Accessory male investment can undermine the evolutionary stability of simultaneous hermaphroditism.
ABSTRACT Sex allocation (SA) models are traditionally based on the implicit assumption that hermaphroditism must meet criteria that make it stable against transition to dioecy. This, however, puts serious constraints on the adaptive values that SA can attain. A transition to gonochorism may, however, be impossible in many systems and therefore realized SA in hermaphrodites may not be limited by conditions that guarantee stability against dioecy. We here relax these conditions and explore how sexual selection on male accessory investments (e.g. a penis) that offer a paternity benefit affects the evolutionary stable strategy SA in outcrossing, simultaneous hermaphrodites. Across much of the parameter space, our model predicts male allocations well above 50 per cent. These predictions can help to explain apparently 'maladaptive' hermaphrodite systems.
investment can undermine
the evolutionary stability
Nico K. Michiels1,*, Philip H. Crowley2
and Nils Anthes1
1Animal Evolutionary Ecology, Institute for Evolution and Ecology,
Eberhard Karls-Universita ¨t Tu ¨bingen, Auf der Morgenstelle 28,
72076 Tu ¨bingen, Germany
2Department of Biology and Center for Ecology, Evolution and Behavior,
University of Kentucky, Lexington, KY 40506-0225, USA
*Author for correspondence (email@example.com).
Sex allocation (SA) models are traditionally based
on the implicit assumption that hermaphroditism
must meet criteria that make it stable against
transition to dioecy. This, however, puts serious
constraints on the adaptive values that SA can
attain. A transition to gonochorism may, however,
be impossible in many systems and therefore
realized SA in hermaphrodites may not be limited
by conditions that guarantee stability against
dioecy. We here relax these conditions and explore
how sexual selection on male accessory invest-
ments (e.g. a penis) that offer a paternity benefit
affects the evolutionary stable strategy SA in out-
crossing, simultaneous hermaphrodites. Across
much of the parameter space, our model predicts
male allocations well above 50 per cent. These
‘maladaptive’ hermaphrodite systems.
Keywords: simultaneous hermaphroditism;
sex allocation; sexual selection; male copulatory
organ; adaptiveness; sexual antagonism
Sex allocation (SA) theory links the evolution of simul-
taneous hermaphroditism and its stability against pure
sex invaders to three prime conditions (Charnov et al.
1976; Charnov 1980; Fischer 1981). First, at least
one sex function should show diminishing fitness
returns, and thus fitness is maximized by combining
optimal yields from both sexes in one individual.
Second, diminishing returns are often associated with
male function (Charnov 1979; Arnold 1994). The
resulting less than 50 per cent male allocation provides
more resources for egg production, so that population
growth exceeds that of gonochorists with a 1 : 1 sex
ratio. Third, conditions causing diminishing male
returns are low density and mobility or poor mate
searching (Tomlinson 1966; Ghiselin 1969), which
reduce sperm competition and thus favour low male
investment (Fischer 1984; Raimondi & Martin 1991;
Scha ¨rer & Ladurner 2003). These models, however,
are constrained in considering conditions for the evol-
ution and stability of hermaphroditism, restricting the
degree to which changes in SA in relation to group
or body size are possible (Cadet et al. 2004; Brauer
et al. 2007). Consequently, they may insufficiently pre-
dict evolutionarily stable SA when phylogenetically
old, well-established hermaphroditic clades (possibly
unable to change to gonochorism) are exposed to
sexual selection. Moreover, few SA models consider
male investments other than sperm, such as mate
searching or seminal fluid compounds (but see
Charnov 1996; Greeff & Michiels 1999; Pen &
Weissing 1999; Crowley 2008).
Here, we explore how selection for male investments
offering a disproportionate fertilization advantage affects
optimal SA in outcrossing, hermaphroditic animals.
In §5, we apply these to extant systems that apparently
violate stability conditions for hermaphroditism.
2. BASIC MODEL
Let the fitness, W, of an outcrossing hermaphrodite be
the sum of its fitness via female (eggs) and male func-
tion (offspring sired in n partners). Individuals mate on
average n times as a donor and as a receiver. The
environment determines mating opportunities, which
are never rejected. Inseminations precede fertilization.
Paternity per receiver depends on the investment, m, a
donor makes per mating (e.g. ejaculate size) relative to
that of the receiver’s other mates. All remaining
resources are allocated to eggs.
The W of a rare mutant introduced in a population
with a SA denoted by overbars
W ¼ ð1 ? rÞR þ n
ðn ? 1Þ? mð? rÞ þ mðrÞð1 ?? rÞR;
where R is the total resources for reproduction, r is the
proportion of R allocated to male function (¼SA),
m(r) is the male investment per female mate as a func-
tion of r and n is the number of mates.
m(r) scales according to the number of matings
n; ? mð? rÞ ¼? rR
The evolutionary stable strategy (ESS) for r is
obtained by setting the first derivative of equation
(2.1) for r equal to zero, replacing ? r by r and solving
for the ESS r ¼^ r
^ r ¼n ? 1
2n ? 1:
This result is the same as that of Charnov (1980) and
Fischer (1981) (figure 1, red line). It predicts ^ r when
sperm is the only form of male investment.
3. ACCESSORY MALE INVESTMENT
IN SPERM COMPETITION
We now implement benefits offered by accessory male
investment that can increase paternity but that trades
off against sperm production per se. This investment
could be structural (e.g. a penis, on which we focus
in what follows) or functional (e.g. sperm plugs,
manipulative seminal compounds, or behaviours that
increase sperm competitiveness). By having a larger
One contribution of 16 to a Special Feature on ‘Sexual conflict and
sex allocation: evolutionary principles and mechanisms’.
Biol. Lett. (2009) 5, 709–712
Published online 15 July 2009
Received 5 April 2009
Accepted 22 June 2009
This journal is q 2009 The Royal Society
penis, own sperm may be put in a better position rela-
tive to rival sperm, offering a fertilization benefit in
sperm competition or cryptic female choice (Eberhard
1985). The proportion of reproductive resources
invested in this organ, p, is considered to be part of
total male allocation r. Hence, r – p is the proportion
of R left for sperm production. The fertilization advan-
tage is modelled as a ‘virtual increase’ in sperm
number by multiplying the resources invested per part-
ner by pa. The dimensionless exponent a (0 ? a)
allows us to control how p affects sperm precedence.
The investment strategy (2.2) is now additionally
dependent on the benefit through a ‘male organ’ and
mðr;pÞ ¼Rðr ? pÞ
? mð? r;? pÞ ¼Rð? r ?? pÞ
with p the cost of the male organ and a an exponent
modifying the beneficial effect of p from nil (a ¼ 0),
decelerating (0 , a , 1), linear (a ¼ 1) to accelerating
(a . 1).
Substituting equation (3.1) into equation (2.1)
and solving for the ESS values of r and p separately
^ r ¼n^ p þ n ? 1
2n ? 1
^ p ¼
a þ 1:
Now solving equations (3.2) and (3.3) simul-
taneously for ^ r and ^ p results in
^ r ¼
ðn ? 1Þða þ 1Þ
n þ ðn ? 1Þða þ 1Þ;
^ p ¼
ðn ? 1Þa
n þ ðn ? 1Þða þ 1Þ:
(Note: second derivatives of ^ r and ^ p are negative, indi-
cating maxima whenever a . 0 and n . 1.) The results
show that even for few mates, adding a competitive
advantage for a larger male copulatory organ (a . 0)
drives ^ r above 50 per cent (figure 1, blue lines).
( f )
semen per partner
relative fitness female
1234 5 6 710
12345 6 7 10
Figure 1. ESS solutions for five values of a as a function of mate number for (a) male allocation ^ r and (b) allocation to a
male organ ^ p. The other graphs were derived from these: total allocation to semen ((c) Rð^ r ?^ pÞ) and semen per partner
((d) Rð^ r ?^ pÞ=n). Total fitness as sum of sired (male) and produced (female) (e) egg expenditure and (f ) relative fitness
of a pure female in a corresponding hermaphroditic population. a ¼ 0 (red line) represents the traditional Charnov model.
710N. K. Michiels et al. Penis investment and sex allocation
Biol. Lett. (2009)
Rð^ r ?^ pÞ=n increases with a, rising to 80 per cent for
accelerating effects. Note that for a ¼ 0 (red line), ^ p ¼ 0,
yielding an ^ r identical to the basic model above.
The model further illustrates the trade-off between
investments in sexually selected male traits (p) and
investment in sperm only (compare ^ p R with total
semen in figure 1). All else equal, a decelerating advan-
tage directs more male resources into sperm rather
than accessory investment; the reverse is more likely
for accelerating returns. The model also shows how
ejaculate sizes are tailored depending on the number
of mates (figure 1d). Under strict monogamy, ^ r
approaches zero but reaches a maximum with only
two sperm donors competing for fertilizations, corre-
sponding to theoretical predictions (Ball & Parker
1997; Wedell et al. 2002). With increasing numbers
of partners, ejaculate sizes decrease owing to the
requirement to divide the available amount of sperm
across n partners.
4. STABILITY AGAINST PURE SEX INVADERS
Hermaphrodites are stable to invasion by females as
long as their per capita egg production is ?0.5 that of
theaveragefemale(assuminga1 : 1sexratiointhegono-
chorists and no paternal provisioning by males).
Consequently, hermaphrodites with ^ r . 0.5 are prone
to invasion by pure females. Under our paradigm, this
space, indicating that such systems are inherently labile.
Figure 1e,f displays the total fitness of a hermaphrodite,
expressed as total amount of resources that contribute
to an individual’s female reproduction plus male fitness
through the female partner (figure 1e) and the relative
success of pure female invaders (figure 1f ).
We show that alternative investment options in addition
to sperm generate selection regimes that diverge
considerably from the original SA models, resulting in
male allocations well beyond the 50 per cent threshold
across a wide range of the parameter space. Such
enhanced male allocation occurs even with a decelerat-
ing effect of the male structure p on sperm precedence
(0 , a , 1). This enhancement strongly depresses
population fitness and makes hermaphrodites inherently
prone to invasion by pure females.
From a theoretical standpoint, pure hermaphroditic
systems should thus be non-existent unless sperm
competition is low. However, some extant hermaphro-
ditic systems may be incapable of producing pure sex
mutants. This appears particularly likely in clades
where internal fertilization requires complicated struc-
tures for sperm transfer and fertilization. Cleanly
switching off either of the two sex functions and
making the resources fully available to the other func-
tion may be non-trivial, suppressing the success of pure
sex individuals. Hence, unless developmental or gen-
etic switches allow a simple breeding system reversal,
hermaphrodites with high marginal benefit from acces-
sory investment (high a) may be phylogenetic dead
ends. As a second obstacle, behavioural systems such
as conditional reciprocity may further lower the fitness
of pure sex invaders, stabilizing hermaphroditism
(Fischer 1981; Anthes et al. 2005). Unless replaced
by a separate sex species that competes for the same
set of resources, maladaptive hermaphrodites such as
these may persist over long periods. An intermediate
compromise may be facultative selfing, e.g. in pulmo-
nate snails (Jarne & Auld 2006). This seems feasible
whenever the cost of inbreeding is surpassed by the
cost of selection for excessive male allocation and
may explain the association of occasional aphally (the
lack of a penis generating inability to donate and, in
some species, inability to receive sperm) with selfing.
escalated male allocation exist among limacid land
slugs. Pairs of Limax corsicus attach themselves to over-
hanging structures to evert and intertwine their gigantic
male copulatory organs, hanging down for up to 92 cm
in a 10 cm slug (Gerhardt 1933; figure 2). Sperm are
exchanged at the penis tips. Large penises are appar-
ently widespread among gastropods (e.g. Anthes &
Michiels 2007; Reise 2007) and flatworms (N. K.
Michiels 1992–1999, personal observation).
It is striking that transitions between hermaphrodit-
ism and gonochorism are frequent only in animals with
external fertilization and
reproductive systems such as cnidarians, bivalves,
Figure 2. Schematic drawing of a mating pair of L. corsicus,
illustrating the excessive size of the entwined male copulatory
organs (drawn after a picture from M. Kaddatz and
Penis investment and sex allocation
N. K. Michiels et al.
Biol. Lett. (2009)
crustaceans, polychaets and fishes (Harrison & Wallace
1990; Bauer 2004; Mank et al. 2006; Rouse & Pleijel
2006; Iyer & Roughgarden 2008). In contrast, clades
with internal fertilization and advanced genital systems
such as flatworms, oligochaetes, molluscs or insects
show such transitions only rarely, if at all (e.g. Heller
1993); the reproductive evolution of these organisms
may be constrained by phylogenetic inertia.
parameter space within which (some) hermaphrodites
operate could be larger than previously assumed.
They should be extended by including costs paid as a
result of sexual conflict (Michiels & Koene 2006),
mate searching (Puurtinen & Kaitala 2002) or selfing.
All of these components may vary depending on the
benefits of multiple mating, e.g. via fertility insurance
or offspring performance (Sprenger et al. 2008).
Finally, while we have alluded to possible systems
that match our predictions, additional empirical
measurements of SA and potential benefits of male
accessory investments are clearly needed.
consider that the
We thank K. Jordaens and two unknown referees for
suggestions and S. Sahm and G. Schulte for figure 2. This
paper has benefited from the workshop ‘Analogies in the
evolution of gender expression and sexual strategies in
animals and plants’ funded by the Volkswagen Foundation,
Neuhausen/Fildern, September 2008.
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