After summarizing the size for the largest baleen whales precisely one year ago, I return to provide an in-depth review for the sperm whale (Physeter macrocephalus). This will serve as a little teaser for the manuscript I’ve recently submitted, a literature review concerned with the maximum attainable size of the sperm whale.
The sperm whale is one of my favorite whale species alongside the bowhead (Balaena mysticetus) and the blue whale (Balaenoptera musculus). The high-quality oil within their spermaceti organ and the ambergris in their intestines made sperm whales a major target of every major nation in the commercial whaling industry. The two waves of commercial whaling in the 19th and 20th century are thought to have caused a 57% decline from a history population of nearly 2 million whales (Whitehead & Shin, 2022). The global population is now thought to be around 840,000. While abundant, this species may still face pressures from anthropogenic influences and are still feeling the effects of their populations having been disrupted.
P. macrocephalus is the only extant member of both the Physeter genus and Physeteridae family. Its closest extant relatives are the much smaller pygmy (Kogia breviceps) and dwarf (Kogia sima) sperm whales within the Kogiidae family. Physeteroids were once a diverse clade, predominantly composed of macrophagous predators such as the Scaldicetus, Acrophyseter, Zygophyseter, Brgymophyseter, and the ever-popular Livyatan. However, even these fierce creatures are much smaller than the extant sperm whale, which remains the largest known species of odontocete to have ever lived.
Life History and Growth
The primary method of estimating age in tooth whales is counting the dentine layers in their teeth (Sergeant, 1962). These dentine layers were thought to form bi-annually (Berzin, 1964, 1972; Nishiwaki et al., 1958), however an annual formation rate akin to earplug laminae in baleen whales has been verified (Lockyer, 1981). Many growth curves have been published for sperm whales across the North Pacific (Berzin, 1972; Nishiwaki et al., 1958; Ohsumi, 1977), North Atlantic (Martin, 1980), and the Southern Hemisphere (Bannister, 1969; Best, 1970; Evans & Hindell, 2004; Gambell, 1972; Gaskin & Cawthorn, 1973). Growth curves are compared in Figure 1, showing relatively little regional difference in adult size.
Getting on to their size, sperm whales are typically born at about 4 m (Gambell, 1972; Matthews, 1938; Nishiwaki et al., 1958; Ohsumi, 1965). Weaning occurs by the second year at an average length of 6.7 m (Clarke, 1956). Female sperm whales sexually mature at 8-9 m in length after 7-10 years and physically mature at around 10.5-11 m after 20-30 years (Berzin, 1964; Best, 1970; Clarke et al., 2011; Evans & Hindell, 2004; Lockyer, 1981). Males continue to grow considerably larger. Sexual maturity in males has been interpreted to occur between 9-12.5 m after 9-20 years (Aguayo, 1963; Berzin, 1964; Clarke, 1956; Matthews, 1938; Nishiwaki, 1955; Nishiwaki et al., 1958). Further investigations revealed males reach full sexual maturity after 25 years and 13.7 m, with growth ceasing after 50 years at an average length of 15.2-16 m (Bannister, 1969; Berzin, 1964; Clarke et al., 1994; Gambell, 1972; Nishiwaki et al., 1958; Ohsumi, 1977). Sperm whales exhibit the most pronounced sexual dimorphism of any cetacean species.
Figure 1
Many of those familiar with fisheries studies and marine ecology are used to seeing growth curves fitted by logistic functions, such as the one shown below (von Bertalanffy, 1934, 1938).
L(t)=L∞–(L∞–l0 ) e-kt
The parameters included are age (t), the growth coefficient (k), length at birth (l0), and the mean asymptotic length when a population is allowed to grow indefinitely (L∞). The above form is how the von Bertalanffy growth model was originally presented, while the reparameterization below is the most widely-used version (Beverton, 1954) .
L(t)=L∞(1-e-k(t-t0))
Here, l0 is replaced with t0, which represents the age at which the length is zero. This constant is not an actual biological character, but an extrapolation of the post-natal growth trend. It should not be interpreted as the length of gestation.
There’s also another parameter, Lmax, which is the maximum size observed within a population. Fish studies canonically interpreted that the Lmax closely approaches L∞ (Beverton, 1963; Parker & Stott, 1965; Pauly, 2002; Taylor, 1958). In reality, Lmax may deviate significantly from L∞, as mortality rates and the degree of individual variation can lead to Lmax being much lower or higher than L∞ (Hordyk et al., 2015; Ricker, 1979; Schwamborn, 2018). Since the latter outcome universally applies to whales, I strictly distinguish these two parameters in contrast to some literature on cetacean growth that use the Lmax notation as a synonym for L∞ (Garde et al., 2007, 2015; George et al., 1999; Lubetkin et al., 2012; Olsen & Sunde, 2002; Rosa et al., 2004).
Many of the earliest growth curves for sperm whales were fitted by hand (Berzin, 1964; Best, 1970; Gaskin & Cawthorn, 1973; Nishiwaki et al., 1958) as the non-uniform growth trends of large whales were poorly modeled by a single mathematical function (Chittlebrough, 1965). While the growth of females could be fitted by a single von Bertalanffy curve like smaller odontocetes (Bannister, 1969; Evans & Hindell, 2004), existing functions for males only provide good fits for post-pubertal growth (Bannister, 1969; Martin, 1980).
Recent studies for the growth of baleen whales obtained strong fits from two-phase models that transition at the age of weaning (Agbayani et al., 2020; Fortune et al., 2012, 2021; Lubetkin et al., 2012). I chose to apply a similar approach for male sperm whales using the raw data published for 3,045 individuals from the North Pacific (Kato, 1995; Ohsumi, 1977), 289 from the North Atlantic (Borrell et al., 2013; IJsseldijk et al., 2018; Martin, 1980; Mendes et al., 2007; Pagh et al., 2016), 240 from the Southeast Pacific (Clarke & Paliza, 1994)1, and 8 from the South Atlantic (Degrati et al., 2011; Ramos et al., 2001).
1(7/22/2023 Update: I’ve recently found that the raw age data that was analyzed in Clarke et al., 1994 was available in the appendix of the previous part of their studies of Southeast Pacific sperm whales. I have since updated figures 3&4 and the accompanying parameters to reflect this change)
Each observation was rounded to the nearest year and whole foot. Due to issues noted with sampling, labeling mistakes, and age estimation errors, I smoothed both the length and age distributions in accordance to a procedure outlined for a refined length key (Ohsumi, 1977). The length distributions obeyed a normal distribution while age distributions at a given length were notably right-skewed (Figure 2). Even after smoothing, the natural variation in size at a given age is very wide (Figure 3).
Figure 2
When fitted using the Solver add-in in Excel, a single von Bertalanffy function yielded the parameters below (r2= 0.720). The curve is plotted against the data in Figure 4. While the estimate for the L∞ is reasonable, t0 is unrealistic. This echoes the aforementioned issues in modeling the growth of large whales.
L(t)=15.02 (1-e-0.094(t-0))
Figure 3
Plotting the average length for each age (Figure 4) allows one to observe an inflection at around 16-17 years and 11.5 m in length. This represents the secondary growth spurt in male sperm whales (Best, 1970; Nishiwaki et al., 1963; Ohsumi, 1977). The same occurrence has been observed in the male growth curves of other polygynous odontocetes with pronounced sexual dimorphism such as pilot whales (Betty et al., 2022; Kasuya et al., 1988; Kasuya & Matsui, 1984; Sergeant, 1962), northern bottlenose whales (Benjaminsen & Christensen, 1979) and killer whales (Christensen, 1984). I used this point to mark the transition for a two-phase model listed below (r2=0.998). Phase 1 was fitted to the average size at birth (4.05 m) and weaning (6.7 m, age 2) reported in literature. The two-phase model was overall a considerably better fit over the single-phase model and provides a more reasonable estimate of 4.35 m for the size at birth.
Phase 1 (Ages 0-16): L(t)=11.99(1-e-0.1385(t+3.25))
Phase 2 (Ages 17 and older): L(t)=15.81 (1-e-0.0741(t-0.0162))
Figure 4
Figure 5 below shows the major growth stages for sperm whales outlined from using my two-phase model for males and an average curve for two von Bertalanffy functions for females (Bannister, 1969; Evans & Hindell, 2004). The stages of reproductive development in males adhere to the following definitions (Best, 1974).
- Puberty-The stage at which 50% of whales are immature at the center of the testes, which corresponds to around 8.7-10.3 m at 9-10 years old (Bannister, 1969; Best, 1969; Clarke et al., 1994). Puberty appears to be what was referred to as sexual maturity by some early authors (Berzin, 1972; Clarke, 1956; Nishiwaki et al., 1958).
- Sexual maturity– The stage at which 50% of whales are immature and 50% are maturing or mature at the periphery of the testes. This occurs at an average length of 11-12.9 m at 19 years old (Best, 1969, 1970; Clarke et al., 1994; Lockyer, 1981). This stage coincides with a growth spurt in the testes (Clarke et al., 1994; Gambell, 1972) and body size (Best, 1970, 1979; Best et al., 1984). By extension of the latter, this stage may occur at around 16 years for North Pacific males taken in the 1950-1970s (Ohsumi, 1977) .
- Social maturity– The stage at which equal proportions of males are immature and mature at the periphery of the tests. Corresponds to a length of 13.7-14.4 m at 25 years old (Best, 1970; Clarke et al., 1994; Gambell, 1972). This parameter coincides with the deceleration of growth, sudden increase in testes size, full attainment of breeding status, and transition towards solitary living (Best, 1970, 1979; Clarke et al., 1994; Clarke & Paliza, 1988; Gambell, 1972; Gaskin, 1970; Kato, 1984).
Figure 5
Taxonomic history and anatomical differences between regions: multiple subspecies?
Linnaeus originally described 4 species of sperm whales : P. catadon, P. macrocephalus, P. microps, and P. tursio (Linneaus, 1758). As these names were synonymized, the latter two were phased out early and P. macrocpehalus ultimately won out over P. catadon due to first reviser priority (Husson & Holthuis, 1974). Apparent differences in size and external proportions have tempted Soviet authors to suggest that northern and southern sperm whales form distinct subspecies like in baleen whales (Berzin, 1972; Heptner et al., 1988; Tomilin, 1967). While analyses of external proportions show some clustering between individual regions (Machin, 1974), there was no clear division of northern and southern hemisphere whales. The growth curves (Figure 1) also suggest that apparent differences in average length of total catches are skewed by age segregation.
Genetic analyses have shown that there’s little genetic diversity across the global population of sperm whales (Lyrholm et al., 1999). While maternal genetic lineages within the mitochondria shows significant differentiation between populations, the biparentally-inherited nuclear DNA showed far less differentiation(Engelhaupt et al., 2009; Mesnick et al., 2011). This provides evidence for significant interoceanic male-mediated gene flow. The main exception to this trend is for Mediterranean sperm whales, appear to be very distinct from the Eastern North Atlantic population (Drouot, Berube, et al., 2004; Engelhaupt et al., 2009; Violi, 2020). IPI data revealed nearly no males exceeding 14 m (Caruso et al., 2015; Drouot, Gannier, et al., 2004; Pavan et al., 1997). In addition, two males measuring 12.2 and 12.8 m were found to be 40-44 years old (Frantzis et al., 2002; Maio et al., 2022). These whales would have likely physically matured around 12.5-13 m, approaching the minimum value of of 13.3 m reported in literature (Clarke et al., 1994). This evidence suggests that sperm whales from the Mediterranean are generally much smaller due to either genetics or possibly lower prey abundance in their low-latitude environment.
While there’s evidence suggesting that nutrition can lead to significant differences in growth between sperm whale populations (Best et al., 2016; Clarke et al., 1994; Kahn et al., 1993; Kasuya, 1991), the average difference in male growth is < 1 m. In Figure 6, I present the length frequencies of stranding records for male sperm whales from the Mediterranean (Cagnolaro et al., 1986; Centro Studi Cetacei, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994b, 1994a, 1995, 1996, 1998; Frantzis et al., 2002; Maio et al., 2022; Mazzariol et al., 2011). 35% of these males were reported reaching 15-19 m, which is congruent to the typical size range of mature bulls in other regions. All of these are from Italian strandings from between 1986-1995. While I am certainly convinced that sperm whales in the Mediterranean likely grow smaller on average, I doubt that slower growth is solely responsible for the apparent absence of males over 15 m in recent studies. I believe this discrepancy is a matter of some as-of-yet uncovered age segregation for Mediterranean males.
Figure 6
Maximum size
Like the blue whale, the precise maximum size (Lmax) of the sperm whale has been a matter of contention. Historical records reported individuals measuring up to 23.1-27.4 m (Beale, 1839; Bennett, 1840; Starbuck, 1878). However these measurements were likely curvilinear lengths, leading experts to place the maximum length closer to around 18.3 m (Flower, 1868; Rice, 1989). It’s certainly correct that 18.3 m is exceptional for male sperm whales, although this may be a bit conservative for the precise maximum size. Interestingly, there are multiple records of bulls measuring between 18-18.6 m that were shown to be physically immature (Andrews, 1916; Boschma, 1938; Clarke, 1956; Kasuya, 1991), indicating they were still capable of further growth.
Reported measurements within the whaling data became more reliable after regulations and operational standards improved during the 1930s and 1940s (Branch et al., 2007; Donovan, 2000). Within this data, Guinness records recognizes a 20.7 m bull reported from the Kuril Island land stations in 1950 (Wood, 1972, 1976, 1982). While intentional data falsification plagued Soviet whaling data (Ivashchenko et al., 2011), this occurred more so during the 1960s. Data from the Kuril land stations from between 1948-1964 showed no signs of falsification (Ivashchenko et al., 2014). Prior to Guinness records, this whale was also cited as a record-holder by a very prominent Soviet cetologist (Zenkovich, 1954), who was unlikely to have been provided falsified data. Furthermore, the measurements within non-falsified Soviet data was among the most reliable of major whaling nations, as the Soviet industry was very keen on providing data to be utilized for biologists (Ivashchenko, personal comm., 2023). With all this in mind, the length of this individual was likely neither falsified nor an inaccurate measurement.
There are very few records of larger males that are considered reliable. A review of marine megafauna reports a bull captured in 1933 that measured 24 m (McClain et al., 2015). I will say that I have been recently analyzing the IWC catch data and saw that this whale was reported by Chilean fleets. As far as I’m aware, there were no regulations for Chilean whaling that would ensure accurate measurements prior to the formation of the Comisión Permanente del Pacífico Sur in 1952. In my upcoming article, I investigate whether such a size is even attainable.
The maximum size for females is a more complicated issue. Some literature have cited whaling records of females measuring of 15.9-17.4 m (Haldane, 1906; Nishiwaki, 1972; Tomilin, 1967) and a recent review has found that females reported from the Southern Ocean land stations had size-distributions that were nearly identical to males (McClain et al., 2015). However, records of such large females are often owed to typographic errors (Thompson, 1928) and whalers misidentifying the sex of males with retracted penises (Berzin, 1964; Matthews, 1938). The latter issue is prevalent even within modern whaling data, thus making it more difficult to precisely determine the limit in maximum size for female sperm whales.
The matter of sex misidentification becomes evident whenever comparisons are made to data collected by biologists. A 12.3 m female examined in the Azores was, at the time, the largest verified record known to most experts (Clarke, 1956). Since then, only a few other females measuring between 12.5-12.72 m have ever been reported (Andrews, n.d.; Guiler, 1978; Haase & Félix, 1994; Robson & Bree, 1970). I’ve performed some filtering within the IWC catch database that provided me a more reliable dataset of accurately identified females. This maximum I’ve arrived upon ended up being very interesting, which I will delve more into in my upcoming article.
Now in my previous posts, I tend to provide some emphasis on weight-length relationships, but that will also have to wait until my article is published. I worked very hard on it and had to delay it several times to follow up on some interesting leads, but I’m glad to say that it’s finally out of the way and I hope the peer-review process goes well.
For anyone interested in the dataset I’ve developed for my growth curve, contact me on cetologyh@gmail.com
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