0 15.6 0
Years research 0.0 73.0 15.6 0
Lag years of 90% captures 0.0 73.3 15.9 0
Null random effects − 75.9 18.5
Null fixed effects − 286.5 229.1
Table 3. Meta-regression models of the growth rates of the
global humpback whale populations as functions of differ-
ent explanatory variables. % Het = percentage of among-
study heterogeneity explained; AIC = Akaike’s information
criterion; ΔAIC = AIC difference between the model and the
best model (lowest AIC value). Akaike weight measures the
weight of evidence in favor of the model and may be inter-
preted as the model probability
Fig. 4. Annual population growth rates of humpback whales
according to hemisphere as reported by studies included in
the meta-analysis (n = 14). The black line within the box in-
dicates the median, box indicates the 1st and 3rd quartiles,
and the whiskers indicate range of values. White asterisks
indicate the predicted population growth rates for both
hemispheres based on the meta-regression model with
hemisphere as an explanatory variable
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Wedekin et al.: Population growth rates of humpback whales
sity as an explanatory variable was the model that
accounted for the most among-study heterogeneity
(~39%). This model predicts higher rates of growth
with increasing genetic diversity. The model that
included hemisphere as a moderator also ac counted
for substantial heterogeneity (~34%), predicting
higher growth rates in the Southern Hemisphere
(12.21% yr−1) and lower rates in the Northern Hemi-
sphere (7.74% yr−1) (Fig. 4). Other models that
included variables related to methodology or the his-
tory of hunting did not fit the data well and did not
explain much of the among-study heterogeneity.
DISCUSSION
Potential biases in the growth rates
Two types of errors resulting from animals being
missed by observers may affect distance sampling
methods (Marsh & Sinclair 1989): availability bias,
which is caused by animals that are not available to
be detected, and perception bias, which is caused by
the ability of an observer to detect the animals. If the
parameter of interest was the absolute abundance of
the population, a correction factor to ac count for
availability bias caused by animals that were under-
water when the airplane passed should be applied
(Barlow et al. 1988). It is reasonable to assume that
the availability bias for humpback whales did not
vary among years, and thus the uncorrected esti-
mates of abundance were used as proxies for the
total population size to obtain the growth rates. How-
ever, our assumption of constant perception bias
among years remains to be tested. An important
improvement for future aerial surveys is to include a
double observer platform (Borchers et al. 1998) to test
whether perception bias plays an important role in
the estimates of abundance and growth rates, and
whether it varies among years. Any change in the
survey method, however, needs to be done in a man-
ner that still allows comparisons over the long term.
Distance sampling estimates of growth rate may
also be affected by temporary or permanent migration.
It has been hypothesized that the high growth rates of
some populations of humpback whales may be the re-
sult of a combination of true growth and temporary
immigration, driven by a tendency to aggregate for
mating (Clapham & Zerbini 2015). In essence, whales
would abandon former breeding grounds in favor of
other sites with higher densities. Such unidirectional
movements could bias growth rate estimates from
both mark−recapture and distance sampling methods.
Movements between breeding grounds were de -
tected in the Southern Hemisphere, including a
whale that was sighted in Madagascar and Brazil
(Stevick et al. 2011) and another whale sighted in
Ecuador and Brazil (Stevick et al. 2013). Connections
between the stocks of Africa and Brazil have been
suggested by song behavior and genetics (Darling &
Sousa-Lima 2005, Rosenbaum et al. 2009), despite
the fact that the majority of whales from Brazil retain
their fidelity to this breeding ground (Rosenbaum et
al. 2009). These authors estimated an immigration
rate from stock B (West Africa) to stock A (Brazil) of
approximately one individual per year (or 29 per
generation). Such few migrants per generation may
allow some genetic exchange among breeding stocks
but would not be enough to significantly affect their
population structure (Rosenbaum et al. 2009). Thus,
the contribution of migration to the population
growth rate for Brazilian humpback whales is as -
sumed to be small or negligible.
Growth rate of the stock of Brazilian
humpback whales
Humpback whales from Brazil were intensively
hunted both in their feeding and breeding grounds,
with figures in the order of tens of thousands of
whales caught (Williamson 1975, Findlay 2001, de
Morais et al. 2017). It has been estimated that this
population reached a depletion level of 1 to 13% and
remained low for 4 decades (Zerbini et al. 2011).
Almost 10 years after the commercial whaling mora-
torium issued by the IWC in 1966, the occurrence of
this species in the whaling grounds of the northeast-
ern coast of Brazil was considered rare (Williamson
1975).
In recent decades, multiple lines of evidence have
indicated that the Brazilian stock of humpback
whales is growing. Previous studies reporting the
growth rates of these whales, however, have shown
contrasting growth rates (Freitas et al. 2004, Ward et
al. 2011). The first study considered a mark−recap-
ture dataset collected from the Abrolhos Bank, esti-
mating an annual growth rate of 31% from 1996 to
2000 (CV = 48%; Freitas et al. 2004). Such a high
growth rate may be overestimated by the use of a
population model with 100% survival or by the fail-
ure to control for differences in effort in terms of
space or time among years. The mark−recapture esti-
mates for this period are apparently overestimated
when compared with the growth rates obtained
through count methods.
201
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Mar Ecol Prog Ser 575: 195–206, 2017
Counts of whales from boat surveys around the
National Marine Park of Abrolhos (same core sam-
pling area and period of the mark−recapture effort)
yielded a growth rate of 7.4% yr−1 from 1995 to 1998
(CV = 48%; Ward et al. 2011). The limited area cov-
ered by the boat surveys used to count whales, how-
ever, could result in a negative bias in the growth
rate determined in this study because only core habi-
tats were surveyed, and these areas may become sat-
urated first relative to more marginal habitats (Ward
et al. 2011).
The aerial surveys covered a wider study area and
show that the growth rate may vary among regions
(see Supplement 4). The highest density area ob -
served in this study in the central region of the Abrol-
hos Bank roughly matches the area covered by the
boat counts and indeed has lower growth rates than
adjacent regions. This provides further evidence for
the hypothesis that the growth rate presented by
Ward et al. (2011) was an underestimate, as their
study did not sample the entire habitat of this popu-
lation. Some regions within the Brazilian breeding
ground presented growth rates too high to be caused
only by births (see Supplement 4). The spatial organ-
ization resulting from movements of whales may bias
growth rate estimates because whales born in a high
density region of the breeding ground may occupy
adjacent regions in following seasons. Moreover,
potential biases of the studies reviewed by us in the
meta-analysis, including growth rates too high to be
biologically plausible, may be due to sampling a par-
ticular region within the breeding ground.
The dataset presented here, which was collected
during a later time period than those discussed
above, yielded relatively high estimates of annual
growth for this population. As judged by its good pre-
cision, a more rigorous sampling procedure and
broader spatial coverage of the breeding area, we
consider that aerial surveys provided a robust empir-
ical estimate of the instantaneous growth rate (r) for
this population. The estimate of an increase of 12%
yr−1 is very close to what was proposed as the bio -
logically plausible limit using a theoretical popula-
tion model (Zerbini et al. 2010) and thus is most likely
close to the intrinsic growth rate for this species.
Moreover, the confidence interval of the growth rate
presented here covers the theoretical maximum pro-
posed for the species, suggesting that they are not
significantly different.
Whaling activities did not last long enough to ham-
per the genetic diversity of the Brazilian stock, which
is one among the highest of the humpback whale
populations of the Southern Hemisphere (Engel et al.
2008). Recent abundance estimates for this stock sug-
gest that the population is nearly half of its pre-
exploitation abundance of 24 558 whales (Zerbini et
al. 2011). According to the logistic model and other
models of population growth with density depend-
ence, this population is growing at its maximum rate.
Furthermore, with the depletion of most populations
of other baleen whales in the Southern Hemisphere,
millions of tons of krill were available for other
whales and consumers in the Southern Ocean (Laws
1977). This ‘krill surplus’ may have favored con-
sumers in the Southern Ocean, creating the neces-
sary conditions for the observed growth of this popu-
lation (but see Balance et al. 2006 for a more complex
picture).
The recovery of humpback whale populations
world wide through the moratorium of commercial
whaling may be regarded as an emblematic example
of conservation success. Recently, the International
Union for Conservation of Nature has revised the
Red List status of humpback whales worldwide to
Least Concern (IUCN 2016) and the Brazilian Min-
istry of the Environment reclassified the species in
national waters to Near Threatened (ICMBio 2014).
Unfortunately, commercial whaling had many nega-
tive consequences, some of which were irreversible.
Humpback whales were once abundant around
South Georgia in the Southern Ocean and now are
recorded at low numbers, despite the presence of
krill in the region (Moore et al. 1999). Furthermore,
the moratorium occurred too late to preclude the
local extinction of some species (e.g. gray whale in
the North Atlantic, blue whale at South Georgia and
off Japan), and other species have not yet achieved
full recovery (e.g. North Atlantic right whale, hump-
back whales at South Georgia and New Zealand)
(Clapham et al. 2008, Clapham 2016).
Among-population differences in growth rate
The meta-analysis suggests that a substantial
amount of the heterogeneity among studies in the
growth rates of humpback whales is attributable to
geographical differences. The predicted growth rate
of humpback whales in the Northern Hemisphere
was lower than that in the Southern Hemisphere. A
remarkable difference between the polar ecosystems
of the south and the north is the absence of geo-
graphical barriers in the Southern Hemisphere.
The Antarctic Circumpolar Current runs eastward
around the Antarctic continent, creating gyres and
upwellings, and therefore enhancing the mixing and
202
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Wedekin et al.: Population growth rates of humpback whales
productivity of the Southern Ocean ecosystem (see
Murphy et al. 2007). The absence of geographical
barriers in the Southern Hemisphere may also affect
the population dynamics and structure of baleen
whales. Migration of whales between different stocks
may decrease the risk of extinction through a ‘rescue
effect’ (Hanski 1999).
The extension of sea ice in the Arctic is smaller
than that in the Antarctic, and has decreased in re -
cent decades, while it has increased in the Ant arctic
(NOAA/NSIDC 2014). Sea-ice habitats are known to
favor the recruitment of krill (Atkinson et al. 2004).
Additionally, the primary productivity of the North
Pacific Ocean has decreased over recent decades
(Schell 2000). Most rorqual whales in the Southern
Hemisphere are larger in size than in the north,
which may be related to higher primary productivity
in the south or may be a product of selection for ener-
getics (Brodie 1975). Furthermore, humpback whales
in the Northern Hemisphere feed on a larger variety
of prey and have a longer feeding season than their
counterparts in the south (Brodie 1975). In contrast,
prey of humpback whales in the Southern Hemi-
sphere largely consists of dense swarms of krill, which
may extend over 10s of kilometers (Nicol 2006). Nev-
ertheless, the distribution and abundance of krill
around the Antarctic continent is not uniform and the
Scotia Sea is the region that has the highest abun-
dance of krill (Atkinson et al. 2004) and is where the
Brazilian humpback whales feed (Stevick et al. 2006,
Zerbini et al. 2006b, Engel & Martin 2009). Thus,
there are likely differences in the marine biological
productivity and availability of prey across distinct
feeding grounds of the humpback whale.
Human impact in the Northern Hemisphere is
higher and can act with biological processes to create
the hypothesized differences in the growth rates of
whales between the hemispheres. Shipping lanes
and traffic that may threaten some baleen whales are
much more widespread and intense in the Northern
Hemisphere (Halpern et al. 2008). For example, the
North Atlantic right whale Eubalaena glacialis is
struggling to recover from whaling (Caswell et al.
1999) due to high shipping traffic and collisions
(Conn & Silber 2013), among other factors. In con-
trast, most southern right whale populations are
recovering from whaling, with high growth rates
reported in recent decades (e.g.Best et al. 2001,
Cooke et al. 2001). Shipping strikes may not be an
issue for Northern Hemisphere populations of hump-
back whales but may act synergistically with other
human impacts and decrease the overall habitat
quality for this species.
Patterns of exploitation by whalers also varied geo-
graphically and may account for the hemispheric and
longitudinal differences in the population growth
rates of this species. In the Southern Hemisphere, the
past total catches in the Atlantic and Indian oceans
were much larger than in the Pacific Ocean (Mori &
Butterworth 2006). Moreover, the breeding stocks of
the North Pacific, Brazil and eastern Australia were
those that experienced the largest catches (see Sup-
plement 6). The peak period of catches also differed
among the populations and, together with the total
catches, may determine how far each population is
from reaching the carrying capacity and, conse-
quently, its growth rate. However, the explanatory
variables related to hunting patterns did not explain
the heterogeneity in the growth rates among the
populations.
Haplotype diversity explained the largest amount
of heterogeneity among the studies. Higher genetic
diversity was observed for populations in the South-
ern Hemisphere; the lowest genetic diversity was
observed for the population in the North Pacific
(Jackson et al. 2014). Populations that may have
passed through a population bottleneck due to com-
mercial whaling and loss of genetic diversity, as in
the North Pacific and North Atlantic populations,
have the lowest genetic diversity and rates of growth.
Loss of genetic diversity may impact populations
over the long term by adversely affecting the ability
to cope with environmental change (Frankham 2005).
Concluding remarks
The growth rate estimated for the Brazilian breed-
ing population of humpback whales in recent
decades (r= 0.114) is near the maximum possible
growth rate for the species. Allometric models pre-
dict lower intrinsic growth rates for this species, with
rmax ranging from 0.037 (based on the model by
Caughley & Krebs 1983) to 0.058 (based on Schmitz
& Lavigne 1984). Thus, its large size could place the
humpback whale on the slow extreme of the range of
life histories within cetaceans. Moreover, using
known demographic parameters, such as the age of
first reproduction, inter-birth interval and survival,
the instantaneous population growth rate for the
humpback whale was estimated to be 0.05 (Taylor et
al. 2007). Contrary to most theoretical expectations,
at least temporarily, humpback whales show high
population growth rates typical of fast living and/or
smaller-sized cetaceans. One exception is the predic-
tion based on the relationship between rmax and age
203
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Mar Ecol Prog Ser 575: 195–206, 2017
at first reproduction (Hone et al. 2010), which yields
an estimate of rmax = 0.118 for the humpback whale,
considering that first reproduction of this species
occurs at 6 yr of age (Clapham 1992). It is reasonable
to state that humpback whales may decrease inter-
birth interval, increase survival and possibly breed at
a younger age when conditions are favorable.
The cessation of commercial whaling, the high
genetic diversity of humpback whales and the high
abundance of krill were likely the conditions that
allowed such a remarkable population growth rate
for some stocks. Commercial whaling set the stage
for the study of population growth and ecosystem
shifts at a global scale. Here, an empirical estimate of
the instantaneous growth rate (r) for the humpback
whale breeding stock of Brazil is provided. This esti-
mate is close to the intrinsic growth rate of the spe-
cies (rmax), which is rare to observe for wild animal
populations. Our study also highlights the impor-
tance of long-term studies in population ecology and
conservation biology (Caughley 1977, Gaillard et al.
1998). These studies are invaluable for our under-
standing of how the Southern Ocean will change
with the recovery of large whales, including compet-
itive inter actions among krill consumers. Another
interesting project would be to study the demo-
graphic transition of large whales from high popula-
tion growth to an equilibrium state and determine
how density-dependent processes will act on the
population dynamics of this species.
Acknowledgements. This study was part of a PhD thesis in
the Graduate Program in Zoology at the Federal University
of Paraná (UFPR). PNPD-CAPES provided a post-doc
scholar ship for L.L.W.; we acknowledge grant 2013/19250-7
from the São Paulo Research Foundation (FAPESP); CNPq
and FAPESP provided research grants for P.I.P. Projeto
Baleia Jubarte is sponsored by Petróleo Brasileiro S.A.
(Petrobras). Financial support for the data collection was
also provided by Fibria Celulose, Veracel Celulose, Com-
panhia de Navegação Norsul and Centro Mamíferos Aquá -
ticos (CMA − ICMBio). We thank IBJ’s staff, researchers,
interns and volunteers for assistance in the field and labora-
tory and many aerial survey observers, especially Cristiane
Albuquerque Martins and Alexandre Azevedo. We are
grateful to Emygdio Monteiro-Filho, Eduardo Secchi, Marta
Cremer and Daniel Danilewicz for comments on an early
draft of this manuscript. We thank Phil Clapham, Dave Haas
and 2 anonymous reviewers for providing comments that
greatly improved this paper.
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Submitted: August 19, 2016; Accepted: May 23, 2017
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