Download MATE CHOICE FOR OPTIMAL (K)INBREEDING

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doi:10.1111/j.1558-5646.2010.01217.x
MATE CHOICE FOR OPTIMAL (K)INBREEDING
Mikael Puurtinen1,2
1
Department of Biological and Environmental Science, Centre of Excellence in Evolutionary Research, P.O. Box 35, FI-40014
University of Jyväskylä, Finland
2
E-mail: [email protected]
Received September 21, 2010
Accepted November 23, 2010
Mating between related individuals results in inbreeding depression, and this has been thought to select against incestuous
matings. However, theory predicts that inbreeding can also be adaptive if it increases the representation of genes identical by
descent in future generations. Here, I recapitulate the theory of inclusive fitness benefits of incest, and extend the existing
theory by deriving the stable level of inbreeding in populations practicing mate choice for optimal inbreeding. The parsimonious
assumptions of the model are that selection maximizes inclusive fitness, and that inbreeding depression is a linear function of
homozygosity of offspring. The stable level of inbreeding that maximizes inclusive fitness, and is expected to evolve by natural
selection, is shown to be less than previous theory suggests. For wide range of realistic inbreeding depression strengths, mating
with intermediately related individuals maximizes inclusive fitness. The predicted preference for intermediately related individuals
as reproductive partners is in qualitative agreement with empirical evidence from mate choice experiments and reproductive
patterns in nature.
KEY WORDS:
Inbreeding, incest avoidance, inclusive fitness, kin selection, mate choice, relatedness.
Adaptive explanations for mate choice concentrate on the benefits
that can be accrued by discriminating among potential reproductive partners. The benefits of mate choice can be classified as
direct benefits, genetic benefits, and inclusive fitness benefits.
Direct benefits of mate choice include factors that affect the number of surviving offspring, for example, mate’s ability to provide
shelter and nutrition for the offspring. Genetic benefits are factors
affecting offspring genetic quality, that is, heritable differences in
fitness (good genes) or differences in genetic compatibility between mates (compatible genes) (Puurtinen et al. 2009). Inclusive
fitness benefits of mate choice refer to the increased genetic representation in future generations that can be gained by increasing
the reproductive success of relatives via mate choice (e.g., Parker
1979).
Previous theoretical work has shown that inclusive fitness
benefits can favor close inbreeding even when this results in substantial reduction in offspring fitness. These models have identified the boundary level of inbreeding depression limiting the
evolution of inbreeding among first-order relatives, that is, between full siblings, or between parents and offspring (Parker 1979;
C
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Smith 1979; Waser et al. 1986; Lehmann and Perrin 2003; Kokko
and Ots 2006). Although these models can easily be extended to
study the boundary level of inbreeding depression limiting incest
among any pair of relatives, they do not address the important
question: What level of inbreeding maximizes fitness? As natural
selection ought to maximize fitness, deriving the optimal relatedness for adaptive inbreeding is warranted. Apart from the cursory
note in the appendix D of Lehmann and Perrin (2003), optimal
inbreeding for inclusive fitness benefits has not been studied before. Here, I will first recapitulate the calculation of threshold
inbreeding depression that limits the evolution of incest, and the
calculation of optimal level of inbreeding under the simplifying
assumption of an outbred population. Then, I extend the analysis
to find the long-term evolutionarily stable level of inbreeding in
populations practicing optimal mate choice for inbreeding. In the
end, I will discuss the implications of the model to understanding
mate choice, population structure, and mating system evolution.
The model is developed primarily for species with separate
sexes. For convenience of writing, I will use the term female for
the sex that has high parental investment and whose reproduction
C 2011 The Society for the Study of Evolution.
2011 The Author(s). Evolution Evolution 65-5: 1501–1505
B R I E F C O M M U N I C AT I O N
is not limited by mate availability but by resource availability, and
male for the sex that is primarily limited by mate availability. For
mathematical convenience, let fitness from outcrossing be one.
We can then write the net inclusive fitness effect for a female
from incestuous mating with a male with relatedness r as
Ifemale = (1 − δ) + r (1 − δ) − 1 − rc,
(1)
where δ is inbreeding depression and c denotes the opportunity
cost for a male from incestuous mating (when c = 0 incest does
not affect male’s opportunities for outcrossing, and when c = 1
incest precludes outcrossing).
In (1), the first term denotes genes passed directly from the
female to the offspring, the second term denotes genes identical
by descent (IBD) with the female passed to the offspring from the
related male, the third term denotes the loss of one unit of direct
fitness that would have been obtained if the female outcrossed,
and the fourth term denotes loss of inclusive fitness from lost
outcrossing opportunity by the related male. Analogically, we
can write the effect of incestuous mating on male fitness as
Imale = (1 − δ) + r (1 − δ) − c − r,
(2)
where the first term denotes genes passed directly from the male
to the offspring, the second term denotes genes IBD passed to
the offspring from the related female, the third term denotes the
lost outcrossing opportunities for the male, and the fourth term
denotes the lost indirect fitness that could have been obtained if
the related female had outcrossed.
Solving I = 0 with respect to δ, we get the strength of inbreeding depression that will limit evolution of incest. For females
this value is
δfemale = (r − rc)/(1 + r )
(3)
Figure 1.
To find the optimal relatedness that maximizes inclusive fitness, inbreeding depression needs to be defined as a function of
parental relatedness. Assuming that the effects of different loci
combine additively, inbreeding depression is a linear function of
offspring inbreeding coefficient F (Falconer and Mackay 1996).
Linear inbreeding depression is the most typical pattern found in
empirical studies. Noting that in an outbred population offspring
inbreeding coefficient is one-half of parental relatedness (F =
r/2), and denoting the slope of the relationship between F and
inbreeding depression as b (as in Crnokrak and Roff 1999), inbreeding depression can be written as a function of relatedness of
the parents
δ = bF = b(r/2).
and for males
δmale = (1 − c)/(1 + r ).
(4)
Equivalent equations have been derived previously by Waser
et al. (1986), Lehmann and Perrin (2003) and Kokko and Ots
(2006). When c = 0 and relatedness between partners is 0.5 (e.g.,
full siblings in an outbred population), the equations yield the
familiar inbreeding tolerances of two-thirds for males and onethird for females (Parker 1979; Smith 1979; Waser et al. 1986;
Taylor and Getz 1994; Lehmann and Perrin 2003) (Fig. 1). Waser
et al. (1986) also give a full discussion of the implications of
varying the opportunity cost (c) to benefits of incest. The conflict
of interests between sexes over inbreeding has been extensively
discussed in the studies cited directly above. Here, I will focus on
mate choice that maximizes the inclusive fitness of the choosing
sex (generally females).
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Threshold inbreeding depression (δ) limiting the evo-
lution of inbreeding as a function of parent relatedness (r) in an
outbred population assuming male opportunity cost c = 0.
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(5)
Substituting (5) to equations (1) and (2) yields after rearrangement
Ifemale = 1/2(2r − br − 2cr − br2 )
(6)
Imale = 1/2(2 − 2c − br − br2 ).
(7)
and
Figure 2 shows the effect of incest on female and male fitness
for various values of b when the opportunity cost c = 0. From the
male perspective, outcrossing always yields the highest fitness,
but incestuous matings also yield positive fitness returns unless
relatedness is very high (r is close to 1) and inbreeding depression
is very severe. For females, there often exists an optimum level of
relatedness that maximizes fitness, and this optimum depends on
B R I E F C O M M U N I C AT I O N
1
male,bb==11
male,
1.33
male,bb==1.33
male,
male,bb==1.6
1.6
male,
female,bb==11
female,
Effect of incest on fitness
0.8
1.33
female,bb==1.33
female,
0.6
1.6
female,bb==1.6
female,
0.4
0.2
0
FJJ = (1 + F)/2, where F is the individual’s inbreeding coefficient (Bulmer 1994). Because relatedness does not have the same
relation to familial relationships in an inbred population as in an
outbred population, deriving solution in terms of relatedness is
of little practical or heuristic value. It is more useful to derive
the stable level of inbreeding (offspring inbreeding coefficient F
which is equal to parental consanguinity FJK ), as this is easily
measured from real populations as reduction in heterozygosity
O
from that expected with random mating, F = HEH−H
.
E
Denoting consanguinity of mates in the current generation as
FJK and the inbreeding coefficient of the choosing female as F,
and assuming c = 0, the net inclusive fitness effect for a female
mating with male with consanguinity FJK is
-0.2
0
0.125
0.25
0.375
0.5
0.625
0.75
0.875
1
Ifemale = (1 − bFJK ) +
r
Figure 2.
The effect of incestuous mating on male and female
fitness for various values of inbreeding depression (b), assuming
an initially outbred population and male opportunity cost c = 0
(equations 6 and 7). For males, outbreeding is always more beneficial than incest. Incest however yields positive fitness returns
for realistic values of inbreeding depression, especially when relatedness to the female is not extreme. For females, there often
exists an optimum relatedness that maximizes fitness (see text for
details).
the strength of inbreeding depression. The optimum relatedness
for female mate choice in an outbred population is found by
solving ∂Ifemale
= 0 with respect to r, which yields
∂r
∗
=
rfemale
2 − b − 2c
.
2b
(8)
When male opportunity cost c = 0, female fitness in an
initially outcrossed population is optimized by outbreeding when
b ≥ 2, by full-sibling mating when b = 1, and in simultaneous
hermaphrodites by self-fertilization when b ≤ 2/3 . Thus, when
2
/3 < b < 2, there exists an intermediate r∗ that maximizes female
fitness. As Figure 2 shows, the stronger the inbreeding depression,
the less closely related optimal mates are. For example, when b =
1.6, female fitness is maximized by reproducing with first cousin
(r = 0.125) and reproducing with full brother (r = 0.5) yields
lower fitness than full outbreeding.
The above derivation of r∗ applies only to an initially outbred
population. Obviously, if incestuous matings are common, the
population becomes inbred and equation (8) no longer applies. I
will next derive the stable level of inbreeding in populations where
females are practicing mate choice for optimal inbreeding. For
simplicity, I also assume negligible male opportunity cost (c = 0).
In the context of inclusive fitness, relatedness is defined as
rJK = FJK /FJJ , where FJK is consanguinity between individuals and FJJ is the consanguinity of an individual with itself, and
2FJK
(1 − bFJK ) − 1.
(1 + F)
(9)
Equation 9 assumes that inbreeding and consanguinity coefficients are at their equilibrium values. The optimal consanguinity
= 0 with respect to FJK :
is found by solving ∂∂Ifemale
FJK
FJK =
2 − b(1 + F)
.
4b
(10)
Equation 10 has been derived earlier by Lehmann and Perrin
(2003, eq. D1b). Because parental consanguinity (FJK ) equals inbreeding coefficient of the following generation (F), equation (10)
is a recurrence relation that can be solved for stable level of inbreeding (F ∗ )
F∗ =
2−b
.
5b
(11)
Thus, for 1/3 < b < 2, there exists a stable intermediate level
of inbreeding (Fig. 3). This stable level of inbreeding is 80% of
the predicted from equation (8) which applies to a completely
outbred population. For b ≤ 1/3, complete inbreeding is expected.
For b > 2, disassortative mating avoiding relatives is expected,
leading to stable negative F ∗ values approaching −1/5 as b → ∞.
Discussion
The analysis of optimal inbreeding reveals that (some degree of)
inbreeding is expected to evolve under a wide range of inbreeding
depression strengths, even when mate choice is done by the sex
with the lower inbreeding tolerance. This result corroborates the
earlier findings that inbreeding can be adaptive even when it
results in appreciable inbreeding depression (Parker 1979; Smith
1979; Waser et al. 1986; Lehmann and Perrin 2003; Kokko and
Ots 2006). However, the analysis also reveals that the expected
amount of inbreeding is considerably lower than the previous
analyses insinuate. For example, it has been suggested that in an
outbred population incest among first-order relatives (r = 0.5)
should evolve whenever δ < 1/3 (assuming c = 0) (Parker 1979;
Smith 1979; Waser et al. 1986). The current analysis however
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The stable level of inbreeding (F ∗ , equation 11) in populations practicing optimal inbreeding as a function of the strength
Figure 3.
of linear inbreeding depression (b). When 1/3 < b < 2, population
is expected to be partially inbred (F ∗ is between 0 and 1), and
when b > 2, dissassortative mating leading to negative F ∗ values
is expected.
suggest that when b = 4/3 (which gives δ = 1/3 for full-sibling
matings in an outcrossed population), female inclusive fitness in
an outcrossed population is maximized at r = 0.25, and that the
stable level of inbreeding in a such a population is only F ∗ =
0.1 (from eq. 11), instead of F ≈ 0.25 that might be inferred by
extrapolation from the previous models.
It has been argued that there is a mismatch between theory and data regarding the prevalence of inbreeding in nature:
previous models suggest that close inbreeding should be fairly
common in nature, yet empirical studies seldom find evidence for
preferential close inbreeding (Kokko and Ots 2006). The analysis
of mate choice for optimal inbreeding suggests that the expected
degree of inbreeding has been overestimated: as explained above,
the optimal long-term levels of inbreeding are much lower than
the previous studies suggest. Intriguingly, when preference for
related individuals has been found in empirical studies, preference is usually not for immediate but for slightly more distant
kin. In a review on inbreeding avoidance in animals, Pusey and
Wolf (1996) list experimental studies on mate preferences. Five
of the seven studies with relevant information found evidence for
preference of intermediately related individuals (first or second
cousins) while full siblings were avoided. Preference for intermediately related mates may be a common phenomenon also in
natural environments. In a recent review of mate choice in birds,
Mays et al. (2008) found that in general preference seems to be
for genetically similar rather than for genetically dissimilar mates,
and this pattern is evident in both choice of social mate (five out
of eight studies) and extra-pair mate choice (14 out of 18 studies).
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It certainly seems that the empirical evidence is in qualitative
agreement with the prediction that intermediately related individuals should be preferred as reproductive partners. Inbreeding
depression (b) on fitness components has been estimated to range
between 0.55 and 0.82 in the wild (Crnokrak and Roff 1999). As
inbreeding depression for total fitness is probably considerably
higher than inbreeding depression on components of fitness, values of b predicting preference for intermediately related mates
(1 < b < 2) are expected to be common in natural populations.
The analysis of optimal inbreeding predicts that for a range
of realistic values of inbreeding depression, positive F values
should be observed in populations practicing mate choice for optimal inbreeding. This immediately suggests an empirical test of
the model: the level of inbreeding in a population (F) should relate to strength of inbreeding depression (b) as in equation (11).
Although such analysis comparing inbreeding depression and inbreeding would be very welcome, it must be noted that deciding
the proper F statistic for inferring inbreeding may prove difficult. Inferring inbreeding will be easy if the population has clear
boundaries and the individuals can easily choose partners from
the entire population. In this type of scenario, inbreeding will be
detected as positive F IS at conception. If the population is more
widespread, and/or dispersal of individuals is low in relation to
the distribution of the population, it is more difficult to decide
on the correct reference population. If there is isolation by distance, breeding can be random at local scale but nonrandom at
larger scales. Even with random local mating, F IT will be positive
because of the spatial structuring of the population, and hence
inbreeding is taking place. The intriguing viewpoint emerging
from the current analysis is that the isolation by distance may
arise as a consequence of mate choice for optimal inbreeding: if
mating with kin maximizes inclusive fitness, this will select for
short dispersal distances and hence give rise to spatial structuring
in the population. Short dispersal distances and population structuring could thus plausibly evolve in the absence of any costs to
dispersal, simply as a mechanism to maximize inclusive fitness
via mate choice (see also Lehmann and Perrin 2003).
The analysis also suggests a new approach to the theory of
mating system evolution in hermaphroditic organisms. The main
question in hermaphrodite mating system evolution has been to
understand the forces directing the evolution of self-fertilization
versus cross-fertilization. This approach is conceptually identical
to the study of evolution of incest among first-order relatives versus complete outcrossing discussed at length above. The very basic theory of hermaphrodite mating system evolution predicts the
evolution of full selfing when self-fertilization depression is less
than one-half, and complete outcrossing when self-fertilization
depression is more than one-half, although many ecological and
genetic forces are known to cause deviations from this prediction (see e.g., Uyenoyama et al. 1993; de Jong and Klinkhamer
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2005). The current analysis however suggests that biparental inbreeding, not selfing, is expected for self-fertilization depression
values between 1 and 1/3 , without any assumptions about purging,
pollen discounting, or linkage between fitness loci and mating
system modifiers (see Uyenoyama et al. 1993). Unfortunately,
most analyses of hermaphrodite mating systems have not distinguished between biparental inbreeding and self-fertilization
as sources of inbreeding, leaving open the question of the role
of biparental inbreeding on estimated rates of self-fertilization
(Goodwillie et al. 2005). New methods employing multilocus
genetic estimates of mating system parameters and information
about population spatial genetic structure provide tools for simultaneous estimation of selfing and biparental inbreeding, and data
are starting to accumulate (Herlihy and Eckert 2004; Vekemans
and Hardy 2004; Jarne and Auld 2006; Jarne and David 2008). It
seems that for populations characterized by high F values, selfing
is indeed the main source of inbreeding. Because self-fertilization
can function as a reproductive assurance mechanism, and because
physiological mechanisms of selfing differ from biparental reproduction, it is to be expected that a model derived for optimal
biparental inbreeding will not capture all key aspects affecting
the evolution of self-fertilization. Nevertheless, considering the
possibility that biparental inbreeding may be adaptive might yield
important insights to evolution of hermaphrodite mating systems.
The analysis presented in this article ignores many aspects
likely to influence mating system evolution in nature. As a simplified model, the analysis however pins down the finding that
in absence of any complicating factors related to ecology or the
specifics of genetic systems, selection should favor nonzero inbreeding for wide range of inbreeding depression strengths. In
future work, it will be worth studying the consequences of factors
such as costs of mate choice, sexual conflict over mate choice
(Parker 1979; Pizzari et al. 2004), kin recognition mechanisms,
purging of genetic load with inbreeding, and possible nonlinear
inbreeding depression (synergistic epistasis) (Charlesworth et al.
1991) on model predictions. Broadening the scope of adaptive
inbreeding from incest between close relatives to inbreeding optimized with respect to relatedness holds promise of a rewarding
avenue for both theoretical and empirical research.
ACKNOWLEDGMENTS
I thank J. S. Kotiaho for inspiring discussions, R. Paatelainen for help
with the recursion solution, and two anonymous referees for constructive comments. This study was funded by Academy of Finland (grant
7121616).
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Associate Editor: S. West
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