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Postcopulatory sexual selection influences baculum evolution in primates and carnivores

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The extreme morphological variability of the baculum across mammals is thought to be the result of sexual selection ( particularly, high levels of post- copulatory selection). However, the evolutionary trajectory of the mammalian baculum is little studied and evidence for the adaptive function of the baculum has so far been elusive. Here, we use Markov chain Monte Carlo methods implemented in a Bayesian phylogenetic framework to reconstruct baculum evolution across the mammalian class and investigate the rate of baculum length evolution within the primate order. We then test the effects of testes mass (postcopulatory sexual selection), polygamy, seasonal breeding and intromission duration on the baculum in primates and carnivores. The ances- tral mammal did not have a baculum, but both ancestral primates and carnivores did. No relationship was found between testes mass and baculum length in either primates or carnivores. Intromission duration correlated with baculum presence over the course of primate evolution, and prolonged intro- mission predicts significantly longer bacula in extant primates and carnivores. Both polygamous and seasonal breeding systems predict significantly longer bacula in primates. These results suggest the baculum plays an important role in facilitating reproductive strategies in populations with high levels of postcopulatory sexual selection.
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Cite this article: Brindle M, Opie C. 2016
Postcopulatory sexual selection influences
baculum evolution in primates and carnivores.
Proc. R. Soc. B 283: 20161736.
http://dx.doi.org/10.1098/rspb.2016.1736
Received: 5 August 2016
Accepted: 4 November 2016
Subject Areas:
evolution
Keywords:
baculum, postcopulatory sexual selection,
prolonged intromission, primates, carnivores,
Bayesian phylogenetics
Authors for correspondence:
Matilda Brindle
e-mail: matilda-jane.brindle.14@ucl.ac.uk
Christopher Opie
e-mail: kit.opie@ucl.ac.uk
Electronic supplementary material is available
online at http://dx.doi.org/10.6084/m9.fig-
share.c.3583481.
Postcopulatory sexual selection influences
baculum evolution in primates and
carnivores
Matilda Brindle and Christopher Opie
Department of Anthropology, University College London, 14 Taviton Street, London, WC1H 0BW, UK
CO, 0000-0002-3379-4703
The extreme morphological variability of the baculum across mammals
is thought to be the result of sexual selection (particularly, high levels of post-
copulatory selection). However, the evolutionary trajectory of the mammalian
baculum is little studied and evidence for the adaptive function of the baculum
has so far been elusive. Here, we use Markov chain Monte Carlo methods
implemented in a Bayesian phylogenetic framework to reconstruct baculum
evolution across the mammalian class and investigate the rate of baculum
length evolution within the primate order. We then test the effects of testes
mass (postcopulatory sexual selection), polygamy, seasonal breeding and
intromission duration on the baculum in primates and carnivores. The ances-
tral mammal did not have a baculum, but both ancestral primates and
carnivores did. No relationship was found between testes mass and baculum
length in either primates or carnivores. Intromission duration correlated with
baculum presence over the course of primate evolution, and prolonged intro-
mission predicts significantly longer bacula in extant primates and carnivores.
Both polygamous and seasonal breeding systems predict significantly longer
bacula in primates. These results suggest the baculum plays an important
role in facilitating reproductive strategies in populations with high levels of
postcopulatory sexual selection.
1. Introduction
The morphology of male intromittent organs is argued to be subject to more
rapid divergent evolution than any other form in the animal kingdom [1].
The baculum, or penis bone, does not buck this trend and has been described
as ‘the most diverse of all bones’ ([2], p. 1), varying dramatically in length,
width and shape across the Mammalia.
The baculum is not uniformly present across mammals. It was thought only to
exist in eight of the mammalian orders: Afrosoricida, Carnivora, Chiroptera,
Dermoptera, Erinaceomorpha, Primates, Rodentia and Soricomorpha [3,4]. How-
ever, it has recently beendiscoveredthat a Lagomorph, the American pika (Ochonta
princeps), also has a small baculum [5]. This discovery suggeststhat baculum pres-
ence may be more prevalent across mammals than historically assumed. Certain
orders have a mixture of baculum presence and absence across species; these are
the Carnivora, Chiroptera, Primates and Rodentia. In Primates, for example,
humans, tarsiers and several Platyrrhines lack a baculum. The Lagomorphia
may be similarly divided. Aside from documenting the presence and absence of
the baculum across the mammalian orders,the evolutionary history of thebaculum
had not been studied until recently, leaving many questions unanswered.
Genital (and hence bacular) morphology is suggested to be subject to sexual
selection [6]. The few empirical tests conducted to date may support this hypoth-
esis. Stockley et al. [7] found that baculum width in polygamous house mice (Mus
domesticus) was a significant predictor of male reproductive success. Simmons &
Firman [8] were able to manipulate baculum width experimentally by altering
&2016 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution
License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original
author and source are credited.
the level of sexual selection pressure in populations of house
mice. After 27 generations, populations with artificially
enforced high levels of postcopulatory sexual selection
pressure had significantly thicker bacula than populations in
which monogamy was enforced and sexual selection pressure
was therefore absent. These studies indicate that intra-sexual
selection, in particular postcopulatory sexual selection
pressure, may be driving bacular evolution. If this is the case,
the bacula of populations under high levels of intra-sexual
selection pressure, such as those with polygamous (multi-
male, multi-female) or seasonal mating systems, should be sub-
ject to stronger evolutionary forces.
Different mating systems generate variation in levels of
postcopulatorysexual selection pressure and therefore morpho-
logical variability; for example, species with high levels of
sperm competition tend to have large testes relative to their
body mass [9]. Residual testes mass is thus considered to be a
reliable measure of the mating system of a population and
therefore the degree of sexual selection pressure [9]. Orr &
Brennan [10] found that relative testes mass was a significant
predictor of baculum presence across Chiroptera, Eulipotyphla,
Primates and Rodentia. However, the same study found no
relationship between baculum presence or width and mating
system, indicating that a third variable may be at play. Ramm
[11] tested for a relationship between testes mass and baculum
length in four orders by first establishing the level of phylo-
genetic dependency between species and then conducting
appropriately corrected regressions. A positive relationship
between testes mass and baculum length was noted in Rodentia
and Carnivora, but the same test found no relationship in
Primates or Chiroptera.
The adaptive function of the baculum, under high levels
of intra-sexual selection, is yet to be established. A potential
strategy by which a male could increase their reproductive
success, by outcompeting rival males, is through prolonging
intromission and consequently delaying a female mating
with another male [12]. The prolonged intromission hypoth-
esis argues that the baculum helps to facilitate this prolonged
duration of intromission by supporting the penis [13].
In this context, the proximate mechanism of the baculum
is to act as a supportive rod, strengthening the penis and
protecting the urethra during prolonged intromission [12].
A recent study on three different species of bat found that
the baculum formed a functional unit with the corpora caver-
nosa, which protected the glans tip and the shaft of the
penis when erect [14]. The authors posit that the baculum
also helps to limit constriction of the distal urethra and ure-
thral opening in the erect penis during intromission,
facilitating sperm flow. In many species of primate in
which the baculum is elongated, the distal end of the bone
projects slightly from the urethra while the penis is erect
[15]. This could bring the baculum into contact with a
female’s cervix during intromission, facilitating the transfer
of semen into the cervical canal [12,15].
Evidence for the prolonged intromission hypothesis has
so far proven controversial. Early studies found that pro-
longed intromission was correlated with elongated bacula
in primates and carnivores [13,16]; however, these studies
did not take into account the statistical non-independence
of data that arises due to a shared evolutionary history
between species. A later study, corrected to account for
phylogeny, tested for a correlation between prolonged intro-
mission and baculum length in North American carnivores,
but did not find support for the hypothesis [17]. However,
data to test this hypothesis were only available for 18 species,
of which only two were characterized as having short intro-
mission duration. Dixson et al. [18] argue that this sample is
not representative enough to decisively refute the prolon-
ged intromission hypothesis, and carried out their own
phylogenetically corrected analysis in a sample of 57 species
of mammal. This time, a significant correlation was found
between the two variables. Although both studies were cor-
rected for phylogeny, if the degree of phylogenetic
dependency is not established before an analysis is adjusted,
correcting for phylogeny can produce misleading or incorrect
results, as the level of relatedness between species varies
across a phylogeny [19]. Bayesian Markov chain Monte Carlo
(MCMC) analyses enable species’ phylogenies to be incorpor-
ated into an analysis, rather than simply correcting for
phylogeny, and can thus produce more reliable results [20,21].
In a new study, Schultz et al. [22] used the earlier phylogenetic
methods of stochastic mapping to model the presence and
absence of the baculum in 954 mammalian species, and argue
that the baculum independently evolved a minimum of nine
times in mammals. However, this sample is unlikely to reflect
the course of evolution across the entire mammalian class,
particularly as baculum absence was only noted in 103 species.
Here, we use phylogenetic comparative methods within a
Bayesian MCMC framework [23] to examine the evolutionary
history of the baculum and investigate the hypothesis
that increased levels of intra-sexual selection affect baculum
evolution. We first reconstructed the evolutionary trajectory
of the baculum across the entire mammalian class and exam-
ined the rate of bacular evolution in the primate order. Then,
we tested for a relationship between baculum length and
testes mass in both primates and carnivores. We then further
tested for correlated evolution between baculum presence
and intromission duration in primates, before conducting
phylogenetic t-tests to establish whether primates and carni-
vores with prolonged intromission durations have longer
bacula than those with short intromission durations. Finally,
we used the same tests to examine whether increased levels of
postcopulatory sexual selection pressure caused by (i) poly-
gamous mating systems and (ii) seasonal breeding patterns
led to an increase in baculum length in primates. Primates and
carnivores are likely to be particularly rewarding groups to
study, because there is a mixture of baculum presence and
absence within each order. This means that differences
between those with and without bacula can be tracked at
the species level, rather than across orders. Furthermore, as
these orders are arguably more extensively studied than
other mammalian groups, there are more data available.
If the baculum facilitates prolonged intromission and
increased proximity to the cervix in order to reduce the level of
sperm competition and increase reproductive success, then sev-
eral predictions can be made and tested. It would be expected
that there would be a relationship between baculum length
and testes mass, which can be used as a proxy for the level of
postcopulatory sexual selection pressure in a population. Intro-
mission duration would be expected to correlate with baculum
presence across the course of evolution. Species with prolonged
intromission durations should have elongated bacula. Finally,
groups in which postcopulatory sexual selection pressure is
highest, such as those in which mating is polygamous or
occurs seasonally, should have longer bacula than groups
with lower levels of postcopulatory sexual selection pressure.
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
2
2. Material and methods
Ancestral state reconstructions, tests of correlated evolution, tests
of trait relationships and phylogenetic t-tests were all conducted
using BAYESTRAITS (v. 2) [24]. Trait data were compiled from the
literature (electronic supplementary material).
A supertree phylogeny of 5020 extant mammals was used to
reconstruct the ancestral states of baculum presence across the
mammalian order [25]. All analyses of the primate and carnivore
orders were conducted on a posterior distribution of 10 000 mol-
ecular phylogenies inferred using Bayesian MCMC methods [26].
Chronograms were used in all ancestral state reconstructions and
tests of correlated evolution, whereas phylograms were used in
tests of trait relationships and phylogenetic t-tests.
A reversible-jump MCMC method with an exponential hyper-
prior ranging between 0 and 0.07 was used to estimate discrete
ancestral states [27]. Each chain was run for 5 million iterations with
a burn-in of 50 000 iterations; this was the case for all analyses aside
from the variable-rates model. We were interested in inferring seven
key nodes across the mammalian phylogeny, as well as the ances-
tral state of baculum presence for both the primate and carnivore
orders (electronic supplementary material, figure S1). Nodes were
constructed using the ‘add MRCA’ procedure in BAYESTRAITS [24].
A variable-rates model was used to reconstruct the course of
baculum length evolution across the primate order (following
Venditti et al. [28]). The model allows the rate of evolution to
change across a phylogeny over time, identifying when and
where evolutionary rates have differed without prior knowledge.
Stretched branches of the phylogenetic tree indicate that a trait
has evolved quickly and compressed branches indicate slow
rates of trait change. The model was run for 10 million iterations,
with a burn-in of 100 000 iterations.
Baculum length and testes mass were tested for a relationship
using a multiple regression between baculum length, testes mass
and adult male body mass. The model was run three times and
the chain with the median log marginal likelihood was chosen;
this approach was also taken when conducting correlated evolution
and hypothesis tests.The proportion of the slope parameter (
b
)that
crossed zero was used to establish the p-values (following Organ
et al.’s [29] method for phylogenetic t-tests).
To test for correlated evolution between baculum presence and
intromission duration, we compared the log marginal likelihood of
independent (traits constrained to evolve separately) and depen-
dent models. An exponential hyperprior with a range of 0–0.05
was used. The two models were compared using log natural
Bayes factors (BFs), calculated as two times the difference in log
marginal likelihood between the models [24]. BFs were interpreted
following Kass et al. [30]: 0–2, minimal support; 2–6, positive sup-
port; 6– 10, strong support; more than 10, very strong support.
Recent literature has highlighted several issues with using the
harmonic mean as a measure for estimating the log marginal like-
lihood of a model and the relative merits of the stepping-stone
sampling method, which is argued to be more accurate [31,32].
We therefore used the stepping-stone sampling method to esti-
mate the log marginal likelihood. One hundred stones were used
per 10 000 iterations of the Markov chain. Following Xie et al.
[32], a beta (
a
, 1.0) distribution was employed and
a
was set at
0.3. Stepping-stones were used in this way for all tests of trait
relationships, correlated evolution and phylogenetic t-tests.
MCMC phylogenetic t-tests were used to test hypotheses
accounting for the statistical non-independence of the data, due
to shared evolutionary history (following Organ et al. [29]).
3. Results
AmultistateanalysisinBAYESTRAITS [24] (n¼1818) indicates
that the ancestral mammal did not possess a baculum (baculum
absence, mean probability ¼0.98). Ancestral state reconstruc-
tions across six nodes (table 1; electronic supplementary
material, figure S1) suggest that the baculum first evolved
after non-placental and placental mammals split (baculum
absence, mean probability ¼0.93), but before the most recent
common ancestor (MRCA) of primates and carnivores evolved
(baculum presence, mean probability ¼0.99). The ancestral pri-
mate and carnivore both had a baculum (baculum presence,
mean probability ¼1.00 and 1.00, respectively).
The evolutionary trajectory of baculum length was visual-
ized using the variable-rates model, which stretches or
shrinks the branches of a phylogenetic tree according to
differing rates of trait evolution (figure 1; electronic sup-
plementary material, figures S2– S4). Primates show marked
variation in baculum length and this is reflected in their
evolutionary history. Very little change has occurred in
platyrrhines and tarsiers, which tend to have small or
absent bacula, indicating that the baculum of the ancestral
primate was fairly small. By contrast, strepsirrhines and
catarrhines have undergone relatively fast evolutionary
change, and generally have longer bacula than the platyr-
rhines and tarsiers. The apes represent an interesting group
as they have undergone high rates of change, yet have very
small or absent bacula. This suggests that after the
platyrrhine and catarrhine lineages split, the baculum of the
ancestral catarrhine underwent a high rate of evolution and
became a lot longer. When apes subsequently split from
Old World monkeys this trend reversed and the ape
baculum underwent further high rates of evolution, this
time reducing in length. (See electronic supplementary
material for variable-rates trees depicting carnivore baculum
length evolution and primate and carnivore testes mass
evolution, figures S2– S4.)
Baculum length could not be predicted from testes mass
in either primates (n¼46, p¼0.139, R
2
¼0.03) or carnivores
(n¼32, p¼0.231, R
2
¼0.37) (electronic supplementary
material, table S2).
Table 1. Probability of baculum presence or absence at the root and six
nodes of the mammalian phylogeny (see electronic supplementary material,
figure S1, for nodes). Probabilities of baculum presence or absence of
ancestral primates and carnivores are also given.
baculum absent baculum present
mean
probability s.e.
mean
probability s.e.
root 0.98 0.0011 0.02 0.0011
node 1 0.93 0.0020 0.07 0.0020
node 2 0.51 0.0016 0.49 0.0016
node 3 1.00 0.0000 0.00 0.0000
node 4 0.01 0.0000 0.99 0.0000
node 5 0.3 0.0010 0.7 0.0010
node 6 0.01 0.0000 0.99 0.0000
primates 0.00 0.0000 1.00 0.0000
carnivores 0.00 0.0000 1.00 0.0000
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
3
We found positive evidence for correlated evolution
between baculum presence and intromission duration in
primates (n¼299, log BF ¼4.78; table 2). Ancestral state recon-
structions and model rates indicate that baculum presence and
short intromission durations (mean probability ¼0.73) pre-
ceded a shift to prolonged intromission (figure 2). After long
intromission durations had evolved, the baculum was rarely
lost. However, the baculum was often lost if intromission dur-
ation remained short. Long intromission durations rarely
became short again when a baculum was present. By contrast,
when a baculum was absent, intromission duration switched
frequently between being long and short.
The hypothesis that postcopulatory sexual selection influences
baculum length was tested through a series of phylogenetic
t-tests (table 3). In line with our predictions, we find that species
in both the primate and carnivore orders in which intromission
is prolonged have significantly longer bacula than species in
which intromission is short (n¼53, p¼0.000 and n¼41, p¼
0.018, respectively). Primates in polygamous mating systems
werefoundtohavesignificantlylongerbaculathanthosein
Tarsius_lariang
Galagoides_demidoff
Tarsius_bancanus
Cheirogaleus_medius
Varecia_variegata_variegata
Trachypithecus_francoisi
Hapalemur_griseus
Microcebus_murinus
Pan_troglodytes_troglodytes
Lemur_catta
Ateles_paniscus
Piliocolobus_badius
Erythrocebus_patas
Colobus_guereza
Tarsius_syrichta
Alouatta_pigra
Alouatta_seniculus
Macaca_sinica
Daubentonia_madagascariensis
Otolemur_crassicaudatus
Mandrillus_sphinx
Colobus_polykomos
Homo_sapiens
Nasalis_larvatus
Papio_papio
Cercocebus_torquatus
Chiropotes_satanas
Alouatta_palliata
Alouatta_sara
Rhinopithecus_roxellana
Theropithecus_gelada
Saguinus_bicolor
Pan_paniscus
Miopithecus_talapoin
Loris_tardigradus
Perodicticus_potto
Saimiri_boliviensis
Papio_cynocephalus
Saguinus_fuscicollis
Cercopithecus_mona
Presbytis_comata
Callithrix_jacchus
Chlorocebus_aethiops
Callithrix_pygmaea
Saguinus_mystax
Ateles_fusciceps
Lagothrix_lagotricha
Alouatta_belzebul
Cercopithecus_solatus
Macaca_nemestrina
Cebus_apella
Macaca_fuscata
Papio_hamadryas
Pygathrix_nemaeus
Cacajao_calvus
Cercopithecus_mitis
Lophocebus_albigena
Cebus_capucinus
Eulemur_fulvus_fulvus
Callimico_goeldii
Macaca_thibetana
Papio_ursinus
Macaca_arctoides
Saguinus_oedipus
Propithecus_verreauxi
Aotus_lemurinus
Macaca_fascicularis
Alouatta_caraya
Tarsius_dentatus
Alouatta_guariba
Gorilla_gorilla_gorilla
Macaca_assamensis
Pongo_pygmaeus
Macaca_nigra
Ateles_geoffroyi
Leontopithecus_rosalia
Cacajao_melanocephalus
Galago_senegalensis
Ateles_belzebuth
Macaca_mulatta
Cercopithecus_neglectus
Saguinus_midas
Callithrix_humeralifera
Callithrix_argentata
Papio_anubis
Mandrillus_leucophaeus
Procolobus_verus
Hylobates_lar
Figure 1. A primate phylogeny scaled to reflect the rate of bacular evolution. Darker red branches indicate lower rates of evolution; blue branches indicate
particularly high rates of evolution.
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
4
other mating systems (n¼65, p¼0.032). Finally, seasonally
breeding primates have significantly longer bacula than primates
that do not breed seasonally (n¼63, p¼0.045).
4. Discussion
Our results have uncovered the evolutionary trajectory of the
baculum across the mammalian class, showing that the bacu-
lum first evolved after placental and non-placental mammals
split around 145 million years ago (Ma), but before the
MRCA of primates and carnivores evolved around 95 Ma
[25]. We show for the first time that both the ancestral
primate and the ancestral carnivore had a baculum, a result
bearing important implications for how the baculum should
be studied within these orders. Analyses should focus on
examining why the baculum was retained in certain species
and lost in others, not why the baculum might have evolved;
it was already present in their ancestors.
We found no relationship between baculum length and
testes mass in primates or carnivores, supporting previous find-
ings in primates, but not carnivores [11]. This discrepancy
is probably explained by the use of a Bayesian phylogenetic
framework for our analyses; our finding suggests that any
observed relationship between baculum length and testes
mass could have evolved by chance. Although these results
do not provide support for the hypothesis that baculum
length is sexually selected, they do not refute it. It is possible
q12
z: 0.00%
baculum,
long intromission
no baculum,
short intromission
baculum,
short intromission
no baculum,
long intromission
q31
z: 62.24%
q21
z: 80.72%
q43
z: 0.46%
q13
z: 0.02%
q24
z: 98.18%
q34
z: 0.16%
q42
z: 0.02%
root
Figure 2. Coevolution between primate baculum presence and intromission duration. zpercentages show the posterior probability that a transition rate from one
state to another is zero (i.e. how often a given transition does not occur). Thick black arrows indicate that a transition happened frequently; thinner or absent arrows
indicate that a transition was rare or practically non-existent. (Online version in colour.)
Table 2. Likelihood of dependent and independent models of correlated evolution between baculum presence and intromission duration in primates. The Bayes
factor indicates positive support for the dependent model of evolution over the independent model. Bayes factors were interpreted following Kass et al. [30]:
O2, minimal support; 2– 6, positive support; 6 10, strong support; more than 10, very strong support.
coevolution analysis
dependent model independent model
log likelihood log likelihood log natural Bayes factor
intromission duration 245.77 248.16 4.78
Table 3. Phylogenetic t-tests of baculum length and intromission duration in primates and carnivores, and mating system and breeding seasonality in primates.
model
primates carnivores
b
s.e.
b
p-value
b
s.e. bp-value
baculum length and intromission duration 16.64 +0.05 p¼0.0000 64.90 +0.41 p¼0.018
baculum length and mating system 23.45 +0.03 p¼0.0318
baculum length and breeding seasonality 23.55 +0.03 p¼0.0448
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
5
that aspects of baculum morphology, such as width or shape,
are more likely to vary with testes mass. For instance, baculum
shaft width is a significant predictor of the number of offspring
sired by male house mice [7]. Indeed, Orr & Brennan found
that testes mass predicted baculum width in four orders of
mammal; however, when this relationship was tested using a
phylogenetic model, baculum width was no longer a significant
predictor [10]. It is possible that these results would have
remained significant if the relationship had been examined at
the order level, as bacular function may vary from order to
order. Our results serve to highlight the importance of using
full phylogenetic methods when examining trait evolution.
This study has been the first to demonstrate that baculum
presence has correlated with intromission duration over the
course of primate evolution. The result highlights the inter-
play between morphological and behavioural phenotypes
over evolutionary time. The baculum physically supports
and protects the male’s penis [12,14], and assists the transfer
of semen towards a female’s cervix [12,15]. However, it also
plays an important role in facilitating prolonged intromission,
which itself may be a sexually selected behaviour, aimed at
increasing reproductive success by delaying females from
re-mating [12].
Our results confirm that the prolonged intromission
hypothesis remains robust when analysed within a rigorous
phylogenetic framework. Phylogenetic t-tests show that the
baculum is significantly longer in both primate and carnivore
species in which intromission is prolonged. This suggests that
the elongation of the baculum over the course of mammalian
evolution was probably driven by its utility in prolonged intro-
mission. Two more phylogenetic t-tests showed that primates in
polygamous mating systems and seasonally breeding primates
had significantly longer bacula than primates in other mating
systems and those without a seasonal breeding pattern, high-
lighting the importance of postcopulatory sexual selection as
a driver of bacular evolution.
The finding from the test of correlated evolution, coupled
with the results of the phylogenetic t-tests, allows us to begin
piecing together the proximate and ultimate functions of the
baculum. Polygamous mating systems and limited breeding
seasons create high levels ofpostcopulatory sexual competition.
In this environment, prolonging intromission could delay a
female from re-mating, thus increasing a male’s chance of suc-
cessfully fertilizing her under competitive conditions. Ensuring
that the urethra is unrestricted and there is as little distance as
possible for sperm to travel is a way of increasing the amount
of sperm transported to the cervical canal. The baculum
serves as a supportive structure duringprolonged intromission,
both protecting the urethra and preventing it from being
constricted [14].
These results do not necessarily apply to other orders within
the mammalian class, but they do highlight potentially reward-
ing lines of enquiry. It is also important to note that, even within
the primate and carnivore orders, other factors are likely to
influence whether a baculum is retained or not and how its
morphology evolves. Studies of bacular evolution tend to
focus on why it is present in certain species, or why it might
have increased in length or width; factors driving the reduction
or disappearance of bacula have largely been ignored.
Ingenious studiesare beginning to pick apart the proximate
mechanism of the baculum, as well as some of the factors
driving its evolution in different mammalian orders [8,14].
By comparing these findings across orders and examining
the baculum through a phylogenetic framework, we can
begin to build a more comprehensive picture of the proximate
and ultimate functions of the baculum, and how it evolved in
extant species and their ancestors.
Data accessibility. Data are available from Dryad Digital Repository [33].
Authors’ contributions. M.B. and C.O. designed research; M.B. and C.O.
performed research; M.B. and C.O. analysed data; M.B. and C.O.
drafted the manuscript. All authors gave final approval for
publication.
Competing interests. We have no competing interests.
Funding. M.B. is supported by a NERC Doctoral Training Studentship,
and C.O. is supported by a Leverhulme Early Career Fellowship.
References
1. Eberhard W. 1993 Evaluating models of sexual
selection: genitalia as a test case. Am. Nat.142,
564–571. (doi:10.1086/285556)
2. Patterson BD, Thaeler CS. 1982 The mammalian
baculum: hypotheses on the nature of bacular
variability. J. Mammal.63, 1– 15. (doi:10.1890/
0012-9623(2004)85[22b:ASOMTA]2.0.CO;2)
3. Perrin WF, Wursig B, Thewissen JGM (eds). 2009
Encyclopaedia of marine mammals, 2nd edn.
London, UK: Academic Press.
4. Martin RD. 2007 The evolution of human
reproduction: a primatological perspective.
Yearb. Phys. Anthropol.50, 59– 84. (doi:10.1002/
ajpa.20734)
5. Weimann B, Edwards MA, Jass CN. 2014
Identification of the baculum in American
pika (Ochotona princeps: Lagomorpha) from
southwestern Alberta, Canada. J. Mammal.95,
284–289. (doi:10.1644/13-MAMM-A-165)
6. Hosken DJ, Jones KE, Chipperfield K, Dixson AF.
2001 Is the bat os penis sexually selected? Behav.
Ecol. Sociobiol.50, 450–460. (doi:10.1007/
s002650100389)
7. Stockley P, Ramm SA, Sherborne AL, Thom MDF,
Paterson S, Hurst JL. 2013 Baculum morphology
predicts reproductive success of male house mice
under sexual selection. BMC Biol.11, 66. (doi:10.
1186/1741-7007-11-66)
8. Simmons LW, Firman RC. 2013 Experimental
evidence for the evolution of the mammalian
baculum by sexual selection. Evolution 68,
276–283. (doi:10.1111/evo.12229)
9. Harcourt AH, Harvey PH, Larson SG, Short RV. 1981
Testis weight, body weight and breeding system in
primates. Nature 293, 55– 57. (doi:10.1038/
293055a0)
10. Orr TJ, Brennan PL. 2016 All features great and
small—the potential roles of the baculum and
penile spines in mammals. Integr. Comp. Biol.56,
635–643. (doi:10.1093/icb/icw057)
11. Ramm SA. 2007 Sexual selection and genital evolution
in mammals: a phylogenetic analysis of baculum
length. Am.Nat.169, 360 –369. (doi:10.1086/510688)
12. Dixson AF. 2012 Primate sexuality: comparative
studes of the prosimians, monkeys, apes, and human
beings, 2nd edn. Oxford, UK: Oxford University
Press.
13. Dixson AF. 1987 Baculum length and copulatory
behavior in primates. Am. J. Primatol.60, 51– 60.
(doi:10.1002/ajp.1350130107)
14. Herdina AN, Kelly DA, Jahelkova
´H, Lina PHC,
Hora
´c
ˇek I, Metscher BD. 2015 Testing hypotheses
of bat baculum function with 3D models derived
from microCT. J. Anat.226, 229– 235. (doi:10.1111/
joa.12274)
15. Dixson AF. 1987 Observations on the evolution of
the genitalia and copulatory behaviour in male
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
6
primates. J. Zool.213, 423– 443. (doi:10.1111/j.
1469-7998.1987.tb03718.x)
16. Dixson AF. 1995 Baculum length and copulatory
behaviour in carnivores and pinnipeds (Grand Order
Ferae). J. Zool.235, 67– 76. (doi:10.1111/j.1469-
7998.1995.tb05128.x)
17. Larivie
`re S, Ferguson SH. 2002 On the evolution of the
mammalian baculum: vaginal friction, prolonged
intromission or induced ovulation? Mamm. Rev.32,
283– 294. (doi:10.1046/j.1365-2907.2002.00112.x)
18. Dixson A, Nyholt J, Anderson M. 2004 A positive
relationship between baculum length and
prolonged intromission patterns in mammals.
Acta Zool. Sin.50, 490–503.
19. Freckleton RP, Harvey PH, Pagel M. 2002
Phylogenetic analysis and comparative data: a test
and review of evidence. Am. Nat.160, 712– 726.
(doi:10.1086/343873)
20. Opie C, Atkinson QD, Dunbar RIM, Shultz S. 2013 Male
infanticide leads to social monogamy in primates. Proc.
Natl Acad. Sci. USA 110, 13328–13332. (doi:10.
1073/pnas.1307903110)
21. Shultz S, Opie C, Atkinson QD. 2011 Stepwise
evolution of stable sociality in primates. Nature
479, 219–222. (doi:10.1038/nature10601)
22. Schultz NG, Lough-Stevens M, Abreu E, Orr T, Dean
MD. 2016 The baculum was gained and lost multiple
times during mammalian evolution. Integr. Comp.
Biol.56, 635– 643. (doi:10.1093/icb/icw034)
23. Huelsenbeck JP, Ronquist F, Nielsen R, Bollback JP.
2001 Bayesian inference of phylogeny and its
impact on evolutionary biology. Science 294,
2310–2314. (doi:10.1126/science.1065889)
24. Pagel M, Meade A, Barker D. 2004 Bayesian
estimation of ancestral character states on
phylogenies. Syst. Biol.53, 673– 684. (doi:10.1080/
10635150490522232)
25. Fritz SA, Bininda-Emonds ORP, Purvis A. 2009
Geographical variation in predictors of mammalian
extinction risk: big is bad, but only in the tropics.
Ecol. Lett.12, 538–549. (doi:10.1111/j.1461-0248.
2009.01307.x)
26. Arnold C, Matthews LJ, Nunn CL. 2010 The 10KTrees
website: a new online resource for primate
phylogeny. Evol. Anthropol.19, 114– 118. (doi:10.
1002/evan.20251)
27. Pagel M, Meade A. 2006 Bayesian analysis of
correlated evolution of discrete characters by
reversible-jump Markov chain Monte Carlo. Am. Nat.
167, 808–825. (doi:10.1086/503444)
28. Venditti C, Meade A, Pagel M. 2011 Multiple routes
to mammalian diversity. Nature 479, 393– 396.
(doi:10.1038/nature10516)
29. Organ CL, Shedlock AM, Meade A, Pagel M,
Edwards SV. 2007 Origin of avian genome size
and structure in non-avian dinosaurs. Nature 446,
180–184. (doi:10.1038/nature05621)
30. Kass RE, Raftery AE. 1995 Bayes factors. J. Am. Stat.
Assoc.90, 773–795. (doi:10.1080/01621459.1995.
10476572)
31. Baele G, Lemey P, Bedford T, Rambaut A,
Suchard MA, Alekseyenko AV. 2012 Improving
the accuracy of demographic and molecular
clock model comparison while accommodating
phylogenetic uncertainty. Mol. Biol.
Evol.29, 2157– 2167. (doi:10.1093/molbev/
mss084)
32. Xie W, Lewis PO, Fan Y, Kuo L, Chen M-H. 2011
Improving marginal likelihood estimation for
Bayesian phylogenetic model selection. Syst. Biol.
33, 104–110.
33. Brindle M, Opie C. 2016 Data from: Postcopulatory
sexual selection influences baculum evolution in
primates and carnivores. Dryad Digital Repository.
(doi:10.5061/dryad.412gv)
rspb.royalsocietypublishing.org Proc. R. Soc. B 283: 20161736
7

Supplementary resource (1)

... Different mating systems vary in the level of postcopulatory selection and associated behavioural and morphological phenotypes they generate [24]. For example, multi-male mating systems produce high levels of postcopulatory male-male competition, and are associated with large testes to body mass ratio [5,25] and elongated bacula [24]. ...
... Different mating systems vary in the level of postcopulatory selection and associated behavioural and morphological phenotypes they generate [24]. For example, multi-male mating systems produce high levels of postcopulatory male-male competition, and are associated with large testes to body mass ratio [5,25] and elongated bacula [24]. We therefore employ mating system and testes mass (controlled for body size) as proxies for postcopulatory selection, using the compilation of data in Brindle & Opie [24]. ...
... For example, multi-male mating systems produce high levels of postcopulatory male-male competition, and are associated with large testes to body mass ratio [5,25] and elongated bacula [24]. We therefore employ mating system and testes mass (controlled for body size) as proxies for postcopulatory selection, using the compilation of data in Brindle & Opie [24]. ...
Article
Full-text available
Masturbation occurs throughout the animal kingdom. At first glance, however, the fitness benefits of this self-directed behaviour are unclear. Regardless, several drivers have been proposed. Non-functional hypotheses posit that masturbation is either a pathology, or a byproduct of high underlying sexual arousal, whereas functional hypotheses argue an adaptive benefit. The Postcopulatory Selection Hypothesis states that masturbation aids the chances of fertilization, while the Pathogen Avoidance Hypothesis states that masturbation helps reduce host infection by flushing pathogens from the genital tract. Here, we present comprehensive new data documenting masturbation across the primate order and use these, in conjunction with phylogenetic comparative methods, to reconstruct the evolutionary pathways and correlates of masturbation. We find that masturbation is an ancient trait within the primate order, becoming a more common aspect of the haplorrhine behavioural repertoire after the split from tarsiers. Our analyses provide support for both the Postcopulatory Selection and Pathogen Avoidance Hypotheses in male primates, suggesting that masturbation may be an adaptive trait, functioning at a macroevolutionary scale.
... Three key theories have been suggested, including: (i) the 'vaginal friction hypothesis' (Long & Frank, 1968), where the additional rigidity of the bacula facilitates intromission, specifically in taxa presenting high levels of sexual size dimorphism (SSD) or where the act of mounting occurs before erection (Lariviere & Ferguson, 2002); (ii) the 'prolonged intromission hypothesis' (Ewer, 1973), in which the bacula enables successful sperm deposition by preventing the urethra from becoming occluded during long periods of intromission and (iii) the 'induced ovulation hypothesis' (Greenwald, 1956), whereby the additional stiffness and/or tip shape provided by the baculum stimulates the reproductive tract of the female, triggering ovulation and increasing the likelihood of fertilisation. Support for all three hypotheses has been only sporadically found across mammals (André et al., 2021;Brindle & Opie, 2016;Dixson et al., 2004). Partly this is due to the challenges and invasiveness associated with testing these hypotheses in vivo. ...
... Previous studies have used large intraspecific datasets to examine baculum characteristics, including bone weight and length (Özen, 2018), and allometry ( Both alpha shapes PC1 and ariaDNE PC1 were significantly correlated to two proxies of post-copulatory sexual selection. These results suggest that high shape complexity, as determined by both alpha shapes and ariaDNE, may be driven by increased intromission duration across the group, supporting previous comparative studies in mammals (Brassey et al., 2020;Brindle & Opie, 2016;Dixson et al., 2004). In addition to intromission duration, there has been broad support for the prediction that relative testes mass indicates intensity of sperm competition (Birkhead & Møller, 1996;, with a recent quantitative meta-analysis justifying the use of these assumptions in research (Lüpold et al., 2020). ...
... In experimental studies, baculum form has been shown to vary with post-copulatory pressures. Artificially altered levels of sexual selection led to a significant increase in bacula width (Simmons & Firman, 2013) and baculum size was significantly associated with reproductive success (Stockley et al., 2013), suggesting that intra-sexual post-copulatory sexual selection pressure may be driving bacula evolution (Brindle & Opie, 2016). ...
Article
Full-text available
The penis bone, or baculum, is present in many orders of mammals, although its function is still relatively unknown, mainly due to the challenges with studying the baculum in vivo. Suggested functions include increasing vaginal friction, prolonging intromission, and inducing ovulation. Since it is difficult to study baculum function directly, functional morphology can give important insights. Shape complexity techniques, in particular, are likely to offer a useful metric of baculum morphology, especially since finding homologous landmarks on such a structure is challenging. This study focuses on measuring baculum shape complexity in the Musteloidea ‐ a large superfamily spanning a range of body sizes with well‐developed, qualitatively diverse bacula. We compared two shape complexity metrics – Alpha shapes and AriaDNE and conducted analyses over a range of six different coefficients, or bandwidths, in 32 species of Musteloidea. Overall, we found that shape complexity, especially at the baculum distal tip, is associated with intromission duration using both metrics. These complexities can include hooks, bifurcations and other additional projections. In addition, alpha shapes complexity was also associated with relative testes mass. These results suggest that post copulatory mechanisms of sexual selection are probably driving the evolution of more complex shaped bacula tips in Musteloidea and are likely to be especially involved in increasing intromission duration during copulation. This article is protected by copyright. All rights reserved.
... Gómez et al. (2016) suggested that sociality was an important mediator of conspecific aggression in mammals, so we also reconstructed an additional three components of sociality: the extent of female cooperation, the presence of bisexual groups containing multiple males, and the mating system. Furthermore, mating systems and strategies are strongly linked to the degree of competition between males (Emlen and Oring 1977;Brindle and Opie 2016), with greater variation in male reproductive success leading to higher rates of aggression, sexual dimorphism, and adaptations in response to post-copulatory competition (Clutton-Brock 2016). We therefore reconstructed infanticide along with four traits associated with the intensity of intrasexual male competition: sexual dimorphism in body size and canine size (pre-copulatory competition), the presence or absence of the penis bone (baculum), and testes size (post-copulatory competition). ...
... Infanticide was reconstructed as it represents a lethal act of conspecific violence (n=183), and high rates are reported for all African apes except bonobos (Opie et al. 2013). Also reconstructed were cooperation among females (n=41), since this can mitigate male dominance over females (e.g., in bonobos); the presence of multi-male groups (n=206), which are a prerequisite for the formation of all-male alliances; and the degree of competition between males, which can influence rates of aggression and violence (Emlen and Oring 1977;Brindle and Opie 2016). A further four traits indicative of the intensity of male-male competition were reconstructed: sexual dimorphism in body size (n=213) and canine size (n=119), mating systems (n=221), baculum presence (n=300), and testes size (n=101, details of trait states, SI table S1). ...
Preprint
Full-text available
The origins of human intergroup conflict are poorly understood despite the volume of attention the topic has received. Recent research suggests that, among mammals, violence is especially commonplace in primates, particularly social and territorial species. Here we use Bayesian phylogenetic methods to reconstruct the evolution of lethal violence across the ape lineage to understand better the roots of human lethal violence. Of the five key traits underpinning lethal violence, our reconstructions suggest that male coalitions, male dominance over females, and male-biased territorial defence were all present in the Pan-Homo last common ancestor. However, there was no support for the presence of exclusively hostile interactions with other groups or male natal residence, contrasting with extant chimpanzees. Our results suggest humans evolved from an ancestor whose lethally violent tendencies may have been tempered, compared with extant chimpanzees, by low male relatedness and coalitions between unrelated females.
... The presence of multiple functions may partly reflect the baculum's multiple evolutionary origins (Schultz et al. 2016). Analysis of bacular size and form in isolation from functional considerations therefore has limitations, but the presence of informative systematic patterns through simple analyses of size and scaling indicates that such analyses nevertheless contribute meaningfully to our understanding of bacular evolution (Arnqvist 1997;Brindle and Opie 2016;Orr and Brennan 2016). ...
Article
Full-text available
Growth, allometry, and characteristics of a sexually selected structure in wolverine (Gulo gulo (Linnaeus, 1758)), northern river otter (Lontra canadensis (Linnaeus, 1758)), and sea otter (Enhydra lutris (Linnaeus, 1758))
... Implications for reproductive biology. Several studies have explored the relationship between baculum length and the reproductive biology of the living carnivorans [e.g., [8][9][10][37][38][39][40]. These relationships can thus be used to draw inferences about the reproductive biology of the Borophaginaes. ...
Article
Full-text available
The baculum of mammals offers the opportunity to study the reproductive biology of extinct species given that it is a fossilizable part of the male genitalia and that its size and shape correlate with several aspects of the reproductive biology of extant mammals. Fossil bacula, however, are rare. Currently, bacula have been described from only two extinct species of canids, one from the subfamily Caninae and the other from the extinct subfamily Hesperocyoninae. Here, I describe the bacula of five extinct species of Borophaginae, each of which was found with other skeletal elements that have enabled identification to the species level. Two specimens (Aelurodon ferox and Aelurodon stirtoni) are largely complete, while the baculum from Carpocyon compressus is complete but still embedded in matrix that obscures some of its features. The bacula of Paratomarctus euthos and Desmocyon thomsoni are incomplete, but they provide useful information nonetheless. These borophagine bacula are similar to extant canines in being robust, having a urethral groove, and a simple distal end. These features suggest that the Borophaginae had long-lasting copulation and possibly spontaneous ovulation, similar to the extant canines. However, unlike the straight baculum of extant canines, borophagine bacula are ventrally curved (arched), which is also observed in the hesperocyonine baculum. The implication of this curvature for the reproductive biology of these animals remains unknown.
Article
While the mammalian baculum shows enormous morphological variability, the baculum of canids is highly conserved, with most variation restricted to size. Here, we explore the allometric relationship between baculum length and body size in extant and extinct canids. Examination of 26 species in the extant subfamily Caninae using standard linear regression revealed isometry. Phylogenetic regression also revealed an allometric slope indistinguishable from isometry. This pattern differs from the substantially negative slopes seen in other mammalian clades. The strength of the canid allometric relationship (r2) is also greater than in other clades, suggesting functional constraints on their baculum size. The constraints may be related to the copulatory tie that is characteristic of canids, and/or their monogamous mating system. Complete bacula are known from just four extinct species. The two complete bacula from the extinct subfamily Borophaginae (Aelurodon ferox and Aelurodon stirtoni) fall on the same allometric relationship as the living canids. However, the baculum of the extinct dire wolf (Aenocyon dirus, from the extant subfamily Caninae) and from the extinct subfamily Herperocyoninae, Hesperocyon gregarius, are significantly longer than expected based on their body sizes, suggesting that they may have had a different reproductive biology from that of extant canines.
Article
Full-text available
Allometric analyses of sexually selected structures have revealed many patterns of evolutionary and behavioural significance, for example, in weapons, ornaments, and genitalia. We investigated allometry of the baculum (penis bone) relative to body size in post-growth adults of three large mustelids: wolverine (Gulo gulo (Linnaeus, 1758)), northern river otter (Lontra canadensis (Linnaeus, 1758)), and sea otter (Enhydra lutris (Linnaeus, 1758)). The baculum grew over a longer period than did body size. Correlations among bacular variables were positive in post-growth adults. No regression slopes expressed positive allometry (i.e., slope > 1 for linear variables). These trends point to the possibility that bacular size is adapted to the average size of the reproductive tract of sexually mature female northern river otters and possibly sea otters, and that pre-ejaculatory (“pre-copulatory”) selection is highest in those species. Bacular size varied more than skull or limb-bone size, and bacular shape also varied greatly. Species differed in size and complexity of the urethral groove and bacular apex, suggesting functional differences in intromission. Substantial variation in bacular shape resulted from healed fractures, especially in sea otter. Knowledge of copulatory behaviour, age of breeding, female reproductive anatomy, and genitalic interactions during intromission is needed for comprehensive understanding of bacular anatomy, allometry, and variation for these species.
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Full-text available
Brindle & Opie. Postcopulatory sexual selection influences baculum evolution in primates and carnivores. Supplementary information on data, methods and analyses
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Data from the literature on the baculum and our own studies are used to evaluate two conflicting hypotheses for bacular variation. The first hypothesis states that bacular differences arise incidentally as pleiotropic by-products of phyletic divergence. The second hypothesis attributes precise reproductive function to the baculum (and phallus), which in turn allows the baculum to function as a reproductive isolating mechanism. Several patterns of bacular variation are used to test these hypotheses: bacular length versus body size (both among and within taxa), baculum length versus vaginal length, and bacular variability versus baubellar (os clitoris) variability. The results of these analyses lead us to propose that, by determining gross phallic morphology, different bacular morphologies probably elicit different behavioral and neuroendocrine responses from the female during copulation. Changes in bacular morphology that produce differential responsiveness on the part of the female may thus provide a basis for species-specific reproduction. Additional analyses of phyletic and geographical patterns of bacular variation corroborate this proposal, and the systematic and reproductive implications of these results are briefly considered.
Article
Full-text available
The baculum (os penis) has been extensively studied as a taxon-specific character in bats and other mammals but its mechanical function is still unclear. There is a wide consensus in the literature that the baculum is probably a sexually selected character. Using a novel approach combining postmortem manipulation and three-dimensional (3D) imaging, we tested two functional hypotheses in the common noctule bat Nyctalus noctula, the common pipistrelle Pipistrellus pipistrellus, and Nathusius' pipistrelle Pipistrellus nathusii: (i) whether the baculum can protect the distal urethra and urethral opening from compression during erection and copulation; and (ii) whether the baculum and corpora cavernosa form a functional unit to support both the penile shaft and the more distal glans tip. In freshly dead or frozen and thawed bats, we compared flaccid penises with artificially 'erect' penises that were inflated with 10% formalin. Penises were stained with alcoholic iodine and imaged with a lab-based high-resolution x-ray microtomography system. Analysis of the 3D images enabled us to compare the changes in relative positions of the baculum, corpora cavernosa, urethra, and corpus spongiosum with one another between flaccid and 'erect' penises. Our results support both functional hypotheses, indicating that the baculum probably performs two different roles during erection. Our approach should prove valuable for comparing and testing the functions of different baculum morphologies in bats and other mammals. Moreover, we have validated an essential component of the groundwork necessary to extend this approach with finite element analysis for quantitative 3D biomechanical modeling of penis function. © 2015 Anatomical Society.
Article
Mammalian penises are morphologically diverse, including a highly variable and taxonomically informative baculum (os penis), and variable penile spines, both of which are possessed by many—but not all—species. To understand the evolution of genital morphologies, as well as the potential role of both the baculum, and penile spines that directly interact with female reproductive tract, we undertook a comparative study of male penile spines and their relationship with the baculum across all mammalian orders. Specifically, we investigated several factors that may explain the presence or absence of penile spines in mammals, including mating system, risk of sperm competition, female reproductive physiology, presence and width of the baculum, and phylogenetic history. We observed that the presence of both the baculum and penile spines is correlated with residual testes size, suggesting a potential role in sexual selection for these traits. We found no association between the presence of spines and mating system, or with the presence/width of the baculum, although relative testes mass was marginally associated with baculum width. We found no relationship between baculum presence or width and mating system. We also noted that spines presence or absence have an order-level distribution, and clear phylogenetic patterns of distribution across mammals. It is likely that spine morphology and distribution, not just presence, play an important role in genital evolution in mammals, but these features are poorly described in most groups. Quantitative data collection in most mammalian taxa would be useful to further elucidate the evolution of the complex genital morphology of this group.
Article
The rapid evolution of male genitalia is a nearly ubiquitous pattern across sexually reproducing organisms, likely driven by the evolutionary pressures of male–male competition, male–female interactions, and perhaps pleiotropic effects of selection. The penis of many mammalian species contains a baculum, a bone that displays astonishing morphological diversity. The evolution of baculum size and shape does not consistently correlate with any aspects of mating system, hindering our understanding of the evolutionary processes affecting it. One potential explanation for the lack of consistent comparative results is that the baculum is not actually a homologous structure. If the baculum of different groups evolved independently, then the assumption of homology inherent in comparative studies is violated. Here, we specifically test this hypothesis by modeling the presence/absence of bacula of 954 mammalian species across a well-established phylogeny and show that the baculum evolved a minimum of nine times, and was lost a minimum of ten times. Three different forms of bootstrapping show our results are robust to species sampling. Furthermore, groups with a baculum show evidence of higher rates of diversification. Our study offers an explanation for the inconsistent results in the literature, and provides insight into the evolution of this remarkable structure.
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In a 1935 paper and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P-values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this article we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology, and psychology. We emphasize the following points:
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This thorough revision of the classic first edition brings this authoritative book right up-to-date. Articles describe every species in detail, based on the very latest taxonomy, and a host of biological, ecological and sociological aspects relating to marine mammals. The latest information on the biology, ecology, anatomy, behavior and interactions with man is provided by a cast of expert authors - all presented in such detail and clarity to support both marine mammal specialists and the serious naturalist. Fully referenced throughout and with a fresh selection of the best color photographs available, the long-awaited 2nd edition remains at the forefront as the go-to reference on marine mammals. * More than 20% NEW MATERIAL includes articles on Climate Change, Pacific White-sided Dolphins, Sociobiology, Habitat Use, Feeding Morphology and more * Over 260 articles on the individual species with topics ranging from anatomy and behavior, to conservation, exploitation and the impact of global climate change on marine mammals * New color illustrations show every species and document topical articles FROM THE FIRST EDITION "This book is so good... a bargain, full of riches...packed with fascinating up to date information. I recommend it unreservedly it to individuals, students, and researchers, as well as libraries". - Richard M. Laws, MARINE MAMMALS SCIENCE "...establishes a solid and satisfying foundation for current study and future exploration" - Ronald J. Shusterman, SCIENCE.