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Biologically plausible rates of increase for Antarctic blue whales



Basic biology limits the possible rate of increase in natural populations. Simply put, no population closed to immigration can increase more rapidly than is allowed by survival rates, pregnancy rate, age at first parturition, and the proportion of female births. Using a basic equation that relates values of these parameters to the implied rate of increase, a biologically plausible distribution and an upper bound are estimated for rates of increase in Antarctic blue whales (Balaenoptera musculus intermedia). The literature is reviewed to obtain distributions for each of the input parameters: adult survival S ~ N(0.963, 0.02 2), calf survival S j ~ N(0.84, 0.15 2), annual pregnancy rate p ~ U(0.33; 0.5), age at first parturition t p ~ N(10, 2 2), and the proportion of births that are female q f ~ N(0.473, 0.001 2). Lower and upper bounds were also placed on S, S j , and t p ; most important of these is the restriction that S j < S. The resulting distribution for the instantaneous annual rate of increase is ~ N(0.040, 0.019 2) with an upper 99 th percentile of 0.082, corresponding to annual rates of increase ~ N(0.041, 0.019 2) and 0.085 respectively. Estimated rates of increase from surveys of Antarctic blue whales (7.4% from JARPA, 8.2% from IDCR/SOWER) are close to this theoretical maximum of 8.5%, and have 95% confidence intervals that exceed the biological maximum possible rates.
Biologically plausible rates of increase for Antarctic blue whales
Basic biology limits the possible rate of increase in natural populations. Simply put, no population closed to
immigration can increase more rapidly than is allowed by survival rates, pregnancy rate, age at first parturition,
and the proportion of female births. Using a basic equation that relates values of these parameters to the implied
rate of increase, a biologically plausible distribution and an upper bound are estimated for rates of increase in
Antarctic blue whales (Balaenoptera musculus intermedia). The literature is reviewed to obtain distributions for
each of the input parameters: adult survival S ~ N(0.963, 0.02
), calf survival S
~ N(0.84, 0.15
), annual
pregnancy rate p ~ U(0.33; 0.5), age at first parturition t
~ N(10, 2
), and the proportion of births that are female
~ N(0.473, 0.001
). Lower and upper bounds were also placed on S, S
, and t
; most important of these is the
restriction that S
< S. The resulting distribution for the instantaneous annual rate of increase is ~ N(0.040, 0.019
with an upper 99
percentile of 0.082, corresponding to annual rates of increase ~ N(0.041, 0.019
) and 0.085
respectively. Estimated rates of increase from surveys of Antarctic blue whales (7.4% from JARPA, 8.2% from
IDCR/SOWER) are close to this theoretical maximum of 8.5%, and have 95% confidence intervals that exceed
the biological maximum possible rates.
Rates of increase in any population are limited by biology, providing a key piece of information that can be incorporated in
population assessments. The key biological factors are survival rates, inter-birth intervals, age at first parturition, and the
proportion of females in the population, which can be combined using a simple equation to provide estimates of both the
average and maximum possible rates of increase for biological populations. When this method is applied to humpback whales
(Balaenoptera novaeangliae), biologically plausible average rates of increase are 4.7% per annum (Clapham et al., 2006) and
the maximum rates are 12.6% (Clapham et al., 2001), 13.8% (Brandão et al., 2000) and 10.6% (Clapham et al., 2006); when
applied to southern right whales (Eubalaena australis), the average rate of increase of 7.2% almost exactly matches the
growth rate of 6.9% per annum from surveys (Best et al., 2005); and when applied to Antarctic blue whales (B. m.
intermedia), the average annual rate of increase is 4.3%, and the maximum rate is 11.9% (Branch et al., 2004).
Since the Antarctic blue whale distribution was published (Branch et al., 2004) new data have been presented for several
of the biological parameters, particularly for survival in northern blue whales (B. m. musculus) (Ramp et al., 2006), and for
survival, age at first parturition, and inter-birth intervals in pygmy blue whales (B. m. brevicauda) (Branch, 2008b); and
many studies have been published for other mysticetes. Here, we update the previous estimates of average and maximum
rates of increase for Antarctic blue whales.
Equation for estimating rate of increase
The Euler-Lotka equation, derived from Leslie matrix theory, can be used to directly estimate the instantaneous rate of
increase from biological parameters (Brandão et al., 2000):
(1) 1
tt t
δ is the instantaneous rate of increase,
is the age at first parturition (yr), assumed to be one year after the age at sexual maturity,
S is adult survival rate
is first-year survival rate
p is the annual pregnancy rate, or the inverse of the inter-calf interval
is the proportion of births that are female
Estimated distributions were obtained for each of the parameters from a literature review of known blue whale biology
and the biology of other large mysticetes. To obtain the distribution for the rate of increase, Monte Carlo simulations were
conducted where 50,000 sets of values were drawn from the parameter distributions and δ calculated for each. The maximum
possible rate of increase for Antarctic blue whales is assumed to be the upper 99
percentile of this distribution. The highest
20504 86
Pl, Edmonds WA 98026, USA, e-mail:
rate recorded for any one draw would be misleading, because this would increase as the number of draws increased, whereas
the 99
percentile is a stable estimator.
IWC catch database
The IWC individual catch database has recently been updated and now includes corrected Soviet catches (C. Allison, IWC
individual catch database Version 3.5, 11 February 2008). For several of the parameters, data from the database is extracted.
In each case, only the data for blue whales south of 56°S are used, because in this region >99% of blue whales are Antarctic
blue whales according to length frequencies of sexually mature females (Branch et al., 2007a) and relationships between
length and ovarian corpora (Branch et al., 2008).
Age at first parturition ( )
Most available estimates are for mean age at sexual maturity, t
, which is generally presumed to be about 1 yr before mean
age at first parturition, t
(e.g. Brandon et al., 2007). Existing estimates of the age at sexual maturity, t
, are sparse for
Antarctic blue whales. The best method for ageing mysticetes is by counting earplug layers, a method pioneered in the 1950s
(Purves, 1955; Laws and Purves, 1956). Earlier papers interpreted these layers by assuming that two earplug layers were
added each year (e.g. Chittleborough, 1959), but later analyses examining monthly changes in earplug formation have
confirmed that only one earplug layer is added per year for a variety of mysticetes (Roe, 1967; Rice and Wolman, 1971;
Lockyer, 1972, 1974, 1984). Earplugs were rarely collected before this ageing method was developed, and as the Antarctic
blue whale population was substantially depleted by this time, only limited earplugs were collected before the ban on
catching Antarctic blue whales was implemented in the early 1960s. As a result, estimates of t
are based on limited data for
Antarctic blue whales, and although good estimates are available for pygmy blue whales, no estimates are available for any
other blue whale population.
The little that has been published on earplug ageing of Antarctic blue whales is contradictory. Ohsumi (1979) reports that
limited Antarctic blue whale earplug data imply t
= 10 yr, and the few data points plotted in Figure 9 of Ichihara (1966) for
Antarctic blue whales also seem to imply that t
is about 8–12 yr. However, Lockyer (1981), aged earplug of 20 females and
16 males (data not reported) and states that t
is 5 yr, noting that this estimate is consistent with estimates of t
from baleen
plates made by Ruud and Jonsgård (1950) and Nishiwaki (1952).
For pygmy blue whales, estimates of t
come from Japanese and Soviet data. Japanese data presented by Ichihara (1966)
include ovarian corpora and earplug counts for 32 females shorter than the legal minimum catch length (70 ft, 21.3 m). These
data were reanalysed by regressing ovarian corpora counts against earplug laminae counts, resulting in an estimate of t
= 9.9
yr (95% CI 8.0–11.8) (Branch, 2008b). Most of the Soviet whaling on pygmy blue whales was illegal (Yablokov, 1994;
Mikhalev, 2000), and analyses on these data have been unknown in the West until recently. Part of the Soviet pygmy blue
whale data were analysed in a paper by Sazhinov (1970), only recently translated into English, and the author reported that
the length at sexual maturity is 19.2 m and that two female blue whales that were 19.2 m long, each with one corpus luteum,
had 9 and 11 earplug layers respectively, implying that t
= 9–11 years. The complete Soviet ovarian corpora data from the
recovered original logbooks, recently analysed, confirm that the length at maturity is 19.2 m (95% credibility intervals 19.1–
19.3 m) (Branch and Mikhalev, accepted). When combined with the complete earplug data presented in Sazhinov’s PhD
dissertation (Sazhinov, 1980), only recently obtained, the estimate of t
was 9.9 yr (95% credibility interval 9.0–11.0) for
female pygmy blue whales (Branch, 2008b), essentially confirming the preliminary estimates of Sazhinov (1970).
Rather more extensive data are available for humpback whales than for other mysticetes due to the recent surge in photo-
identification studies. In the Gulf of Maine, age at first calving, t
+ 1, is 5.92 yr (95% CI 5.47–6.37) (Clapham, 1992). In
south-eastern Alaska, though, age at first calving is substantially higher: t
+ 1 is 11.8 yr (95% CI 10.3–13.3) (Gabriele et al.,
2007). If the results of Chittleborough (1959) are reinterpreted assuming that there is one growth layer laid down in the
earplug per year, as is now believed (e.g. Best, 2006), then the age at sexual maturity was 8–12 yr off Australia in the mid-
Estimates of t
for other mysticetes show a similar range of estimates. For fin whales (B. physalus), t
apparently declined
from 10–11 yr in the 1930s to 6–7 yr during 1960–65 (Lockyer, 1972). For sei whales (B. borealis), t
also declined from
11–11.5 yr before 1935 to 8.4 yr in the 1960s in the Antarctic (Lockyer, 1974) and t
was 8.2 yr (95% CI 7.3–9.0 yr) in
1962–63 in South African waters (Best and Lockyer, 2002). Antarctic minke whale (B. acutorostrata) estimates of t
declined from ~11 yr for cohorts born in the 1950s to 7 yr for those in the 1970s (Thomson et al., 1999). North Atlantic right
whales (Eubalaena glacialis) produce their first calves at t
+ 1 = 9.53 yr (95% CI 8.39–10.67) (Kraus et al., 2001),
compared southern right whale estimates of t
+ 1 = 7.69 yr (95% CI 7.06–8.32) for South Africa (Best et al., 2005); and t
1 = 9.1 yr (95% CI 8.5–9.9) for Península Valdés, Argentina (Cooke et al., 2001). Eastern Pacific gray whales mature at t
8 yr (range 5–11 yr) (Reilly, 1984). A much higher estimate of t
of 20 yr (95% CI 14–26) is obtained from the Bering-
Chukchi-Beaufort Seas population of bowhead whales (Brandon et al., 2007), which is known to contain very long-lived
whales (e.g. George and Bockstoce, 2008).
In summary, the limited data available for Antarctic blue whales supports t
= 10 yr, but one study indicates t
could be 5
yr; data from pygmy blue whales strongly supports t
= 10 yr (95% CI 9–11 yr); and t
for humpback, fin, sei, northern right,
southern right and Antarctic minke whales has ranged from 5 yr to 11 yr, with most recent estimates falling in the 6–9 yr
range. It is difficult to amalgamate these contradictory assessments in a consistent manner. Although the most likely value of
for Antarctic blue whales is 10 yr, other evidence supports a lower value for t
. To introduce the possibility of a lower t
one year is subtracted from the most likely value, and a high standard deviation of 2 yr is assumed, thus t
~ N(9, 2
) and t
N(10, 2
). To prevent the high standard deviation resulting in draws of t
falling outside the range observed for species other
than bowhead whales, draws from this distribution were bounded to lie within the interval [5, 12] yr.
Adult survival rate (S)
Survival rates have not been calculated for Antarctic blue whales. For pygmy blue whales, the estimated survival rate from
combined age frequencies of Soviet and Japanese data is 0.94 (95% CI 0.93–0.95) (Branch, 2008b). For northern blue whales
in the Gulf of St Lawrence, a long-term photo-identification study produced an estimate of 0.975 (95% CI 0.960–0.985)
(Ramp et al., 2006). For North Pacific blue whales, survival was 0.927–0.951 based on earplug layers collected in 1957–
1965, but this is a lower bound on survival in the absence of whaling given the long history of whaling on this population
(Ohsumi, 1979).
Estimates of adult survival for other mysticetes vary considerably, but are generally higher than the 0.94 estimated for
pygmy blue whales. Survival rates for South African right whales are 0.990 (95% CI 0.983–0.997) (Best et al., 2005); for
Argentine right whales, 0.981 (95% CI 0.971–0.991); for Bering-Chukchi-Beaufort bowhead whales, 0.984 (95% credibility
interval 0.948–1.000) despite annual whaling mortality of 0.005 (Zeh et al., 2002); for western Pacific gray whales, 0.951
(95% CI 0.917–0.972) (Bradford et al., 2006), or 0.97 (95% CI 0.96–0.98) (Cooke et al., 2005); for Gulf of Maine humpback
whales (most recent estimate): 0.950 (95% CI 0.928–0.972) (Clapham et al., 2003); for Hawaiian humpback whales, 0.963
(95% CI 0.944–0.978) (Mizroch et al., 2004); for southeastern Alaskan humpback whales, 0.957 (95% CI 0.943-0.967)
(Mizroch et al., 2004); and for Prince William Sound humpback whales, 0.984 (95% CI 0.954–0.995) (Mizroch et al., 2004).
For north Atlantic right whales, adult survival was estimated to be 0.979 (95% CI 0.973–0.985) during 1980–1992
(Knowlton et al., 1994), but are now thought to have declined over time from 0.99 in 1980 to 0.94 in 1994, resulting in a
prediction of extinction in at most 191 yr (Caswell et al., 1999). When separated by stage, the survival of mothers declined
from 0.95 to 0.63 during 1980–1995, while non-mother adult females had constant survival of 0.99 during 1980–1995
(Fujiwara and Caswell, 2001). However, given that since these estimates were published, this population has increased from
under 300 (Fujiwara and Caswell, 2001) to 396 in 2006 (Anon, 2006), survival rates have probably increased again in recent
In summary, there are two blue whale survival estimates, neither from Antarctic blue whales. The Gulf of St Lawrence
estimates are closer to the estimates from other mysticetes, while the estimates from pygmy blue whales are lower than for all
other species. A weighting of 2:1 is applied to the Gulf of St Lawrence: pygmy blue whale mean estimates, to obtain an
overall mean of 0.963, while a broad standard deviation of 0.02 is assumed, i.e. S ~ N(0.963, 0.02
). Bounds of [0.927; 0.990]
reflect the lower limit for North Pacific blue whales, and the maximum survival rate of 0.990 for South African right whales.
First-year survival rate (S
Calf survival rates have never been estimated for blue whales, but Branch et al. (2004) and Brandão et al. (2000) assumed
that calf survival should be less than adult survival, since suckling calves would presumably die if their mothers died.
Although this assumption is retained here, North Atlantic right whale calf survival was consistently higher than the survival
of mothers during 1980–1995 (declining from 0.96 to 0.85 compared to declines from 0.94 to 0.63 for mothers) (Fujiwara
and Caswell, 2001).
Calf survival rate estimates in other mysticetes vary greatly: 0.99 (95% CI 0.97–1.00) for Argentine southern right whales
(Cooke et al., 2001); 0.85–0.96 for north Atlantic right whales (Fujiwara and Caswell, 2001); 0.875 (range 0.828–0.922) for
Gulf of Maine humpback whales (Barlow and Clapham, 1997); 0.818 (95% CI 0.482–0.977) for Pacific humpback whales
(Gabriele et al., 2001); 0.734 (95% CI 0.518–0.95) for South African southern right whales (Best et al., 2005); and either
0.701 (95% CI 0.492–0.850) (Bradford et al., 2006) or 0.73 (90% credibility interval 0.61–0.83) for western Pacific gray
whales (Cooke et al., 2005).
Estimates for this parameter are based entirely on other species. The mean of the population means is 0.84. The upper
bounds of those estimates range from 0.83 to 1.00, and these upper bounds are close to the adult survival estimate assumed
above for most populations, while lower bounds range from 0.492 to 0.97. Values for S
were therefore assumed to be
distributed ~ N(0.84, 0.15
) with bounds of [0.492, S]. The upper bound is based on adult survival, S, to ensure that juvenile
survival is always less than adult survival, as discussed above.
Annual pregnancy rate (p)
Ongoing photo-identification studies have not yet produced estimates of the inter-calf interval (the inverse of the pregnancy
rate) for blue whales. Many studies have recorded pregnancy rates, which vary between 0.11 and 0.84 (Laws, 1961; Mizroch,
1981), with a mean of 0.43 (SD = 0.17) (Branch et al., 2004), but these estimates are not as direct an estimate of pregnancy
rates as might be imagined, because it was illegal to catch females with calves and because of likely segregation by
reproductive class both by time and in space. Ovulation rates have been calculated by regressing ovarian corpora counts
against earplug laminae, producing inter-ovulation estimates of 2.5 yr (no CI calculated) for Antarctic blue whales caught in
1956/57–1958/59 (Ohsumi, 1979) and 2.6 yr (95% CI 2.2–3.0) for pygmy blue whales caught in the early 1960s (Branch,
2008b). Although the rate of accumulation of ovarian corpora places a theoretical upper bound on the pregnancy rate, both of
these estimates are based on very small sample sizes.
All studies on blue whales have concluded that the inter-calf interval is 2–3 yr (e.g. Mackintosh and Wheeler, 1929;
Laurie, 1937; e.g. Mackintosh, 1942; Tomilin, 1967). The upper bound of 3 yr essentially comes from the high observed
pregnancy rates in the catches. The lower bound of 2 yr follows directly from observations that pairing occurs in June–July
and calving in May–June the following year, and weaning only occurs 7 months after birth (Mackintosh and Wheeler, 1929;
Mackintosh, 1942). Assuming that females only rarely are simultaneously lactating and pregnant, it is improbable that female
Antarctic blue whales could give birth annually. In the IWC catch database, there are 25,515 pregnant females, 173 lactacting
females and only 2 records of females both lactating and pregnant. However, it should be noted that multiple instances of
annual calving has been reported both for Alaskan humpback whales (Straley et al., 1994) and for east Australian humpback
whales (Kaufman et al., 2006), including one east Australian female observed with a calf for five consecutive years.
It should be noted that multiple births are ignored here since it is unlikely that more than one fetus would survive to
maturity. Excluding multiplets would have negligible effect in any case: in the IWC database, there were 24,560 single
fetuses, 206 twins, 5 triplets and 1 quadruplet, for an average of 1.009 fetuses per pregnancy, similar to previous estimates of
1.007–1.008 (Risting, 1928; Tomilin, 1967).
Inter-calf intervals are available for other species of mysticetes, with the greatest information available for humpback
whales. For humpbacks off east Australia, the mean calving interval was 2.39 yr (95% CI 2.20–2.62) (Kaufman et al., 2006);
off California, 2.30 (95% CI 1.85–3.04) (Steiger and Calambokidis, 2000); in south-eastern Alaska, 2.78 (95% CI 2.31–3.52)
(Baker et al., 1992); in the Gulf of Maine, 2.56 yr (95% CI not given) (Clapham et al., 2003); and around Hawaii, 1.72 (95%
CI 1.33–2.44) (Baker et al., 1987). North Atlantic right whales have experienced fluctuations in the inter-calf interval from
3.67 yr (95% CI 3.46–3.89) during 1980–1992 (Knowlton et al., 1994), to over 5 yr in 1993–1998 (Kraus et al., 2001)
decreasing to 3.2 yr in 2006 (Anon, 2006). Southern right whales have inter-calf intervals of 3.15 yr (95% CI 3.11–3.18) off
South Africa (Best et al., 2005); 3.28 (95% CI 3.16–3.40) off southern Australia (Burnell, 2001); and 3.35 (95% CI 3.25–
3.45) at Peninsula Valdéz, Argentina (Cooke et al., 2001).
The above summary of available information sheds little light on what is a reasonable value to assume for Antarctic blue
whales average annual pregnancy rates. The most likely values of 0.39–0.43 yr
are problematic because of their underlying
assumptions or small sample sizes, while the “upper bound” on inter-calving intervals for pygmy blue whales imposed by the
inter-ovulation interval has wide 95% confidence intervals ranging from 2.2 to 3.0 yr. In light of these uncertainties, I
decided to assume a uniform interval between 2 and 3 yr for the inter-calving interval, corresponding to p ~ U(; ½).
Proportion of births that are female (q
A previous review of published estimates (Branch et al., 2004) found that 5,637 out of 11,942 fetuses examined were female
= 0.472) and that the catches listed in the same sources comprised 87,098 females out of 184,280 (q
= 0.473)
(Mackintosh, 1942; Nishiwaki and Oye, 1951; Tomilin, 1967). That review noted that sexed catches represent a near census
of the population since virtually all Antarctic blue whales were caught.
The IWC catch database was examined for sex ratios south of 56°S. More sexed whales were contained in the database
than presented in previous sources (229,023), of which 108,332 were female, thus q
= 0.473 is identical to the previous
estimate. The proportion of females among sexed fetuses (9,643 out of 19,915) is slightly higher than previously estimated: q
= 0.484.
Since nearly all of the catches listed in the database were sexed (98.8%), and the catches comprised a virtual census of the
population, the sex ratio in the catch (0.473) is assumed to be the best estimate of the proportion of whales that are female.
Given the high sample sizes, the binomial distribution is practically identical to a normal distribution, therefore the 95% CI is
0.471–0.475, and this factor is distributed q
~ N(0.473, 0.001
The distribution of values for δ, the instantaneous rate of increase, is N(0.040, 0.019
), with a maximum rate (the 99%
quantile) of 0.082. These correspond to annual rates of increase of 0.041 (SD = 0.019) and 0.085 respectively.
The estimated distribution for the instantaneous rate of increase (mean 0.040, sd = 0.019) is similar to that obtained for
Antarctic blue whales previously (mean 0.043, SD = 0.019) by Branch et al. (2004), but the maximum of 0.082 is
considerably lower than previously assumed (0.12). If the distribution was incorporated as a prior on the rate of increase (or
the maximum taken to be an upper bound), this would decrease the estimated rate of increase in Branch et al. (2004).
Based on surveys, the estimated current rate of increase for Antarctic blue whales is 8.2% per year (95% CI 1.6–14.8%)
from the IDCR/SOWER surveys (Branch, 2008a), and 7.4% per year (CV=1.19) from the JARPA surveys (Matsuoka et al.,
2006). These survey-based estimates are close to the maximum annual rate of 8.5% and a substantial proportion of the
confidence intervals of these estimates are above the maximum estimated here. It might be tempting to conclude from these
surveys that Antarctic blue whales are increasing at near maximal possible rates, but the confidence intervals around these
survey-based rates of increase are high, and include substantial probability of lower rates of increase.
The biologically plausible distributions developed in this paper rely heavily on biological parameters for pygmy blue
whales and other mysticete species, which may not be directly applicable to Antarctic blue whales. Given that Antarctic blue
whales were depleted to much lower levels than pygmy blue whales (Branch et al., 2007b), it is possible that they may have a
lower age at first parturition, higher survival, or shorter inter-calf interval, because of the relatively lower densities and higher
food availability. If so, the rates of increase estimated here would be biased low. In support of this idea, age at first parturition
appears to have declined for fin, sei and minke whales in response to depletion by whaling (Lockyer, 1972, 1974; Thomson
et al., 1999; Best and Lockyer, 2002), although these findings have been questioned by Mizroch (1981).
As pointed out by Branch et al. (2004), the estimates obtained here assume that the distributions for each of the input
parameters are independent, except for the constraint that calf survival must be smaller than adult survival. For purists this is
problematic, but the practicality of the matter is that no data exist to estimate a variance-covariance matrix between each of
the parameters for any whale population, let alone Antarctic blue whales. In any case, reducing the uncertainty in the
estimated values of the input parameters would most likely have a greater impact on the estimated rate of increase, than
attempting to estimate the variance-covariance matrix of the parameters. Therefore, we assume independence between these
parameters, as other authors have done in the past (Best et al., 2001; Clapham et al., 2001; Branch et al., 2004; Clapham et
al., 2006).
T.A.B. is grateful for funding for this project from the International Whaling Commission, and wishes to thank Y. Mikhalev
for providing the earplug data in Sazhinov (1980), L. Flynn for translating Sazhinov (1970), and I. Mikhalev for translating
email exchanges with Y. Mikhalev.
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... Continuous models of population dynamics are used to estimate the intrinsic growth rate and other demographic characteristics of blue whale populations. The basis of my investigation is an article by Branch (2008), who estimated with the Euler-Lotka equation the mean annual growth rate as 4.1%, using a simple survival function. He chose a stochastic model. ...
... For each of the input parameters, he assumed biologically plausible distributions: adult survival, calf survival, annual pregnancy rate, age at first parturition, and the proportion of births that are female. In my article, I adopt the variables and data from Branch (2008). However, I restrict myself to a deterministic representation. ...
... However, I restrict myself to a deterministic representation. The approach of Branch (2008) is extended by considering alternative life tables and by calculating additional parameters. The focus is on a simple life table model, which has also been used implicitly by Branch: the piecewise exponential distribution. ...
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Lecture Note on Demography: Continuous models of population dynamics are used to estimate the intrinsic growth rate and other demographic characteristics of blue whale populations.
... Since then, considerable progress has been made in reducing key uncertainties in the input data and in the model parameters. The catch series has been updated (Branch et al., 2008a), the circumpolar abundance estimates have been finalized (Branch, 2008a), new JARPA abundance estimates have been produced (Matsuoka et al., 2006), a minimum abundance estimate based on mitochondrial DNA has been obtained (Branch and Jackson, 2008) using the method of Jackson et al. (2008), and the range of biologically plausible rates of increase has been narrowed considerably (Branch, 2008b). Additionally, the possibility that some of the blue whales encountered in the Antarctic were pygmy blue whales (B. ...
... Given estimates for these parameters, a distribution was developed for plausible rates of increase using the method of Branch et al. (2004). The updated distribution for annual rates of increase is ~ N(0.041, 0.019 2 ), with an upper 99 th percentile (assumed to be the maximum possible) of 0.085 yr -1 (Branch, 2008b). In the base case models presented in this paper, the upper limit on the rate of increase is set to 0.085 yr -1 . ...
... The abundance was constrained so that it could not fall below 214 in any year, based on the genetic minimum abundance (Branch and Jackson, 2008). Additionally, the δ and r parameters for rate of increase were constricted to have a maximum value of 0.085, as discussed above (Branch, 2008b). The logistic parameterization results in problematic posterior convergence given the very low population size at the bottleneck. ...
Full-text available
The status of Antarctic blue whales is assessed using a Bayesian logistic population model fitted to three long-term datasets. Due to unsustainable levels of whaling from 1926 to 1971, except during World Was II, the population declined from 256,000 (95% credibility interval 235,000–307,000) to a low of 395 (235–804), which was 0.15% (0.10–0.28%) of pre-exploitation levels. The low point was reached in 1971 or 1972 after which the introduction of international observers halted catches of Antarctic blue whales by Soviet fleets. Since then, the population is estimated to have been increasing with probability 0.998, at an annual rate of 6.4% yr-1 (2.4–8.4%). However, despite this increase, the most recent abundance estimate of 2,280 in 1997 is only 0.9% (0.7–1.0%) of pre-exploitation levels.
... These could be individuals that are sexually or physically immature, or as also suggested for humpback whales 78 , mature females that are currently not breeding. Sexual maturity in blue whales is only reached at 10 years, and physical maturity afterwards [79][80][81] . Female blue whales are not thought to breed each season as they have a two to three year inter-calf interval, gestation lasting at least 10 months, weaning lasting seven months, and simultaneous pregnancy and lactation is rare 80,81 . ...
... Sexual maturity in blue whales is only reached at 10 years, and physical maturity afterwards [79][80][81] . Female blue whales are not thought to breed each season as they have a two to three year inter-calf interval, gestation lasting at least 10 months, weaning lasting seven months, and simultaneous pregnancy and lactation is rare 80,81 . However, the vocalizations that are geographically distinct in blue whales and appear as songs are likely only produced by males 17,18 , and the distinct Antarctic blue whale vocalization was used to report the year-round presence of blue whales in the Antarctic 63,64 . ...
Population-level conservation is required to prevent biodiversity loss within a species, but it first necessitates determining the number and distribution of populations. Many whale populations are still depleted due to 20th century whaling. Whales are one of the most logistically difficult and expensive animals to study because of their mobility, pelagic lifestyle and often remote habitat. We tackle the question of population structure in the Antarctic blue whale (Balaenoptera musculus intermedia) – a critically endangered subspecies and the largest extant animal – by capitalizing on the largest genetic dataset to date for Antarctic blue whales. We found evidence of three populations that are sympatric in the Antarctic feeding grounds and likely occupy separate breeding grounds. Our study adds to knowledge of population structure in the Antarctic blue whale. Future research should invest in locating the breeding grounds and migratory routes of Antarctic blue whales through satellite telemetry to confirm their population structure and allow population-level conservation.
... To have a chance to disprove our hypothesis, it would be interesting to follow up groups of whales acoustically separated from their original group. We consider that the actual context of recuperation of the populations of blue whales (Branch, 2008) is favourable to the apparition of vagrant whales or groups of whales re-colonizing old territories, making such observations possible. On the other hand, long term follow up of known acoustical groups are fundamental, while we expect that some change in the frequency decrease is bound to appear at a decadal timescale, since the frequency cannot decrease linearly for ever. ...
Full-text available
The linear decrease in the frequency of blue whale songs around the world is, to date, an unexplained phenomenon. We show it can be reproduced by a mathematical model considering two antagonistic behavioral trends: first, a bias towards conformity in the song, and second, a tendency to try and sing lower than the other whales. We check the robustness of our model by considering some more complex premises. First, different hierarchical relations between the singers are explored, adapting methods used in the flocking motion studies. Then a population-dependant simulation shows that even considering the gradual addition of new whales, the evolution is still globally linear. Finally, we show that intra-annual variations surging from different causes can be naturally incorporated into the model. We then conclude that, unlike other explanations, a cultural hypothesis seems compatible with the observed linearity of the blue whales's songs frequency shift.
... Multiparous pregnancies have been described in several species of Mysticetes including sei whale (Balaenoptera borealis) (Gambell, 1968;Kawamura, 1969); humpback whale (Megaptera novaeangliae) (conjoined twins; Zemsky & Budylenko, 1970;and non-conjoined twins;Kimura, 1957); common minke whale (Balaenoptera acutorostrata) (conjoined twins; Zinchenko & Ivashin, 1987; and non-conjoined twins Kato, 1982), Antarctic minke whale (Balaenoptera bonaerensis) (Kato, 1982), blue whale (Balaenoptera musculus) (Branch, 2008) and fin whale (Balaenoptera physalus) (Kimura, 1957;Laws, 1961). Furthermore Jonsgård (1953) reported a fin whale with six foetuses of varying sizes. ...
The present study is the first record of twinning in Lagenorhynchus acutus and indeed any Lagenorhynchus sp. Both foetuses were male and located in the left uterine horn, had distinct grossly normal placentas and amniotic sacs, and were therefore likely dizygotic twins. The twins were an incidental finding in an animal that died of a systemic Brucella ceti infection.
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Many baleen whales were commercially harvested during the 20th century almost to extinction. Reliable assessments of how this mass depletion impacted whale populations, and projections of their recovery, are crucial but there are uncertainties regarding the status of Southern Hemisphere whale populations. We developed a Southern Hemisphere spatial “Model of Intermediate Complexity for Ecosystem Assessments” (MICE) for phytoplankton, krill (Euphausia superba) and five baleen whale species, to estimate whale population trajectories from 1890 to present. To forward project to 2100, we couple the predator–prey model to a global climate model. We used the most up to date catch records, fitted to survey data and accounted for key uncertainties. We predict Antarctic blue (Balaenoptera musculus intermedia), fin (Balaenoptera physalus) and southern right (Eubalaena australis) whales will be at less than half their pre-exploitation numbers (K) even given 100 years of future protection from whaling, because of slow growth rates. Some species have benefited greatly from cessation of harvesting, particularly humpbacks (Megaptera novaeangliae), currently at 32% of K, with full recovery predicted by 2050. We highlight spatial differences in the recovery of whale species between oceanic areas, with current estimates of Atlantic/Indian area blue (1,890, <1% of K) and fin (16,950, <4% of K) whales suggesting slower recovery from harvesting, whilst Pacific southern right numbers are <7% of K (2,680). Antarctic minke (Balaenoptera bonaerensis) population trajectories track future expected increases in primary productivity. Population estimates and plausible future predicted trajectories for Southern Hemisphere baleen whales are key requirements for management and conservation.
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Between 1991 and 1997 right whales were studied on their wintering grounds on the southern coastline of Australia, predominantly at theHead of the Great Australian Bight, where over 350 individuals have been identified. The observed mean inter-calf interval for females was3.33±0.10 years (±SE, n = 57) at the Head of the Bight and 3.64±0.13 years (±SE, n = 117) in the wider Australian population. Wheninter-calf intervals of six or more years were excluded, the mean intervals became 3.28±0.09 years (±SE, n = 56) and 3.28±0.06 years (±SE,n = 107), respectively. Inter-calf intervals of two years were recorded following the early death of a neonate on two separate occasions andthe implications of these ‘shortened’ intervals and of calvings that were not observed are discussed. The mean age at which yearlings wereobserved to be fully weaned was calculated to be 365±8 days (±SE, n = 18) from the estimated birth dates of individual calves andsubsequent associations, or lack of them, between the yearlings and their cows the following year. A total of 108 movements greater than200km in length were made by individual whales. The mean within-year movement was 730±84 km, made over 34±4 days (±SE, n = 18),whilst the mean between-year movement was 1,036±45km (±SE, n = 87), made over a mean interval of 3.3±0.3 years (±SE, n = 90). Thenumber and direction of coastal movements observed suggest that the right whales off southern Australia comprise a single populationwhich may undertake an almost circular, anti-clockwise migration to the south of the Australian continent. A significantly greaterproportion of females displayed a level of between-year fidelity to the Head of the Bight aggregation area (92%, n = 61) than did males(68%, n = 19) or whales of unknown sex (63%, n = 8).
Cetaceans are compared on a global basis with N-of-the-equator representatives measured in relation to their southern hemispheric counterparts. Terms of reference for comparison include: age determination, maximum body length, natural mortality coefficient, and maximum life span. Specific comments are made for Balaenoptera acutotostrata.-from Current Antarctic Literature
The conclusion of researchers in the 1950s that humpback whales reached sexual maturity at about age five was largely influenced by their interpretation of baleen tracings, and to achieve consistency with these tracings the accumulation rate of ear plug laminations (growth layer groups: GLGs) was assumed to be two per year. However, ovulation and natural mortality rates calculated by these researchers under the same assumption produced estimates that are difficult to reconcile with other biological data or with more recent estimates using individual re-sighting data. Such disparities are reduced or disappear when an annual accumulation rate is used, in which case their ear plug data would have indicated a mean age at sexual maturity of 9-11 years. Recent estimates of the age of female humpback whales at first calving using longitudinal studies of photoidentified individuals have produced conflicting results, some (from southeastern Alaska) being compatible with the earlier age-determination studies, others (from the Gulf of Maine) suggesting a much younger age.