I... A..-

    

      
   
       

‘ll

1

l
\

Lulumm

WM“Wt

a 1le

4w
Ioo
mm

IHL‘Sab

2 (”2‘0

This is to certify that the

thesis entitled
Female Choice and Extra-Pair Copulations

presented by

Christopher D. Wilson

has been accepted towards fulfillment
of the requirements for

Master of Science Zoology

degree in

 

 

 

Date

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

 

LIBRARY
Michigan State
University

 

 

 

PLACE IN REfURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIFiCIDateDuost-nts

FEMALE CHOICE AND EXTRA-PAIR COPULATIONS
By

Christopher David Wilson

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Zoology

2000

3 II... 'IIiar
.Illlll

[0"

l‘.‘

t

i‘

Ivn’lln. [the

ABSTRACT
FEMALE CHOICE AND EXTRA-PAIR COPULATIONS
By

Christopher David Wilson

The discovery that social monogamy does not always lead to genetic monogamy
has forced us to reassess our understanding of sexual selection. Comprehension of the
factors that are important in causing the inconsistencies between the social and sexual
relationship is essential if we are to understand the evolution of mating systems.
Empirical work on this subject has been largely focused on avian species and much data
has been accumulated that demonstrates the considerable variation in levels of sexual
infidelity within and between socially monogamous species. It has been reasoned that the
motivation behind these extra-pair copulations (EPCs) is the acquisition of indirect good
genes benefits, so within such a framework, a probability model of female choice at the
point of EPCs is presented. The model takes the assumption that the female appraises the
genetic quality of her partner in relation to the genetic quality of the population of
potential males (probably at the point of initial mate choice) and along with benefit-cost
information, resolves whether or not to make a cuckold of her partner. The model allows
us to quantify the indirect benefits and costs of EPCs to females from observational data,
and results in an explanation for the variation in the frequency of extra-pair copulations,

with population levels of variation for fitness related genes being the important factor.

T 0 Doreen and Ernie

iii

ACKNOWLEDGMENTS

I would particularly like to thank Dr. Donald Beaver for his professional and
personal help, support and encouragement throughout my time at Michigan State
University and I wish him every happiness in his retirement. I would also like to express
my gratitude to Dr. Thomas Getty and Dr. Scott Winterstein for serving on my committee
and for providing invaluable advice on this work, as well as Dr. Jeff Connor, Dr. Donald
Hall and Dr. Danny Rozen for assisting me in my Ph.D. applications. As for everyone

else, you know who you are, and you know I'm grateful.

TABLE OF CONTENTS

LIST OF TABLES .............................................................................................................. vi
LIST OF FIGURES ............................................................................................................ vii
INTRODUCTION ................................................................................................................ 1
HELENA DERIVED ............................................................................................................ 7
HELENA, THE P-VARIABLE AND BENEFIT-COST RATIOS ................................... 10
THE STRATEGIES COMPARED .................................................................................... 17

Helena ...................................................................................................................... 1 7

Hermia ..................................................................................................................... 18
EPCs AND GENETIC VARIATION ................................................................................ 23
EPCs, GENETIC VARATION AND POPULATION SIZE ............................................. 32
A NOTE ON INBREEDING DEPRESSION .................................................................... 36
MAIN CONCLUSIONS .................................................................................................... 39
SOME FUTURE DIRECTIONS ....................................................................................... 40
BIBLIOGRAPHY .............................................................................................................. 41

LIST OF TABLES

Table 1. Hypothetical field observations of EPC behaviour from a subset of a
population .............................................................................................................. 12

Table 2. The relationship between the benefits and costs of EPC behaviour for the
subset of individuals .............................................................................................. 13

Table 3. Comparisons of predicted EPC activity under strategies of Hermia and Helena
in populations of ten couples ............................................................ 21

Table 4. Average benefits and costs of participating in EPCs for each female in three
populations with different levels of genetic variation ........................................... 26

Table 5. Predicted number of females that would accept or reject EPCs in three
populations with different levels of genetic variation ........................................... 28

Table 6. The probabilities that any accepted EPC will be with a male equal or
superior to the female's attending male, in three populations of differing
genetic variation .................................................................................................... 30

vi

LIST OF FIGURES

Figure l. Proportions of males superior to the female's attending male for females

mated to males of differing genetic quality ....................................................... 8
Figure 2. The minimum benefit-cost ratios required for a strategy of accept to be

adopted ............................................................................................................. 11
Figure 3. Hypothetical field observations applied to the minimum benefit-cost

curve ................................................................................................................. 14
Figure 4. A Gaussian distribution of male quality and the Hermia strategy ..................... 17

Figure 5. Discrete distribution of male quality in a population of ten males mated
to ten females ................................................................................................... 18

Figure 6. Three discrete populations with differing levels of male genetic variation ....... 24

Figure 7. The females that have the propensity to engage in EPCs in three
populations of differing levels of male genetic quality ................................... 29

Figure 8. As additive genetic variation in the population of males increases, the
frequency of females participating in EPCs also increases, yet the
probability that any one of these EPCs is with a male superior in
quality to her partner decreases ........................................................................ 31

Figure 9. Example of distributions used to calculate required levels of variation ............ 33

Figure 10. The genetic variation required for x-number of EPCs decreases with
increasing population size ................................................................................ 35

Figure 11. Distributions reflecting the quality of potential EPC-males with respect
to the quality of the current partner (dashed line). (a) Increasing the
genetic variation of the offspring; any EPC male will do just fine.
(b) “Hermia”; only superior males are considered. (0) “Helena”; most
EPCs are with superior males .......................................................................... 37

vii

INTRODUCTION

Content with Hermia! No; I do repent
The tedious minutes I with her have spent.
Not Hermia but Helena 1 love:

Who will not change a raven for a dove?
The will of man is by his reason sway ’d;
And reason says you are the worthier maid.

A Midsummer Night’s Dream. Act 11, Scene 2.

In his writings on sexual selection, Darwin did not consider why females should
copulate with more than one male, since he believed that females were strictly
monogamous. We are now familiar with the various mating systems that are present in
different species, these being traditionally described as being the result of the spatial and
temporal distribution of resources. However, if we are to take this definition, the mating
systems themselves determine only the social bond and not the sexual relationship of
individuals. If individuals are constrained in their mate choice by the mating system, they
will attempt to improve this situation through sperm competition, and it is sperm
competition that dictates many aspects of the sexual relationship above that of the social.
Sperm competition as a field of study is concerned with processes on a number of levels,
from the physiological processes in the female reproductive tract, to the subject of this
work: explanations for extra-pair copulations.

Extra-pair copulations (or EPCs) are a prevalent behaviour in avian breeding
systems. This discovery has revolutionized our understanding of sexual selection, since

until the recent application of genetic markers, 90% of bird species were categorized as

1

monogamous. We are now more than aware that social monogamy does not always lead
to genetic monogamy.

We therefore not only have situations of female choice at the time of mating, but
also a second round of active female selection, the difference in propensity to participate
in the latter being predisposed by the quality of male attained during the original mating.
The original mate choice, and therefore the degree of inclination to participate in EPCs,
may be a function of the original female mating order8 (be it controlled by the time of
arrival on the breeding territories or the physical ability to initiate reproduction“) and
consequently the quality of the female, i.e. both male and female quality control the
predisposition to take part in EPCs.

There are a number of possible benefits of EPCs to females ranging from the
direct and non-genetic (such as insurance against sterile mates or increased parental care)
to the indirect and genetic (such as good genes or increased genetic diversity). However,
if females are participating in EPCs for apparently non-genetic benefits (because future
matings are necessary to ensure reproductive success) genetic differences between males
will be the factor that prompted the EPC in the first instance. That is, multiple mating for
purely non-genetic benefits is unlikely as it invariable leads to the possibility of genetic
benefits as well”. Intraspecific analyses of the patterns of extra-pair behaviour have
suggested that the main benefit females gain from extra-pair matings is an improvement
in the genetic quality of their offspring, i.e. indirect good genes benefits” 28.

There is also great variation in frequency of extra-pair paternity (EPP) both at the

species level and the population level (natural populations vary in the level of EPP from

0% to more than 75%”) and understanding this variation will provide us with an
opportunity to understand which factors are important in promoting polygamy.

Females usually participate in extra-pair copulations more readily with males that
are of high quality. This preference for quality has been shown to operate on the age“ 2' 3' 4,
the dominance ranks, health“, and the degree of expression of secondary sexual

characteristics” 8- 9’ ‘°~ n. 17

of the males concerned, these factors being indicators of the
potential genetic quality and sex appeal of the offspring. Furthermore, there is much
evidence that suggests that a female's desire to participate in EPCs, along with their
choice of EPC partner, is a function of the difference in quality between her original mate
and the EPC male”; the practice of females performing EPCs with males that are more
attractive in terms of their secondary sexual characteristics than their partners being the
most obvious example.

The male quality evidence is usually interpreted in the following way. Paired
females actively accept or reject individual extra-pair solicitations (or decide whether or
not to solicit themselves) depending on the difference in quality of her mate and the
extra-pair male, i.e. if the extra-pair male is of sufficiently greater quality than her partner
she will accept the EPC, if he is not sufficiently superior, she will reject. We may assume
that the degree of expression of a secondary sexual characteristic is equivalent to quality,
specifically genetic quality, since other female choice criteria associated with original
mate choice, such as ability to provide parental care or territory quality, rarely apply to

EPCS6.

If we are to think of the female behaviour in terms of adopting a particular

strategy, then for the above behaviour we would have something along the lines of 'only
have extra-pair copulations with males of sufficiently greater quality than my own
partner.’ The data which has been interpreted as supporting this idea shows an expected
distribution of EPC male quality, but a significant portion of this lies below the level of
quality of the original mate, i.e. a notable number of EPCs take place with males of
poorer quality than the mate; contradictory to the suggested strategy” '5' '6' '7 .In order to
explain these EPCs with poorer quality males, along with providing us with an alternative
explanation of why females mated to relatively poor quality males have a higher
propensity to engage in EPCs, the following is presented.

I propose a model in which females are not selective of individual extra—pair
males. Depending on the quality of their current partner in relation to the rest of the
population of potential male mates, they adopt a strategy of 'accept EPCs' or 'reject EPCs'
(or again, decide whether or not to solicit themselves), regardless of the quality of the
specific individual EPC males. This assumption requires some clarification, since if
females are able to assess male quality, then why are they not selective of the individual
extra-pair male? There are a number of advantages that arise from making the decision to
accept or reject prior to the EPC proposition, especially if active solicitation on the part of
the female is involved, which is often the case. These advantages regard not incurring
certain costs that may arise if the female puts herself in the position of assessing
individual extra-pair male quality. Parker“ suggested that when the duration of copulation
is short (as it is in birds) it might be less costly for females to accept an EPC rather than

wasting time avoiding or rejecting persistent non-mates. If the female has decided on a

strategy already, she will not find herself in this position and therefore incur neither cost.
Furthermore, she is much less likely to be subject to a forced EPC in which she might get
injured or her eggs damaged that may occur if the female assesses an individual male and
then rejects. Further, she avoids increased predation risks and harassment from males that
may reduce her foraging efficiency. The assumption that such a strategy is employed
seems highly justified.

It will be shown that this approach allows us to begin quantifying the relative
power of the costs and benefits of extra-pair copulations, through translating EPC and
male quality data back to marginal benefit: cost ratios, and predictions regarding levels of
polygamy may be made by working in the opposite fashion. With the intention of
simplifying matters, the strategy of only accept EPCs from superior males shall be
referred to as Hermia, while the strategy that I propose involving assessing the quality of
the population of available males shall be referred to as Helena. The two are young
women involved in the love triangle in A Midsummer's Night's Dream, rather fitting for a
study on cheating and extra-pair antics.

The study proceeds by comparing the two strategies in terms of the expected
proportions of EPCs that will be with superior males. The intention here is to show that
Helena, even with what may be seen as looser selection criteria still achieves a
comparable proportion of EPCs with superior males.

The next section of this work essentially examines the variation in extra-pair
copulation frequencies (data here is usually obtained from extra-pair offspring data since

EPCs are notoriously difficult to observe in the field) both within and between species.

Previous studies that have addressed this question have come up with a variety of origins
for the variation, based around such factors as local breeding density'8 and the degree of
breeding synchrony”. Since these possible explanations are controversial, with no clear
support, I have focused my attention on the degree of variation in male fitness-related
traits (as a correlate of total genetic variation) within the population. By applying the
Helena strategy to populations with differing variations it is shown that one should expect
EPC frequencies to be greater in populations containing more variation. This is quite
logical since if one takes female choice of fitness related traits to be a general explanation
for the occurrence of extra-pair patemity, then it follows that one would expect that more
females would seek to modify the paternity of their clutch when there are greater
differences between the genetic quality of potential fathers. The effect of population size

on the whole equation is also examined.

Helena Derived

 

When should females adopt strategies of 'accept' and when should they adopt
strategies of 'reject'?
Let p = the proportion of males in the population of potential mates that are of
higher quality than her partner.
So (1 — p)= the proportion of males of lesser quality
We need to know the relative fitness of the two strategies:
1) The fitness of 'reject“.
Just has the basic fitness of 1, which arises solely from interactions with her
partner.
2) The fitness of 'accept'.
Has the same basic fitness of 1 from copulations with her partner.
Add to this the benefit b when EPCs are performed with superior males, occurring
at frequency p.
Subtract the cost c when EPCs are performed with inferior males, occurring at
frequency 1— p.

Giving the fitness of 'accept' to be 1+ bp — c(1— p)

1+bp-c(1—p)
1

 

So the relative fitness of the two strategies is:

So if bp — c(1— p) > 0 then the strategy of 'accept' should be adopted.

 

bp — C(l — p) > 0 translates to p >
b + c

So females should choose the strategy of 'accept' extra-pair copulations (or again, decide

to actively solicit EPCs themselves) if the proportion of males in the population better

6
b+c

. This is Helena.

 

than their own is greater than p >

It is important to remember that b and c are not the benefits and costs of a single
EPC, but simply the benefits of copulating with a superior male, and the costs of
copulating with an inferior male, both with respect to the quality of the original partner.

If we assume a normal distribution of male quality in the population, then the

females mated to each individual male have the p -variables indicated:

Frequency

 

 

 

 

 

p = 0.875 0.75 0.5 0.25 0.125

Male Quality

Figure l. Proportions of males superior to the female's attending male for females mated
to males of differing genetic quality.

But not only are the p-variables different for each individual female, the values of

b and c are also, since if a female has a p-variable of 0.125, she will obviously not

benefit from an extra-pair copulation with a superior male as much as a female with
p = 0.875. It is the differences between b and c (or the ratios of % ) that are crucial in

determining which strategies are adopted, these required ratios being easily calculated as
follows:

If p = 0.25 (i.e. the female's partner is better than 0.75 of the population) then for

 

'accept' to be adopted then 0.25 > , which translates to b > 3c , i.e. the benefits must

b+c

be at least three times as great as the costs.

If p=0.5,then0.5 >—c——,giving b>c.
b+c

And if p = 0.75, then 0.75 > b—c—, giving b > y , i.e. the benefit of an EPC
+ C

with a superior male need only be a third as much as the cost of copulating with an
inferior male. This is perfectly logical since when p = 0.75 , on average three out of four
interactions will be with superior males, i.e. p may not only be seen as proportion of
superior males in the population, but also as the probability of accepting an EPC from a

superior male, given that a strategy of accept has been adopted. For example, arbitrarily,

 

 

if p = 0.75, b = 5 and c = 16 (b c = 0.76) then 'reject' should be adopted, however if
+ c
p = 0.75 , b = 5 and c = 14 (b c = 0.73) then 'accept' should be adopted. If the latter
+ 6

turns out to be the case, then the probability of that EPC being with a superior male is

0.75.

Helena, the p-Variable and Benefit-Cost Ratios

Figure 2 shows the minimum benefit: cost ratios required for a strategy of ‘accept’

to be adopted.

If the benefit-cost ratio is greater than that given by the Helena Curve for any
given p-variable, then a strategy of accept should be adopted, and below the line; reject. It

is now theoretically possible to determine p for each female; observe whether or not

 

females perform EPCs for any given value of p; then tracking back (using the p > b c
+ c

equation and fig. 2) to find the relative values of b and c.

10

 

 

 

 

 

 

 

0 0.25 0.5 0.75 1

p-value

 

 

 

 

 

Figure 2. The minimum benefit-cost ratios required for a strategy of accept to be
adopted.

11

For example, suppose the following data from a group of 7 females:

Table l. Hypothetical field observations of EPC behaviour from a subset of a population.

 

 

 

 

 

 

 

 

p - variable Accept or Reject EPCs
0.9 Accept
0.75 Accept
0.67 Accept
0.5 Accept
0.33 Accept
0.25 Reject
0.1 Reject

 

 

 

 

From the change from accept to reject between p—variables of 0.33 and 0.25, and

from looking back to c

 

and fig. 2, it can be seen that these represent y ratios of 2
+ c C

and 3 respectively. One cannot assume from this data that for all females, the benefits of
copulating with a superior male are between 2 and 3 times as great as the costs of
copulating with an inferior male, since as stated above, b and c values are different for

each p-variable. We can only deduce a relationship between b and c for each individual:

Table 2. The relationship between the benefits and costs of EPC behaviour for the
subset of individuals.

 

 

 

 

 

 

 

 

p - variable Accept or Relationship
Reject EPCs between b and c

0.9 Accept b > %
0.75 Accept b > %
0.67 Accept b > %
0.5 Accept b > c

0.33 Accept b > 2c
0.25 Reject b < 3c
0.1 Reject b < 9c

 

 

 

 

 

We can now go on to plot this information onto figure 2, in order to show in
which portions of the graph our population lies (shown by the ‘Accept’ and ‘Reject’

regions below).

13

 

b/c

 

Accept

    

1 4 Reject

 

B-—————— ——_———————-_-—_-———_—_——————

 

_—————_————

 

o 0.23 0.33 0,5 1
p-value

 

 

 

 

 

 

 

Figure 3. Hypothetical field observations applied to the minimum benefit-cost curve.

14

No conclusions may be drawn concerning the area between p =0.25 and p =0.33,
since we have no data from within this transitional area.

It is important to note that this graph only represents one moment in time. Both
the costs and benefits of the EPCs are transient quantities, liable to change at any time
due to a number of factors, such as changes in the male population structure, the time in
the breeding season or even participation in an EPC. This point also influences one of the
predictions of the original proposition:

Since females are choosing strategies of ‘accept’ or ‘reject’ even before being
confronted by a prospective EPC male, one would expect them to either reject all
solicitations or accept the first that comes along,

I.e. (where R = reject and A = accept)

Either R, R, R, R
Or A, A, A, A
But not R, R, R, A

But since b and c may change, and performing an EPC is one factor that may
change these quantities, we may get A, R, R, R.

As a consequence, interesting insights into the factors that mediate such sexual
behaviours may be gained from observing a change in strategy. For example, instead of
interpreting the behaviour of rejecting a number of EPC propositions and then accepting
one as being characteristic of a female only wishing to copulate with a male of preferred
quality, rather we may investigate the factor that have caused a change in the cost: benefit

ratio to now make EPCs preferable.

l5

One of the predications of the model outlined above is that the predisposition of a
species or population to engage in EPCs will depend upon the degree of variation in
perceivable male quality. The important determinants of EPC behaviour are not only
those factors that affect the relationship of b and c, but also those that control p and the
female’s interpretation of p. It is therefore reasonable to presume that the a larger
distribution of male quality (i.e. of greater variance) will lead to a higher frequency of
EPCs, since with a reduction in male quality variance we have a resultant drop in the
possible values of b and c, and a corresponding drop in the female’s ability to assess

graduations in p. This prediction is examined later in this work.

16

The Strategies Compared

 

The Hermia strategy (only accept EPCs from superior males) predicts that all
EPCs that are observed will be with males superior to the female’s current partner
(assuming perfect discrimination on behalf of the female). Will Helena result in some
EPCs being with inferior males (as is often the case in the data) and will the proportions

of EPCs with superior males be comparable between the two strategies?

1) Hermia.

Frequency

 

 

 

 

Male Quality

Figure 4. A Gaussian distribution of male quality and the Hermia strategy.

I.e. A female mated to male Y will accept an EPC from Z, but not with X. So

100% of EPCs will be with superior males. It is important to remember that we are only

17

concerned with EPCs in which the females choose (i.e. Accept or Reject, or actively seek)

and not forced EPCs.

2) Helena.

Take 10 females mated to 10 males, with male quality distributed as follows:

 

 

 

 

 

 

 

 

 

 

 

D
E
B F H
A c G 1 J
Male Quality

Figure 5. Discrete distribution of male quality in a population of ten males mated
to ten females.

The p—variables (proportion of males in the population superior to their own mate)

will be as follows:

A: p=l
B&C: p=%
D,E,F&G: p=%
H&I: p=%
J: p=0

l8

Let us make the assertion that:

Moving up one place gives a benefit of one, up two gives two and so on.
Similarly, moving down one place has a cost of one, down two gives a cost of two, and so
on. For example, if a female mated to B accepts an EPC with H, she will receive a benefit
of 2. For the purposes of this example, there are no costs or benefits associated with
accepting an EPC from a male of equal quality to their own.

We can now calculate the average benefit and cost to each female of accepting an EPC:

 

 

For A: Benefit: ((2 x 0+ (4 x 2); (2 x 3)+(1x 4)) = 2.22
Cost: 0
ForB & C: Benefit: ((4XI)+(2:2)+(1X3»=1.57

Cost: (1x1)=1

 

For D, E, F & G: Benefit: ((2 x I): (1" 2»=1.33

Cost: «2"1)+(1"2» 1.33

For H & I: Benefit: (1 x 1) :1

Cost: ((4x1)+(2:2)+(1x3))=1.57

For J: Benefit = 0

Cost = ((2xl)+(4x 2);.(2x3)+(1x4)) : 2.22

19

9

. . . . c
Now puttlng these values 1n to the equation ‘Accept 1f p > —b—— :
+ c

For A: 1 > ——O—— Therefore Accept
(2.22 + 0)
1
For B & C: 7 > —— Therefore Acce t
A (1.57 +1) p
For D, E, F & G: /9<1 33 Therefore Reject
(1. 33 + 1. 33)
For H & I: /<1 57 Therefore Reject
(1 +1. 57)
For J: 0 < —2'2—2— Therefore Reject
(0 + 2.22)

So with Helena, the only females that should accept EPCs are those mated to A, B
and C, whilst with Hermia, all females except that which is mated to male J will
potentially participate in EPCs. The word ‘potentially’ is important here, since although 9
out of 10 Hermia females could plausibly partake in such behaviour, the likelihood that
they would do so depends on the quality of the male encountered, since not all encounters
will be with superior males. We can calculate the probability of any individual EPC
proposition being accepted by simply totaling the fraction of superior males for each

female and dividing by the total number of females:
1 I+(lit—Zitfihhthan
10 9 9 9 9 9 9 9 9

20

Since this prerequisite of higher quality does not apply to the Helena females,
then for them the probability of any EPC proposition being accepted is simply the
fraction of females that fall into the accept category, i.e. 3 out of 10.

It is also interesting to compare the two strategies in relation to the fraction of
EPCs that are with inferior and superior males. For Helena, 100% of A’s EPCs will be
with superior males, and 8 from 9 (88.9%) of B and C’s will be with equal or superior
males. So any single EPC observation will have a probability of

(1+ 0.889 + 0.889)
3

 

= 0.926 of being with an equal or superior male, and 1 minus this

number (7.4%) will be with inferior males. Needless to say that with Hermia, all EPCs
will be with superior males.

All this is shown with greater clarity in Table 3 below.

Table 3. Comparisons of predicted EPC activity under strategies of Hermia and Helena
in populations of ten couples.

 

 

 

 

 

 

 

Hermia Helena
Number of females. 10 10
Number of females potentially participating in EPCs.

9 3

Probability of any EPC proposition being accepted. 0.411 0.3
Probability of any one of the EPCs being with an equal or
superior male. 1 0.926
Probability of any one of the EPCs being with an inferior male. 0 0.074

 

 

 

2]

 

So what insights may be gained from this? First of all, with Helena we can expect
some EPCs to occur with males of lesser quality than the attending male, which as
mentioned above, is in line with most published data. We may also test empirically the
difference in the probability that any EPC proposition in the population will be accepted
(in this case: Hermia 0.411, Helena 0.3). Further modelling would need to be performed
to assess how these figures vary over different p0pulation sizes and different levels of
genetic variation (see later), but it appears possible that once a predictor of this factor had

been developed, one could distinguish between Hermia and Helena in the field.

22

EPCs and Genetic Variation

 

Let us now examine the relationship between EPC frequencies and genetic
variation that I mentioned briefly on page 16.

The model outlined above assumes that females are able to assess the quality of
their partner with respect to that of the other males in the population and make their
decision to accept or reject EPCs based on this assessment along with the average benefit
gained from an EPC with a superior male and the average cost of an EPC with an inferior
male. As a consequence, the number of females participating in EPCs will be a function
of the amount of variation in male quality, since more females will have the propensity to
engage in EPCs when there are greater differences in the quality of potential fathers. The
connection between the variation in male quality and genetic variation is made by
assuming that total genetic variation is positively correlated with the additive genetic

variation of the fitness-related traits”.

Below (figure 6) we have three populations, each consisting of nineteen females

mated to nineteen males, with male quality distributed as indicated.

23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F
G Population]
o=0.92

H Population2

I / O'=l.49

J H
B K O D I M
C L P E J N
D M Q B F K O Q

A E N R S A C G L P R S

Population3

o = 2.70 \

CEGJLNP

 

 

 

 

 

 

 

 

 

 

 

 

 

ABDFHKMOQRS

 

 

 

Figure 6. Three discrete populations with differing levels of male genetic variation.

24

To keep things simple, let us take the same cost-benefit payoff system as we did
previously, i.e. moving up one place gives a benefit of one, up two gives two and so on.
Similarly, moving down one place has a cost of one, down two gives a cost of two, and so
on. The actual cost-benefit payoff system that we choose to use is unimportant; varying it
in terms of making the costs or benefits more or less important with relation to the other
will only increase or dampen the resulting trends. Under this scenario, the average
benefits and costs to each female of participating in an EPC can be calculated, as is

shown in table 4.

25

Table 4. Average benefits and costs of participating in EPCs for each female in three
populations with different levels of genetic variation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2 Population 3
Female Benefit Cost Benefit Cost Benefit Cost
A Mail 0 WA” 0 l+4+6+8+15+li:+14+l6+9+10=5” 0
2.11 3.17 5.27
B ETTJH” 1 4+IO+‘162+8+5 =2,“ 1 2mm.»12+11(;+12+14+8+9‘S3 1
1.43 2.44 4.53
C 1.43 1 2.44 1 2+4+9+s;;°+12+7+8 223.
4 1.5
D 1.43 1 .5"_sl‘2_°*_4=1,92 2:243: 4 1.5
1.92 1.33
E 1.43 1 1.92 1.33 2’6+°+:’3"°’6+7 =3.46 3%”.75
3.46 1.75
F L‘s—1:12 1.2 1.92 1.33 3.46 1.75
1.2
G 1.2 1.2 1.92 1.33 W491 M=216
2.91 2.16
H 1.2 1.2 ""3 =1.57 1.57 2.91 2.16
1.57
I 1.2 1.2 1.57 1.57 22:12.”, 2.63
2.63
J 1.2 1.2 1.57 1.57 2.63 2.63
K 1.2 1.2 1.57 1.57 2.63 2.63
L 1.2 1.2 1.57 1.57 2.16 2.91
M 1.2 1.2 1.33 1.92 2.16 2.91
N 1.2 1.2 1.33 1.92 1.75 3.46
O 1 1.43 1.33 1.92 1.75 3.46
P 1 1.43 1.33 1.92 1.5 4
Q 1 1.43 1 2.44 1.5 4
R 1 1.43 1 2.44 1 4.53
S 0 2.11 0 3.17 0 5.27

 

26

 

The p-variables can then be calculated as before, and by applying these, along

 

with the benefits and costs to our original p > b 6 equation, we get table 5. Only the
+ c

females up to and including the first to reject are shown, since all females mated to higher
quality males will reject also. The females participating in EPCs are shown more clearly

in the shaded regions in figure 7.

27

Table 5. Predicted number of females that would accept or reject EPCs in three
populations with different levels of genetic variation.

 

Population 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Females Accept or Reject? Total
p > ?
b + c
A
1 > 0 Accept
211+0 5
B D & E A t Acce t
, C, 0.77 > 1 ccep P
L43+1
F, G, H, I, J, K, L, 1.2 Reject
0.277 <
M & N 1.2 +1.2
Population 2
A
1 > 0 Accept
3J7+0
B, C A t
0.89 > 1 ccep
2.44 +1
D, E, F & G 0. 67 > 1.33 Accept 7 Accept
1.92 +1.33
K & L R ' t
H. I. J. 039 < 1.57 6160
1.57 +1.57
Population 3
A 1 > 0 Accept
527+0
B A t
0.94 > 1 ccep
453+]
C & D A t
tang-:5 a...
+
‘ 8 Accept
E & F A t
0.72 > ————I '75 ccep
3.46 +1.75
G H A t
8‘ 0.61 > ———2'16 ccep
2.91+ 2.16
K R ' t
I, J & 0.44 < 2.63 ejec

 

 

2.63 + 2.63

 

 

 

Population 1

Population 2

 

Population 3

 

 

7C Boi‘J L N P

IAIB D ,F Hf: K M 0 Q Rlil

Figure 7. The females that have the propensity to engage in EPCs in three populations of
differing levels of male genetic quality.

 

 

 

 

 

 

 

 

 

 

29

So one factor that appears to be important in determining levels of EPP are the
population levels of variation for fitness related genes, so it appears possible to use these
measures of variation to predict levels of polygamy. This idea is beginning to gain

1.23 has found differences in

increasing support from the literature; a study by Pertie et. a
the proportion of extra-pair young were significantly positively correlated with the
proportion of polymorphic loci, whilst another by Griffith“ has compared island

populations with those on the mainland and found that island populations are indeed

characterized by low levels of EPP.

In addition, the probability that any of the EPCs are with an equal or superior

male also varies between the three populations. These probabilities are as follows:

Table 6. The probabilities that any accepted EPC will be with a male equal or superior to
the female’s attending male, in three populations of differing genetic variation.

 

 

 

 

p 1 ti 1 17
0P“ a 0“ 1+ 4:48) 0.956
Population 2 1+ 2(1%87+ 4(1513) 0.889
P0P“'afi°“ 3 1+ (1%8i“ 211% 8 + 2(1418)+ 20213) 0 826
8 = .

 

30

So as variation in male genetic quality increases, the probability that any extra-

pair copulation is with an equal or superior male decreases. One more testable prediction.

Genetic = EPC ___ Probability of EPC
Variation Frequency Being With a Superior Male

Figure 8. As additive genetic variation in the population of males increases, the
frequency of females participating in EPCs also increases, yet the probability that
any one of these EPCs is with a male superior in quality to her partner decreases.

31

EPCs, Genetic Variation and Population Size

 

We now have a clear relationship between the number of females in a population
that will potentially participate in EPCs and the amount of additive genetic variation in
the population, so let us now examine how this relationship varies with regard to the
population size.

Four conceptual populations of differing sizes were set up, containing 11, 21, 31
and 41 mated couples, i.e. 22, 42, 62 and 82 individuals in total. The variation in male
quality was assumed to follow as close to a normal distribution as was possible. You may
recall from the three populations examined above that in the case of symmetrical
distribution of quality, the model predicted that all females mated to males to the left of
the median bar would potentially participate in EPCs, and all those on and to the right of
the median bar fell into our reject category. This statement, although true in this case,

only applies to this specific benefit-cost scenario. If one refers back to figure 2 and the
calculations that surround it, we can see that when b = c (i.e. % =1, the cost-benefit

ratio used in this analysis) then the p-variable that we find on the accept / reject crossover
line is 0.5. Since the median bar in this inquiry is representative of p = 0.5 one would
therefore expect (strongly, because within the confines of this model and its cost-benefit
payoff system, no other result is possible) that those females that are unfortunate enough
to have males that fall shy of this condition (left of the median bar, and p > 0.5) to slide
into the accept category, whilst the males of high quality (right of the median bar, and
p < 0.5 ) avoid the embarrassment of cuckoldry.

32

Taking this, we can now vary the number of females participating in EPCs by
simply varying the size of the median bar, and then calculating the variation in the
population. The size of the median bar is calculated by simply subtracting 2 x the number
of females participating in EPCs from the population size. The measure of variation used
was the standard deviation. How this relates to the ratio of polymorphic loci or gene
diversity measure is another question, but since all three attempt to measure essentially
the same thing, the standard deviation will suffice. An example of how the variation

measures were calculated is shown below.

In this example (figure 9), n =11 (the number of couples) and e represents the

number of females participating in EPCs.

 

Figure 9. Example of distributions used to calculate required levels of variation.

33

This process was repeated for each number of females that would potentially
participate in EPCs (i.e. up to 25:1 , re. Left of the median bar statement above) for each

of the four population sizes. The results are shown in Figure 10 below, in terms of an
estimate of the variation required in a population for one to observe x-number of females
participating in EPCs. The data has been significantly smoothed since each distribution
(such as those above) could have been set up in a number of different ways (e.g. for the
set on the left consider 3-5-3 instead of 1-2-5-2-1), besides, we are only concerned with
relatively general trends. Once again, It refers to the number of couples (or males, or
females). Despite the fact that in my calculations the number of females participating in
EPCs was the dependent variable, the axes could be switched to represent the actual order

of biological dependency.

34

14

 

12 . -

n._ _ /

 

 

 

 

 

 

 

 

 

Standard Deviation of Male Genetic Quality
0)
3
11
f1.“
\

0 5 10 15 20 25
Number of Females Potentially Participating in

Figure 10. The genetic variation required for x-number of EPCs decreases with
increasing population size.

The trend is self-evident. At larger population sizes, the genetic variation required
for a fixed number of females to have the potential to participate in EPCs decreases.
Looking at it another way, a fixed level of variation will result in a greater number of
females inclined to partake in EPCs in larger populations. What observations would
authenticate such a prediction? Proportionally higher EPC frequencies at higher

population sizes.

35

A Note on InbreedingDepression

 

With the present model, we so far have increasing EPC frequencies with
increasing male genetic variation, a trend that may be attributed to the increase in the
probability of an EPC resulting in a step up the good genes ladder, and is one that rings
true with the published data on the subjectn' 23’ 2". We must now consider the other
potential indirect genetic benefit to the female of participating in EPCs, that being
increasing the genetic variation of her offspring. If females were participating in EPCs to
reduce the risk of inbreeding then one might expect an EPC frequency - genetic variation
trend contrary to that expected under a good genes strategy since the risk of inbreeding
will decrease with increasing genetic variation. That is, one would expect higher
frequencies of EPCs in populations with low genetic variation, rather than the opposite as
Helena predicts. However, it is difficult to see the significance of such a prediction since
as mentioned above, not only does the published data, however limited, support the good
genes trend, but also the occurrence of inbreeding depression has been observed so rarely
in wild bird populations (Donald Beaver; personal communication) that the strength of
selection against it is unlikely to be particularly strong. It has also been pointed out that
competition between unrelated individuals within broods would probably negate any
advantages that may ensue from increased diversity'z' 25.

If increasing offspring variation were the sole motivation behind EPCs, then we

would see drastically different selection criteria by the females when choosing EPC males

than with the strategies discussed above. As is shown below, one would expect there to

36

be no female preference for EPC-male quality, since as is with recombination itself, any

initial reduction in offspring mean fitness would theoretically be offset by the greater

I
(a) (b) (C) l

___—__—
-———

 

 

 

variation within the brood.

Figure 11. Distributions reflecting the quality of potential EPC-males with respect to the
quality of the current partner (dashed line). (a) Increasing the genetic variation of
the offspring; any EPC male will do just fine. (b) “Hermia”; only superior males
are considered. (c) “Helena”; most EPCs are with superior males.

Finally, it is often found that the distribution of extra-pair offspring between
broods is skewed, with most broods having either all or no offspring fathered by an extra-
pair male”, thereby negating the EPC’s genetic variation benefit. Be sure to note that this
reasoning does not necessarily apply to the male’s motivation for engaging in EPCs, but
his concerns are outside the realms of this piece of work (although having more offspring
sounds like a pretty safe bet).

These arguments are probably sufficient to excuse me from attempting to squeeze
genetic variation benefits into my model of female choice, but I shall mention one more

reason for their exclusion. If inbreeding depression countermeasures were allowed entry

37

then one would be pushed to justify leaving out the myriad of other potential costs and
benefits of EPCs that one sees in the literature from time to time. As with the avoidance
of inbreeding depression, these direct factors (such as guarding against defects from
prolonged sperm storage or the avoidance of rejection costs, see reference 6 for a
comprehensive list) only apply, if at all, to certain species, populations or even
individuals, and so have no real place in a general model of choice behaviour. One is
therefore forced to return to the one thread that runs throughout all female birds’ attitudes

towards extra-pair copulations, that being the genetic quality of their offspring.

38

Some Conclusions

 

. Helena appears to be a viable alternative strategy to Hermia and allows us to begin

quantifying the indirect genetic benefits of EPCs to females.

- Helena predicts that a small number of EPCs will take place with males that inferior

in quality to the female's attending male, in line with the literature.

I If we are to assume that females' motivation to participate in EPCs is to increase the

genetic quality of their offspring, then we can expect higher levels of EPP with higher

population levels of variation for fitness related genes.

' Helena predicts that he variation required for a fixed number of EPCs decreases with

increasing population size.

39

Some Future Directions

 

I To develop a more general predictor of levels of EPCs and EPP to allow distinction

between Hermia and Helena in the field.

I To model Helena analytically to avoid the constraints and lack of clarity that arises

from the probability approach with discrete populations.

I To develop field studies to test the various predictions of Helena.

40

BIBLIOGRAPHY

41

 

10.

11.

12.

13.

BIBLIOGRAPHY

. Afton, A. D. (1985) Forced copulation as a reproductive strategy of male lesser scaup:

a field test of some predictions. Behaviour 92: 146-167.

Moller. A. P. (1985) Mixed reproductive strategy and mate guarding in a semi-
colonial passerine, the swallow Hirundo rustica. Behav. Ecol, Sociobiol. 17: 401-408.

Westneat, D. F. (1987) Extra-pair copulations in a predominantly monogamous bird:
observations of behaviour. Anim Behav. 35: 865-876.

Bollinger, E. K. and Gavin, T. A. (1991) Patterns of extra-pair fertilizations in
bobolinks. Behav. Ecol. Sociobiol.

Smith, S. M. (1988) Extra-pair copulations in black-capped chickadees: the role of the
female. Behaviour 107: 15-23.

Birkhead, T. R. and Moller, A. P. (1992) Sperm Competition in Birds. Academic
Press

Moller, A. P. (1988) Female choice selects for male sexual tail ornaments in the
monogamous swallow. Nature, Land. 322: 640-642.

Moller, A. P. (1991) Frequency of female copulations with multiple mates and sexual
selection. Am. Not.

Moller, A. P. (1991) Parasites, sexual ornaments and mate choice in the barn swallow
Hirundo rustica. In Bird-Parasite Interactions: Ecology, Evolution and Behaviour. J.
E. Loye and M. Zuk (eds), pp. 328-343. Oxford University Press, Oxford.

Moller, A. P. (1990) Sexual behaviour is related to badge size in the house sparrow
Passer domesticus. Behav. Ecol. Sociobiol. 27: 23-29.

Burley, N. T. and Price, D. K. (1991) Extra-pair copulation and attractiveness in zebra
finches. Proc. Int. 0m. Congr. 20

Trivers, R. L. (1972) Parental investment and sexual selection. In Sexual Selection
and the Descent of Man, 1871-1971. B. Campbell (ed.), pp136-179. Aldine-Atherton,
Chicago

Zuk, M, Thomhill, R. and Ligon, J. D. (1990) Parasites and mate choice and red
jungle fowl. Am. Zool. 30: 235-244.

42

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

Graves, J, Ortega-Ruano, J. and Slater, P.J.B (1993) Extra-pair copulations and
paternity in shags: do females choose better males? Proc. R. Soc. Land. B.

Moller, A. P. (1988) Female choice selects for male sexual tail ornaments in the
monogamous swallow. Nature 332: 640-642.

Cordeo, P.J., Wetton, J.H. and Parkin, D.T.(1999) Extra-pair paternity and male
badge size in the House Sparrow. Journal of Avian Biology. 30: 97-102.

Kempenaers, B. Verheyen G. R., Broeck, M., Burke, T., Broekhoven, C. and Dhondt,
AA. (1992) Extra-pair paternity results from female preference for high quality males
in the blue tit. Nature 357: 494-496.

Moller, A. P. and Birkhead, T. R. (1993) Cuckoldry and sociality: a comparative
study of birds. Am Nat 142: 118-140.

Stuchberry, B. J. and Morton, ES. (1995) The effect of breeding synchrony on extra-
pair matings in song birds. Behaviour 132: 675-690.

Jennions, M. D. and Petrie, M. (2000) Why do females mate multiply? A review of
the genetic benefits. Biol. Rev. 75: 21-64.

Parker, G. A. (1974) Courtship persistence and female guarding as male time
investment strategies. Behaviour 48: 157-184.

Petrie, M. and Kempenaers, B. (1998) Extra-pair paternity in birds: explaining
variation between species and population. TREE 13: 52-57.

Petrie, M., Domus, C. and Moller, A. P. (1998) The degree of extra-pair paternity
increases with genetic variability. Proc. Natl. Acad. Sci. 95 9390-9395.

Griffith, S. C. (2000) High fidelity on islands: a comparative study of extra-pair
paternity in passerine birds. Behavioural Ecology 11 265-273.

Parker, G. A. (1984) Sperm competition and the evolution of animal mating
strategies. In Sperm competition and the Evolution of Animal Mating Systems. R. L.
Smith (ed.),pp1-60. Academic Press, Orlando.

Moller, A. P. (1987) Mate guarding in the swallow Hirundo rustica: and experimental
study. Behav. Ecol. Sociobiol. 21: 119-123.

Mulder, E.S., Dunn, P. 0., Cockburn, R. A., Lazenby-Cohen K. A. and Howell M. J.
(1994) Helpers liberate female fairy wrens from constraints on extra-pair mate choice.
Proc. R. Soc. Land. B 255: 223-229.

43

 

28. Hasselquist, D., Bensch, S. van Schantz, T. (1996) Correlation between male song
repertoire, extra-pair paternity and offspring survival in the great reed warbler. Nature
381: 229-232.

44

 

       

  
     

IIIIIIIIIIIIIIIIIIIIII

1111111211111 i:iiiiliiiiil

021 7