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LIFE HISTORYAND SEXUALSELECTION

Patrick D. Lorch University of Toronto at Mississauga

A thesis submittecl in conformity with the recpirements for the degree of Doctor of Philosophy Graduate Department of Zoology University of Toronto

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Life History and Sexual Selection

Patrick D. Lorch University of Toronto at Mississauga Doctor of P hilosophy Graduate Department of Zoology University of Toronto 2000

Three of my thesis chapters use the fecundity by numbers of mates regression slope (Bate- man slopes) to understand how life history allocation patterns can influence the strength of sexual select ion. Males may typically experience st ronger sexual selection because the Bateman slope is Iarger for males than for females. In fact, the ratio of male over female slopes is a way of yuantifying sexual conflict over mating frequency. This conflict may explain the typically higher male motivation to remate relative to females. as well as most other sexual differences (e.g.. shoiviness of peacocks). Animals can allocate energy to different aspects of their life history. and how this allocation affects the strmgth of sexual selection is the central question of most of my thesis.

Chapter 2 develops a mode1 for hou sexual selection can be affected by particular life history allocation patterns. 1 focus on reversais in the strength of sexual selection (e.g. females compete for mates), using Bateman slopes for translating changes in allocation to mating effort into changes in the strength of sexuai select ion.

My third and fourth empirical chapters test predictions (from Chapter 2) about how the upper limit on sexud selection differs for males and females. Chapter 3 quantifies the effects of a life history t rade-off (between having functional wings and fecundity) on sexual differences in these upper limits. Chapter 4 tests predictions about the relationship between the male and female upper limits and the potential for sexual conflict over mating frequency. This chapter also examines why the male upper limit is not greater than the female upper limit as expected.

The last two chapters of my thesis are theoretical and do not involve Bateman slopes. Chapter 5 estimates the statistical power of a test designed to ask whether two traits are evolving in a correlated way across a phylogenetic tree. Chapter 6 contains an analytical mode1 of the forces that can cause sexual selection on females to increase. The mode1 examines how the potential sterility of male mates. or less costly risks like mates with ser-ratio distorters. can cause sexual selection for multiple mating in females. Dedicat ion

1 dedicate this thesis to our first child, coming soon, as if to give me something to do when the thesis is done. Acknowledgement s

Rather than repeat acknowledgements found in each of the chapters, I will use this space to thank my parents and my partner, and to acknowledge the role of my CO-authorsand rny supervisor. Without the tremendous faith, encouragement and support of my parents

I would not have been able to make it this far in what must seem to them an obscure and arcane profession. My wife. Andrea Case. has providd me wit h inspiration. corn fort and all kinds of support. She is the light of my life, the rose of my hcart . While working as a summer lab assistant. Luc Bussière conducted the matings involved in Chapter 3 along with entering most of the data. He went on to write the methods of that chapter and to critique drafts of it. Darryl Gwynne suggested the ex- perimeots that led to Chapter 3 and played a major role in designing them. He also guided rny thinking and writing for this and al1 the other chapters of this thesis. 1 am indebted to bot h Luc and Darryl for their tirne and enthusiasm. In the two remaining co-authored chapters. I did al1 the simulations and al1 the initial writing. John Eadie (in Chapter 5. which appeared in a recent issue of Systematic Biology) kept me from stepping too far out on a limb by applying his experience in using comparative phylogenetic tests to do behavioral ecology. He also devised the way we simulated perfect co-evolution and reigned in my unwieldy prose. Lin Chao (in Chapter 6. submitted to .-Lmerican .Vatu- ralist) realized that multiple rnating in fernales would only evolve under a limited set of conditions and suggested 1 work out exactly what the conditions were. He then came up wit h t hr Taylor expansion as an improvernent on my numerical solution to the problem

(though taking the partial derivative of this approximation was my idea). 1 would also like to thank both Lin and Xick Collins for encouraging me to build models. Finally.

1 would especially like to thank Darryl. everyone else at Erindale and Locke Rowe for providing such a wonderful atmosphere in which to work. Chapter 2 has been subrnitted to Arnerican .Vaturalist. Contents

1 General introduction

2 Role reversal and Bateman's principle . 5 2.L hbstract ...... 6 - 2 [ntroduction ...... 1

2.3 Themodel ...... 15

2.3.1 SIating ...... I5

2.3.2 Reproductive energy and fecundity ...... 17

2.3.3 Gift values and sperm allocation ...... 19

2.3.4 Uating distributions ...... 21 2.3. Sexual select ion gradients ...... *Pl-- 2.3.6 Error in previous analyt ical results ...... 25

2.4 Results ...... '16

2.4.1 Upper limit on sexual select ion ...... 26

2.4.2 Mode1 resuits ...... 30

5 Discussion ...... :38

1 Simmons and Parker ...... 4%

2-52 Arnold and Duval1 ...... 45

2.5.3 Futurework ...... 50

4 Summary ...... 51 2.6 Acknowledgments ...... 5%

2.7 Appendix ...... 53

3 Wing-dimorphism and the upper limit of sexual selection. 54 3.1 Abstract ...... 54

3.2 Introduction ...... 57

3.2.1 Backqoiind ...... fi2

2.2 Predict ions ...... 65

3.3 Materiais and Methods ...... 66 3.3.1 Collection and rearing ...... 66

3.3.2 Matings and courtship observations ...... 68 3.3.3 Egg counting. egg laying rates and hatching siiccess ...... 70

3.3.4 Measuring the upper limit on sexual selection ...... 71

3.3.5 Sperm transfer during copulation ...... 72 3.3.6 Statistics ...... 73

3 .4 Results ...... 74 3.4.1 Upper iimits on sexual selection for females and males ...... 74

- c. 3.42 Hatching success ...... 4,

3.1.3 Courtshipeffects ...... 79

3.5 Discussion ...... SO

3.5.1 Upper lirnits on sexual selection for females and males ...... 80

3.5.2 Courtship effects ...... 83

3.6 Conclusions ...... 86

3.7 Acknowledgements ...... $7

4 Potential for sexual conflict over mating frequency. 89 1.1 Abstract ...... 89 4.2 Introduction ...... 91

vii 4.3 Methods ...... 98

1.3.1 Rearing ...... 98

4.3.2 Datacollection ...... 100

1.3.3 Analysis ...... 102

3.4 Results ...... 101

4.1.1 Fernale body size ...... 107

4.4.2 Upper limits on sexual selection ...... 108

4.4.3 Spermatophore weight ...... 109

1.4.1 Failure of sperm transfer ...... II2

4.5 Discussion ...... 11-4

4.6 hcknowledgements ...... 1'11

5 Power of the concentrated-changes test . 122 5.1 Permissions ...... 123

5.2 Abstract ...... 124

5.3 introduction ...... 125

5.4 Methods ...... 132

5.5 Results ...... 143 5.5. 1 The effect of allowing gains only or both gains and losses ..... 1-14 5.5. The effect of white branches ...... 144

5.5.3 The effect of tree shape ...... 151

5.5.4 Number of taxa versus proportion of white branches ...... 156 5.5.5 Actual versus reconstructed changes ...... 160 5.6 Discussion ...... 161 5.6.1 The effect of white branches ...... 163

5.6.2 The effect of tree topology ...... 164

5.6.3 The effect of number of taxa ...... 166 5.6.3 The effect of the mode1 of evolution ...... 167 ... Vlll 5.6.5 Recommendations for Future studies ...... 169 5.6.6 Assumptions of our analyses ...... 171 5.7 Conclusions ...... 173

5.8 hcknowledgrnents ...... 174

6 Selection for multiple mating in females . 176 6.1 Abstract ...... 177

6.2 Introduction ...... 178

6.3 The mode1 ...... 182 6.3 Results ...... 186 6.5 Discussion ...... 194 6.5.1 Fitness gains with sterile mates ...... 195

6.5.2 Fitness gains with less costly mates ...... 197 63.3 Assessrnent of males by females ...... 198 6.5.4 Evidence frorn nature ...... '200 6.6 Acknowledgments ...... 204

7 General discussion 205 .1.1 Future directions ...... 108

References List of Tables

2.1 Example mating matrix for simulated populations ...... 15 2.2 Surnmary of variables used in nuptial gift mode1...... 55

4.1 Fernale size measurements and PCA coefficients ...... 107

5.1 Effect of mode1 of evolut ion . proportion of white branches and t ree balance on CCT significance ...... 1-16

5.2 Regression of two CCT probabilities on tree shape statistic ...... 151 5.3 Effect of mode1 of evolution . the proportion of white branches and the number of taxa on CCT significance ...... 157 5.4 Results summary...... 16.1

6.1 .4 symmetric changes in & ratio and relative fitness due to remating .... 191 List of Figures

2.1 Relationship between fecundity and number of mates ...... 8 2.2 Upper limi ts on sexual selection for males and females...... 27

'3.3 Sexual selection when fernale mate distribution is random ...... 31

2.4 Results based on empirical Mormon cricket distributions...... 32

2.5 Results based on empirical .\letaballus lit us distributions...... 33

2.6 Six empirical mating distributions ...... 3'7

3.L Predictedrelationshipsbetweentheupperlimitsonsexualselection.... 64

3.2 Mating protocol for estimating both male and female upper limits on sex-

tia1 selection ...... 69 3.3 Estimatesoftheupperlimitsonsexualselection...... 76

4.1 Estimates of the maximum fecundities of once and twice mated females . . 110

4.2 Effects of failure to transfer sperm on average maximum fecundity..... 115

5.1 Effect on the concentrated changes test of including white branches .... 1% 5.2 Relationship betiveen CCT and the proportion of white branches when

only gains are allorved ...... 1-15

5.3 Relationship between CCT and the proportion of white branches with both gains and losses ...... 149 5.4 Relationship between CCT and tree shape when only gains are allowed . . 152 5.5 Relationship between CCT and tree shape with gains and losses...... 154 5.6 Taxon number effects on the relationship between CCT probability 2 and

the proportion white branches when only gains are allowed...... 159

6.1 Female relative fitness as a funct ion of the proportion of "costly" males . 184 6.2 Proportional advantage to remating as a function of the fitness functioo shape...... 188

6.3 Proport ional advantage to remating as a function of the nurnber of mates. 189

6.4 Proportional advantage to reniating as a function of the proportion of costly males in the population...... 192 Chapter 1

General introduction

This thesis represents an attempt to find new ways to integrate life history theory with sexual selection theory. Natural selection acting on an animal's life history may affect the intensi ty of sexual select ion. t here by changing the effec t iveness of Iater kind of select ion in causing evolution. In what follows. I explore this possibility and a number of related issues t hat have corne up along the way.

Sly long-standing interest in combining life history theory and sexual selection theory began with a paper by McLain [1991]. In it he proposed (based on what is now a somewhat discredited dichotomy) that males in Ii selected organisms (with low fecundity and high levels of parental care) would erperience stronger sexual selection than r selected organisms (with high fecundity and low levels of parental care). McLain pointed out that variation in mating success explains a much higher proportion of variation in overall fitness in Ii selected as compared to r selected organisms. Variation in fitness would be dominated by juvenile mortality in r selected organisms. swarnping out effects of variation in mating success. Rather than view them as separate entities. McLain's paper combined life history theory and sema1 selection theory. After reading this paper.

1 began to try to find other ways to integrate these two bodies of t heory. CHAPTER1. GENERALINTRODUCTION 9-

The problem whose solution originally got me interested in finding a more integrated approach is the evolution of size dimorphism in birds [Andersson. 19941. In polyandrous birds (e.g. red phalaropes), sex roles are often reversed (females compete for mates. males do most of the parental care), and females are often larger than males. The conventional explanation for female-biased size dimorphism in polyandrous species has been that females are larger because sexual selection in the context of competition over mates has increased female body size relative to males [see references in Andersson. 1994.p. 2691.

However. there are a fairly large nurnber of bird species where the female is iarger than the male. but there is no evidence of sexual selection acting on females [e.g. most birds of prey: -4ndersson. 199.11. Which came first, the polyandrous phalarope or the egg? 1s reversed sexual six dimorphism a result of competition among females over mates. or did it arise first in the context of life history evolution [i.e. natural selection for increased female size: Andersson. 19941 and t hen lead to the evolution of polyandry*?

To answer questions like the one in the preceeding paragraph. i felt it would be use- hl to have a model for how changes in the allocation of energy to various aspects of an animal's life history affect the strength of sexual selection. One of the main goals of my thesis was to develop such a model based on the pioneering work of Bateman (1948. and Arnold and Duvall. 1994). 1 use the relationship between an individual's nurnber of offspring and number of times it mates as the basis for such a model. When the slope of the regression of fecundity on numbers of mates ( Bateman slope) is greater for females than for males. for example. sexual selection is presumed to be stronger on females than males. In Chapter 2 I use the Bateman slope approach. along aith distributions of nurnbers of mates for fernale katydids. to understand how sex-role reversa1 can occur when the arnount of energy adable for reproduction is reduced relative to the value of food gifts provided during mating (nuptial gifts). In this chapter 1 also develop CHAPTER1. GENERALINTRODUCTION 3 theory to understand what sets the upper limits on sexual selection for males and females.

The next two empirical chapters focus on estirnating the upper lirnit on sema1 se- lectioo in each sex. In Chapter 3, 1 use the Bateman dope approach to test predictions

(from theory in Chapter 2) about how a trade-off between Fecundity and having functional wings affects the upper limits on sexual selection for males and females. In insects such a trade-off is common. Long-winged individuals often have lower egg hying rates in females. and reduced remating rates and smaller nuptial gifts in males. These differences from short-winged forms should result in lower fecundity for both sexes. In long-winged forms there should also be a reduction in the upper limit of sexual selection and in the potential for conflict over mating frequency relative to wliat is expected in the short- winged case. The male iipper limit on sexual selection should exceed the female upper limit. Chapter 4 represents an attempt to measure the male and female upper limits on sexual selection in the absence of any trade-off between functional wings and fecundity.

This chapter also examines some of the pitfalls in estimating upper limits on sexual selection that can lead to female estimates exceeding male est imates.

The question 1 posed earlier. about the origins of female biased size dimorphism in birds. could be answered in a comparative phylogenetic context. Quantitative methods exist for testing hypotheses about evolutionary origins. However. when I began my thesis. nothing was known about the power and potential sources of bis in most of these methods. Chapter 5 represents an examination of poiver and bias for one test ( the concentrated changes test ) which allows test ing hypot heses about w het her one trait is more likely to evolve in the presence or absence of mot her trait. In the future 1 plan to use the statistical approach used in this chapter to test various hypotheses about the relationship bet ween life history evolution and sexual select ion. My penultimate thesis chapter has less to do with life history evolution t han it does with sexual selection. There is a fairly healthy subdiscipline in behavioral ecology dealing with the evolution of female multiple mating. Only rarely is it noted that hypotheses that can explain this phenornenon are basically explanations of what can cause sexual selection on females. This point becornes obvious when you think of t hese hypot heses as ways of producing positive Bateman slopes for females. For example if Fernales remate to obtain addi tional nuptial gift resources. their fecundity can increase wi t h additional matings. which will increase the intensity of sexual selection on females. Chapter 6 describes a mode1 for understanding the evolution of female multiple mating as a way of' reducing the cost of mating with males with genetic defects t hat can reduce female fitness (e.g.. males carrying driving X chromosomes that can cause females to 1ay al1 female broods). In other words.this cliapter examines the conditions under which a certain kind of explanation for female remat ing can cause sexual select ion on females. Chapter 2

Understanding reversals in the relative strength of sexual selection on males and females using Bat eman's principle.

BY Patrick D. Lorch

Biology Depart ment

University of Toronto at Mississauga CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 2.1 Abstract

Whenever the strength of sexual selection (SS gradient) is greater

on females than males, sex-role reversa1 is likely (Le.. females are

more cornpetitive for mates and males are rnore choosy). How-

ever, there is little understanding of how changes in life history

strategy (e.g.. allocating more energy to reproduction and less

to survival) affect SS gradients. To provide a direct link between

the evolution of changes in life history and SS. 1 constructeci a

mode1 that uses the relationship between fecundity and numbers

of mates to translate changes in the allocation of reproductive

energy into changes in male and female SS gradients. 1 show that

the amount of energy available for reproduction affects the up-

per liinit of these gradients for each sex. Nutritious nuptial gifts

increase the upper limit of SS on females. but the upper limit for

males keeps pace. Role reversa1 can occur only when nuptial gift

production reduces a male's ability to compete for fertilizations

within females. The shape of the distribution of mates among

females is also important. The difference between the gradients

for males and females shrinks and sex-role reversa1 is more likely

to occur both when large numbers of females have not rnated

and as the mean number of mates increases during a season. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 7

My mode1 represents a realistic way of converti~igchanges in life history strategy into changes in the SS gradients for males and females wit h important implications for understanding sex-role reversa1 and SS.

2.2 Introduction

Typical sex-roles are those in which males are more cornpetitive for mates than females and females are more choosy among mates than males. Un- derstanding what causes these sex-roles to reverse is critical to understanding what controls sema1 selection and the evolution of mating behavior because the same mechanisms involved in this reversa1 are believecl to ex-

plain most of the variation in the strength of sexual selection and tlius variation in mating systems [defined in terms of which sex has higher variance in mating success: Trivers. 1972. Clutton-Brock and Parker. 1993.

Andersson. 1994. Arnold and Duvall. 19941. Typical sex-roles are thought

to prevail in most animals because males that mate multiple times generally stand to gain more fitness than females. due to the stronger correlation

between the number of offspring his mates produce (fecundity) and num-

bers of mates [Figure 2.1: referred to hereafter as Bateman curves: Bate-

man. 1948, Arnold and Duvall, 19941. This asymmetry causes stronger CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIP LE.

O I 2 3 4 Number ot mates

Figure 2.1: The relationship between fecundity (offspring number) and number of mates

(line graphs) for a hypothetical population with typical sex-roles (Le.. males more cornpetitive. females more choosy). The histograms show the distribution of mates. The line graph and the histogram both represent factors that contribute to the strength of sexual selection. Females gain enough sperm from their first mating to fertilize their eggs. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 9 sema1 selection on males which can result in the evolution of exaggerated male secondary sexual characters and predominately polygynous mating sys tems.

Occasionally, the sex-roles are reversed- males are choosy. fernales are more cornpetitive for mates. and may have exaggerated secondary sexual characters [Darwin. 1871. Andersson, 199.11. Such reversals are thought to occur because females gain more fecundity by mating multiple times than males can. resiilting in a reversa1 in the strength of sexual selection so that it is stronger on females than on males [Bateman. 1948. Arnolcl and Diivall.

19941. In most eramples of sex-role reversal. females are able to increase their fecundity because each additional male offers t hem eit her siibstan- tial paternal care (of young or eggs) or meals (nuptial gifts). Examples involving paternal care include giant waterbugs [Smith. 1979. Iiruse. 19901. pipefishes [Berglund et al.. 1989, Vincent et al.. 1992. Berglund, 19951. and spotted sandpipers [Oring and Lank. 19861, among others. Examples t hat involve nuptial gifts are generally found in insects siich as prey-donating dance flies [Svensson and Petersson. 1987, Cumniing. 199.11, and liatydids that donate edible spermatophores [Vahed. 19981. If males provide al1 (or most) of the parental care or if nuptial gifts are relatively valuable (compared to female energy intake from foraging), then by mating multiple t imes. females gain access to additional care-giving males or additional CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 10 valuable food. It is believed that the strength of sexual selection can then be stronger on females than males, and sex-role reversa1 is likely. So sex- role reversal can occur when females gain more fecundity than males do by mating multiple times, but what causes reversals in the relative gains males and females receive from remating?

Sexual select ion t heoïy provides an answer to t his question. however . it is not integrated very well with Our understanding of how other aspects of animal life histories evolve. Current sema1 selection theory states that the relative parental investment of males and females changes the relative availability of the sexes as mates (operational sex ratio or OSR). thereby changing their poteritial rate of reproduction (PRR). and that parental investrnent is the important factor in determining which sex gains more by mating multiple times [LVilliams. 1966, Trivers. 1972. Emlen and Or- ing, 1977, Clutton-Brock ancl Vincent. 1991. Clutton-Brock and Parker.

19921. Because the overall level of parental investment determines the population growth rate. any parental investment by one sex is potentiallp available to members of the opposite sex [Trivers, 1942. Thornhill. 19861.

Therefore, the sex that will gain more fecundity by remating is the one that invests less effort (energy, time or risk) into the production or rearing of offspring [see Appendix B in Arnold and Duvall. 1994,for a proof by

Thomas Nagylaki]. So current sexual selection theory gives us a qualitative understanding of what controls sex-role reversal. But, without a more quantitative understanding, it is difficult to know how to translate changes in the allocation of effort to reproduction (i.e., changes in the life history) into changes in the strength of sexual selection. An example will clarify this last point.

Consider the origin and evolution of nuptial feeding in an insect mating system without parental care. Because the cost of making individual gametes is lower for males than for females. ancestral non-gift providing males will likely gain more by remating than females [as seen by Bateman.

1948.for Droaophila melanoguster],and the Bateman curves will be as de- picted in Figiire3.1. However. once nuptial gifts evolve [e.g.. in the context of occupying a female with a meal while inseminating her: Boldyrev. 1915.

Thornhill. 19761. remating females stand to gain fecundity from additional matings by converting food from males into additional eggs. This could cause the slope of the Bateman curve for females to rise in the direction of

that shown for males in Figure3.1. The evolution of nuptial gifts represents a change in life history strategy for males where they are allocating energy

to gifts that was previously used for other aspects of their life histoiy. The cost of gift production may be paid by a reduction in a male's ability to

remate [Gwynne, 19901. or to provide females with as valuable a gift or as

many sperm during each mating. Nuptial gifts can also reduce a malek CHA?TER0. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 1'2 ability to gain offspring by remating. These nutritious gifts may induce femaies to mate more often, increasing the likelihood of sperm competition, and thereby reducing the average rate of fecundity gain in males. In mating systems with nuptial gifts, females may gain more fecundity than males by remating and sex-role reversa1 may be the result . but this is not

always the case. For example. in several katydids role reversa1 does not

occur when high protein food is abundant (see below). Understanding

why nuptial gifts result in sex-rolc reversa1 in some cases and not in others

requises a more quantitative understanding both of the forces acting to

produce Bateman curves and of horv these forces are affectecl by changes

in the allocation of effort to reproduction.

Sex-role reversa1 occurs in several katydids where females gain addi-

tional fecundity mith each additional mate [and thus each nuptial gift:

Gwynne, l984a.b] . In Mormon crickets ( Anablus simplex. Ort hoptera.

Tettigoniidae). for example. the nuptial gift that males give to females

during mating is important enough to females to cause ses-role reversa1 in environments where food is scarce [Gwynne. 1981. 1984al. The same is true for another katydid. Kawunaphila nartee [Simmons and Bailey. 19901.

Sex-role reversa1 can be experimentally induced in these two katydids by limiting access to high protein food [Gwynne and Simmons, 1990. Gwynne.

19931. Nuptial gifts in Mormon crickets can weigh as much as 25% of a CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 13 male's body weight [Gwynne, 19811, and in environments where food is scarce, males do not reduce the size of the nuptial gift [relative to body mass; Gwynne, 1984al. This last fact means that in poor environments males are not likely to produce as many spermatophores even though there is increased demand for them from females [Gwynne. 1984al. In a third katydid, Metaballus litus. sex-role reversal has also been described as occurring in some habitats but not in others (Gwynne. 1985. for a dynamic model of M. litvs mate clioice in high and low cpality environments see

Crowley et al., 1991). Finally. for two of these katydid species there are data available on how frequently females niate with different numbers of males in field samples. And. for most populations sampled. there is information on whether they are typical or ses-role reversed [t hree for Mormon crickets and three for the Aiistralian katydid M. litus: Gnynne. 1981.

1984a. 19851. Together these facts make Iratydids. a iiseful mode1 system to examine conditions under which sex-role reversa1 is expec ted.

In this paper 1 develop a model for nuptial gift mating systems to assess the consequences of changes in the allocation of reproductive effort (e.g.. toward nutritious nuptial gifts) for sexual selection. This model uses the relationship between fecundity and numbers of mates (Bateman curves.

Figure 2.1) to understand how changes in the pattern of energy allocation to reproduction can translate into changes in the strength of sexual CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 14 selection on males and females separately. This novel approach allows an understanding of the causes of sex-role reversa1 that can be connected to the evolution of changes in an animal's life history. My goal is to explore some of the conditions under which sex-role reversa1 is expected to occur. 1 start with an examination of the upper limit on the rate at which male and female fecundity increases with multiple mating. 1 then use an individual based model to simulate a mating system witli nuptial gifts. and with that explore some of the links between life history evolution and sexual selection. This model allows me to explore the role of gift value and the frequency distributions of numbers of mates (the marginal distributions in

Figure 2.1) in determining the strength of sexual selection on males and females. The model can utilize arbitrary distributions of numbers of mates for females which allows me to test the effects of various theoretical and empirically derived mating distributions on the relative strength of sexual selection on males and females. Next, 1 compare my simulation results to results from an analytical model by Arnold and Duval1 [1994]. who predict that sex-role reversa1 should occur in a nuptial gift system only in very limited circumstances. Finally, 1 discuss the conseyuences of my model for

Our understanding of sexual selection and sex-role reversal. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 15

Table 2.1: Example mating matrix for simulated populations. A simple 5-by-5 mating matrix that represents how the individual-based model works. The rows and columns representing number of mates and fecundity are used to calculate the sexual selection gradients (partial regression coefficients removing the effects of trait values) shown in

Figures 2.3. 2.1 and 2.5. The box at the lower right shows means (same for males and females) and variances for number of mates and fecundity. See the model description (section 2.3.1) for details.

Mates Fccun- Sperm Energy Female

dity stored for t rni t

1 -3 3 4 5 "B@

Female ID

I Fecundity O 0 38 138 81 Male ( Sperm per mating o 0 3401 6325 2711 hleans !dale Female

Energy for mating 61.66 -15.94 68.02 126.5 54.23 Xlates 1 .I3 2.6 2.8

Male trait -0.77 -1.08 -0.44 0.93 -0.62 Fecundity 51 2714 45SO

2.3 The model

2.3.1 Mating

The model tracked individuals using a "mating matrizc" (see example in

Table 2.1) to represent all the matings in populations of 100 males and 100 females [see Arnold. 1994. Arnold and Duvall. 19941. I filled the mating matrix by following these steps in a computer program (T"code available CHAPTER3. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. upon request ) :

1. From a standard normal distribution, the program randomly assigned each individual a trait value which was used both to determine exactly how much energy it had available for reproduction and. for each male. his maximum iiumbers of mates and the chances that he mated successfully when he encountered a potential mate. This trait coiild repreeent a metric trait like body size [Partridge and Farquhar. 1983, Partridge et al..

19861 or a secondary sex character [Andersson. 19941. or it could represent condition [defined as resources available for siirvival and reproduction:

Rowe and Houle. 19961, and it was assiimed to positively influence both reproductive energy and mating success.

3. The program then randomly assigned each female a number of mates

based on either a Poisson distribution (with mean of 4: see section 2.3.4 below for justification) or an empirical distribution (Figure 2.6 and see section 2.3.4 below).

3. For each female. a male ntas randomly chosen from a pool of eligible

males. Males were removed from the pool when they had mated more than a maximum number of times. determined by dividing the amount of reproductive energy a male had (which depended on his trait value. see below) by the sum of the value of the nuptial gift (for a round of simulations. see below) plus two arbitrary energy units (defined below) set aside for sperm costs for each mating. Actual numbers of sperm per CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 17 mate were determined based on actual numbers of mates (see section 2.3.3 below) . 4. The program then decided whether the pair mated based on the nile: mate with a probability that is a linear function of the male trait value

[as in the open ended preference of Lande. 1981]. A rule like this would be expected to act when the outcome of male-male cornpetition or female choice depends on some trait of males that is correlated to the amount of energy he devotes to reproduction. Such a rule will also act in nuptial gift systems when there is a positive correlation between the speed at which a male produces gifts and his trait valiie. This rule had the desirable effect

of preventing males that mated often from giving fewer sperm per female

than less successful males. 1 determined male mating success this way

because male mating distributions are not known for most species where female mating distributions are known.

5. The program then repeated steps 3 and 4 until al1 females had mated their predetermined number of times.

2.3.2 Reproductive energy and fecundity

For simplicity 1 chose to focus on reproductive energy rather than the broader reproductive effort (which includes energy. time and risk). Before

mating, 1 arbitraxily assumed the reproductive energy available to each

individual (E; see Table 2.2 in section 2.7 for summary of symbols used CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 18 in the model) to be in linear proportion to their trait value (slope = 0.5) so that individuals with a trait value of O had the basic amount of reproductive energy ( Eo). Those wit h a positive trait had proportionally more than Eo, and those with negative values proportionately less. This linear relationship with a slope of 0.5 was assumed because 1 found no data to suggest any other sort of relationship. The linear relationship had the effect of producing equal variance in E regardless of Eo . Eo was fixed at either 100 or 200 arbitrary energy units for both males and females in

a given round of simulations. 1 set an energy unit to eclual the cost of

producing one egg. Males used reproductive energy for both nuptial gifts

and sperm: females used it only for eggs. Each time a fernale mated with a

given male she gained s, sperm (see below) that siibsecluently mixed with al1 other sperm stored in her reproductive tract. Females gained energy

with each mating in proportion to b (gift value in energy units. sec below)

and produced (E+bx/)/v, eggs (where v, = the cost of an egg or 1 energy

unit. xf = number of mates for females). Her fecundity was then eclual to

the number of eggs she prodiiced. Male fecundity by each fernale was pro-

portional to his share in her stored sperm (sperm lottery. see section 2.3.3

below). and his total fecundity was the sum of the number of offspring he

gained with each female. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

2.3.3 Gift values and sperm allocation

1 measured nuptial gift value in units of reproductive energy. Gifts cannot be so large that males give al1 their reproductive energy as gift and none as sperm. To ensure this, males with too little energy to mate once. successfully. were not allowed to mate. and the maximum number of mates was determined as described earlier. Thus one of the costs of multiple rnating and giving away multiple nuptial gifts is a liniit on the number of mates for a given male. 1 varied gift value (6) in units of 5 from 5 up to the largest value that did not result in fewer male mates than female mates (15 for Eo = 100 and 25 for Eo = 200) so that males could not give away al1 of their energy as gift and none as sperm. The nimber of sperrn males ejaculated into each mate at each mating was calculated as s, = (E - bx,)/u,/~, (where Eand b are as above. x, = number of mates for males. v, = cost of a sperm or 0.001 energy units. and Fm = mean number of mates fxmales in a simuiated population). With this moclel for sperm partitioning 1 assumed that the cost of nuptial gifts was also paid in part by reducing the number of sperm ejaculated into each female. which reduced a male's ability to compete for fertilizations mithin each of his mates (for other possible methods of paying this cost, see the Discus- sion. section 2.5). The mode1 also assumed that no sperm were transferred without a gift, a realistic assumption for most nuptial-gift systems [forced copulation in Panorpa scorpionflies being an exception; Thornhill, 19861. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 20

1 assumed sperm competition was by lottery (a male's fertilization success is proportional to the relative abundance of his sperm in a female), and no first or lat male sperm precedence occurred (as appears to be the case in two cricket genera Allonenobivs and Gyllodes; Howard and Gregory. 1993, Sakaluk, 1986: and in the katydid genus Decticw Wedell. 1991).

1 chose to make the number of sperm in an ejaculate (and therefore a male's sperm competitiveness) depend positively on the same trait that determines male mating success rather than make it depend on nuptial gift size. 1 did this both to keep the model simple. without too many unsupported assumptions. and so that 1 could fis nuptial gift value (at a constant proportion of average energy availability. Eo ) for a given round of simulations. Where it has been measured [Sakaluk. 1986. Wedell. 1991.

Gwynne and Snedden. 19951. success in sperm competition is correlatecl

to nuptial gift size. Rather than try to model specifically how nuptial gift value affects sperm allocation (with no data to suggest how this should be done). 1 fixed gift value for a given set of simulations and made s, proportional to E (where E depended positively on the male's arbitrary trait value). This meant that the number of sperm in a male's ejaculate and his sperm cornpetitive ability were positively related to his trait value. which

makes sense if the male trait value was related to his general condition.

Males in good condition should have more energy to allocate to al1 aspects CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. '21 of their life history [Houle, 19911. The way 1 modeled sperm competition has the advantage of making fewer assumptions about the exact relationship between sperm competition and nuptial gifts. Unless in nature there is a negative relationship between a male's trait value and his nuptial gift size, I would not expect the way 1 mode1 sperm allocation to give different results than making sperm numbers depend on nuptial gift value. which itself would probably be positively correlated with trait value.

2.3.4 Mating distributions

In al1 simulations 1 constrained the mating distribution of females to fit ei-

ther a Poisson distribution (mean of 4) or one of six empirical distributions

(Figure 2.6). The Poisson was used to simulate a random distribution of

female mates. .A mean of four was used because it is the upper limit of

field estimates from the distributions. Smaller mean numbers of mates

would make sex-role reversa1 less likely. and field estimates of the mean

numbers of mates acyuired by females range from two to four in Mormon

crickets [Gwynne, 1981. 1984aI and from two to three in the Australian

katydid Metaballus litus [Gwynne. 19851. The six empirical distributions

were derived from field caught female katydids from these two species. Col-

lection localities and the methods used to determine mat ing distributions

have been described elsewhere for both sex-role reversed and non-reversed

Mormon cricket populations [Gwynne, 1984a], for a Mormon cricket pop- CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 22 ulation whose mating system was unknown [Gwynne. 19931, and for both role reversed and non-reversed populations of M. litus [Gwynne. 19851.

Gwynne sampled the non-reversed population of M. litus twice over a two week period, which allowed me to examine the effects of within season changes in the mating distribution on the relative strength of sexual selection (on males and females). (Male mating distributions are determined by step 4 under Mating above (2.3.1).)

2.3.5 Sexual selection gradients

.Arnold ancl Duval1 (1994: Arnold. 1994) suggest using partial regression to measure the effects of remating on fecundity (slope of the Bateman curve) as a way of estimating the sexual selection gradient while controlling for the effects of correlated traits. The partial regression approach allows the removal of what many woiild consider natural selection effects from estimates of sexual selection gradients [Iietterson et al.. 19981. For example. if sperm numbers or nuptial gift value are positively correlated to male trait size. some of his increase in fecundity with each additional mate will be related to his trait size and not his ability to obtain more matings (though these may be correlated. as they are in my simulations). Likewise. if more fecund females are more attractive to males. part of their higher fecundity may be the cause of having more mates and not a result of it [Ketterson et al., 19981. For this reason 1 have used the partial regression approach. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 23

After simulating mating according to the rides described above, 1 used the mating matrix to find the actual fecundity and nurnbers of mates for each male and female. Then for each simulated population. 1 calculated the partial regression of fecundity on numbers of mates, controlling for the effect of trait value. The approach of Arnold and Duvall [1994] was sub- stantially different with regard to measuring sexual selection gradients for males, but riot so different for fernales. They estimate the sexual selection gradient for females as the slope of the regression of female fecundity on the niimber of female mates (Cov(m,x)/Var(x)) so that

mli [(l- k)q~!+ f emale gradient =

(where mll = mean fecundity of females who mate once. q = proportion of females that do not mate. k = the fractional increase in fecundity gained from each nuptial gift (see below). Zf = average female mating success. and of-! = variance in mating success among females) [see Arnold and Duvall. 19941. The way Arnold and Duvall modeled nuptial gifts was slightly different from the way 1 modeled them. They used a nuptial gift which was a fixed proportion (O 5 k 5 1) of the mean fecundity of females who mated once, while 1 used several arbitrary gift values in units of fecundity (no more than 0.13 of the mean fecundity of females who mate once). Their approach to measuring sesual selection on females will give results similar to the partial regression approach 1 use whenever numbers CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 24 of mates among females is not positively correlated to trait size (as was the case in my simulations).

For reasons of mathematical tractability, rather than use the regression coefficient. Arnold and Duvall estimatecl sexual selection on males as the partial derivative of mean male fecundity with respect to the mean number of mates among males,

- male gradient = -"If P& (where mf = mean fernale fecundity (mated and unmated). p = proportion of females that mate (1-cl), and H, = the harmonic mean mating success of females with one or more mates): calculating mean male fecundity as

(where +,= mean number of mates for males) [Arnold and Duvall. 19941. This approach assiimed no correlation between mating success and fecundity, and no cost to mating for males. My approach allowed a correlation

between mating success and fecundity and assumed a cost to remating for

males. It was important to include these improvements because without

them. the sexual selection gradient acting on males can be overestimated

(see Discussion (Section 2.5)). In order to compare my mode1 to that of

Arnold and Duvall, 1 calculated the sexual selection gradients using both CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 25 partial regression coefficients [Solial and Rohlf. 1981. hereafter referred to as the L method] and the two methods used by Arnold and Duvall (the -4D method; Equations 2.1 and 2.2 above). 1 used the mating and fecundity distributions from the simulations described above to calculate the partial regression coefficients and to estimate the parameters to be used in

Equations 3.1 and 3.3. 1 used means of the four sexual selection gradients thus obtained. based on 100 simulated populations, to decide whether role reversa1 had occurred (Le.. when sexual selection was stronger on females than males). for a particular combination of average reproductive energy and value of nuptial gifts.

2.3.6 Error in previous analytical results

By solving the inequality Eq. 2.2 > Eq. 2.1 (using Equations 2.1 and 2.2 from above). Arnold and Duvall [1994] show analytically that the strength of sexual selection will be stronger on males as long as plq is greater than . Due to an error in the derivation. this solution will only be approximately true when ~f is nearly ecpal to pH, (an unlikely event if female mating distributions have significant skew). The error cornes from substituting ~f for p Hz on the wrong side of the ineqiiality, making the inequality invalid except when T! is approximately equal to pH,. For this reason 1 do not report this inequality for the simulations. Instead. I have compared the estimates of the sexual selection gradients based on the two models CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. directly (as described above).

2.4 Results

2.4.1 Upper limit on sexual selection

1 begin by considering the upper limit on sexual selection. generated by remating. in order to describe the effect of different levels of reproductive energy on the strength of sexual selection independent of the effects of nuptial gifts. There is an upper limit on senal selection which is set for females by nuptial gift value and for males by the fecunclity of their female mates. First. for a hypothetical species assume that: al1 females have equal fecundity: there is no parental care; matings are not costly: and to start with there are no nuptial gifts (Figure 2.2.4. Females do not gain fe- ciinclity by remating (beyond the sperm from their first mating) so there is no slope to the line relating their maximum fecundity to number of mates

(no sexual selection on females). On the other hand t here is expected to be an increase in maximum male fecundity with each additional mate. and the rate at which it increases equals the female fecundity (if niales only engage in "ideal" matings where there is no sperm cornpetition. i.e.. they only mate wi th virgin females). Alternatively, if the hypot hetical males are allowed to transfer nuptial gifts to females. maximum female fecundity CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

-t- High. Mule -c. HLyh. Fzmulc & Low. Mukc & Luw . Pcinatc

Figure 2.2: The upper lirnit on sema1 selection is represented by the slope of the lines

where there is a large amount of mating energy (High) and a srnaIl amount (Low).Male

and fernale lines are shown separately. A represents the case for no nuptial gifts. B

represents the case where nuptial gifts are 0.5 fecundity units. and C represents the case

where nuptial gifts are 0.5 fecundity units (see text for details). The difference in slope

between male and female lines (AS) is not affected by nuptial gift value. Zluptial gifts

increase the upper limit on sexual selection on females. but males who mate with these females also get this advantage. When less energy is available for mating, the difference

between the upper limit of sexual selection on males and females is reduced (compare

ASH for High to ASL for Low). CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 28 can increase with additional mates (Figure 2-23 and MC).It increases at a rate equal to the effect of the nuptial gift on her fecundity. How- ever, nuptial-gift giving males (with ideal matings) keep Pace with these females. Their maximum fecundity now increases at a rate equal to the fernale's fecundity plus the boost in fecundity that she receives from the nuptial gift. When energy for reproduction is low. the relative uppeï limit of sexual selection on the two sexes (represented by the slope of the lines in Figure 2.2) will be more nearly ecpal euen when there are no nuptial gifts (compare ASH and ASL in Figure 2.2.1-C). Nuptial gift value has no effect on the difference between the maximum potential sexual selection on males and females. These results represented algebraically are as follows:

where F is the maximum fecundity (for females or males). A is the fecundity of a female before mating, 6 is the size of the nuptial gift (in units of eggs). and x is the number of mates (for males or females). In Figure 2.2 high and low reproductive energy levels are represented as differences in

A. The upper limit of sexual selection on males will be greater than for females whenever A + 6 > bor when il > O. The difference in the maximum strength of sexual selection (due to remating) on males and females (AS = A + 6 - b = A) depends on A alone and not on 6. Therefore, while nuptial gifts alone can cause substantial increases in the upper limit of sexual selection on females. they cannot cause role reversa1 except by reducing a male's mating potential and his success at cornpeting for fer-

tilizations (e.g., sperm competition. see below ). However. a reduction of the difference between the sexes in the upper limit on sexual selection can

result from reductions in energy available for reproduction. This makes it

more likely for sex-role reversal to occur when matings are not ideal and

some critical resource (such as protein rich food for katyclicls or parental care in shorebirds) is in limited supply.

For sex-role reversa1 to occur then. the average male must gain less

feciindity by reniating t han t lie average female-some t hing must prevent

males frorn obtaining their maximum rate of gain in fecunclity due to

remating. 1 believe sperm competition is principally responsible for pre-

venting males from reaching this ~naximum.When females mate multiple

times, a male's sperm have to compete with sperrn from her other mates

in order to fertilize her eggs. Kuptial gifts can increase the extent to mhich

sperm competition occurs if they cause females to mate more often. Also.

if males pay the cost of making nuptial gifts by reducing sperm production

(as 1 have assumed in my simulations) or by reducing the size of future CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 30 nuptial gifts, they will transfer fewer sperm to each mate, making the male less cornpetitive for fertilizations. It is important to note. however. that if males pay the cost of making nuptial gifts by simply mating less often (maintaining nuptial gift size and sperm number) and there is no increase in mean female mate number leading to increased sperm competition, the rate at which males gain fecundity by remating is not affected.

Individual males will be less able to clirnb up the Bateman ciirve. but this effect acting alone is not expected to lower the slope of that curve and

therefore is not likely to produce sex-role reversal. When. as in the case

in Mormon crickets. males are unable to produce as many nuptial gifts in

poor environments yet they rnaintain nuptial gift size [Gwynne. 1984a].

sel-role reversa1 woiild 11ot occur without sperm cornpetition. 111 other

words. if females did not mate multiple times. 1 would not expect sex-role

reversai to occur. 1 believe that this is a new perspective which may help

to explain why so few insects with nuptial gifts exhibit sex-role reversal.

2.4.2 Mode1 results

The mode1 results shown in Figures 3.3. 2.4 and 2.5 represent the aver-

age of 100 estimates of the four senual selection gradients (two partial regression coefficients using the L method and the partial derivative and regression coefficient for the AD method) for populations with 100 males and 100 females. Standard errors were less than 1.3 (smaller than symbols) CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

GiR value within basic mating energy level

+Malt L gdient +Fernale L gradient + Mdt AD gradient 6 Fcmole AD gradient

Figure 2.3: Sexual selection when female mate distribution is random. Females are assigned a mate number from a Poisson distribution (mean = 4). Points represent the average of 100 partial regressions of fecundity on mate number after removing the effects of trait size for males (filled symbols) and females (open symbols) separately for both

AD and L methods (see text section 2.3.5). SE of means are less than 1.3 and are not shown. The probability of rnating with a randomly encountered male depends on male trait value. The figure shows that the difference in sexual selection gradients between males and femdes is smaller and that role reversal occurs at smaller gift values when mating energy is lower. The negative male sexual selection gradient results from the fact that males in the low energy system cannot mate more than 5 times. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

A. NRR - Indim mcrdawi, CO; luiy 19111

- B. IU1- Antelop (I.U UT; Juiy 1981

I 1 s 10 15 ?U 3 5 il) 1s ?O 3 I1U :w Glfl value wlthin bdcmrlfng rnergy kvel

Figure 2.4: Simulation result s based on empirical Mormoncric ket distri butions. Females are assigned numbers of mates From: A. a population that \vas not role reversed (NRR. Figure 2.6A), B. a population that was role reversed (RR. Figure 2.6C). and C. a population whose mating system was not known ( UNIi. Figure 26E). Males in both sets of simulations mated with a probability proportional to tlieir trait value. Bars represent the average of 100 partial regressions of fecundity on mate number after removing the effects of trait size for males and females separately. SE of means are less than 1.3 and are not show. The distribution used in B (UNI{. Figure 2.6E) is dorninated by a large

number of females who had not mated (Figure 2.6E). In B. reversa1 only occurs at low mating energy levels. and in C the overall difference between male and female gradients is smaller than in A and B. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

2 C. RR - Vue. WA: Jin. 28.1981

Figure 2.5: Simulation results based on empirical .\.letaballus litus distribut ions. Fernales are assigned numbers of mates from a distribution from: A. a population that was not role reversed ( NRR. Figure 2.6B). B. the same population 12- 13 days later (RR. Figure 2.6D), and C. a role reversed population (UNI;. Figure 2.6F). Maies in both sets of simulations mated with a probability proportional to their trait value. Bars represent the average of 100 partial regressions of fecundity on mate number after rernoving the effects of trait size for males and fernales separatel- SE of means are less than 1.3 and are not shown. Sex-roie reversal does not occur in the simulations based on M. litus distributions. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 34 for al1 means and are not shown. Males and females are shown separately for both my model (L) and the Arnold and Duvall [1994] model (AD). All three figures show simulations of mean reproductive energy levels of 100 units on the left and 200 units on the right. Role reversa1 is considered to occur whenever the sexual selection gradient is larger for females than males (i.e., when male and female lines for each model cross).

The differences between my model and that of Arnold and Duvall are striking and consistent for al1 female mating distributions. Estimates of serual selection gradients on females are similar for both models (Fig- ures 3.3-2.5). They diverge only slightly at higher gift values (mith the L method yielding slightly higher gradients). The male estimates for the two models. however. differ greatly for all of the distributions. The AD

method estimates sexual selection on males to be rniich higher than the estimates from the L method. The estimates also continue to increase

wit h increased gift value making role reversa1 extremely ~inlikelywit h t his

model. The difference between the strength of sexual selection on males

and females is smaller when less energy is devoted to reproduction. as

was predicted for the upper limit on sexual selection. but role reversa1 is

not likely since male gradients keep Pace with female gradients regardless

of gift value. In what follows 1 will focus on the results based on the L

method, coming back to the difference between my model and the Arnold CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. and Duval1 model in the discussion.

The results shown in Figure 2.3 indicate that for a given gift value, the difference in sexual selection gradients between males and females is lower when the basic amount of reproductive energy is halved. This is in agreement with the results presented in the previous section. In acldition. when sex-reversal in Bateman curve slopes occurs in the siniulations. it occurs at a lower gift value with lower mean reproductive energy (Figure 2.3).

These results from the model match well with the observation in the field that role reversa1 occurs in environments where food is relativelp scarce.

Species that do not reduce the size of nuptial gifts in poor environments

[e.g., Mormon crickets and Requena verticalzs: Gwynne. 19901 would be more likely to reverse sex-roles in these environments. The negative mean sexual selection gradient seen in Figure 3.3 emphasizes the effects of the positive correlation between trait value and mating success among males.

It is only after removing the effects of male trait value that this gradient is negative. Since males with larger trait values have both higher average mating success and more reproductive energy. and because in this model

males (of a given size) who mate more frequently transfer marginally fewer sperm. the sexual selection gradient is negative after the effects of trait size axe removed. For the particular model parameters used to generate this negative gradient, larger males are mating so frequently that they CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 36 are transferring relatively small numbers of sperm and losing fecundity as a result of such frequent mating. (However, there is not a negative correlation between numbers of mates and numbers of sperm per female, r = 0.01). I will deal more with this result in the discussion. as it raises some important issues.

Figure 2.4 shows that in addition to the effects of the level of reproductive energy and of gift value. the distribution of fernale matings is important (see Figure 3.6 for empirical female mating distributions). A sex reversa1 in Bateman curve slopes did not occur when data from the

.'typical roles" or non-reversed Mormon cricket population were iisecl to constrain female matings (Figure 2.4X, though the gradients are very close for low average reproductive energy with a large gift). Sex-role reversa1 only occurred at low reproductive energy levels when the distribution from the sex-roie reversed Mormon cricket population were used to constrain female matings (Figure -AB).Sex-role reversa1 occurred at both reproductive energy levels in simulations based on the unknown sex-role distribution for Mormon crickets (Figure 2.E). Interestingly. the differences between male and female gradients were dramatically lower with the unknown distribution which contained fernales who had not mated (even for the gradients using the AD rnethod). CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

b NRR - Indh mcdowr. CO; B. NRR Du-, WA; Jin. IS, 1981 0.71

C. RR - AaIciOp nciU UT; P. NRR - Dunrbomub.- WA; ,,,, Jm.n-u, 1981 C 0.35, 3 O. 16 O g 1). 12 u."8 * 0.1 PL II

E. UNK - Pduwi. !MT;JUIW 1990 F. RR - Vur. WA: 0.4 1

Figure 2.6: Cornparison of the six empirical distributions (Mormon crickets on the left and i\.letabulus litus on the right) for numbers of mates among females used in the mating simulations represented in Figures 2.4 and 2.5. Lines represent the Poisson erpectation with the sarne mean (2.95 for A, 1.61 for B, 3.71 for C, 2.29 for D. 2.39 for E and 3.25 for F). NRR = not role reversed. RR = role reversed and UNI< = unknown. Names and dates indicate population descriptor used in original papers (see Section 2.5.4). CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 38

When the female mating distribution is constrained using the field data on Metaballus litus. sex-sole reversa1 does not occur (Figure 2.5A). The male and female gradients are close (within one standard error of each ot her) for relatively expensive gifts at low reproductive energy levels when the distribution of the behaviorally role reversed population is used to constrain female matings. The two time-staggered saniples (almost two weeks apart) from the same population at Dunsborough (Figure 2.6B and

D) give us some insight into how changes in the average female mating success can affect the relative strength of sexual selection on males and females. .As the modal number of mates for females shifts from one to two. the difference in the strength of sexual selection on the two sexes shrinks

(compare Figure 2.5A and B). As was the case for al1 female inating distributions. the sexual selection gradients for males and females are more similar when the amount of energy available for reproduction is lower.

2.5 Discussion

Using the relationship between fecundity and number of mates. 1 have developed a mode1 for understanding how changes in energy allocation translate into changes in the relative strength of sexual selection on males and females. The rate at which the upper liniit of sexual selection in- CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE, 39 creases with additional mates for males ecpals the fecundity of females

(including any increases in fecundity she gains by mating) and for females the upper limit equals the value of nuptial gifts. The difference between male and female upper limits decreases when there is less energy available for reproduction and does not depend on nuptial gift value. Sex-role reversal. therefore, is more likely to occur when there is less reproductive energy available simply because the upper limit on the strength of sexiial selection is more nearly equal for males and females. This is in agreement with empirical observations that show sex-role reversa1 can be induced by experimentally reducing the protein content of food. requir- ing males to have less to allocate to reproduction [Gwynne and Simnions.

1990. Gwynne. 19931. or when the presence of gut parasites reduces nutri- ent uptake [Simmons and Zuk. 1992. Simmons. 19931. Nuptial gifts allow females to gain fecundity by remating and are therefore necessary to cause sex-sole reversal. but they are not sufficient by themselves. Without sperm cornpetition to psevent males from reaching their maximum rate of gain in fecundity due to remating, sex-role reversal will not occur. If. on the other hand, giving additional nuptial gifts reduces a male's sperm cornpetit ive abilities, nuptial gifts can play a role in leading to ses-role reversal.

1 have also developed a mode1 that explores some of the effects of nuptial gift value and the frequency distribution of female matings on the CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 40 strength of sexual selection. The model links changes in the allocation of energy to reproduction directly to changes in the relative strength of sexual selection on males and females. Sex-role reversa1 is more likely. based on my model. when nuptial gift value is a large proportion of reproductive energy, and tliis is because in my model males that mate often transfer marginally fewer sperm (though not enough to produce a negative correlation between a male's nurnber of mates and the number of sperm he transfers to each female). In contrast. the results described here. based on the model of Arnold and Duval1 [1994], show that if there is no variation in the sperm competitive abilities of males. the likelihood of sex-role reversa1 does not increase with nuptial gift value. The distribution of mates arnong females also has important effects on the likelihood of sex-sole reversal. If there rire large numbers of females that have not mated (Figure 2.6E).the difference between females and males in the strength of sexiial selection is smaller (Figure 2.K). This is true primarily because having large numbers of females unmated (as might occur early in the mating season) increases the average sexual selection gradient for females that do mate-there are relatively more males available for mating and nuptial gifts.

Using Bateman curves to understand the upper limit on sexual selection and the resulting realization that sex-role reversa1 will not occur without sperm cornpetition to prevent males from obtaining their maximum fe- CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 41 cundity has important consequences for our understanding of sexual selection. For example, this new perspective highlights the asymmetry between males and females in their certainty of seeing returns on investments in reproduction. Investment by females in making and laying eggs cannot be wasted or diverted in the way that niale investment in sperrn and nuptial gifts can, when his mates have copulated with other males. When overall reproductive energy is scarce. sex-role reversa1 is more likely to occur. not only because males will have difficulty producing nuptial gifts. but also because females may gain relatively more fecundity by remating than by foraging, giving them incentive to remate. This incentive coiild lead to higher average levels of sperm cornpetit ion. furt her reducing average male

Bateman slopes. In other words. nuptial gifts. which may have evolved as a way of increasing insemination success [Boldyrev. 1915. Thornhill.

19761 and therefore sperm cornpetitive ability. rnay have made possible a situation where fernale mating frecpency increases. leading to subsequent reduct ions in siring success.

Ultimately. the new perspective 1 am proposing could also affect how we view the evolution of mating systems. The difference in the strength of sewal selection on males and females is what is important in explaining the evolution of mating behavior [and of sexual dimorphism generally: see Figure 7 in Arnold and Duvall, 19941. The Bateman dope perspective CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 42 makes this explicit. A primary determinant of the magnitude of the difference between male and female Bateman dope is the extent to which male sperm compete for fertilizations within the average female. If males pro-

vide females with nuptial gifts or provide parental care, females can gain

fitness by remating. Once this is true. the average number of mates among

females will determine how intense sperm cornpetition will be. which will

in turn determine the difference between the sexual select ion gradients

acting on males and females. When this difference is large. we expect the

sex experiencing stronger sexual selection to compete actively for mates.

It is the outcome of this cornpetition. along with whether or not both

sexes gain some fitness by remating. that mil1 determine the distributions

of mates among the sexes, which in turn determines the niating system.

For example. in a species where there are relatively valuable nuptial gifts

(or paternal care). the higher the average number of mates among females.

the more likely sex-role reversa1 is because the sexual selection gradient

acting on females is likely to be greater than the one acting on males.

2.5.1 Simmons and Parker

1 am claiming that sperm cornpetition (and in particular reduced compet-

itive ability with increased numbers of mates) is important in determining

whether sex-role reversa1 occurs. This claim seems to contradict the results

of Simmons and Parker [1996]. These authors found that sperm compe- CHAPTGR2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 43 tition cannot affect male PRR and therefore cannot affect the likelihood of role reversal. However, their model depends on two assumptions: a) that there be no variation in male sperm competitive ability and b) that there is no correlation between male "time out" (defined as the time, due to mating, that males are out of the pool of potential mates) and factors like the number of matings a male has already obtained. In my model. both of these assumptions are violated (as rnight be expected in katydids or similar animals with nutritious nuptial gifts). The number of sperm the simulated males transfer depends both positively on male trait value and negatively on the numbers of mates he has, so there is definitely variation in nurnbers of sperm transferred by each male and consequently in sperrn competitive ability. Making the niimbers of mates a male obtains (x,) depend positively on his trait value (z,,,). is equivalent to making male time out negatively correlated to 2, and to x,. Simmons and Parker

[1996]make the important caveat that adaptive changes in time-out may occiir as a result of selection due to increased sperm cornpetition intensity. This in turn can lead to reductions in male PRR and to sex-role reversals

[Simmons and Parker, 19961. Males may allocate more sperm to each female to improve fertilization chances, which may require longer recovery times between matings ( particularly when large nuptial gifts are involved).

Indeed there is some evidence that in katydids with large nuptial gifts and relatively high numbers of mates per female, males are transferring CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 34 more sperm to females than do male crickets. with smaller nuptial gifts [Kawanaphila nartee and Repuena verticah females receive one and two orders of magnitude more sperm. respect ively, t han Gryllodes supplicans : Figure 6-7 in Gwynne, 19971.

There are two advantages (over previous explanations) of the model 1 have described for understanding sex-role reversal. First . this model advances Our understanding of role reversa1 by showing how the strengt h of selual selection is affected by changes in the allocation of energy to reproduction. In addition to being able to Say, for example. that sex-role reversal occurs in a species because the female potential reproductive rate

[PRR. Clutton-Brock and Vincent. 1991. Clutton-Brock and Parker. 19921 is greater than the male PRR. we can predict the consequences of changes in life history strategy (in terms of the allocation of energy to reproduction) for sesual selection. Second. we can use this model to examine conflicting selection pressures acting on traits such as nuptial gifts. For esample. nuptial gifts may have evolved as a way of increasing a male's insemination success [Boldyrev, 1915. Thornhill, 19761. However. t hese costly gifts also reduce a male's ability to remate. The relative importance of these two pressures on the strength of sexual selection can be evaluated using the model I describe. 2.5.2 Arnold and Duvall

The striking differences between rny model and that of Arnold and Duvall make the latter model of mating systems with nuptial gifts seem unre- alistic. When their model is applied to female mate distributions from populations that exhibit sex-role reversal. even when costly gifts are involved, sex-role reversa1 does not occur in the simulations. Indeed. the difference between the male and female sexual selection gradients is not noticeably srnaller with role reversed distributions as compared to simulation results for non-reversed distributions. This is in contrast to the results using my model. where wit h certain distributions. when gifts are cost ly. sex-roie reversal does occur. The difference between est imates of the strength of sexual selection on males from the L metliod and the AD method has two compouents. First. since in the simulations. males with larger trait values mate more often. removing the effects of trait value

using partial regressions explains part of the difference. This does not

explain al1 of the difference. however. The AD partial derivative method

always yields the highest estimates of sexual selection gradients. the re-

gression of offspring number on numbers of mates (without rernoving trait

effects) is next highest (the data are not shown), and the partial regression estimate (the L nlethod) is the lowest. So something additional is required

to explain the difference between the two methods. CHAPTER3. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 46

The second part of tohedifference between oiir two methods raises what some may consider weaknesses with rny approach to modeling nuptial gift mating systems. The rest of the difference between the gradients estimated using our two models arises from the fact that in Arnold and Du- vall's model. only sperm competition can reduce male fecundity as they continue to mate; males pay no fecundity costs when they mate with many fernales. In my model. sperm competition and the number of mates interact to reduce maximum male fecundity without reducing feniale fecundity. Though it is often assumed that male fecundity should depenci only positively on the niimber of mates he obtains (because sperm are relatively cheap). it seems reasonable to assume in nuptial gift systems

(especially when proteinaceous food is scarce) that males must pay for additional matings somehow. 1 have chosen to include this cost by reducing the number of sperm that males who mate several times transfer to each female. Another reasonable way to model this woulcl be to allow marginal decreases in gift value with increased numbers of mates for males

[Gwynne, 1984a, 19901. This effect alone would reduce the likelihood of sex-role reversa1 because female sexual selection gradients would be reduced. If the numbers of sperm males transferred also decreased with gift value [this is expected when the number of sperm inseminated depends on gift consumption time, as in some katydids. e.g.. Wedell. 19911, it is hard to predict the consequences for sex-role reversal. To make such a CHAPTER2* ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 44 prediction, it would be necessary to know the relative rates of decrease in both the average female fecundity (due to reduced gift value) and in male sperm competitive ability. To my knowledge, no such data currently exist.

If al1 that is needed to produce sex-role reversa1 is a positive Bateman slope for females and sperm cornpetition, 1 would have expected to see role reversals occurring using the AD method for at least some of the parame-

ter values. The fact that this was not the case emphasizes the importance of factors such as a trade-off between gift numbers and numbers of sperm among males (or other trade-offs that reduce the sperm competitive abil-

ities of males that mate multiple times). The AD method scales the male sexual selection gradient by the harmonic mean number of mates among females. However. it does not take variation in male sperm competitive

ability into account, nor does it take into account any correlations be-

tween these abilities and numbers of mates among males. Under these circumstances, sex-role reversa1 is very unlikely with the parameter values

1 have chosen. My method on the other hand results in sex-role reversals occurring with at least some of the parameter values in ways which match

fairly well with what has been seen in the field.

The mode1 1 am advocating is flexible in three important ways. First, the exact reason for changes in the energy available for reproduction is CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 48 not important for the results presented here. The consequences for sexual selection and for sex-role reversa1 are expected to be the same whether

the amount of reproductive energy varies due to changes in food availability [as is the case in three htydids: Gwynne. 1981, 1985. Simmons and Bailey, 19901, changes in foraging effort (e.g., when predation pres- sure decreases foraging), if parasites reduce food intalce [as with gregarine gut parasites of crickets and katydids: Sinimons and Zuk, 1992, Simmons.

19931, or if allocation patterns Vary for relatively constant resources [as is

seen when some insects rnaintain long wings for dispersal: Crespi. 1988. Iiaitala and Dingle, 1993, Mole and Zera. 1993. Crnokrak and Roff. 1995.

Roff and Bradford, 1996. Sakaluk. 19971. If less reproductive energy is

available. the strength of sexual selection on the two seses will be more nearly ecpal. making sex-role reversa1 more likely. This will be especially

true in animals with nuptial gifts (or paternal care) when the value of

the gift (or care) is a large part of the energy females otherwise devote

to their fecundity. So any change in the acquisition of resources or in

the allocation of those resources to reproduction can have important consequences for sexual selection and the likelihood of sex-role reversal. A

second important flexibility of this mode1 is that, as Arnold [1994] points

out, the exact nature of the relationship between fecundity and number of

mates need not be known. For most of the possible relationships between

these two variables, the partial regression estimate of the sexual selection CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCtPLE. 39 gradient will be a very good approximation of the more precise weighted average of tangents to any curve describing the fecundity by number of mates relationship [Lande and Arnold, 19831. Finally, since any arbitrary distribution of numbers of mates cm be used in the model. the model will be useful for examining the effects of the distribution of niates on sexual selection in more detail. For erample. it is possible that the female mate distribution from Polson, Montana (Figure 2.6E) represents a sample taken eariy in the reproductive season and that some females had not mated yet. When the season starts and as females hecome sexually mature, many will be unmated. As the season progresses, the distribution will stretch out and the relative nurnber of unmated females will shrink.

The difference in the strength of sexiial selection on males as compared to females should shift as the season progresses. We see evidence for this in the two staggered samples for fernales of Metaballus litus from the Duns- borough site. .As the modal number of mates for females increases. the difference in the strength of serual selection on males versus females decreases (compare Figure 2.3A and B). Exactly how the relative strength of sexual selection on males and females changes as the season progresses has important consequences for the evolution of mating behavior. however, it is largely unstudied up to this point [but see Iiruse. 19901. My model should make it possible to better understand the theoretical importance of these effects. Clearly, it would also be nice to know how sexual selection CHAPTER3. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

changes in the field over the course of a season.

2.5.3 Future work

In fact. this work calls attention to the la& of certain kinds of empiri-

cal data that would be useful in evaluating how life history evolution and

sexual selection interact. Because very little is known about how males

allocate reproductive energy to sperm and nuptial gifts. 1 have been somewhat arbitrary in the way 1 model this process. Therefore the model 1

present here should be seen as a first approximation that should be im-

proved upon when more is known about reproductive energy allocation.

We need to know how males dynamically allocate energy to the production - of nuptial gifts and sperm. and we also need to know how males allocate sperrn to their mates [but see Galvani and Johnstone. 1998. Wiklund

et al.. 19981. In addition to information on reproduct,ive energy alloca-

tion. there is clearly a need for data on parentage at the population scale

in the form of parental tables (as in Table 2.1). Only a few exaniples

of this kind of parental table exist [Meagher. 1988, Gibbs et al.. 1990. Meagher. 1991. Webster et al.. 1995. Prodohl et al.. 19981. Parental tables

such as these could be used to compare the relationship between fecundity and number of mates and to actually measure the relative strength

of sexual selection on males and females separately. Cornparison of these

tables between species or populations with different life history strategies CHAPTER2, ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 51 would be very useful for testing predictions arising from the model 1 ad- vocate here. For example, one could test the prediction that reducing reproductive energy (e.g., by manipulating diet quality) will decrease the difference between the strength of sexual selection on males and females even in systems where sex-role reversa1 does not occur. One coiild also use such parental tables to partition the effects of different sources of selection. for example, by comparing the sema1 selection gradients before and after juvenile mortality has occurred. Juvenile mortality might mag- nify, reduce or have no affect on the difference between the strength of sexiial selection on males and fernales [McLain. 1991.malies the daim that high juvenile mortality reduces the potential for sexual selection]. Arnold

[1994] also makes a plea for more "parental table" data and outlines ways that the parameters of interest can be estimated when they are not available. Finally. it is interesting to note that even if sex-role reversa1 does not occur in a species with valuable nuptial gifts (or paternal care). sexual selection on females can be quite strong, and the consecpiences of this for our understanding of sexual selection and mating system evolution remain unexplored.

2.5.4 Summary

The model 1 have outlined represents an example of how life history theory and sexual selection can be directly linked in such a way as to improve CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE. 52 our understanding of sex-role reversa1 and of sexual selection. Specifically, this mode1 allows a better understanding of how changes in the allocation of energy to reproduction can be translated into changes in the relative strength of sexual selection on males and females. We need just such in- sights to better understand the evolution of mating systems and sexual dimorphism.

2.6 Acknowledgments

Special thanks to Darryl Gniynne for providing mating distributions for

Mormon crickets and Metaballus litus. Thanks to Darryl. .Andrea Case.

Luc Bussière. Nick Collins and Locke Rowe for helpful comments. This

work was supported by a grant from National Science and Engineering

Research Coiincil of Canada to Darryl Gwynne. CHAPTER2. ROLEREVERSAL AND BATEMAN'SPRINCIPLE.

2.7 Appendix

Table 2.2: Summary of variables used in nuptial gift model. Variable Defini t ion

Reproductive energy available to an individual Reproductive energy available to an individual with an average trait value

Cost of making a single egg (one energy unit)

Cost of making a single sperm (0.001 energy units)

Nuptial gift value (in units of eggs)

Xumber of mates for females

Number of mates for males

Average number of mates for males

Proportion of females that mate

Proportion of females that do not mate ( 1 - p) Trait value (niales or females)

Xumber of sperm males ejaculate into each fernale Maximum fecundity (males or females)

Potential fecundity of females before receiving any nuptial gifts

Difference between the two sexes in the upper limit on sexual selection Chapter 3

Effects of wing-dimorphism on courtship and the upper limit of sexual selection in the swamp ground cricket Allonemobius socius (Ort hoptera: Gryllidae)

3.1 Abstract

Life history t rade-offs t hat affect fecundity have the potent ial

to influence sexual selection. and this influence may be differ-

ent for males than for females. For example, in species with

two wing lengths (wing-dimorphism),short-winged females may

have higher fecundity t han long-winged females. Males rnay gain CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 55

different numbers of offspring by mating with the two types of

females, and this will influence the potential for sexual selection

on males by changing the way males can gain offspring with ad-

ditional mates. If by mating with more fecund. short-winged

females, males can increase the number of offspring they sire

more rapidly. males may treat short and long-winged females

differently during courtship. Sirnilarly. long-winged males (who

must devote energy to wing-maintenance and flight) may also

have reduced ability to court fernales. or to provide them with

sperni or other substances while mating. This can influence the

potential for sesual selection on females by influencing whether

and how much fecundity they gain by remating. To assess the

importance of this influence. I staged matings between courtship-

feeding swamp ground cricket pairs ( Allonerno bius socius ) to es-

timate the upper limit on sema1 selection from the difference in

the fecundity of once and twice mated males and females. These

upper limits for males and females determine the potential for

sexual selection on the two sexes. The sex that has the potential

to gain more fitness by remating is expected to evolve more elab-

orate mating behavior and morphology [Bateman. 19481. 1 make

predictions for how the upper limit on sema1 selection will de-

pend on male and fernale wing morph assuming certain relative CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 56

values for courtship gifts and female pre-mating fecundity. 1 then test these prediction using the data on fecundity gains from remating in the staged ground cricket matings. In line with my pre-

dictions, there is a trend for female ground crickets to gain more

"potential" fecundity (higher than actual fecundity under natu-

ral conditions) when they mate with short rather than mith long- wingecl males. and long-winged females gain significantly more

than short-winged females. Male upper limits do not resemble

any of the predicted patterns. 1 discuss several reasons why this

rnight be the case. When feniales mate twice. the total time

pairs spend copulating-while the female feeds from the male's

hind tibia1 spur and while sperm transfer is occurring -is longer

wi th short-winged males than with long-winged males. Whether

or not a female has previously mated does not influence copulation duration. The time females spend carrying spermatophores

after the end of copulation does not depencl on male or female

wing morph. or on the whether or not a female has previously

mated. The total time double-mated males spent copulating was significantly shorter when long winged-males mated with short-winged females than the other three wing morph combina-

tions. A double-mated male's spermatophore remained attached

to females for less time in matings when both male and female were long-winged as compared to matings between long-winged

females and short-winged males. Finally, neither copulation du-

ration xior spermatophore carrying time were affected by whet her

or not a male had mated. I discuss the relevance of these results.

3.2 Introduction

Several authors have recognized that life history patterns can influence the strength of sexual selection. &lcLain [199l,based on what is now a somewhat discredited dichotomyl suggested that males in K selectecl organisms would experience stronger sexual selection t han r selec ted organisms because variation in mating success eiplains a much higher proportion of variation in overall fitness in the former as compared to the latter. Vari- ation in fitness would be dominated by juvenile mortality in r selected organisms. swamping out effects of variation in mating success. Other au- t hors [Andersson. 1994, Reynolds. 19961 have construct ed pat h cliagrams that included the influence of life history trade-offs on the strength of sexual selection, but these authors do not give specific examples of how these paths operate. Andersson (1994,Table 72.21, for example, says only t hat *'. . .life history and sexual selection will often be strongly interdependent." The goal of this paper is to give a specific example of how life history evo- CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 58 lution and sexual selection interact by demonstrating the effects of a life history trade-off on the potential for sexual selection acting on males and females separately.

1 will focus on insects with no parental care wliere both long and short- winged individiials occiir in one population (wing climorphism). because this trait is generally associated with a trade-off between the ability to disperse and female fecundity [Denno et al., 1989. Roff. 1986. Roff and

Fairbairn. 1991. Harrison, 1980. Zera and Denno. 19971. It is an example of a life history trade-off that in many insects is likely to affect the strength of sexiial selection (defined here as the rate of increase in fecundity with additional mates). Long wings are accompanied by muscles and estra fat* stores necessary for flight. while short wings often are not. Long-wingecl females in many such insects have reduced feciindity comparecl to short- winged females [Denno et al., 1989. Roff. 1986. Roff ancl Fairbairn, 19911.

If a male could mate with several virgin females who do not mate again

(ideal matings, i.e. no sperm cornpetition), the maximum rate at which he would gain offspring with additional mates equals the feciindity of an average female. So, the upper limit on sexual selection for males is set by the average fecundity of virgin females who mate once (Chapter 2).

Therefore, a male with only long-winged mates will experience less potential for sexual selection compared to a male with only short-winged mates. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 59

As a result, males might treat long and short-winged females differently during courtship.

A male's ability to provide nutritious gifts to females during copulation (nuptial gifts: seen in a number of crickets and katydids [Vahed. 19981) may be reduced by having and maintaining flight wings [Sakaluk. 19971. and this, in t urn. may influence the strength of sexual selection t hat acts on females. In mating systems where males offer nuptial gifts. females have the potential to gain fecundity by mating multiple times because the fernales can convert nuptial gifts into additional eggs. Therefore. there is the potential for sexual selection on females. In contrast to the situation for males. the strengt h of sexual selection on females is determined by the value (in terms of increased fecundity) of nuptial gifts. and the upper limit on the strength of this selection is set for females by the average value of nuptial gifts (Chapter 3). If a male's wing morph affects his ability to provide females with resources. females mating with only long-wingecl mates will experience lower potential for sexual selection relative to females mating with only short-winged mates. The trade-offs involved in having long wings can therefore influence sexual selection on males and females differently because the upper limit on sema1 selection depends on average female fecundity for males and average nuptial gift value for females. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 60

In fact. the force that produces elaborate courtship behavior and sexual dimorphisms in morphology is the difference between actual levels of sexual selection on males and females (as opposed to upper limits). This difference can be called "sema1 conflict over mating frequency" because differences in the rate at which the two sexes gain from remating can lead to conflict over mating frequency. When it is in the fitness interests of one sex to mate more frequently than the other. the conflict acts as a diver- sifying force that shapes mating behavior and morphological differences between males and females.

It is important to distinguish the upper limits that define the 'potential' for both sexual selection and sexual conflict over mating frecpency from the *actualqlevels of secual selection and conflict. In this paper 1 focus on the former because the upper limits on sexual selection can be quantified using controlled matings in the lab (see also Chapter 4) and because wing-morph should have a clear influence on these upper limits

(as explained earlier). Focussing on upper limits allows me to concen- trate on how the life history trade-off associated with wing dimorphism influences the potential for sexiial selection wit hout the complications in- troduced by sperm cornpetition in natural populations. Actual levels of sexual selection on males and females should be estimated from parentage information [e.g. rnolecular parentage data; Eiet terson et al.. 19981 from CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 61 natural populations. Trying to estimate actual levels of sexual selection in the lab requires the unsupportable assumption t hat sperm competition patterns in the lab are similar to natural patterns.

Note that in species with nuptial gifts. the upper limit on sexual selection for males will always ecpal or exceed the female upper limit. since males with each ideal mating (see below) will fertilize the eggs a female had before mating (her pre-rnating investment in eggs) plus any additional eggs made possible by nuptial gift resources. Additional matings for females only increase her fecundity by the the value of the nuptial gift.

The distinction between actual and potent id sexual select ion is impor-

tant because sperm competition can cause the actual strength of sexual selection on males to be lower than the potential in some cases (Chap-

ter 2). When this occurs, it is possible for females to gain more fecundity

than males from remating (on average) wliich can lead to a reversa1 in

the typical sex roles with females competing for mates and males becom-

ing choosy [Gwynne. 1991,and see Chapter 21. In this paper 1 focus on a

wing-dimorphic cricket species that is not known to e-xhibit sex role rever-

sa1 but where males feed females during copulation leading to the potential

for sexual selection on females. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 62

3.2.1 Background

The swamp ground cricket (Allonemobius socius, Orthoptera: Gryllidae:

Nemobiinae) is wing dimorphic throughout its range and the proportion of long-winged individuals (both male and female) increases sout hward in a north-south cline [Mousseau and Roff. 19891. Males engage in a complex. four phase courtship that includes: (1) pre-mounting calling by males which ends with a brief initial moiinting where genital coupling occurs briefly: (3) a second calling phase, where the male produces a small spermatophore. ending mith the female moiinting the male again: (3) copulation. where the female feeds on haemolymph that is extruded from a modified spur on the male's hincl tibia [Pantel. 1896, Fulton. 19311 while the male attaches an external. spherical spermatophore: and (4) post- copulatory guarding. after male and fernale separate. which ends when the female removes the spermatophore (often eating it ). Fiilton [1931] describes nemobine cricket courtship and mating behavior in more detail. The duration of phase three is the copulation duration. while the spermatophore remains attached through both phases three and four.

Males appear to have glands inside the tibia for adding substances to the haemolymph in tibial secretions (Mousseau. persona1 commiinication). Though much is known about the physiological differences between long and short-winged crickets [Roff et al., 1997. Zera and Mole. 19941. little is known about the function of tibial spur feeding [but see Fulton. 1931. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAI, SELECTION. 63

Bidochka and Snedden, 19851. If resources in this gift allow females to produce more eggs (or increase hatching success), females could gain fitness by remating and sexual selection could act on them. If long-winged males provide females wit h fewer resources than short-winged males, t his may affect the female upper limit on sema1 selection. Even if this is not the case. since long-winged A. socius females are known to procluce fewer eggs

[at least early in life: Roff and Bradford, 19961, different combinations of long and short-winged females are likely to produce different upper limits on sexual selection for males.

1 can estimate the upper limit on sexual selection for the sexes separately by mating males to two virgin females in succession and mating females to either one or two virgin males (ideal matings). The difference between estimates of "ideal" fecundity from once and twice mated individuals obtained in this way is an estimate of the upper limit on sexual selection (see Methods for details). It is possible to predict how these upper limits will depend on different combinations of long and short-minged mates based on female pre-mating investment in eggs and on the value of nuptial gifts (in terms of additional eggs). CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 64

Figure 0.1: Predicted relationships between the upper limits on sexual selection for males (open symbols and dotted heu) and females (closed symbols and solid lines) engaging in "ideal" matings in the four wing-morph combinations (e.g. L-S indicates a long-winged female mated with a short winged male), shown for various arbitrary levels of gift value and female pre-mating investment. [n cases A. B and D, female pre-mating investment was assurneci to be enough for 100 eggs by long-winged fernales and

200 eggs by short-winged females. For case C, females invested enough for either 50 or 100 eggs for long and short-winged females respectively. Short-winged males always give a gift that is twice as valuable

(in terms of eggs) as long-winged males unless (as in D) the gift has no value in terms of additionai eggs.

In case A long and short-winged males give gifts worth 50 and 100 eggs respectively. while in B and C they give gifts worth 100 and 200 respectively. The tables to the right of each part of the figure compare the upper limits on sexual selection for males and females (slopes of the lines connecting points on left). CHAPTER3. WING-DIMORPNISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 65

3.2.2 Predictions

Figure 3.1 shows predicted upper limits on sexual selection for a range of gift values and pre-mating fecundities. Since female upper limits are determined by the value of the nuptial gifts (and should not depend on female wing-morph), the value of the upper limit equals the nuptial gift value. and females almost always gain more fecundity by mating with short-winged males whenever these males give more resources (long-winged female with short-winged male matings (L-S: female-male notation used hereafter) and

S-S matings in Figure 3.1). If there is no gift or it cannot be convertecl into eggs, females do not gain more fecundity from short-winged males

(Figure 3.1D) and would not be expected to prefer to mate with short- winged males. Likewise. if male wing-morph does not affect male nuptial gift value, female upper limits should not be greater when they mate with short-winged males (not shown).

Male upper limits on sexual selection depend on both the gift value and on female pre-rnating fecundity (two components of average female fecundity). The relative value of these two factors determines the relative magnitude of the male upper limits for each of the four wing combinations (Figure 3.1). L-L matings will always produce the lowest potential for sexual selection on males regardless of the relative value of nuptial gifts. If gifts are less valuable than female investment in fecundity, S-S CHAPTER3. ~ING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 66 matings will produce the highest potential for sexual selection on males. S-L the next highest, and L-S the next highest (Figure 3.1A). If male and female investment are equally valuable (female investment in pre-mating fecundity = male investment per nuptial gift), 1 predict S-S matings will produce the highest potential for sema1 selection. with S-Land L-S matings the next highest (Figure 3.1B). If the gift is relatively more valuable than female investment. 1 predict that S-S matings will produce the highest potential for sexual selection on males. L-Sthe next highest. and S-L the next highest (Figure 3.1C).Finally. if there is no value to the gift (or no gift), the male upper limit on sexual selection depends on female wing morph and is greatest for S-L and S-S. and less for L-L and L-S matings

(Figure 3.lD). So, unless the nuptial gift has no value. the potential for sexual selection on males will be strongest in S-S matings and weakest in L-L matings.

3.3 Materials and Methods

3.3.1 Collection and rearing

1 collected approximately 17 male, 11 female and 99 nymphal crickets between 25 July and 10 August 1995 from around drainage ditches on the grounds of Southeastern Community College in Whiteville, North Car- CHAPTER3. WING-DI~IORPHISMAND THE UPPER LlMIT OF SEXUAL SELECTION. 67 olina. 1 used these individuals to found two laboratory populations, each in a 10 gallon glass aquarium (60 X 30 X 30 cm) with tops constructed of a wooden frame covered with silk screen cloth. Both cages were kept in an environmental chamber at 30°C. at high humidity and with a 14:10

(1ight:dark) light cycle. These rearing conditions averted diapause, producing a generation time of approximately 30 days. 1 fed crickets with fresh purina@ Classic catchowTM(ground in a blender) and apple slices. and provided water from cotton stoppered glass test-tubes (12 X 75 mm).

The cat food was changed once weekly, the apple was changed twice weekly and the water tubes were changed when dry. For egg laying substrate. each aquarium contained three moistened rolls of cheese-cloth in (5 drarn. 31 X 52mrn) glass vials. These rolls were replacecl on approxiniately 38 day intervals. and rolls containing eggs were unrolled and placed into ventilated clear-plastic boxes (10 X 6 X 6 cm. .AM.X.' Plastics). Nemly hatched nymphs were shalien from the cheesecloth into the populations cages twice a week for two months. For shelter and molting substrate. each cage had several pieces of paper towel and two hahes of an egg carton. Popula- tion cage densities ranged from 20 to 200 adults with varying numbers of nymphs. Roughly 50% of females ernerged as long-winged adults: a slight ly lower proportion of males were long-winged. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 68

3.3.2 Matiiigs and courtship observations

1 obtained virgin adults by separating groups of 5-10 late instar nymphs by sel, into clear plastic boxes (18 X 10 X 10 cm). On emergence, I isolated each adult into a smaller clear plastic cage (10 X 6 X 6 cm) for at least 5 days before mating. Feeding was as described for the population cages (see section 3.3.1 above).

From 1 July and August 1996, 1 paired both long and short-winged females with virgin, long and short-winged males according to the mating scheme shown in Figure 3.2. The resulting matings fell into four wing morph combinations (female-male: L-L. L-S. S-L and S-S). 1 paired half of the once-mated females with a second virgin male on each day after her first mating until she rernated: the other half were allowed to 11 eggs.

Between matings. females destined to mate twice were also allowed to lay eggs. A11 males used as a female's second mate were killed by freezing. 1 paired the males used as first mates for females with a second virgin female on each day after their first mating until they remated. After they remated thep were frozen. This scheme resulted in males who had mated twice in the same four wing-morph combinations as for females. Second mates were always of the same wing morph as first mates. 1 did not use males who failed to mate in two sequential pairings in the analyses of male upper limits on sexual selection. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 69

Fust matings Count eggs and measure lifespan

Second matings

Count eggs and 1 Count eggs and 1 measure lifespan 1 measure lifespan 1

Figure 3.2: Mating protocol for estimating both male and female upper limits on sexual

selection. The letter 'v' next to the male and female symbols indicates a virgin individual. Al1 males used in first matings were remated. Half of females were mated once and the other half were mated twice. hfter each female mated she was allowed to oviposit. The

fende upper lirnit on sexual select ion is the difference between the average fecundity

of fernales who rnated twice (box C) and females who mated once (box A). The male upper limit on sexual selection is simply the average fecundity of second mates (box B:

see Methods section 3.3.2 on p. 68 for details). CHAPTER3. WING-DI~~ORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 70

1conducted matings with one malelfernale pair in an open, clear-plastic box, lined with moistened blotter paper. These boxes contained a slice of apple and a paper label with identifying numbers and wing morphs for the pair. Two video cameras were used to record groups of four boxes

(separated from the rest of the room by a cardboard blind) so that various courtship parameters could be determined. Since spermatophore removal is sometimes clifficult to score from the video tapes. 1 verified spermatophore removal by checking pairs visually at five minute intervals after the pair separated. 1 therefore was able to estimate copulation duration to the nearest second and spermatophore attachment tirne to at least the nearest five minutes.

3.3.3 Egg counting, egg laying rates and hatching success

After mating (and between matings for twice-mated fernales) I placed females in individual cages containing rolls of cheesecloth for oviposition and fed them as described earlier (see section 3.3.1 above). Egg laying rolls were replaced on feeding days or when females remated. 1 counted eggs by unrolling the cheese cloth and inspecting it under a dissecting microscope.

Females were allowed to continue to lay eggs until they died. 1 recorded female lifespan in days, and 1 excluded females wlio lived less than a week af'ter mating from analyses. CHAPTER3. W~NG-DIMORPHISMAND THE UPPER LIMlT OF SEXUAL SELECTION. 71

For the sa.ke of cornparison to work on A. socius published since this study began [Roff and Bradford, 19961, I removed egg-laying rolls çeven days or less after a female's last mating and estimated egg laying rates for

the first week. This method was used to estimate egg laying rate because 1 rernoved rolls on feeding days (three or four day intervals) rather than on fixed intervals after a female's last mating [as in Roff and Bradford. 19961.

Due to time constraints, I coiild not follow the hatching success of al1

34.575 eggs laid by 148 females to determine how fecundity translated into fitness. Instead. during the experiment I uiirolled a subsample of

egg laying rolls (from 57 females) in the same ventilated cages described

earlier. and the eggs were allowed to hatch. 1 counted first instar nymphs to estimate hatching success.

3.3.4 Measuring the upper limit on sexual selection

1 estimated the female upper limit on sexual selection by subtracting the average fecundity of once-mated females (box A in Figure 3.2) from the av-

erage fecundity of twice-mated females (box C in Figure 3.2), estimating a separate upper limit for each of the four wing-morph mating combinations.

1 estimated male upper limits for each of the wing-morph combinations CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 72 differently. Since each male in the experiment mated twice, a more precise estimate of the male upper limit (which controls for inter-male effects: see also Chapter 4) is the average fecundity of each male's second mate

(box B in Figure 3.2). The fecundity of his second mate is precisely the number of offspring he gains by remating. Since both males ancl females were engaging in what we hoped were ideal matings. in what follows. we refer to gains in fecundity as gains in potential fecundity to indicate that these are upper limits on the amount of fecundity that can be gained from remat ing.

3.3.5 Sperm transfer during copulation

During this experiment. 1 found that sperm are transferred during copulation rather than after spermatophore transfer (as has been assumed in crickets in the past). When 1 accidentally interrupted the copulation of one esperimental pair. resulting in the spermatophore remaining attached to the male. the female laid 231 eggs. 1 allowed the last 19 eggs she laid to develop and al1 of theni hatched. 1 subsequently interrupted two pairs after five and 10 minute copulations and in both cases. in spite of the fact that the spermatophore remained attached to the male after separation. upon dissection 1 found her sperm storage organs contained live sperm.

These results clearly indicate t hat sperm are being transferred, not just after copulation, but during copulation as well. This pattern of sperm CHAPTER3. WING-DIMORPHISM.4ND THE UPPER LIMIT OF SEXUAL SELECTION. 73 transfer is known for several katydids that remain in genital contact during extended copulations [Boldyrev. 1915, Vahed, 19981 but has not been reported in crickets. Clearly both copulation duration and spermatophore attachment time are important determinants of how much sperrn is transferred to fernales.

3.3.6 Statistics

To determine how the upper limit on sexual selection was affected by male and female wing morph, 1 used different methods for the two sexes. For

the female upper limit. 1 used a fully factorial three-way ANOVA with female wing morph. male wing morph, and numbers of mates as nominal

factors. Significant interactions between number of mates and either or

both of the other factors would indicate differences between the female up-

per limits on sexual selection for the different wing morphs combinations.

For the male upper limit on sexual selection. 1 usecl a tnro way AY0V.A

on the fecundity of second mates mith female and male wing morph as

factors. Significant differences between the four wing morph combinations

would appear as significant main effects of either male or female wing

morph, or a significant interaction between male and female wing morph.

To examine whether male wing morph. female wing morph or numbers of

mates influenced eit her copulation durat ion or spermatophore attachment

time. 1 used a fully factorial repeated measures ANOVA with female and CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 74 male wing morph as factors and repeated measures of both response variables for first and second matings. To examine hatching success (hatching proportion of eggs sampled). 1 used a three-way ANOVA with the same factors as the analysis of female iipper lirnits on sexual selection (1 used untransformed proportions since 1 coiild find no transformatiori that would normalize the data). Since a number of the females whose hatching success was determined had no eggs hatch, 1 report likelihood ratio y' (' - R~') statistics from a logistic regression analysis that quantifies the association between whether a fernale's eggs al1 failecl to hatch and female wing morph. male wing morph or nurnbers of mates. When 1 report means. they are least squares means (& SE) from the above analyses. generated using JMP [SAS. lggi].

3.4 Results

3.4.1 Upper limits on sexual selection for females and males

There was a trend supporting the prediction that the feniale upper limit on sexual selection should depend on male wing morph. Female upper limits increased more when they mated with short-winged males (male wing morph by number of mates interaction: Fiees= 3.69. p = 0.06).

This trend was primarily driven by long-winged females gaining signifi- CHAPTER3. WING-DIMORPH~SMAND THE UPPER LlMIT OF SEXUAL SELECTION. 75 cant amounts of fecundity (really potential fecundi ty, since t hese are ideal matings) when they remated with short-winged males (L-S in Figure 3.3

, 153.1 f 49.5 eggs, t = 3.09, p = 0.003). though the second largest upper limit was for S-S matings as would be expected. The female upper hm- its for the other wing combinations were not distinguishable from zero (p values for al1 contrasts 2 0.65).

Although there was no significant effect of wing-morph on female lifetime fecundity = 0.16. p = 0.69), there was an effect on her egg laying rate early in life. Estimates of egg laying rate during the first mek of egg laying were only affected by female wing-morph ( FiVaî= 8.07. p = 0.006: and not by male wing-morph Fi,a2= 0.05. p = 0.82: or number of mates Fi,a2= 1.01, p = 0.32). which indicates that. although short- winged females laid eggs at a significantly higher rate than long-winged females (long = 12.3 f 1.6 eggs/day, short = 18.7 f 1.6 eggs/day ) , there was no evidence of an effect on the female upper limit on serual selection

(al1 interactions between numbers of mates and male and female wing morph had p 2 0.14). The difference in egg laying rate between female wing morphs disappeared in the second week (results not shown). Fernale lifespan is also not affected by her wing morph (long = 46.80, short =

42.91; = 2.48. p = 0.12), the number of mates she had (Fi,7a= 1.61. p = 0.21) or her mate's wing morph = 1.61, p = 0.21), nor any of CHAPTER3. WING-D~~~ORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 76

-- Male 746 133.3 242.4 181.1 Femde -37.3 153.1 7.3 21.9

Figure 3.3: Estimates of the upper limits on sexual selection acting on male and female A. socius engaging in "ideal" matings in the four wing-rnorph combinations (see Fig- ure 3.1 for notation). The table indicates the values of male and females upper limits

(the slopes of the lines in the plot ). CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 77 the interactions of these variables.

My results show that there was no significant effect of either male or female wing morph on the number of eggs laid by a male's second mate

(male wing: = 0.36, p = 0.55; female wing: Fi,3s= 1.22. p =

0.28: male*female wing: = 0.26, p = 0.62). Therefore. 1 could not statistically distinguish any of the predicted relationships between the male upper limits on sexual selection for the different mating combinat ions

(in Figure 3.1). A11 males gained potential fecundity by remating (pooling across wing morphs, mean fecundity of second mates = 219.45 It 18.34 eggs. t = 11.83. n = 40. p 5 0.0001). There was no significant difference between the fecundity of a male's first and second mates (pairecl t ratio =

0.20. p = 0.85). indicating that male A. socius appear to have the potential to gain as much fecundity from second as from first mates. Because most females do not gain fecundity by remating (females in L-S matings being the exception). while males gain in al1 wing-morph combinations. my data seem to most closely resemble the predictecl case where the nuptial gift has no value in terms of increased fecundity (Figure 3.1D).

3.4.2 Hatching success

Because the number of times that bot h males and females had mated did not affect the hatching success. and because only one twice-mated S-L CHAPTER3. ~ING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 78 female was sampled (al1 other combinations had between three and eight replicates), 1 dropped numbers of mates from the analysis of hatching success.

The proportion of eggs (from a sarnple female) that hatched was significantly affected only by the interaction of male and female wing morph

(Fi,5n= 5.97. p = 0.02). This effect was explained by a significantly lower hatching success in L-L matings than any other combination (contrast of L-L with the other three: = 7.183, p = 0.01). This coiild be due to a higher proportion of L-L matings failing completely (leading to more fernales with zero feciindity for this wing morph combination than for the other three). On the contrary, logistic regression results showed that the significant male by female wing morph interaction effect on the proportion of femaies whose eggs al1 failed to hatch (L - R~'= 4.04. p = 0.04) re- sultecl from S-L matings having the lowest success (4 out of 13 failures for S-L, compared with 2/11 for L-L. 2/13 for L-S. and 4/20 for S-S). Mat- ings involving long-winged males also resulted in a significantly higher proportion of failures (L- RXL= 8.57. p = 0.003) than for short-winged males (6124 compared to 6/33). Because 1 was unable to include number of mates in the analysis. it is difficult to say how these hatching success effects would affect estimates of the upper limits on sexual selection. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SGXUAL SELECTION,79

3.4.3 Courtship effects

I report results for two courtship parameters: copulation duration and spermatophore attachment time. Neither the number of mates nor the interactions of this variable with male or fernale wing morph had any effect on either of the courtship parameters. This was true for both females and males who had mated twice (p values for within subject effects > 0.3 for females and > 0.1 for males).

Females who had mated tswicespent significantly more time. over both matings. copiilating with short-winged as opposed to long-winged males

(sum of two copulation clurations for short = 1991.2 f 131.3 sec.. long

= 1536.2 f 146.5 sec.: Fi,Î4= 5.35. p = 0.02). There was also a trend for short-winged females to carry the spermatophore longer t han long- wingecl feniales (sum of two spermatophore attachment times for short =

3026.9 I 196.6 sec.. long = 3481.9 f 206.3 sec.: Fi,Î4= 3.66. p = 0.06).

So for single matings copulation durations averaged 996 sec. for matings with short-winged males and 768 sec. for long-winged male matings, and spermatophore attachment times averaged 15 13 sec. for matings involving short-winged females and 1241 sec. for mat ings involving long-winged females.

The only variable to affect both the total time spent copulating and the CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 80 total spermatophore attachment time for double-mated males was the interaction between male and fernale wing morph (total copulation duration:

= 5.38, p = 0.03; total spermatophore attachment time: = 5.73, p = 0.02). These interactions were of opposite sign, however, suggesting that they each had different explanations. The total time spent copulating in two S-L matings was significantly less than for the other three categories of matings (1381 sec. for S-L matings and an average of 2180 sec. for the other three: = 8.18, p = 0.007). On the other hand. two L-L matings resulted in marginally less total spermatophore attachment time than L-S matings (2120 sec. for L-L matings and 2903 sec. for L-S: = 3.73. p = 0.06).

3.5 Discussion

3.5.1 Upper limits on sexual selection for females and males

In line with my predictions, there was a trend (p = 0.06) for female ground crickets to gain more potential fecundity when they mated with short rather than with long-winged males primarily because long-winged females increased their pot ential fecundity significantly by remating wit h short-winged males. This indicates a trend toward a positive upper limit on sexual selection acting on females. Females in L-S matings have a sig- CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMlT OF SEXUAL SELECTION. 81 nificant upper limit on sexual selection (p = 0.003). Female wing morph did affect her egg laying rate during the first week (p = 0.006),but not her lifetime fecundity. There was no evidence from egg laying rates that male or female wing morph influenced female upper limits on sexual selection (interactions of male and female wing morph with number of mates. p 2 0.14). Male upper limits on sexual selection do not resemble any of the predicted patterns. While only females in L-S matings have significant potential for sema1 selection. males in al1 wing combinations significantly increased their potential fecundity by remating. These results most closely resemble the predictions for matings where the nuptial gift does not increase fernale feciindity.

The trade-off between fecundity and having functional wings that occurs in A. socius appears to affect the potential for sema1 selection only in females. and then only when long-winged females mate with short-minged

males. It might be the case that 1 would have detected more pronounced effects if the crickets had been under food stress during the experiment.

This would have made the gift more valuable relative to food from other

sources [Gwynne. 19881. In nature. animals will rarely encounter ad li-

bitum food, and detecting the phenotypic effects of life history t rade-offs

may be easier when the animals are food stressed. CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. g?

Roff and Bradford [1996]found significantly higher total fecundity (in the first 24 days after mating) and higher egg laying rates early in life (up to 17 days after mating) in short-winged females compared to long- winged female A. socius. 1 did not find significant effects of female wing morph on lifetime fecundity. but 1 did find that short-winged females laid eggs at a higher rate during the first week after they mated. The extra 2-3 weeks of egg laying by females in this experiment combined with slightly higher lifespan of long-winged feniales (average of 4 days) could allow long-winged females to make up for their lower fecundity early in life. Long-winged crickets can remove their wings and histolyze their wing muscles. allowing females to convert the energy and space saved into additional eggs [Tanaka. 1986. Zera and Mole, 19941.

Hatching success was lowest with L-L matings. Complete failure to hatch any eggs wu more common in matings involving long-winged males and most common as a result of S-L matings. One explanation for these results could be that long-winged males provide cues in the tibial spur se- cretion that trigger diapause in the eggs. 1 did not assess this possibility. Another unexamined possibility is that long-winged male tibial secretions provide less of substances required for proper development of eggs. There is evidence in two other cricket species. Acheta domesticvs and Teleogryllvs

comrnodus, that males provide enzymes or prostaglandins required to ini- CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 83 tiate oviposition. Whatever the explanation for reduced hatching success, the reduction could provide a selective force to increase female preference for mating with short-winged males [as seen in Gryllus fimus; Crnokrak and Roff, 19951. Some of the evidence from my data on copulation duration are consistent with female preference for short-winged mates (longer total copulation duration by females copulating with short -winged males).

The fact that males gain equal amounts of potential fecundity from first and second mates supports the point 1 made earlier (Chapter 9) that the male upper limit on sexual selection should equal the fecundity of an average virgin female who does not mate again.

3.5.2 Courtship effects

To summarize the courtship effects. there was no effect of remating on the two courtship parameters (copulation duration and spermatophore attachment time) when either males or females were remated. However, the total time double-mated females spent copulating-while the female fed from the male's hind tibia1 spur and while sperm transfer was occurring-was longer with short-winged males than with long-winged males(p = 0.02).

There was a trend for the total time double-mated females spent carrying short-winged male spermatophores to exceed time carrying those of long- winged males (p = 0.06). Double-mated long-winged males spent more CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 84 time over two matings copulating with short-winged females than any other wing niorph combination (p = O.OO7), and the total spermatophore attachment time for double-mated males was marginally lower for L-L matings than L-S matings (p = 0.06). In these last results, there is evidence that long-winged males show preference to short winged females. perhaps allocating more of their limited resources to more fecund females.

The finding that sperm were transferred during cop~ilation-even when females never carried the spermatophore-has consequences for previous and future work on the function of tibial spur feeding. For example.

Bidochka and Snedden [1983] only consider matings as having been successful when a spermatophore was transferred. These authors painted over the tibial spurs of some males. leaving others with their spur esposed and then examined the effect painting had on mating siiccess. copulation durat ion and spermatophore attachment time. Including copulations where the spermatophore was not transferred in estimates of copulation duration and spermatophore attachment time would likely have reduced these estimates for the painted treatment. improving support for the hypothesis that tibial spur feeding increases the amount of sperm transfer. Excluding matings where males failed to transfer the spermatophore in the present experiment is unlikely to have affected my conclusions, since there was no association between failures and either male or female wing morph CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 85

(male wing: L - R~'= 0.02, p = 0.90; female wing: L - lZX2= 1.81, p = 0.18). This indicates that the 36 failures out of 184 observed matings were evenly distributed among the four wing-morph combinations. Future work should take into account both copulation duration and spermatophore attachment time when considering factors that affect sperm transfer in nemobine crickets.

Because sperm transfer takes place during copulation. the fact that double-mated females spend more time copulating with short wingecl males is consistent with the hypothesis that females prefer short-wingecl males.

By staying in copula for longer with some males. a female is likely to increase the proportion of her stored sperm that belong to these males. increasing t heir siring success. Females did not leave the spermatophores of her two short-winged mates attached significantly longer. However. if sperm transfer was completed when copulation ended. there would be no

need to continue to carry the spermatophore. If the crickets had been food stressed. males may not have been able to prolong copulation effectively which may have made spermatophore attachment time more important.

This would explain why males are sometimes seen to pursue females after copulation [Bidochka and Snedden, 19851, and to antennate and sometimes butt their heads into females that are trying to remove the spermatophore. This conspicuous post-copulatory guarding behavior seems to CHAPTGR3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 86 indicate t hat prolonging spermatophore attachment increases male siring success at least in some circumstances.

1 am unsure what to make of the relationship between the two courtship parameters for double-rnated males and male and female wing morphs.

The longer total copulation duration in S-L pairings may reflect a larger investment in the nuptial gift given by long-winged males to more fecund short-winged females. Shorter spermatophore attachment times for L-L matings as compared to L-S may reflect lower effectiveness or intensity of post-copulatory mate guarding for this combination of wing rnorphs or that females discriminated against long-winged males by removing t heir spermatophores more cpickly.

3.6 Conclusions

This study tests predictions based on the hypothesis that a life history trade-off between having functional wings and fecundity can affect the upper limit on sexual selection for males and females differently. While the upper limit on sexual selection for male A. socius is equal to the fecundity of an average virgin female who mates once, there are no detectable differences between the upper limits on the four wing morph combinations CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 87 for males. In this experiment only one wing combination (L-S) produced a female upper limit on sexual selection greater than zero. This seems to indicate that, for the other wing combinations, nuptial gifts do not increase fernale fecundity. The fact that with one wing morph combination females can gain fecundity with additional mates is weak support for a direct effect of a life history trade-off on the strength of sexual selection. It would be interesting to see whether food stress increases the magnitude of this effect. The negative effect on hatching success of L-L matings also de- serves further investigation. This wing morph combination. which might be fairly common in areas colonized by dispersing, long-winged crickets could select for female preferences favoring short-winged males. 1 found evidence consistent wit h female preference for short-winged males in the form of double mated females spending more total time in copula with short-winged males.

3.7 Acknowledgement s

1 tliank Dixie Duncan and Southeastern Community College for hosting me while 1 collected crickets. Marianne Meidzlek-Feaver helped me to find information on collecting sites. Cynthia Thomas and Jenny McEwan helped me in many ways in the lab. Darryl Gwynne and Luc Bussière CHAPTER3. WING-DIMORPHISMAND THE UPPER LIMIT OF SEXUAL SELECTION. 88 helped me with experimental design and discussion and comments on earlier drafts of this paper. Chapter 4

Quant ifying the potent ial for sexual conflict over mating frequency using Bateman slopes

BY Patrick D. Lorch. Luc F. Bussière and Darryl T. Gwynne

Biology Department

University of Toronto at Mississauga

4.1 Abstract

The difference between the sexes in the number of offspring by

number of mates correlation is believed to drive much of the evo-

lution of morphological and behavioral differences between the CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 90

sexes. These correlations have traditionally been represented

by slopes from regressions of number of offspring on number of

mates (Bateman slopes). Typically the Bateman slope is as-

sumed to be large for males and non-existent for females. How-

ever, the two exaniples where males and females slopes have been

measured show there can be appreciable slopes for females. The

actual slopes for males and females can be estimated in the field

using molecular parentage data. In the lab it is possible to es-

timate the upper limits on these Bateman slopes for the two

sexes. We do that here in a katydid (Conocephalus nigropleu-

rum) where males provide females with a large food gift during

rnating (nuptial gift). By mating males and fernales to either one

or two virgin mates. we estimated the way maximum fecundity

increased with additional mates for each ses. From estimates

of average maximum fecundity, we estimated the upper limit of

sexual selection on each sex and compared these estiniates to

predictions based on the relative value of the nuptial gift and

female pre-mating fecundity. Cont rary to what we espected, the

male upper lirnit did not exceed the female upper limit. Both the

fact that a male's second nuptial gift was smaller than his first

and that many matings failed to transfer appreciable numbers of

sperm seem to have contributed the unexpected result. CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 91

4.2 Introduction

Semal selection is typically thought to act more strongly on males than females, because males of many animals more frequently have unique structures, are more colorful, larger. loiider. more mobile and more competitive for mates [Darwin. 18711. Current theory explaining clifferences between the sexes states that. due to the relatively lower cost of producing sperm as compaïed to the cost of producing ova [Bateman. 1948. Trivers. 19731. males are relatively more elaborate because they experience a strong correlation between the number of offspring t hey sire ( t heir fecundi ty ) and the number of mates they obtain [their mating success: Bateman. 1948.

.Arnold and Duvall, 19941. It is generally assumed that there is no such correlation for females (based on only part of the data from a famous paper by Bateman. 1948; e.g.. Trivers. 1972. Andersson, 1994 p. 1-17). This asymmetry in the correlation for males compared to females is thought to lead males to try to remate more readily than fernales. resulting in the potential for sexual conflict over mating frequency [for a recent review see

Arnqvist, lggï]. 1s this sort of sexual conflict as ubiquitoiis as recent interest in it would suggest [Arnqvist. 1997, Brown et al., 1997, and references

therein] or is it a result of selective use of the available data*? CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 92

To answer this question wliat is needed is direct evidence for sex differences in the correlation between fecundity and mating success. Un- fortunately, asymmet ry in t his correlation between fecundity and mating success has only been cpantified for a fruit fly [Bateman. 19481 and for the dark-eyed junco [Ketterson et al.. 19981. In these two studies the evi- deiice for sexual conflict over mating frequency was not as strong as rnight be expected. For a number of theoretical and practical reasons [Arnold and Duvall. 19941 the slope of the regression of fecundity on the number of mates (the "Bateman slope") was used in these two stuclies rather than a correlation coefficient. Batemen split the results from an esper- iment on fruitflies (Drosophila melanoyaster) done in six replicates into two groups. The inale slope was 12.3 times greater than the female slope

(29.5/2.4. male / female dopes) in one group (two replicates) but only 1.6 times greater in the other group [23.3/14.T. in four replicates: based on a re-analysis of Batemanns 1948 data by Arnold and Duvall. 19941. The latter results do not show as stïong evidence for sexual conflict over mating frequency as the former results do. Females in these latter replicates had a fairly high slope and gained an average of 14.7 offspring with each additional mate. For sorne unknown reason, this portion of Bateman's results (the majority of his data) are seldom cited [but see Arnold and

Duvall, 19941. The bulk of Bateman's results are suïprising in light of CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 93 recent evidence that multiple mating is costly for female fruitflies but not males [promiscuous females suffer reduced lifespan; Chapman et al., 19951. Under these circumstances, the male slope should fax exceed the female s10~e.l

In a second species, dark-eyed juncos ( Junco hyemalis). Iiet terson et al.

[1998] found no significant difference in the positive Bateman slopes for males and females (sexual conflict index = 0.9 = 2.6312.92. male / fernale slope). Behavioral observations had indicated that t hese birds were socially monogamous (pair bonds forin and both sexes care for yoiing). It was. therefore. surprising to find that females gainecl as niiich fecundity with adclitional mates as niales. and so appeared to be experiencing as much sexual selection as males. Males might have been expected to have a positive Bateman slope. even in a socially monogamous mating system

(with relatively ecliial male and female parental care). due to the relatively lower cost of producing individual sperm [Bateman. 1948. Trivers.

19'721. This would allow males to engage in extra-pair copulations and increase their fecundity. However, since females seem to have a similar Bateman slope to males. there was no detectable sexual conflict over mating frequency in this species. So. in the two species where the correlation

'Even before Chapman et al. [1995], Bateman's second set of replicates were seldom referred to when his work was cited. CHAPTER4. POTENT~ALFOR SEXUAL CONFLKT OVER MATING FREQUENCY. 94 between fecundity and numbers of mates has been measured the evidence for conflict between the sexes over mating frequency is not strong.

These two examples have important implications for sexual selection theory. As Arnold and Duval1 [1994] have pointed out. such studies are changing how we understand the evolution of mating systems and they may also affect our understanding of how sexual dimorphism evolves. The two studies suggest that sexual selection on females may be stronger than predicted by sexual difference theory. Mating systems that have been considered socially monogamous based on behavioral observations. May be better described as promiscuous [Ketterson et al.. 19981. These studies also make clear that, rather than focusing on the strerigth of sesual selection acting on males alone. the important variable to focus on is the difference in the strength of sexual seiection acting on males and females.

What we have been calling sexual conflict over mating frequency is an estimate of this difference.

Research has traditionally focused on the strength of sexual selection on males (often assuming there is no sexual selection on females) not on sema1 conflict over mat ing frequency. For example. lek mating systems have been characterized as having stronger sexual selection on males than is seen in related non-leking species [see Andersson, 1994.p. 16.11. An al- CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 95 ternative view is that lek mating systems occur when the sexual conflict over mating frequency is greater than a certain threshold so that the relative strength of sema1 selection on the two sexes-not the strength on males alone-is the most relevant variable. Sexual dimorphisms of al1 sorts will likely evolve most rapidly when there is a large difference between the strength of sexual selection acting on males and females. .As a result we might expect to see a better correlation between levels of sema1 conflict over mating frequency and the degree of sexual dimorphism than would be expected between dimorphisin and the absolute strength of sexiial selection on males.

In this paper we propose and test methods for quantifying the potential for sexiial conflict over mating frecliiency. quantified as the difference between the upper limit on sexual selection (Chapter 2) for males and females. This upper limit is defined as the maximum rate of gain in fecundity with increasing numbers of ideal mates. For males. the upper limit on sexual selection should be equal to the average fecundity gained from fertilizing virgin females who do not remate (Le.. no sperm competit ion:

Chapter 2). The female upper limit should ecpal the average value (in eggs) of any goods and services that males provide (Chapter 2). To measure this upper limit. we will use regression estimates of the relationship between maximum fecundity and numbers of mates (Chapter 2). CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 96

Estimates of the potential for sexual conflict over mating frequency should not be confused with estimates of actual levels of sexual conflict.

For example, there might be a large difference between potential and ac- tua1 sexual conflict over mating frequency in some waterst rider species

(Hemiptera: Gerridae). Repeated mating is costly to females that have to carry males during edended copulation bouts, making females more vul- nerable to predators fsom below the water surface. There should therefore be a large potential for sexual conflict over mating frequency (Le.. a large difference in the upper limit on male and female Bateman slopes). in species where females increasc the cost of rnating for males by striiggling with them [see Arnqvist. 19971, we niight not espect very liigh actual levels of sexual conflict. The potential for sexual conflict over mating frequency can only be measured in situations where mavimu~nfecundity can be estimated iising controlled matings between virgins. whereas the actual levels of sexual conflict will most commonly be measured using genetic markers in natural [Ketterson et al., 19981 or semi-natural populations [Bateman.

19481. We will focus on estimating the potential for sema1 conflict over mating frequency in a species where we migight expect less conflict than is possible in waterstriders because males provide females with goods that can be converted into additional eggs so that both females and males gain by multiple mating. CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 97

A widespread type of 'goods' that males of many insects provide to their mates is nuptial gifts. These mating meals often increase the number of offspring females produce [Vahed, 19981. Therefore, we would expect females to have a significant positive correlation between fecundity and numbers of mates. reducing the extent of sexual conflict over mating frecpency. Siich correlations have been reported for many insects [Ridley. 19881, including gift-giving katydids in which males feed their mates with a large nutritious spermatophylax attached to the spermatophore [Orthoptera: Tet tigoniidae; Simmons. 1990, Gwynne. 1984a. 19881. In some species the spermatophylax is so important to fernales that they compete with one another for access to matings [leading to a reversa1 in the typical mating roles: Gwynne. 1981. 1985, Simmons and Bailey, 19901. Cnfortunately. no estimates of the correlation between fecundity and numbers of mates have been obtained for male katydids. making it difficult to assess the importance of sexual conflict in this group.

In this paper we focus on another nuptial gift giving katydid Corn- cephalus nigropleurum. ;\ single nuptial gift in this species represents roughly 10% of the males' body weight [Gwynne, 19821. Fernales prefer to mate with heavier males [Gwynne. 1982, De Luca and Morris, 19981 t hat donate larger spermatophores [Gwynne, 19821, indicating that fe- CHAPTER4. POTENT~ALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 98 males place a premium on nuptial gifts. Nevertheless, unlike some other katydids C. nzgropleurum exhibit typical sex roles where males compete for mates and females choose between potential mates based on their Song

[Gwynne. 19821. In this species there is no eviclence of sex role reversal.

The purposes of this paper are to demonstrate that there is the potential for significant sexual selection on females and to estimate the upper limit of sema1 selection acting on males and females. thereby quanti%- ing the potential for sexual conflict over mating freyuency. We will also discuss the importance of this quantity. difficulties in estimating it. and how viewing secual conflict in the way we propose affects esisting sexual selection theory. Our results lead us to propose new theory which details the influence of "failed matings" on the upper limits of sexual selection acting on males and females.

4.3 Methods

In 1at.e April and early May. 1996 we collected Conocephalus nigropleumm eggs from the "pine-cone" galls formed on willow buds by midges

(Rhabdophaga strobiloides : Diptera: Cecidomyiidae) , and found along CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATlNG FREQUENCY. 99 the Credit River in Erindale Park, Mississauga, Ontario, Canada . The katydids hatched from eggs collected in April experienced slightly lower densities than those collected in May (due to an attempt to rear a large number of long-winged individuals from the eggs collected in May for an- ot her study). Preliminary analyses taking t hese rearing t reat nients into consideration revealed that they did not significantly contribute to any of the analyses. so anirnals frorn both treatrnents were pooled in al1 analyses presented here. Only short-winged males and females were used in this st ucly.

We stored eggs on wet filter paper in petri dishes that were placed in an environmental chamber at %OC. 80% humidity. and a 1212 1ight:dark photoperiod. Upon hatching, larvae were treated in two ways. Larvae hatched from eggs collected in April were transferred to fiberglass screen cages measuring 30 X 30 X 30 cm. up to densities of 60 individuals per cage, and fed a diet of apple and katydid cake (a high-protein mixture of rolled oats, millet seed. bee pollen and commercial fish flakes) three times weekly. Larvae hatched from eggs collected in May were reared in plastic cages rneasuring 13 X 11 X 18 cm (~io~ui~@).up to densities of 1.) individuals per cage. We fed them a diet of apple, beef-based canned cat food. and htydid cake three times weekly. To obtain virgin adults for matings. we isolat ed penultimate instar individuals from bot h treatrnents into sep- CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 100 arate cylindrical Plexiglas jars (7 cm diameter and 7.5 cm in height) with fiberglass screen tops.

4.3.2 Data collection

\Ve kept newly molted adults of both treatments isolated for a minimum of six days before pairing them with a member of the opposite ses. We paired individuals of similar age haphazardly, noting the duration of copulation. and the time taken by the female to remove and consume both the spermatophylax (the "meal") and the attached sperm ampulla (eaten by the female when empty of sperm). Only matings that resulted in successful spermatophore transfer were analyzed. We also recorded niale weight loss during mating (assumed to be ecpivalent to combined weight of the nuptial gift (spermatophylax + ampulla)).

After mating, females were isolated and given a small (5-10 cm) section of grass stem (reed canary grass, Phalaris arundinacea) in which to oviposit. Leaf sheaths of this grass were examined weekly for eggs. at which time we provided fresh stems to females.

The day following a mating, we paired one of the members of each successfully mated couple with another virgin partner (except for two males that were mated twice in one day). If this second pairing was unsuccessful, CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 101 another virgin partner was presented on the following day and subsequent days until the focal individual had mated twice. We recorded the interval between rnatings in days. About a third of females mated twice, one third mated once to unmated males, and one third mated once to males who had themselves previously mated once. Most of the males were mated twice.

Male and female maximum fecundities were estimated differently Fe- cundity for a female who had mated either once or twice was simply the total number of eggs laid in her lifetime. Male fecundity was estimated only for twice mated males, and for each male a separate estimate of fecundity from each of his two mates was obtained. Egg counts from some females were used both to estimate the fecundity of once mated females and the fecundity of once mated males. Fecundities measiired in the way we have jiist described give an estimate of an animal's maximum fecundity with one or two virgin mates. rather than the lower fecundity it would

liliely have with one or two matings under natural conditions. This is be-

cause in nature. females may encounter mates that may have fewer sperm

or smaller gifts due to recent mating. Males in nature might encounter females that had already mated, resulting in post-copulatory cornpetition

among males for fert ilizat ions. Measuring maximum fecundi t ies allows us

to cstimate the upper limit on sexual selection (see Analysis below). CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 202

We froze al1 males after their final mating and al1 fernales after their death. We recorded female lifespan after mating. Al1 morphometric measurements were made using a microscope fitted with a digital video Cam- era connected to a Power Macintosh. NIH image (version 1.61). a digital imaging program. was used to compute the following five morphometric measurements: pronotum length, average of left and right front femur. average of left and right hincl femur. average of left and right front wing. and average of left and right hincl wing. After al1 measurements had been made. we dried the specimens (minus the gut) to a constant weight and recorded the dry mass of al1 individiials.

4.3.3 Analysis

In order to obtain a single index of body size for fernales. we condticted a principal components analysis (PCA) on the five morphological measures obtained plus the dry weight. The first principal component (PC1) from

this analysis was used to generate a PC score for each individual from their six size measurements. No PCA was reported for males because. in

preliminary analyses. male size had very little effect on the relationship

between his fecundity and his mating frequency (see below).

Rather than use correlations to determine the relationship between fe- CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 103 cundity and numbers of mates, we follow Arnold and Duval1 [1994] and use regression slope estimates. Since we want to quanti& the potential for sexual conflict over mating frequency using the upper limit on sexual selection for males and females (Chapter 2). we estimated the slope of the maximum fecundity by numbers of mates regression for each ses separately [wliile controlling for the effects of body size, where needed, so that body size effects are not confounded with the effects of multiple mating;

Iietterson et al.. 19981. This was done by mating a focal animal and either one or two virgins of the opposite sex (as described above). For females. we then computed a niultiple regression where the dependent variable was maximum fecundity. and the independent variables were numbers of mates and PC1 (for female size). This was done to reduce variance in estimates of upper limits due to female size variation. The upper limit of sexual selection for fernales was estimated as the partial regression coefficient corresponding to numbers of mates. For males. the fecundity of the first and second mate of a double-mated male can be estimated separately. so we estimated the upper limit of sexual selection for males more simply and with less error than was possible in the case of females. For each male we estimated his maximum fecundity for one rnating from the fecundity of his first mate. We then estimated the same male's maximum fecundity for two matings from his total fecundity ( fecundity from his first mate plus that of his second mate). The upper limit of sexual selection CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER M.4TING FREQUENCY. 104 for males was then estimated using a "repeated measures" regression of fecundity against numbers of mates. The slope was calculated as the difference between the mean maximal fecundity for once and twice mated males (divided by 1).and the significance of the slope was determined using a repeated measures ANOVA. The repeated measures design has the advantage of reducing the effects of differences between males on the variance in the numbers of eggs their mates lay while using smaller numbers of males. (Note: ANOVA is used rather than a paired t - test to emphasize that the approach can be generalized for more than two mates.) In a preliminary analysis of the male slope we used an analysis ecluivalent to the one used to estimate the female slope (multiple regression of fecundity on number of mates and male PC1 for the same six size nieasures). Male PC1 contributed < 0.0001 to the R' of the model (relative to the simple linear regression model of fecundity on numbers of mates) and reduced the value of the slope estimate by only 0.028. For this reason we did not correct the male slope for male size and we used the repeated measures approach for judging whether the slope was different froni zero because this approach should give us more statistical power. We then compared regression siopes for males and females by using the slopes and their variance estimates to compute a t - test [for unequal variances: Sokal and Rohlf. 19811.

Several factors could have affected our estimates of the upper limit of CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 105 sexual selection on the two sexes (and our estimates of the potential for sema1 conflict). We focus on two factors in particular: 1) a possible reduction in the size of the nuptial gift in second matings relative to the first [as in Simrnons. 1995. Reinhold and von Helverson. 19971, and 3) a failure to successfully transfer sperm. With regard to the first factor. double mated males that give smaller nuptial gifts to their second mates are expected to have maximum fecundities that are less than twice the fecundity of single mated males. If males give less to seconcl mates because they se- mate befose they have fully replenished spermatophore glands froni their first mating [see Gwynne, 19901. this behavior will reduce our estimate of the upper limit of sexual selection on males (without affecting estimates for fernales who get two virgin mates). CVe tested for ciifferences in the weight of first and second spermatophores of double-matecl males (using a

Wilcoxon signed-rank test and reporting medians and inter-cpartile ranges

(IQR)).We then tested the hypothesis that males have not fully recovered between matings in two ways. First. we tested for correlations between

the inter-mating interval and the weight difference between first and second spermatophores (using Spearman rank correlations. r,). Second. we should be able to detect whether a male's remating interval affects the fecundity of his second mate above and beyond the effects of nuptial gift

amount (e.g., if the quality as well as the amount of the second gift is

lower than the first ). To do this we estimated the least squares regression CHAPTER4. POTENT~ALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 106 line explaining how the number of eggs laid by al1 single mated females was affected by the weight of the spermatophore they received (this assumes a linear relationship between fecundity and gift size). The equation for this line was then used to predict the number of eggs a male's second mate should produce based on the weight of her nuptial gift. The average difference between the observed and predicted second mate fecundity was compared to zero. If there is a significant difference between the effects of first and second spermatopliores that is independent of their size (e.g.. the second one is of lower quality). we would expect the average difference between observed and predicted fecundity 60 be distinguishable from zero.

The second factor that rnay affect our estimates of the potential for sex-

ual conflict is unsuccessful sperm transfer. We developed a verbal model

to explain how this factor can affect our estimates of the upper limits on

sexual selection for males and females. We then usecl this model to de-

scribe how failures to transfer sperm may have affected our estimates of

the potential for sexual conflict.

To see whether a second mating affected a fernale's lifespan [Brown.

19941 or egg laying rate [Gwynne. 1988, Simmons. 19931. we compared

the number of days a female lived after mating and the number of eggs

laid per day over this period for once and twice mated females (excluding CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 107

Table 4.1: Female body size measurement (with standard error. SE) and coefficients of first principal component.

Factor n Meana SE coefficientb Pronot um lengt h Front fernur lengt h Hind femur lengt h Front wing length Hind wing length Dry weight " -411 lengths are in mm and weight is in grams.

Coefficients are for first eigenvector from the principal components analysis of female size measures. females who dicl not lay any eggs). Errors are reported as f one standard error unless otherwise indicated.

4.4 Results

4.4.1 Female body size

The first principal component (PC1) explains 47% of the variation in female size measurements. Table 4.1 shows the mean and standard errors for each of the six measurements along with how each character loaded in the principal cornponents analysis. Variation in the length of the two wings was mostly independent of other size measures (see low wing coef- CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 108 ficients in Table 4.1). The wing lengths loaded strongly ont0 PC2 (not shown). Female PC1 was significantly correlated with the total number of eggs laid (for once and twice mated females together. r, = 0.49, n = 23, p = 0.02).

4.4.2 Upper limits on sexual selection

The upper lirnit of sexual selection acting on females (i.e.. the partial regression coefficient for number of mates. controlling for the effects of female body size using multiple regression) is 31.0 i 12.83 (see Figure la).

This upper limit is significantly different from zero (MSnUmb,,.f ,,,tes -

4098.89. FLT2-= 5.85. p = 0.03) indicating that females have the potential to gain fecundity by mating multiple times. Multiple mating significantly increased female post-mating lifespan (frorn 38.83 f4.79 days for one mat-

ing to 453.75f 7.18 days for two: t = 2.89. n = 12 and 8. p = 0.01) without

increasing egg laying rate (over a fernale's mated life: from 0.85 f0.15 eggs

per day for one mating to 1.11 f 0.19 for two; t = 1.04. n = 12 and 8. p = 0.31). This indicates fecundity gains due to remating are primarily

the result of increases in female post-mating lifespan as reported by Brown

[1994] for female tree crickets (Oecanthus nigricornis) that receive larger

gift S.

The upper limit on males (estimated as the difference in mean fecundity CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 109 with one and two mates) is 12.55 f 6.89 (Figure 4.1) which is also significantly different from zero (repeated measures: b!lSnumber,f ,,te, = 865.64,

= 10.67, p = 0.009) indicating that males also gain fecundity by remating. They do not gain as much as theory would predict: the male upper limit on sexual selection should equal the fecundity of single mated females (Chapter 2) which in our data is 19.64 f 4.30. However. a t - test comparing male and female upper limits showecl that they were not significantly different (equivalent to a paired t - test comparing the number of eggs by first and second females: t = 1.16. df = 10. p = 0.27). Fur- therrnore. although the female upper limit is more tlian tmice as large as for males. the two are not significantly different (Figure 4.1: t - test for uneyual variances: t' = 1.15. n = 11 and 23. p > 0.2). Therefore. we cannot detect statistically significant potential for sesual conflict over mat ing frequency. However. as the variance about the two estimates (especially

for the females) is large and the sample sizes fairly small. we have low

power to detect a significant difference between slopes.

4.4.3 Spermatophore weight

If the difference between the male and female upper limits is real. the

difference may be a result of a decrease in spermatophore size in second

matings [see Davies and Dadour, 19891 resulting in a smalleï gift in the

second mating and consequently a smaller fecundity gain. This was the CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 110

00 One Two Number of mates

Figure 1.1: Estimates of the maximum fecundities of once and twice mated females (open circles) and males (closed circles). The upper limit on sexual selection (or the rate of gain in maximum fecundity with increased numbers of mates) is calculated as the difference betweea the maximum fecundities of double and single mated individuals ( divided by 1).

The effects of body size were removed from lemale upper limits using partial regession

(see text ). CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATlNG FREQUENCY. 111 case. There was a significant decrease in spermatophore weight between a male's first and second matings (0.013 f 0.008 g (median f IQR) for one and 0.008 f0.004 g (median f IQR) for two mates; Wilcoxon Z = -2.31. n = 11, p = 0.02). There was no equivalent difference between the weights of first and second spermatophores given to females by their two virgin mates (O.OlEt 0.004 g (median f IQR) for one and O.Ol5f 0.006 g (median f IQR) for two mates: Wilcoxon Z = -1.18. n = 8. p = 0.24). If males are providing srnaller second nuptial gifts because they have not fully replenished spermatophore glands. there shoiild be a negative correlation between the difference in spermatophore weight (first minus second) and inter-mating interval. We founcl a negative correlation. although it was not significantly less than zero (r, = -0.37. n = 11. one tailed p = 0.12).

To try to separate the effects of nuptial gift size from other effects on fecundity (e.g.. spermatophore quality), we regressed the number of eggs laid by the 34 single-mated females on the weight of their spermatophore gift (Eggs = 1533.84 * spermatophore weight + 8.13: R' = 0.08) and substituted the weight of the second spermatophore into this ecpation to get predicted egg outputs for males*second mates. We then asked whether the average difference between observed second mate fecundities and the prediction based on the size of the second nuptial gift was different frorn zero. It was not significantly different (mean difference = -8.22. t = -2.08. df = 10, p = 0.06). CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER kIATING FREQUENCY. 112

4.4.4 Failure of sperm transfer

The lower male estimate for the upper limit on sexual selection might also be due to what appears to be the failure of sperm transfer in some matings;

12% (4 of 34) first matings produced no eggs. 35% (12 of 34) produced

< 10 eggs. These failures do not appear to be due to male sterility because. of the four males who failed to transfer sperm during their first mating. three mated a second time and al1 of these mates laid eggs. The failure of sperm transfer can have different effects on the upper limit of sexual selection for males as compared to females. CVe illustrate this more clearly with a graphical model for understanding how failures to transfer sperm affect male and female maximum fecundities and the resulting upper limits on sexual selection. (A quantitative model will be presented elsewhere).

In mating systems in which males supply goods and services to females. when sperm transfer is successf~il.the maximum fecundity of males will always equal or exceed female maximum fecundity (Chapter 2). This occurs because. although female maximum fecundity increases wit h additional matings by an amount equal to nuptial gift value. male maximum fecundity increases by this amount plus any female pre-mating fecundity (equal to her fecundity if she were to receive only sperm and no gift: Chapter 2).

Any matings resulting in nuptial gift transfer but no sperm transfer. as occurs in our experiment, will reduce the average maximum fecundity of CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 113 single mated individuals in proportion to the number of failures (relative to the maximum when there are no failures, since a failure will produce no offspring). It is also clear that the maximum fecundity of males and females who mate once will be equal.

The maximum fecundity of males and females who mate twice is not equal when some matings result in a failure to transfer sperm. This is because twice mated males fa11 into three categories of maximum fecundity

(males with two failures. with one success and one failure. and with two successes) while females fa11 into only two categories (two failures versus one or two successes). Whether a female has one or two siiccessful sperm

transfers is irrelevant to her fecundity (assuming no addit ional effect of ovipositional stimulants from the second ejaculate) because one siiccessful

mating can transfer enough sperm to fertilize al1 her eggs [htydids ejac-

ulate a lot of sperm: e.g.. 6.3 million in Poecilimon veluchianus. Reinholcl

and von Helverson. 19971, while bot11 matings transfer fecundity benefits

from nuptial gifts. Thus. with failed insemination the average maximum

fecundity of twice mated males and females will decrease at different rates

leading to different effects on the upper limit of sexual selection (the rate of

increase in maximum fecundity with additional mates). If we assume that

failures to transfer sperm are relatively rare (presumably they are costly

and natural selection acts to reduce them), failures can actually increase CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 114 the female upper limit on sexual selection while reducing the male upper limit (relative to when there are no failures, Figure 4.2). This can lead to a situation where estimates of the female upper limit can actually exceed those of the male upper limit (Figure 4.2) as was seen in our estimates.

It can also explain why the maximum fecundity of females who mate two times can exceed twice the maximum for females who have matecl once

(Figures 4.1 and 4.2).

4.5 Discussion

The regression slopes expressing the relationship between masimurn fe-

cundity and numbers of mates were significantly positive for both sexes

indicating they both have the potential to gain fecundity by copulating

with more than one mate. In other words there is the potential for sexual

selection on both males and females (Chapter 2). Individuals of both sexes

who are better able to take advantage of this potential leave more descen-

dants. This positive relationship between fecundity and mating success

has always been assumed to be the case for males. but it rnay also be true

for females (and not only when sex roles are reversed). The potential for

sexual selection on females appears to be due to increased fecundity that

cornes from increased lifespan. Mating twice almost doubles post-mating CHAPTER4. POTENTIALFOR SEXUAL CONFLlCT OVER MATING FREQUENCY. 115

Figure 4.2: Effects of the proportion of matings that result in successful nuptial gift transfer but a failure to transfer sperm on the average maximum feciindity for a group of mating individuals. Females are arbitrarily assurneci to have a pre-mating fecundity

(before they receive a nuptial gift ) of 100 eggs. and nuptial gifts allorv fernales to produce

200 extra eggs. Failures reduce estimates of maximum fecundity linearly for single mated individuals (of both sexes; numbers of mates = 1 in A) and for double mated males (male number of mates = 2 in A). However. failures do not reduce the fecundity of double mated females as fast as they do single mated females (females with 1 and 2 mates in A). Estimates of the upper limit on sexual selection (slopes in A plotted on Y axis in B) are decreased by failures for males (closed circles). but failures can increase estirnates for females (open circles: when failures are rare. < 0.5 of al1 matings). CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 116 lifespan of females without increasing t heir egg laying rate over t his period.

Our data do not dernonstrate statistically significant levels of potential for sexual conflict over rnating freyuency. If anything, it appears that males should have less motivation to rernate in C. nigropleurvm than females, since the slope for females was more than twice that of males. However. this difference may have been the result of males remating before they had fully replenished their spermatophore glands. given the trend toward a negative correlation between the inter-mating interval and change in spermatophore weight. Maximum male fecundity (from niatings mith virgin females) is expected to increase with increased nurnbers of niates at a rate eyuivalent to the fecundity of females who have mated once (Chapter

2). In our experiment there mas a trend toward the male upper limit on sexual selection being less than the mean fecundity of once mated females. This is further evidence of the possibility that something [perhaps some aspect of male yuality or coinpatibili ty with particular females: Cunning- ham and Birkhead. 19981 is preventing some males from attaining their maximum rate of gain from remating. The failure of sperm transfer cluring mating attempts can also result in an increase in estimates of the female upper limit on sesual selection while reducing the male upper limit leading to the seerningly paradoxical result where the male upper limit of sexual selection does not exceed the female upper limit. CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 117

Fernale C. nigropleumm have the potential to gain significant fecundity by remating. The potential for sexual selection on females that these gains create is in line with results from the majority of Bateman's [1948] replicates and with work on dark-eyed juncos [Iietterson et al., 19981.

Similar gains in fecundity are known to accrue to females in other nuptial gift-giving systems [Vahed. 19981, t hough t hese gains are generally not thought of as creating potential for sexual selection. In fact. the same potential is expected for nuptial gift giving insects and for anirnals where males contribute significant levels of parental care [Arnold and Duvall.

199.11 because female fecundity rnay increase with addit ional mates.

-4s mentioned in the introduction. there are important differences be-

tween estimates of the potential for sexual conflict (e.g.. niale / female upper limits on sexual selection) and measures of actual levels of conflict

(e.g.. male / female Bateman slopes). Studies that use genetic markers

to estimate the average rate of gain in fecundity witli increased numbers

of mates [Bateman, 1948, Iietterson et al.. 19981 will arrive at estimates

of sexual selection gradients for males and females that are lower than

the upper limits estimated by using maximum fecundities. Even if there

is a large difference between the male and female upper limits on sexual

selection (i.e.. there is high potential for sexual conflict over mating frequency ) , the difference between the actual sexual select ion gradient may CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 118 be small. In fact this discrepancy rnay tell us interesting things about the mating system or environmental constraints acting in a population at the time when the slopes were estimated. Such a discrepancy is likely to be the case in waterstriders, as we mentioned earlier. Estimating both the potential and actual levels of sexual conflict can therefore be informative.

Our results highlight some of the pitfalls in estimating the potential for sexual conflict over mating frequency. As was the case with our data. whenever the estimate of the male upper limit on sexual selection is less than the average fecundity of females who have mated once. there is reason for concern. CVe believe that this cliscrepancy can 'esult partly from males giving smaller second nuptial gifts to ferriales and partly from matings where sperm transfer was unsuccessful. Failure to transfer sperm affects maximum fecundity for double-mated males and females in different ways with consequent divergent effects on estimates of the potential for sexual conflict over mating frequency. In Mormon crickets (Anabms simplex), another katydid with a large external spermatophore. of al1 females observed to mate one to four tirnes (in field cages), 21% had at least one mating that transferred no sperm, while 33% of single matings in the lab failed to transfer sperm [Gw-ynne, 19931. We have argued that when failures to transfer sperm occur rarely and independently of nuptial gift transfer, they can increase estimates of female upper limits on sexual se- CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 119 lection and decrease male estimates of the upper limit. This cmlead to a situation where the female estimate exceeds the male estimate, especially when it is compounded (as it was in our data) with the fact that males were transferririg smaller nuptial gifts during second matings. Such errors in estimating the upper limits on sexual selection could lead to a mistaken impression of the potential for senual conflict over mating frecpency. Es- timating and using more natural remating intervals for males rather than pairing them with a new female everyday until they mate. as was done here. niight eliminate the reduction in nuptial gift size between matings which would reduce error in the estimates.

Xlternatively. to estimate the male upper limit on sexual selection. one could simply use the estimate of the average fecundity of once mated females. The rate at which males gain fecundity witli additional mates should be equal to the fecundity of females who mate once (Chapter 2).

There are two problems with this approach. First, we do not know in

C. nigropleumm whether males always give a large first nuptial gift and smaller ones after that. If this is the case. estimating the male upper limit on sexual selection from the fecundity of his first mate would require knowing the proportion of males that mate more than once and the amount of reduction in nuptial gift size. The second problem is that since sperm transfer failures result in underest imat es of the maximum fecundity CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER MATING FREQUENCY. 120 of once mated females, this approach would result in an underestimate of the male upper lirnit on sexual selection.

It is more difficult to know how to deal experimentally with the effects of failures to transfer sperm. In some situations it may be possible to detect failures by plotting frequency distributions of the numbers of eggs laid by both a male's first and second mates and looking for a bimodal distribution. The lower peak coüld t hen be discarded. We were not able to cletect such bimodality with female C. nigropleumm because of our small sample sizes. Using molecular paternity markers may also prove useful for quantifying failure to transfer sperm.

In conclusion we believe that this work represents one of the first attempts to measure the potential for sexiial conflict over mating frequency.

Measuring the upper limit on sexual selection for males and females separately is a useful way to yuantify sexual conflict over mating frequency.

Conflict over mating frequency plays an importaiit role in determining mating systems (e.g.. whether males or females are more competitive for mates). and the extent of this conflict is also the important quantity in determining the evolution of semial dimorphisms of other sorts. More work in this area, both for animals with typical, male competitive. sexual systems and for systems where sex-roles are reversed, would clearly be useful. CHAPTER4. POTENTIALFOR SEXUAL CONFLICT OVER M.4TING FREQUENCY. 121

4.6 Acknowledgement s

We thank Seaver Som for helping collect eggs. Cynthia Thomas. Vijanti

Ramlogan Murphy and Jenny McEwan helped with measilring and weigh- ing. Chapter 5

The power of the concent rated-changes test for correlated evolution

BY Patrick D. Lorch

Biology Department

University of Toronto at S1ississauga and

John 'V1c.A. Eadie

Department of Wildlife, Fish and Conservation Biology

University of California. Davis. C.4 CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 5.1 Permissions

Systematic Biology A Publication of the Soaety of Systematic Biologists

Richard OLmrnnd. Editor, Systcmitic Biolosy office - (106)543.cwM lhpartmrnt of Bahny, Bax 353325 FAX - (206168E1728 L'niversity of Washington cd1- systbiol(kr.w~shingtnn.rdu Sicirele. WA 98195

September 14,1999 Deu Dr. hch:

I hereby grant you permission to reproduce, as part of his PhD. thesis, any material frorn the paper titled "Power of the concentrated changes test for conelated evalution" publisfieci in Systcmatic Biology. Volume 4û(1), pages 170-191. Sincerely,

Richard Ohtead, Editor, Systematic Biology

Dopariment of Wdlife, F%h 6 Consandon Bidagy One Shkb Avenue Davis, CA O561 6-8751 CHAPTER5. fOWER OF THE CONCENTRATED-CHANGES TEST.

5.2 Abstract

The concentrated changes test (CCT) calculates the probability

that changes in a binary character are distributed randomly on

the branches of a cladogam. This test is used to examine hy-

pot heses of correlated evolu t ion, especially cases where changes

in the state of one character influences changes in the state of

another character. The test may be sensitive to the addition

of branches lacking either trait of interest (white branches). To

esamine the effects of the proportion of white branches and of

tree topology on the CCT probability. we conductecl a simu-

lation aiialysis using a series of randomly-generated 100-taon

trees, in addition to a nearly perfectiy balancecl (symmetrical)

and a completely imbalanced (asymmetrical) 100-taon tree. Vs-

ing two models of evolution (gains only, or gains and losses). we

evolvecl character pairs randomly ont0 these trees to simulate

cases where (1) characters evolve independently (i.e.. no corre-

lation among the traits) and (3) al1 changes in the dependent

character occur on branches containing the independent trait

(i.e.. a strong correlation among the traits). This allowed us to

evaluate the sensitivity of the CCT to type I and type II errors,

respectively. In our simulations, the CCT did not appear to be CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 125

overly sensitive to the inclusion of white branches (low likelihood of type 1 error using both CCT probabilities < 0.05 and

< 0.01). However the CCT was susceptible to type II error when the proportion of white branches is < 20%. The test was also

sensitive to tree shape and was positively correlated to the tree

imbalance statistic I (Colless). Finally. the CCT responded dif-

ferently for simulations where only gains were allowed relative to those where both gains and losses were permitted. Our results indicate that the CCT is unlikely to detect correlation between

characters when no such correlation exists. However. when a

trait can be gained but not Lost. the CCT is conservative and

may fail to detect true correlations among traits (increased type

II error). Determination of the sampling universe (taxa included

in the comparative analysis) can strongly influenced the prob-

ability of making such type II errors. We suggest guidelines to

circurnvent t hese limitations.

5.3 Introduction

The comparative method remains one of the most powerful tools available in evolutionary biology [Brooks and McLennan, 1991, Harvey and Pagel. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 126

1991, Maddison and Maddison, 19921. Recent developments in phylogenetic analysis have made it possible to study evolutionary patterns across diverse taxa while taking into account shared phylogenetic history. These developments have proven particularly valuable for researchers interested in testing hypotheses of correlated evolution between two or more characters [reviewed by Harvey and Pagel, 19911. Of the several techniques now available to test for patterns of correlated evolution between discrete characters [Ridley. 1983. Proctor, 1991. Sillén-Tullberg, 1993. Pagel.

1994b, Read and Nee. 19951. Macldison's concentrated changes test [hereafter referred to as the CCT: hladdison, 19901 has proven to be popular [Donoghue. 1989, Hunter. 1995. Hoglund and Sillén-Tullberg. 1994. Janz and Nylin. 19981 because it is logical. powerful. and readily accessible in the program MacClacle [Maddison and Maddison. 19921. The CCT is particularly ml1 suited to testing hypotheses about whether the evolution of a trait is more likely when another character is in a partic~ilarstate.

The CCT determines whether changes in one character (the dependent character) are concentrated on branches of a tree that have a particular state of a second character (the independent character). The test is performed by first reconstructing the evolution of two characters on a phy- iogenetic tree. The user then counts the number of gains (n) and losses

(m) in the dependent character over the whole tree. and the number of CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 12'7 these gains and losses that occur on branches reconstructed to have the derived state ("black" branches) of the independent character (p gains and q losses on black branches). To calculate the CCT probability, the test calculates (a) the number of ways la gains and m losses can be distributed on the entire phylogeny, and (b) the number of ways p gains and q losses can be distributed ont0 the black branches given n gains and rn losses on the whole tree. The ratio of b/a expresses the probability that the observed number of changes in the dependent character woulci occur by chance on black branches-the smaller the ratio. the more strongly changes in the two traits are associated. The test assumes equal branch lengths and uses the number of gains and losses in the whole tree as a way of weighting how important these two kinds of changes are (a detailed description of how this test is performed nias provided by Macldison. 1990.p. 55 and Maddi- son and Maddison. 1992).

The purpose of our paper is twofold. First. we consider mhether the

CCT is sensitive to the inclusion of clades composed of "white" branches.

that is, branches of a phylogeny reconstructed to have the ancestral state of two characters (neither trait of interest is present). Maddison [1990] recognized that the concentrated changes test would be sensitive to the inclusion and exclusion of taxa. For example, he noted that addition of

taxa in which there has not been a change in any of the characters of CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

ABCDEFGHI JKLMNOPQRSTU OOOOOOnnOnOO.O.0moori

4 gains of dependent character (3 of them on black branches)

,u @ CCT P = 0.049

Figure 9.1: Demonstration of the effect on the coiicentrated changes test (CC'T) of including clades with neither trait of interest (white branches). P values indicate the test probability when the CCT is calculated at each point for four gains in the dependent character (three of them on black branches) given the distribution of the independent character shown. The part of the tree containing taxa A-H is completely balanced. but the part with bI-CT is completely imbalanced. interest coiild result in a situation where "a weak association between changes and black areas in the rest of the tree might becorne a strong association when many species ... are added. because there woiild then be many more white branches on which changes could have occurred but did not" [Maddison. 1990,p. 551. The problem is illustrated in Figure 5.1.

In this example, seven of nine taxa (M-U) possess a trait of interest (two have lost it). This so called independent trait is optimized on the tree as shom by the black branches. Suppose a second. dependent trait has CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 129 arisen four times (in taxa M, O, Q and at the base of clade T-U) and

is illustrated by cross-bars on the branches at the point where these ori-

gins occurred. The CCT allows us to ask whether the dependent trait is

more likely to evolve when the independent trait is present (i.e., do gains

of the second trait occur more often than would be expected by chance

on the black branches, given the tree structure*?). In this example, the

result of the CCT is highly dependent on the position in the tree at which

the test is conducted. At point 1 (Figure 5.1) if we calculate the CCT

probability that three gains and no losses occurred on black branches by

chance (given four gains overall). the test reveals no significant associa-

tion of the two characters (CCT = 0.847). At point 3. the association

is stronger (CCT = 0.326) and at point 3 the association is significant

(CCT = 0.049). The only difference among these tests is which taxa are

sampled: we have progressively added clades (1-L ancl A-H) consisting of

white branches. The CCT appears to be highly sensitive to the inclusion

of taxa lacking either of the traits of interest.

It could be argued that the addition of the white branches simply in-

creases the power of the test to detect a true association. The newly

added lineages could have had changes within them but did not. and as

Maddison points out, al1 statistical methods should react to inclusion of

new sample points. However, we became concerned that weak or even CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 130 random associations between characters might become statist ically significant simply through the addition of taxa with neither trait of interest.

The relationship between the proportion of white branches and the likelihood of making type 1 error (the probability that an association will be detected when there is none) needs to be evaluated. We do so here by simiilating the random evolution of characters on a series of trees. and then asking whether a test for an association between characters using the

CCT is sensitive to the inclusion of white branches.

The problem of aciding white branches leads to the broader question of

-*t&xonsampling7'-hom to define the sampling iiniverse to esamine correlated evolution without influencing the chances of finding a significant correlation [Coddington. 19%. 1994. Sillén-Tullberg, 1993, Pagel, 1994al.

Sillén-Tullberg [1993] considered the sensit ivi tsy of comparative tests to the inclusion and exclusion of taxa at length. However. taxon sanipling involves changes in both the number of taxa ancl in the proportion of branches that are white, an issue that Sillén-Tullberg [1993]did not ad- dress. We attempt to separate these influences by examining variation in the proportion of white branches on 100 taxon trees and on JO and 25 taxon subsets.

A second goal of our study is to examine the extent to wliich the CCT CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 131 is affected by tree shape. The CCT explicitly incorporates tree topology in its calculation of the number of ways that changes in the dependent character could occur on a given tree. However. Maddison [1990]recognized that tree shape may nonetheless influence the value of the test statistic. For example, if a tree is highly asymmetrical or imbalanced [sensu

Heard, 1992. as in the part of tree in Figure 5.1 containing taxa M-U], some branches represent greater lengths of time than others. Xccordingly, apparent correlations could arise between characters. not because of any causal connection, but simply because changes in both characters are more likely to occur on longer branches. If this were true. we would expect that the CCT would be more susceptible to type 1 error as trees become more imbalanced. The CCT may also be sensitive to tree shape due to potential effects on the number of black branches. Imbalanced clades can have a much wider range of black branches than balanced clades [Wedelin and Tullberg, 19951.

Partly in response to concerns about the effects of tree shape. Sillén-

Tullberg [1993]designed a new test. the contingent states test (CST).that is less sensitive to tree topology. This test compares the relative frequency of gains and stasis in a dependent trait and asks whether these frequen- cies depend on the state of an independent trait. Werdelin and Tullberg

[1995] recently compared the performance of the CCT and the CST on two CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 132 extreme tree shapes - perfectly symmetrical and perfectly asymmetrical

64-taxon trees. They found that the tests yield different probabilities in some situations (e.g., for asymmetric trees with small numbers of black branches) and that the CCT is sensitive to tree shape, but they did not examine the power of either test in detail. Because most phylogenies for real organisms are not as estreme as those used by Werdelin and Tull- berg (1995), a further evaluation of the influence of tree shape on the

CCT would be valuable. We use rneasures of tree balance [Colless. 1982.

Heard, 1992, Iiirkpatrick and Slatkin. 19931 to examine the sensitivity of the concentrated changes test to tree shape. CVe also esamine whether the proportion of white branches (rather than the n~imberof black branches) influence the likelihood of making type I and type II errors. Our results provide an assessrnent of the statistical power of one of the more accessible comparative techniques for testing hypotheses of the correlated evolution of discrete charact ers.

5.4 Methods

In setting up the simulations described below, a number of factors had

to be dealt with simultaneously. We wanted to test the effect of adding

white branches and the effect of tree shape using the same trees and char- CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 133 acters so that we could evaluate the importance of these effects relative to each other. Tree shape statistics are sensitive to the number of taxa in the tree [Heard. 1992, Kirkpatrick and Slatkin, 1993. Rogers. 19941. For this reason we held the number of taxa constant at 100 for most of our analyses. We chose to use trees with large numbers of taxa and chose parameters (e.g., transition probabilities, DELTRAN resolving options) for character evolution that would give us a range of white and black branches. This allowed us to do two things. First. it allowed us to look at the effects of white branches using variation in the proportion of white branches between characters without varying the number of taxa as we did in the example above (Figure 5.1). Second. this approach provided sufficient variation in the number of black branches to enable a test for

the effects of interest. Setting the probability of gains too high results in characters wit h large numbers of black branches. Setting the probability

of gains too low leads to the opposite. small numbers of black branches.

Either of these alternative approaches would limit the scope of our examination of the CCT (and the generality of our results) by constraining the range of probabilities possible (i.e.. to be close to one when there are

many independent black branches and close to zero when there are few).

Likewise. we chose to emphasize trees with 100 terminal taxa rather than

smaller trees because this allows a larger range in the number of gains

and losses possible for a trait of interest. For approaches such as the CCT CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 134 t hat depend on convergence for power [Coddington. 19941, large numbers of taxa are desirable. The CCT has been used on trees ranging in size from 52 to several hundred taxa (52 in Hunter, 1995; 64 in Werdelin and Tullberg, 1995; 72 in Hoglund and Sillén-Tullberg, 1994: 80 in Donoghue, 1989; and 437 in Janz and Nylin. 1998).

To assess the effects of tree shape on the CCT, we needed a rnethod of generating random trees with shapes siniilar to real trees. Trees generated using real character matrices have been compared to various kinds of random trees of equivalent size using the shape statistic I (defined below) which indicates the average balance between the number of taxa in the descendent clades for each node in a tree. CVe generated ten random trees containing 100 taxa using the Eyiiiprobable random trees option in Mac-

Clade 3.0 [Maddison and Maddison. 19921 which uses a model equivalent to the equal probability model of Rogers [1994] or the proportional-to- distinguishable arrangements (PDA) model of Savage [1983] and Heard and Mooers [1996]. This method randomly samples al1 possible rooted dichotomous trees. Another model for producing random trees is known as the equal rates Markov (ERM) model [Rogers, 19941. (Although not used in this study. the random joining option in MacClade produces trees equivalent to the ERM model, Maddison and Slatkin. 1991.) Real trees tend to be less balanced than ERM trees and more balanced than PDA CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 135 trees [Rogers, 19941. In other words, mean I values of real trees tend to fa11 between mean 1 values for ERM and PDA generated trees (on average:

ERM I < "real" I < PDA 1), especially for large trees [Rogers, 19941. The expected value of 1 for ERM trees with 100 taxa can be calculated from equation 2 of Heard [1992] as 0.144, and for PD..\ trees with 100 taxa. I can be extrapolatecl from Figure 2 of Rogers [1994] as 0.27. We therefore chose trees with shapes that spanned this range for our stiidy to concen- trate most of out efforts in the range of shapes where real trees would be expected to fall. To show how the CCT behaves on trees with extremes shapes. we also constructed a 100 taxon tree with nearly perfect balance

(symmetrical. as in the part of the tree in Figure 5.1 containing taxa A - H) and one that was completely imbalanced (asymmetrical). (Yote: Perfectly balanced trees can only be constriicted with 3" taxa where n is an integer.)

Once the trees were generated. we evolved 60 random characters ont0 each tree using the Evolve Characters option (a Markov model) with each of the following two models of evolution: 1. Gains only [e.g., evolution of copulation in water mites: Proctor, 19911: transition probabilities of 0.1 for gains (O + 1 transitions), 0.0 for losses (1 + O transitions). 0.9 for O + O transitions, and 1.0 for 1 + 1 transitions; and 2. Gains and losses

[e.g., evolution of dioecy in gymnosperms; Donoghue, 19891 : transition probabilities of 0.1 for gains. 0.05 for losses , 0.9 for O + O transitions. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 136 and 0.95 for 1 + 1 transitions [Maddison and Maddison, 19921. Character changes were reconstructed onto each tree using MacClade. The DEL-

TRAN option was used for resolving ambiguous reconstructions of character evolution in order to increase the number of gains reconstructed.

Remaining equivocal branches were resolved by assuming that the character state at the tree's toot was white (lacked both of the traits of interest) and by allowing only gains for model 1. Dyads of characters were then established by pairing adjacent random characters in the data set. The

CCT was conducted for each of the 720 dyads (12 trees. by 30 pairs of characters, by two models of evolution) using MacClade. Each character contributed to only one test except for the characters on the most balanced tree which were used again for the 50 and 25 tavon subset trees

(described below). We treated the first random character in each dyad as the independent variable and the second character as the dependent variable. Because of the size of the trees and the number of taxa. the

Simulation option was used with 1000 simulations and the Actual changes option was selected.

For each pair of characters. we determined two probabilities:

1. The probability that an association would be detected between

changes in the dependent and independent character when the

characters evolve independently. This analysis allows us to assess type 1 error (the probability that an association will be claimed by the test when none exists). We counted the number of observed gains and losses in the dependent character that occurred on black branches (those reconstructed to have the derived state) of the independent character. In the example show in Figure

5.1, three of the four gains in the dependent character are 011 black branches. We then used MacClade to calculate the probability of getting this many or more gains and as many or fewer losses on black branches given the total number of gains and losses observed for the dependent character (on al1 of the independent branches). Since al1 characters were generated randomly and independently. there shoiild be no significant association- any significant associations observed are due to chance (type 1 error ) .

3. The pîobability that an associatzorz would be detected if alJ of the changes in the dependent character had occurred on black branches of the independent character. This analysis allows us to assess type II error (the probability that an association will iiot be foiind when one exists). We simulated the extreme situation where gains in the dependent character occurred only in the presence of the derived state of the independent character. and t hen asked whet her the CCT would detect such an association. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

To do so, we counted the total number of gains and losses of the dependent variable, on al1 independent branches. In Figure 5.1

for example, there are four gains overall (three on black and one other). We then used MacClade to determine the probability

that as many or more gains (e.g., 4 in Figure 5.1) and as many

or fewer losses would occur by chance on black branches of the

inclependent character. This allowed us to simulate a correlation

between the traits without changing the rate of evolution or the met hods of reconstructing character evolution. The CCT needs

only to know the actual pattern of black and white branches for

the independent characters, not for the dependent characters.

Other ways of approaching this problem are considered in the

Discussion (section 5.6).

CVe next assessed the effect of including white branches on both of these probabilities. The proportion of white branches for each tree and each dyad of characters was calculated using a C program (available from

P.D.L.).Using the MacClade "node list" output format for representing the tree and character reconstruction. we used the C program to count gains and losses as well as white branches. We used nonparametric Spear- man rank correlations (corrected for ties when necessary) to examine the relationship between the probabilities calculated by the CCT and the proportion of white branches. The significance level for these correlations CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 139 were adjusted using sequential Bonferroni because the same test was repeated for each tree [Rice, 19891. We also used nominal logistic regression [Hosmer and Lemeshow, 1989, Trexler and Travis, 1993. SAS, 19971 to test whether an increase in the proportion of white branches (pwb) affected the likelihood that the CCT was significant (less than 0.05 or 0.01). This was done by asking whether pwb contributed significantly to a model that included the model of evolution, pwb and a tree shape statistic considered later (I),so that the relative importance these three factors could be corn- pared. Interactions were not included because they did not contribute significantly to the models. In our logistic regression analyses. a positive coefficient indicates that there was an increase in the proportion of significant CCT probabilities as the continuous variable increases. Where the effect of the model of evolution rvas considered. a positive coefficient indicates a higher proportion of significant CCT probabilities for the gains only model than for the model with gains and losses.

To examine the effect of tree shape on Maddison's CCT. we used the trees generated as described above and, for each tree. calculated a tree balance statistic called the index of imbalance (1, developed by Colless

[1982]and corrected by Heard [1992]and Rogers [1994]). 1 is calculated as where n is the total number of terminal taxa. and r and s are the number of terminal taxa to the right and left, respectively, of a given interna1 node. I is a good indicator of tree shape because it ranges from zero for perfectly balanced (symmetrical) trees to 1 for completely imbalanced

(asymmetrical) trees. This statistic was used because it has been the focus of rnuch recent research on tree shape [Heard. 1993. 1996. Rogers. 1994.

Mooers, 1995, Mooers and Heard. 19971 and because the expected valiie of the statistic for random trees with n end-taxa can be calculated [Heard.

We then examined the effect of tree imbalance on the CCT probabilities.

Each tree provided a single value of I . As in the preceding analysis. we determined both (1) the probability that an association would be detected between the evolution of dependent and independent characters when they are independent (to assess the effect of tree shape on type 1 error) and (2) the probability that an association would be detected if al1 of the changes in the dependent character had occurred on biack branches of the independent character (to assess the effect of tree shape on type II error). To analyze the effect of tree shape. we used two approaches. Linear regression

[for multiple y values at each x; Sokal and Rohlf, 1981.p. 471 was used to CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 141 examine how the CCT probability was influenced by tree imbalance (1 ). The CCT probabilities had highly skewed distributions. Only the logit transformation was strong enough to normalize these distributions. How- ever. there are zeros and ones in out data and the logit is undefined for these values. causing a nonrandom loss of data. For this reason regressions were performed on the untransformed values. CVe consider the regression with and without the extreme trees (most balanced and imbalanced) to test whether the effect of tree shape on the CCT is different in the range where real trees are more likely to fall, than it is across the whole range of tree shapes. CVe also included I in the nominal logistic regression analysis

(see above methocls) to test whether an increase in 1 affected the likelihood that the CCT was significant (for a = 0.05 or CI = 0.01).

To look at the effect of taxon sampling (which varies both the proportion of white branches and the number of tami) while holding tree shape more or less constant. we followecl the analysis of 100 taon trees with an analysis on two subsets of a nearly perfectly balanced 100 taixon tree. We did this by calculating the CCT for a 50 and 25 taxon clade within the larger tree. This was done using the same pairs of characters as in the analyses of the 100 taxon tree with the additional proviso that there be at least one change (gain or loss) in the dependent character within the selected clade. (If there are no changes, the CCT is fixed at either CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 142 zero or one.) CVe estimated the same two CCT probabilities (1 and 2 described above). Logistic regression was used to examine the effect of taxon number and the proportion of white branches together for the two models of evolution on the CCT probability. We used subsets of only the most balanced 100 taxon tree for several reasons. First. taking subsets of the most balanced tree (I = 0.01) does not result in trees with dras- tically different tree balance (0.02 for the 50 tavon sub-tree and 0.04 for the 25 taxon sub-tree), allowing us to ignore the effects of tree shape in this part of the analysis. With trees of intermediate balance. any sub-tree is likely to have a very different shape and I value. It is also difficult to take subsets of a fixed size without changing the structure of the resulting tree and breaking iip clades present in the larger tree. Subsets of the least balanced tree mre not used because when traits were gained but not lost. the subset trees were often entirely black.

The CCT relies on reconstructed ancestral states for the characters of interest to judge the numbers of gains and losses on a tree. The imple- mentation of the CCT in NlacClade also relies on a nul1 mode1 of random distribution of changes ont0 the tree to estimate the probability that dependent changes are concentrated on black branches of the independent character [see Maddison, 1990,for details]. Problems may arise wit h the test if parsimony reconstruction of ancestral states results in a very different distribution of changes ont0 the tree than that produced by the nul1 mode1 of random evolution. Fortunately, the effects from this sort of discrepancy on the CCT can be evaluated using the Reconstruction option in MacClade [for an explanation of the differences between Actual and

Reconstructed. see Maddison and Maddison. 1993,p. 310-311. To ensure that the above simulations were not influenced by this sort of reconstriic- tion error, we repeated the above simulations for 30 character pairs (15 with gains only and 15 with gains and losses) on three of the trees using the i\I.AXSTATE Reconstruction option. Bot h CCT probabilities (1) and (2) obtained in this way were then compared to those obtained using the Actual changes option using the Wilcoxon signed rank test (with sequential Bonferroni adjustment where appropriate). If there is no effect of using reconstructions. we expect there to be no significant difference between the probabilities obtained using the Actual and Reconst ructed simulations. Simulations with the Reconstruction option take consider- ably longer to run so the Actual changes option was used in the original simulations. and we only repeated the analysis with three of the 13 trees

(a. b and c) for both of the models of evolution. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

5.5 Results

5.5.1 The effect of ailowing gains only or bot h gains and losses

The overall effect of the model of evolution was that when both gains and losses were allowed, more gains were reconstructed ont0 the trees (using the independent character as an example: for al1 13 trees. Mean f SE =

8.56 f0.21) than when only gains were allowed (5.88 f 0.20). There were

4.51 f 0.15 losses reconstructed onto the 13 trees. The average number of black branches for the independent character was 106.49 i 1.90 for the model with losses and gains. and 141.80 i 2.26 for the mode1 with gains only. Obtaining significant CCT values was more likely when losses were allowed than when they were not (Figures 5.2 and 5.3. and Table 5.1). .A detailed evaluation of these effects is provicled in the following sections.

5.5.2 The effect of white branches

1. Characters evolve independent1y.-(a) Only gas'ns are a1lowed.-Considering al1 360 pairs of randomly evolved characters (Le.. uncorrelated). only a single significant association was detected at a = 0.05 and none were detected at a = 0.01. This indicates a realized type 1 error of 0.0028 (11360)which is smaller than we would expect: the upper 95% confidence limit based on the Binomial distribution (n = 360) is 0.015. which does not include

0.05. If type 1 errors occurred at a rate of one in twenty tests, we would O a Ob A c O d + e x g h ri ri k a balanceci r imbalanced

Proportion of white branches

Figure 5. 2: The relationship between CCT probabilities and the proportion Of branches with neither trait of interest (white branches) when only gains are allowed to evolve is shown for 30 pairs of characters on 1'2 trees with 100 taxa. Probabilities are for the cases where (a)characters are simulated to evolve independently ( probability 1 ) and where (b) al1 gains in the dependent character occur on black independent branches (probability 2). Dotted lines show CCT = 0.05. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 146

Table 5.1: Logistic regression analysis of CCT probability significance (< 0.05 or < 0.01) as a function of the model of evolution (gains only versus gains and losses), the proportion of white branches (pwb)and the tree balance statistic I . The iikelihood ratio y* (LRy2) indicates the relative contribution of a given effect to the overall best model including the effects shown in that part of the table. Interaction terms were included only if they contributed significantly to the models. Sections 1 and 2 represent the two different probabilities discussed in the text. Variable Coefficient SE LRx2 " pb i. Characters evolve independen tly. a = 0.05 Mode1 of evolutioii - 1.880 0.5 18 36.16'7

pub -5.507 2.051 8.191 1 -0.458 0.934 0.259 intercept -3.301 0.644

2. .AH changes in the dependent character occur on black branches.

û = 0.05

Mode1 of evolution 0.227 0.381 0.36

PW~ 17.526 1.619 2 14.57 1 -7.358 1.190 30.52 Model * 1 -6.253 1.190 17.89 Intercept -0.824 0.446

û = 0.01 Mode1 of evolution -0.030 0.293 1 .O23

PW~ 15.251 1.400 208.596 I -6.0141 1 .-CO5 27.60 1 Mode1 * I -4 -31 1 A06 11.149 intercept -1.813 0.391

a Al1 with df = 1.

* Probability of getting a greater y * by chance. CHAPTER3. POWEROF THE CONCENTRATED-CHANGES TEST. 147 have expected 18 significant tests for a = 0.05 and 4 for a = 0.01. The test is therefore conservative with respect to type I error when only gains are allowed.

The proportion of white branches had a small, but significant effect on the CCT probability. There was a negative correlation between the proportion of white branches and the test probability when analyses for al1 12 trees were pooled (r, = -0.34. n = 360, p < 0.0001: Figure 5.2a). However . when correlations were examined for each tree separately. none were significant (with sequential Bonferroni correction for 13 tests and a table-wide a = 0.05) and iii two cases. the sign was reversecl (range: r, = -0.52, p = 0.005 to r, = +0.31, p=0.09. n =30 in each case).

(b) Both gains and losses are allowed.-Twenty-five out of 360 character pairs produced significant associations at a = 0.05 and 4 out of 360 at a = 0.01. resulting in realized type 1 error of 0.07 and 0.01 respectively The likelihood of making type I errors is not significantly different from what we would expect for a = 0.05: lower 95% confidence limit is 0.045

(for 25 significant out of 360). which includes 0.05, and was exactly what we would expect for cr = 0.01. Neither the overall nor any of the separate correlations were significant at ct = 0.05 (overall: r, = 0.06, p = 0.27: range: r, = -0.19. p = 0.31 to r, = +0.36, p = 0.05, n = 30 in each case). CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

There was a significant negative contribution of proport ion white branches to the significance of the CCT probability (at cr = 0.05) based on the three- variable logistic regression model (Table 5.1). This is entirely explained by the decrease in the proportion of significant CCT probabilities with increased pu76 seen in the data for the model where both gains and losses were allowed (see points above versus below dotted line in Figure 3.3a).

When only gains are allowed, pwb cloes not influence the significance of the CCT since there is only one significant probability under this model. This difference between the models of evolution explains the significant effect of model of evolution on the analysis (Table 5.1). The logistic regression analysis could not be estimated for cr = 0.01 because there were too few significant CCT probabilities at this a level.

2. AII changes in the dependent character occvr on black branches.-

(a) Only gains are allowed.--When al1 changes in the dependent character were presumed to have occurred on "black" branches of the independent character. significant associations were detected for 113 of 360 character pairs for a = 0.05 and 73 of 360 for a = 0.01 (Figure 5.2b). ;\iIoreover. there was a highly significant negative correlation between the proportion of white branches and the CCT probability (r, = -0.79. n = 360. p < 0.0001; data for al1 12 trees pooled). When each tree was examined CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

Q) (b) C 0 k 0 balanced a imbalanced

Proportion of white branches

Figure 5.3: The relationship between CCT probabilities and the proportion of branches with neither trait of interest (white branches) when both gains and losses are allowed to evolve is shown for 30 pairs of characters on 12 trees with 100 taxa. Probabilities are for the cases where (a)characters are simuloted to evolve independently (probability 1) and where (b) al1 changes in the dependent character occur on black independent branches (probability 3). Dotted lines show CCT = 0.05. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 150 separately. al1 of the correlations were significant (with Bonferroni corrected a values for 13 tests) and al1 were negative (range: r, = -0.83. p < 0.0001 to r, = -0.47. p = 0.01: n = 30 in each case).

(b) Both gains and losses are allowed.-When both gains and losses were allowed. 391 of 360 character pairs gave a CCT probability < 0.05. and 247 of 360 were less than 0.01. The proportion of white branches and the CCT probability were highly correlated (r, = -0.65. n = 360. p < 0.0001: data for al1 13 trees pooled: Figure L3b) with 9 of the 12 trees also reaching significance (after Bonferroni correction for 13 tests: range: r, = -0.84. p < 0.0001 to r, = -0.35. p = 0.06: n = 30 in each case). The ability to detect a significant association between the dependent and independent character was greatly reduced once the proportion of white branches was less than 20%. but this loss of power was less marked than it was when only gains were allowed (compare Figures 5.2b and 5.3b).

There was a highly significant positive contribution of pwb to the significance (for both cr = 0.05 and a = 0.01) of this CCT probability based on the logistic regression mode1 (shown in Table 3.1). .As the proportion of white branches increases. so does the fraction of CCT values tliat are judged significant . The mode1 of evolution did not contribute significant ly on its own. (The Model by I interaction will be discussed in the next CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 151

Table 5.2: Coefficients for regression of two CCT probabilities on tree shape statistic

I. Values are shown separately for each mode1 of evolution. and for regressions with and without the two extreme trees. Sections 1 and 2 represent regressions for the two different pro babili t ies discussed in the text .

Including extreme tree s hapes Excluding extreme t ree shapes - - Slope Inter- R2 P" Slope Inter- R' pa cept cept

1. Characters evolve independent ly. Model of evolution Gains only O.il 0.81 0.04 0.046 1.35 0.56 0.06 0.003

Gains and Losses 0.05 0.45 0.001 0.551 0.36 0.39 0.0001 0.593 2. .\II changes in the dependent character occur on black branches.

Model of evolut ion Gains only 0.73 0.16 0.25 0.001 3.78 -0.48 0.19 0.00005

Gains and Losses 0.1 1 0.02 0.0:3 0.073 0.80 -0.13 0.06 0.033

a Represents the significance level of the regression slope.

section.)

5.5.3 The effect of tree shape

1. Chaîacters evolve independent1y.-(a) Only gains are atlowed.-There

was a significant positive relationship between the CCT probability and

the tree imbalance statistic (I ), and this relationship is stronger when

the extreme trees (most balanced and imbalanced) are exchded from the

analysis (Table 5.2 and Figure 5.4a). By excluding the extreme trees, we CHAPTER5. POWEROF THE CONCENTR.4TED-CHANGES TEST.

Tree imbalance (1)

Figure 5.4: The relationship between CCT probabilities and the tree shape statistic 1 when only gains are allowed to evolve is shown for 30 pairs of characters on 1%trees wit h

100 taxa. Probabilities are for the cases where (a) characters are simulated to evolve independeritly (probability 1) and where (b) al1 gains in the depeodent character occur on black independent branches (probability 2)). Dotted lines show CCT = 0.05. solid lines represent least squares regression line for al1 tree shapes. and dashed lines represent regression line when two extreme tree shapes are eucluded. place more emphasis on the range of tree shapes in which real trees are expected to fall, and the effect of tree shape on this CCT value is stronger in this range. As the trees became more balanced (lower I ), the CCT probability decreased slight ly. However, even when the t ree was nearly fiilly balanced. only a single type 1 error was made (at the 0.05 significance level) .

(b) Both gains and losses are al1owed.-The slope of the regression of the CCT value on I was not significantly different from zero (with and without the extreme trees: Table 5.2 and Figure 5.5a).

The contribution of 1 to the logistic regression that included the mode1 of evolution. the proportion white branches and I was not significant (Ta- ble 5.1). The CCT. therefore, appears not to be affected by tree topology. and this variable does not seem to increase the likelihood of making type 1 errors.

2. ALI changes in the dependent chamcter occur on black branches.-

(a) Only gains are al1oured.-Tree imbalance had a sigiiificant effect on the CCT probability in cases where the dependent character changed only on black branches of the independent character (Figure 5.4b). There was again a positive relationship between tree imbalance and this CCT proba- CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

Tree imbalance (1)

Figure 5.5: The relationship between CCT probabilities and the tree shape statistic i

when both gains and losses are allowed to evolve is shown for 30 pairs of characters on 12

trees with 100 taxa. Probabilities are for the cases where (a) characters are sirnulateci to evolve independently (probability 1) and where (b)al1 changes in the dependent character occur on black independent branches (probability 2). Dotted lines show CCT = 0.05. solid lines represent least squares regression line for al1 tree shapes. and dashed lines represent regression line when two extreme tree shapes are excluded. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 155 bility both with and without the extreme trees, and again the relationship is stronger when the extreme trees are excluded (Table 5.2). Moreover, the ability to detect a significant association between characters was strongly influenced by tree shape. The two trees that were most balanced (Le., lowest I: tree most balanced. I = 0.011; tree d. 1 = 0.117) exhibited the greatest proportion of significant associations (27 of 30. and 21 of

30 respectively for a = 0.05 and 24 of 30. and 14 of 30 respectively for cr = 0.01). In contrast 10% or fewer of the associations were significant for the two least balanced trees (for both a = 0.05 and a = 0.01: tree least

balanced I = 1. O of 30 associations significant : tree k: I = 0.968. 3 of 30 associations significant ) .

(b) Both gains and losses are a2lowed.-There was a positive relationship between tree imbalance and this CCT probability both with and without the extreme trees. This relationship was not significant when the extreme trees were included, but was significant when they were excluded

(Figure 5.5b and Table 5.3). The two trees that were most balanced exhib-

ited the greatest proportion of significant associations ( most balanced: 29

of 30. and d: 27 of 30 for a = 0.05 and 29 of 30, and 25 of 30 respectively

for a = 0.01). In contrast. many fewer of the associations were significant

for the two least balanced trees (least balanced: 18 of 30 associations sig-

nificant and k: 17 of 30 associations significant for a = 0.05. and 2 of 30 CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. and 1 of 30 respectively for a = 0.01).

The results in section (a) and (b) above were reflected in the logistic regression results for both a = 0.05 and a = 0.01. There was a significant negative contribution of I to the significance of this CCT probability based on the logistic regression mode1 (Table 5.1). Tree topology clearly has an effect on the power of the CCT-the more balanced the tree, the more likely that a significant association will be detected. This effect is significantly stronger when only gains are considered than when losses are also included (significant negative interaction; see Figures 5 Ab and 5.5b and

Table 5.2). However. the logistic regression results indicate that the proportion white branches has a greater effect on the CCT probability than either tree topology. the model of evolution or the model * I interaction (greater LRy2 in Table 5.1).

5.5.4 Number of taxa versus proportion of white branches

There was only one significant CCT value (with pwb = 0.3: at a = 0.05 and none at

a function of the mode1 of evolution (gains only versus gains and losses), the proportion of white branches (pwb) and the number of taxa. Regressions were only

performed when al1 changes in the dependent character occur on black branches

(probability 2). The likelihood ratio ( L RrZ ) indicates the relative contribution of a given effect to the overall best mode1 including the effects shown in that part of the table.

Variable Coefficient SE LRt2" pb

ci = 0.05

Model of evolution

pvrb

Xumber of taxa

pw6 " Yumber of taxa Intercept

cl = 0.01 Model of evolution

pwb

Yumber of taxa

pu16 * Yumber of taxa Intercept

Al1 with df = 1.

Probability of getting a greater x2 by chance. the cu = 0.05 significance level, pub and the interaction between this variable and number of taxa both contribute significantly to the regression.

Mode1 of evolution and number of taxa by themselves do not contribute significantly. Therefore. once the effect of the interaction is taken into account. as the proportion of white branches increases. the fraction of CCT values that are significant (< 0.05) decreases. The variable pwb is relatively more important than the number of taxa (,CR\' for pwb > LR~" for number of taxa). indicating that tmon sampling effects on the CCT are driven primarily by the proportion of white branches. Hontever. the interaction contributes the most strongly to the regression. The significant interaction term indicates that as the number of taxa decrease (especially from 50 to 25). so does the range of pwb over which the test has power.

Specifically. the point at which tliere is no power to detect an association between characters increases as the number of taxa decrease (e.g.. vertical lines in Figure 5.6) untii there is no range of pwb for which the CCT reliably indicates a significant association. When only gains are allowed. the

point at which the test loses power and makes type II errors is around 0.25 pwb for 100 taxa. 0.43 pwb for 50 taxa and 0.88 pub for 25 taxa (Figure

5.6~~.b and c). Results for when both gains and losses are allowed follow

the same pattern (0.13. 0.28. and 0.88 for 100, 50. and 25 taxa respec-

tively). This seems to be a straightforward result of the decrease in the

number of branches on which character changes could have occurred that CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

Proportion of white branches

Figure 5.6: The relationship between CCT probabiiity 2 (al1 changes are presumed to occur on black branches) and the proportion of branches with neither trait of interest (white branches) wben only gains are allowed to evolve is shown for trees with (a)100.

(b)50. and (c) 25 taxa. The horizontal line indicates CCT = 0.05. and the vertical line represents the point (in terms of the proportion of white branches) below which the CCT begins to make type II errors (power breakdown point). CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 160 accompanies a decrease in the number of taxa. At the 0.01 significance level, the interaction between pwb and number of taxa is the only statistically significant contributor to the regression, and the mode1 of evolution becomes relatively more important than pu16 (Table 5.3).

5.5.5 Act ual versus reconstructed changes

Finally. to test whether using reconstructed character states had an effect on the CCT probabilities. we compared values obtainecl using the Actual changes option and the MAUTATE reconstruction option in MacClade for trees a, b and c. These trees fa11 within the range of tree shapes into which we espect real trees to be most likely to fall. The differences in the values obtained using these two methods were very small (Imedian clifferencesl between O and 0.007). Wilcoxon signed rank tests coniparing the MAXSTATE reconstructed CCT values and the *8.ktual"values for each of the two kinds of probabilities (1 and 2) and models of evolution

(gains only, and losses and gains) for trees a. b and c resulted in one rnarginally significant difference among twelve tests (Wilcoxon z = 3.67. p = 0.008; with Bonferroni correction). For tree c. when only gains were allowed. the Actual changes option caused an underestimate of probability

(1). However. the median difference was very small (-0.006).Only a single

CCT value for probability (1)was significant when only gains were allowed and it was not on this tree but on tree b. Consequently, the difference in CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 161 results between the MAXSTATE reconstruction methods and the Actual changes method appears to be small, indicating that our results are not an artifact of having used reconstructed character states.

5.6 Discussion

One of the limitations in evaluating fully the power of the CCT is that there are so many variables that can potentially influence the outcome of the test. Many of these variables are interrelated. and it becomes difficult to assess the effect of any single variable while holding al1 others constant. In our simulations. it woiild have been possible to consider additional variables such as different transition probabilities or the resolving option ACCTRAN rat her t han DELTRXN. However. each added variable increases the number of simulations dramatically and such an e-xhaustive analysis becomes difficult to present coherently. We chose instead to focus on four variables that we thought might have an impact on the conclusions drawn with the CCT-the proportion of white branches. tree shape, two basic models of evolution, and, in a simple way, the number of taxa. .A summary of Our results for each of these variables is presented in Table

5.4 and we discuss each effect in turn. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

Table 5.4: Summary of the effects of white branches. tree shape, number of taxa, and mode1 of evolution (gains only, or gains and losses) on the outcome of the concentrated changes test .

Probability 1: Probability 2: Characten evolve independcntly AI1 changes in dcpcndcnt character oc-

cur on blrrck branches Effect of white branches a. Gains only Likclihood of type I error is lower Likelihood of type II error incrcascs then expected (CCT is conserva- whcn the proportion of white branches cive) ia < 20% Negative comhtion of propor- Strong, ncgative correlation of propor-

tion of white brancher with Prob- tion O$ tuhite brancher with Probability ability t b. Gains and losdes Type 1 error as expected (CCT is Likelihood of type II error increases accurate) when the proportion of white branches is < 20% :Vo cffect of proportion of white Strong. negativc comlation oj propor- branches on Probability 1 tion of white bronches with Probability -d Effect of tree shape

a. Gains only Likelihood of type i error is low Likelihood of type II error incrcases as tree imbalancc ( f) increues Positive correlation of trcc imbal- Strong, positive correlation uj trcc im-

once (1) with Probability balancc (1) wrth Probability 2 b. Gains and loases Likelihood of type error is low Likelihood of type II error incrcascs as

trce irnbalancc ( 1) increascs

Xo comlation of tnc imbalancc CVcak, positive comlation of tee im-

(I) with Probability 1 balancc (1) with Probability 2 Effcct of nurnber of taxa Gains only and gains and losses Too fcw significant CCT duesto Likelihood of type II error incrcascs as evaluatc nurnber of taxa decreases, but depends on the proportion of white branches Signrficant interaction with proportion of white brancher on Probability 2 5.6.1 The effect ofwhite branches

For the large realistically shaped trees and the extreme trees used in this stucly, character pairs with a larger proportion of white branches were not more likely to have significant CCT values when no association between the characters exists (Probability 1. Table 5.4). Increasing the proportion of white branches decreased the likelihood of type 1 error when gains and losses were allowed, and had no effect when only gains were allowed.

The test therefore seems to behave reasonably with regard to type I error. When there was no association between the characters of interest. the CCT reliably reflected this fact and adding white branches did not increase the chances of obtaining a significant association when none existed.

In striking contrast. the power of the CCT to detect associations between characters (type II error) was strongly influenced by white branches.

Type II errors were made quite cornmonly when there was a low pïopor- tion of white branches (for both models of evolution). We interpret this to mean that the test can be insensitive when there are too few white branches. In our data this occurs when there are fewer than 20% white branches. This result is not entirely unexpected. As more of the branches of a given tree are reconstructed to contain the derived state of the independent character (i.e.. are black), the probability that a change in the dependent character will occur on a black branch by chance will necessar- CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 164 ily increase. The CCT should, and does, reflect this fact. Moreover. we would expect this to be true for trees of any shape because it is a function of how early the characters of interest evolved. Hontever. what has been less appreciated, is that the power of the test is dramatically reduced when one or both of the traits of interest evolved early (and heiice branches for one or both traits are predorninantly black). This power loss is mitigated when both characters can be lost after they have been gainecl. because losses drive the proportion of white branches back up (compare Figures

52b and 5.3b).

5.6.2 The effect of tree topology

Though less influential than the proportion white branches. the tree balance statistic. I . is significantly positively related to the CCT value (Fig- ures 5.4 and 5.5, and Table L'>)-the more balanced the tree. the more likely that a significant association will be detected. This effect is exaggerated when only gains are reconstructed. Maddison [1990] pointed out that imbalanced trees have high variance in the amount of time represented by each branch. Accordingly. we might anticipate that the CCT value would be lower in imbalanced trees because of the greater likelihood of two characters evolving on the longer branches by chance rather than because of a causal connection [Maddison. 19901. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

The CCT could be modified to allow different probabilities of change on different branches by changing the nul1 mode1 from one of random distribution of changes to one where the probability of change on a branch depends on its length [Sanderson, 19911. Pagel [1994b]developed a maximum likelihood approach that gives a measure of the correlated evolution of two traits while taking branch lengths into account. However. our results suggest that the effect of tree shape on the CCT is not due solely to the influence of branch length. Character changes were not more likely in imbalanced parts of the trees because changes occurred with equal probability on each branch regardless of length. Therefore branch length variance alone cannot explain the higher CCT valiles in more imbalanced trees.

Werdelin and Tullberg [1995] noted that there is a reduced range of possible CCT values for imbalanced trees when only gains are allowed. Our data indicate that this may be even more true when both losses and gains are reconstructed (compare Figures 5.4b and 5.5b). We suggest that this pattern results from the different consequences of gains and losses in balanced versus imbalanced parts of trees. There is the potential for higher variance in the number of black branches when changes occur in imbalanced clades. For example, in the imbalanced clade in Figure 5.1, a gain on the branch that forms the root of clade O-Ut one branch CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 166 from the root of clade N-U would result in al1 branches leading to O-U being black (13 branches). A gain on the other branch from the root of N-U results in 1 black branch. On the other hand, in an equal-sized balanced clade A-H, an equally basal gain on either the root branch of clade E-H or clade A-D would result in al1 branches of either clade being black (seven branches). Gains one step away from the root of eacli clade result in very different ranges in the amount of black branches. The consequence for the CCT is that the maximum CCT value possible on imbalanced trees is higher than for balanced trees-if most of a clade is black. the numerator and denominator of the CCT approach each other.

Whatever the cause. tree shape influenced the CCT probability for our

twelve constructed trees which span the range of tree shapes [in agreement

with the results of Werdelin and Tullberg. 19951. Because of the effects

of tree shape on the CCT. we recommend that users of this test calculate the tree balance statistic I for their trees. CCT results for trees with high

I values should be viewed as more conservative than those basecl on trees with low 1 values.

5.6.3 The effect of number of taxa

The magnitude of the effect of white branches on the CCT was related to

the number of taxa (or number of branches) in the tree. Because there were CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 167 so few significant CCT values detected when characters evolved randomly

(probability 1, Table 5.4). we could not assess the effect of the number of taxa on Type 1 error. However, our analysis indicates that the likelihood of type II errors increases as the number of taxa decrease. although this also depended on the proportion of white branches on the tree (Figure 5.6).

For example, in a tree of 100 taxa. type II errors are more likely when the proportion of white branches falls belon, 0.30. whereas in a tree of 25 taxa. type 11 errors become frequent when the proportion of white branches falls below 0.90! (Figure 5.6) This effect occurs because a reduction in the number of taxa reduces the number of places where changes can occur on the tree. leading to higher CCT values and increased possibility of type II error. Our resiilts (Figure 5.6) suggest that researchers should be cautious in applying the CCT to trees with fewer than 50 taxa or with characters reconstructed to have less than 30-40% white branches whenever the gains per branch ratio is 5 0.06.

5.6.4 The effect of the mode1 of evolution: Gains only vs. gains and losses

When only gains are allowed, the CCT is perhaps too conservative with regard to type 1 error. Our results demonstrate a realized type 1 error that is roughly 18 times lower than the generally accepted 5% error rate

(0.0028 as opposed to 0.05). Interestingly, Proctor (1991) found that Ri- CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 168 dley's method (1983) was also "extremely conservative when the trait is never lost." One approach to ameliorate this effect would be to adjust the critical value for statistical significance of the CCT (e.g.. to p < 0.10) when only gains are considered. However, it is difficult to know where to objectively set the critical value for the test. For our data one in twenty results would be deemed significant only if we used a critical valiie of 0.40. a rather extreme adjustrnent.

In contrast, the CCT behaves more as we would expect when losses and gains are both allowed (Table 5.4). It is not clear why the CCT behaves so differently under the two models of evolution. One possibility is that. although the probability of gain was the same for the two models in our simiilations. there may have been a smaller number of realized gains when only gains were permitted simply because losses created the opportunity for more gains. Alternatively, a higher proportion of black branches for the independent character might be expected when only gains are allowed.

Either of these results (fewer gains or more black branches) would lead to higher values of the CCT probability and hence more conservative test results. Our data support both of these possibilities. The average number of gains of the independent trait is less for the model with gains only

(5.88) than for the model including losses (8.56). In addition. there are 1.33 times more black branches, on average, when only gains are allowed CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 169 than when losses are also allowed. However, the relative numbers of gains and black branches are also affected by other factors such as the fact that we are reconstructing the changes ont0 the trees rather than using the .4ctual changes and our use of DELTRAN resolving options.

5.6.5 Recommendations for future studies: How do we define the sampling universe?

Our results clearly demonstrate that inclusion of taxa lacking t.he clerived state of both characters can influence the power of the CCT. as Maddi- son suspected. The question then becomes: what determines which. and how many, taxa lacking the traits of interest can or should be adcled?

Several suggestions have been made about how the scope of a study of correlated evolution shoiild be defined [Coddington. 1992. 1994, Pagel.

1994bl. Coddington [1994] proposed that as wide an array of organisms as possible should be included in the analysis to mavimize the generality of the conclusions. Pagel [1994b], in contrast. argued that tests of correlated evolution make hypotheses about the selective forces producing the correlation of interest and, accordingly. only clades that contain taxa with the independent trait of interest should be considered.

Our results also indicate that spurious correlations are not likely to arise simply because a large proportion of a tree is white with respect to two characters of interest, at least for the simulated data presented here. Thus we believe the risk of expanding the sampling universe should be minimal.

In contrast, if the independent trait is widespread and has evolved only a few times, limiting the study to only clades that contain taxa with the independent trait may mean that there will be very few white branches.

This will make it impossible to use the CCT to detect an association.

Sillén-Tullberg's [1993] CST will suffer a similar loss of power. although it may still be possible to use a test based on sister taxon comparisons such as that of Read and Nee [1995]. Consequently, the value of adding clades containing white branches to reduce type II error would seem. based on

Our data, to offset any small effect (if any) of increasing type 1 error rates.

We are aware of at least one study where the effect of a small propor-

tion of white branches may have influenced the outcome of a test for cor-

related evolution. Hunter [1995] iised Maddison's CCT and several other

methods to test hypotheses about the evolution of reduced wings in forest

Lepidoptera. Because of concern that white branches were "problematic"

for the CCT, large clades (97 species) in the Geometridae were omitted

from the study [Hunter, 1995,p. 271. The proportion white branches was

not calculated for the phylogenies used in the study, but the lack of sig-

nificance of the CCT for al1 hypotheses tested may have been a result of

the omission of white branch taxa. Sillén-Tullberg [1993] also cautions CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 171 researchers using phylogenies from the literature to be sure that the tree has not been resolved in such a way as to limit white branches.

5.6.6 Assumptions of our analyses

We have chosen what sonie may consider a peculiar way of simulating perfect CO-evolution. We have asked what the CCT probability would be if al1 dependent character changes (both on black and white independent branches) had occurred on black branches. Ideaily one woiilci want to make the probability of change in one character depend on the state of

another character so tliat CO-evolutioncould be simulated clirectly. This is

not possible in MacClade currently. As an alternative to the method we

used, one could consider character pairs where al1 changes of the dependent character occur on black branches (six percent of Our character pairs meet this criterion). Unfortunately. this method can have the undesirable

effect of restricting the study to trees that are predominately black (for

our data, the changes in independent characters do not fa11 on black branches unless the tree is > 77% black). We can think of no simple way

to change transition probabilities to deal with this problem. However.

we note that our method should not create an unreasonably high number

of dependent gains as we use the same transition probabilities for both

dependent and independent characters. For example. there were no cases CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST. 172 where there were more changes in the dependent character than there were black branches.

We also used reconstructed character states in our analysis of the CCT and it is possible that this may have affected our results. However. when we compared the results of the MAXSTATE reconstruction methods and the Actual changes method for a sample of trees. the differences were small and, in 11 of 12 comparisons. not significantly different. Consequently, the patterns we describe do not appear to be an artifact of having used reconstructed character states.

Finally. we assumed certain values for transition probabilities of gains and losses. and we used the DELTRAN resolving option throughout al1 of our analyses. Our primary objective in doing so was to generate sufficient numbers of gains of the dependent character and a range of trees with varying degrees of white branches to be able to fully explore the power of the CCT. Different transitions probabilities or different resolving options may yield different patterns and we encourage researchers to continue to evaluate these alternatives. In the interim. we believe our analyses provide new insight into the strengths and limitations of the concentrated changes test and will help guide others in the use of this test in future comparative st udies. CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

5.7 Conclusions

We conclude that the proportion white branches and tree shape do influence the results of the CCT. and they do so to different extents depending on whether or not losses are reconstructed ont0 trees in addition to gains.

When the evolution of two correlated characters is reconstructed ont0 a cladogram, the proportion of the cladograrn branches that have neither trait of interest has an important effect on the concentrateci changes test.

This effect is not to increase the likelihood that the test will be significant. but to constrain its usefiilness. Coiitrary to our initial expectations. the susceptibility of the test to type 1 errors is not increased by including a large proportion of white branches. In contrast. if there are too few white branches or too few taxa. the test is not likely to detect even very strong correlations (i.e., is likely to make type II errors frequently). Tree shape can also affect the CCT probability. althoiigh for our data set it did so

to a smaller degree than the proportion of white branches. Type II errors are more likely in imbalanced trees. and the rate at which their likelihood increases is greater when only gains are considered. Finally. the results of

the test are affected by the mode1 of evolution. In particular, the CCT is very conservative with regard to type 1 error when only gains are recon- CHAPTER5. POWEROF THE CONCENTR.4TED-CHANGES TEST. 174 structed ont0 a tree. Our results have consequences for studies designed to test hypotheses of correlated evolution. It is important not to so limit the scope of the study that clades with neither trait of interest are unnec- essarily excluded. If concerns exist about the effect of white branches on a particular tree, simulations such as the ones undertaken in this study can be used to estimate the power of the CCT for a given set of characters and a particular tree shape. We also recommend that users of the CCT report I for their trees to allow others to assess the extent to which tree shape may influence their results.

5.8 Acknowledgments

We thank Lin Chao. David Carr. and Douglas Gill for suggesting the idea for this paper. Stephen Heard. Wayne Maddison. Darryl Gwynne. Arne

Slooers. Robert Baker. and Luc Bussière gave us helpful discussion. David

Cannatella. Stephen Heard, Wayne Maddison. h mi la Martins. Adrienne Rigler, John Weins, and an anonymous reviewer commented on an earlier nianuscript. P.D.L. was supported by a National Science ancl Engineer- ing Research Council of Canada (NSERC) grant to Darryl Gwynne. J. McA. E. was supported by an NSERC grant, by the Raveling Waterfowl

Endowment. and by the Agricultural Experiment Station. University of CHAPTER5. POWEROF THE CONCENTRATED-CHANGES TEST.

California. Chapter 6

Selection for multiple mating in fernales: sterility and sex-ratio distorters

BY Patrick D. Lorch

Biology Depart ment

University of Toronto at 'ulississauga and Lin Chao

Department of Biology

University of California, San Diego CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 6.1 Abstract

If females are unable to discriminate among males before mating, remating by females that store sperm niay have evolved as

a hedge against having only with 'costly' mates (less preferred

males that reduce her fitness). However, the benefit of rernating

is not guaranteed because she can also mate by chance wit h an-

other costly male. LVe devised a mode1 to explain the evolution

of female remating by representing fernale fitness as a function

of the proportion of costly mates. CVe examined the effect of a

linear, a concave upward, and a concave downward fitness func-

tion and found that only the latter favors the evolution of female

remat ing. Wit h a concave downward function. females mating

with intermediate proportions of costly mates have nearly the

same fit ness as females wit h none. .A biological interpretation

for a concave downward function is that sperm from good males

are better at competing with sperm from costly males. A concave

upward function implies the reverse. whereas a linear funct ion will occur when sperm are equally cornpetitive. We review spe-

cific situations in nature that might produce a concave downward

function and find evidence that sterility and intragenomic conflict are two situations capable of driving the evolution of female CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

remating by our model.

6.2 Introduction

Diverse hypotheses, bot h adaptive and nonadapt ive. have been proposed to explain why females with the capacity to store sperm often mate more than once. One nonadaptive hypotheses is that multiple mating occurs due to a genetic correlation between female and male tendency to remate [Hall- iday and Arnold. 19871. Adaptive hypotheses are more numerous. Females may accept addit ional mat ings to reduce costs of intersexual harassrnent by accepting a behavior that is strongly favored in males. to acquire more nutrients from seminal fluid or nuptial gifts. to obtain parental care from additional males. or to produce genetically diverse or superior progeny

[Halliday and Arnold, 1987, Loman et al.. 1988. Sherman et al.. 1988. Ya- sui. 19981. Females rnay benefit by allowing the most cornpetitive sperm to

fertilize her young (Harvey and May, 1989: but see Curtsinger. 1991, Yasui.

1997). Keller and Reeve [1995] suggest that one mating may not provide

the female with enough sperm to fertilize al1 of her eggs [e.g.. Walker. 1980, Thornhill and Alcock, 1983, Lorch et al., 1993, Lewis and Austad.

1994. Fjerdingstad and Boomsma, 19981 or that females are hedging their

bets against the possible sterility of their first mate [see Olsson and Shine, CHAPTER6. SELECTIONFOR MULTlPLE MATING IN FEMALES. 179

19971. A more recent hypothesis proposes that females remate as a hedge against fitness costs arising from intragenomic conflict when they mate with genetically incompatible males [Zeh and Zeh, 19961. Intragenomic conflict. from the female's perspective, can refer to any genetically based trait in males that reduces her fitness. and it can be attributed to various causes ranging from endosymbionts and transposable elements to inbreed- ing. genomic imprinting and segregation distorters (e.g.. genes that cause deviation frorn a one-to-one sex ratio (sex-ratio distorters. sensu Haig and

Bergstrom [1995]); Zeh and Zeh. 1996).

Both male sterility and intragenomic conflict can provide an advantage to female remating because having sterile mates and having mates with sex-ratio distorters. for example. can reduce female fitness. When females remate. they gain by diliiting the fitness costs of such mates (referred to hereafter as 'costly' males). Male sterility. at one extreme of the range of costs to females. occurs at relatively high frequency in some natural populations (e.g., 4.5% in the sand lizard. Lacerta agilis. [Olsson and

Shine. 199'71: and 20% in two stalk-eyed fly species of the genus Cyrtodz- opszs [Wilkinson et al., 1998a1). Sterility is thought to arise from parasite infections [Alvarez. 1993, Tagashira and Tanaka, 19981 and certain chro- mosomal rearrangements of the sex chromosomes [McICee et al.. 19981.

There are obvious fitness consequences for females who mate only with a CHAPTER6. SELECTIONFOR MULTIPLE hiIATING IN FEMALES. 180 sterile male. Several authors have proposed that females remate to avoid inviable offspring [but see Birkhead and Mdler, 1982. Gibson and Jewell.

1982, Wetton and Parkin, 1991, Lifjeld, 19941. Olsson and Shine [1997] have shown that matings with sterile males can result in females laying eggs that do not develop. So there is some evidence that male sterility can negatively affect female fitness.

As mentioned above. females can also incur fitness costs when mating with genetically incompatible mates siich as males carrying sex-ratio distorter genes [Zeh and Zeh. 19961-our focal example. for this paper, of a type of mate that is less costly than a sterile mate. Ses ratio genes are known in butterflies [Chanter and Owen, 19721 and several species of

Diptera [reviewed in Presgraves et al.. 19971. being recently discovered in wild populations of two species of 'vlalaysian stalk-eyed flies [Cyrto- diopsis whitei and Cyrtodzopsis dalmanni, Diopsidae: Presgraves et al..

1997, Wilkinson et al.. 1998bl. Although there are relatively few examples. Jaenike LI9961 argues that since five of the nine Drosophzla species he has studied carry sec-ratio distorters. distorters are probably more preva- lent than is commonly recognized. Fisher [1930] first pointed out that females producing sex-biased broods would suffer fitness costs because each sex must supply half of the parents of al1 future generations. Thus. ofkpnng from sex-biased broods may be under-represented as the par- CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 181 ents of the next generation if (for a population sex-ratio near unity) some over-abundant female offspring fail to mate or if they have reduced fitness because they do not mate often enough (e.g., when nutritious mating gifts are involved or when females are sperm limited: see Discussion (Section

6.5)). There is niounting eviclence that sex-ratio distorter genes are often accompanied by pleiotropic decreases in the numbers of sperm that carrier males transfer [Beckenbach. 1978, Wu. 1983a.b. Presgraves et al.. 1997'1. which could leave females who mate only once sperrn lirnited. Sex-ratio distorters can also clrive to fixation resiilting in primarily single sex populations, and perhaps local extinctions [Hamilton. 19671 and selection at the level of populations when they are relatively isolated from each other.

With a simple model. we demonstrate that multiple mating can evolve as a hedge against male sterility only under a restricted set of conditions: a fernale's relative fitness must be a concave clownward fitnction of the proportion of her mates that are sterile. In other words. females mated to intermediate proportions of sterile mates must have a fitness similar to females without such mates. CVe extend the results for sterility to show that multiple mating can evolve under a similar range of conditions in the context of intragenomic conflict whenever females encounter males of two levels of quality. The way fernale fitness depends on the proportion of costly mates has largely been ignored in previous theoretical work on the CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES, 182 advantages of female remating [but see Wu, 1983bI. We focus on sex-ratio distorters as an example of intragenomic conflict both because it is fairly well studied and because it is useful to have an example in mind when considering our model. Bear in mind, however. that the model we present may be applicable to other forms of intragenomic conflict producing a range in the costliness of mates. We also discuss the effect on Our results of both the assessrnent of male cpality by females and subsequent selective sperm use [sperm choice, a mechanism of cryptic female choice: Eberhard.

19961, and of competition among sperm from a fernale's different mates

(sperm competition).

6.3 The model

CVe are interested in understanding whether female multiple rnating can evolve as a way to reduce the effects of mating with what we have callecl costly males. To start. we need a model of female fitness in terms of the proportion of her mates that are costly (as opposed to good). The simplest model is a linear decrease in fitness with increased proportions of costly mates. Alternatively. we can imagine that as the proportion of costly mates increases. female fitness decreases either more slowly or more quickly than the linear case. Once we have a female fitness function that CHGPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 183 includes these three possibilities, if we assume that females randomly encounter both costly and good males (in proportion to their frequency in

the population), we can calculate the average fitness of females with vari-

ous numbers of mates. Then we can compare the average fitness of females with m mates to those with m + 1 mates (for a range of m) to see whether remating increases female fitness for a given kind of fitness function.

CVe can define the relative fitness of a female that mates with m mates

of which n are costly as f (n, m). For example in the case of remating to

avoid sterility. female fitness ranges from one when she mates with only

fertile males to zero when she mates with only sterile males. To define the

range of possible fitnesses with different proportions of sterile mates we

can use an equation of the form

f (n,m) = i- (3

where q > O [Figure 6.1: as in Charnov. 1979, Laguérie et al.. 19931. The

variable q determines the shape of the female fitness function (i.e.. how her fitness is affected by the proportion of costly mates she has (E) ). It can be affected by sperm cornpetition and sperm choice by females. When

q < 1 the relationship is concave-up. when q = 1 the relationship is linear.

a.nd when q > 1 it is concave-down. The farther q gets from 1. t.he more concave the functions get and the more intermediate proportions of sterile

mates resemble either the al1 fertile mate case for concave-down or the al1 CHAPTER6. SELECTIONFOR MULTIPLE MATINC IN FEMALES.

Figure 6.1: Fernale relative fitness as a functioo of the proportion of "costly" mâles (z).

The two sets of curves represent a minimum relative fitness (a) of zero or 0.5. Within each set of curves. there is a concave down curve (q = 2). a linear curve (q = 1). and a concave up curve (q = 0.5). CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. sterile male case for concave-up curves.

Equation 6.1 can be generalized for costs less severe than sterility. If

the less desirable mate produces some relative fecundity O 5 a < 1, then

(shown in Figure 6.1).

If we assume that females randomly encounter males of both types.

when the probability of a female mating with costly males is s (O < s < 1). the average fitness of females with m mates is

where g is the binomial distribution n!([L,pn(l - s)"-" and f is as de-

scribecl above. If females cannot discriminate between male types the

variable s represents the proportion of costly males in the population. .Al- ternatively, if females can assess whet her potential mates are costly and

reject them as mates. s represents the product of the proportion of costly

males and the probability of failing to properly assess male type. When

s equals either zero or one. there is no advantage to remating because al1

males have equal fitness.

We derived an approximation for Equation 6.3 using a Taylor series CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 186 expansion that allowed us to assess which shapes of the female fitness function (i.e., which q) result in an advantage to remating. Equation 6.3 was used to verify that error from this approximation does not affect our conclusions and to demonstrate graphically which values of q give an "advantage to remating" which we define as the ratio W,+I /W,for different values of m and s (see Results: Figures 6.2, 6.3. 6.4). When this value is greater than one, there should be selection for remating.

6.4 Results

CVe begin by reporting results that hold for both the sterile mates case and

for the case where females are trying to rediice the cost of mating with

less costly mates. and then we report results specific to each case. We

were unable to obtain an exact analytical solution of Equation 6.3 to show

that q > 1 when m 3 1. An approximation of TV,, is possible using the

first and third terms of the Taylor series expansion of f evaluated at the

mean nurnber of costly mates (E) for a given m [the second term is zero

when you evaluate the expansion at the mean because it contains (n - n):

Hilborn and Mangel. 1997,p. 511 as follows: CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 187 where (since female mate types are assumed to be binomially distributed)

q( l-*)~(q-~)( 1-a) n = ms and Var(n)= ms(1- s),and where fU(n)= mg . This yields

If there is an advantage to remating, then the partial derivative of Equa- tion 6.5 with respect to m should be positive.

is positive when q > 1 and is negative when q < 1. So for al1 rn 2 1. when q > 1. fitness increases with m and remating is advantageous. In other words it is only advantageous for females to remate when they have a concave down fitness function. Xumerical solutions for wt;,can be obtained (e.g.. Figures 6.2 and 6.3) by using Equation 6.3 and substituting values for m. n. q and s to calculate the advantage to remating. We used

these numerical solutions to verify that the approximation (Equation 6.4) is reasonably accurate and that the above result holds for a range of values of m. S. and a.

In addition to the qualitative effect of q just described. q and m have quantitative effects as well. The amount females gain by remating increases as q increases above one (Figure 6.2). There is also a diminishing

return from remating many times to avoid costly mates (seen as a reduced CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

- Figure 6.2: Proportional advantage to remating (fit ness advantage. CC*,+~ /r,)as a

function of the exponent (q) of the female relative fitness function (see text ) for females

that (A)mate twice relative to Females that mate a single time (m = 1). (B)niate three times relative to twice (rn = 2) and (C)mate six times relative to five times (rn = .5). The

proportion of costly males (s)is set at 0.5. The steeper curves in parts A-C represents a

minimum relative fitness (a) of zero and the other curve is for a = 0.5. while the dotted

line represents the point at which t here is no fitness advantage to remating. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

- Figure 6.3: Proportional advantage to remat ing (fit ness advantage. W,+,IVrn ) as a function of the nurnber of mates (m)when the minimum relative fitness (a)is zero (A) or 0.5 (B).The proportion of costly males (s) is set at 0.5. In both A and B the top set of points is for the case w hen the exponent (q) of the female relative fitness funct ion (see text) is two, the horizontal set is for q = 1 and the lower set of points is for q = 0.5. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 190 difference, in terms of fitness advantage. between adjacent points with increasing rn in Figure 6.3a and b for q = 2). This is because as m increases, one extra mate brings a smaller possible change in the proportion of your mates with the costly phenotype (k). When a female has mated once (m = l), her proportion of costly mates is either zero or one. An additional mate will either shift her to a proportion of 0.5 or leave her where she started. When a female has six mates (m = 6). she can have seven possible ratios ranging frorn zero to one. .An extra mate cmonly shift her a fraction less than 117 up or down (as opposed to 112 for rn = 1). So the maximum change in the ratio decreases with increasing m. and this translates into smaller changes in female relative fitness with increasing

m. Finally. the magnitude-and interestingly the symmetry-of the fractional increase or decrease in the :ratio depends on how close to 0.5 a female is before remating. For example. if a female has three costly mates out of six. she will have either three or four out of Severi after remating

-a change of 0.071 (or 112 of 117) either up or down. On the other hand

if she has two costly mates out of six before remating, she will end up with either two or three costly mates out of seven. Two out of seven rep-

resents a decrease of 0.048 in the proportion of costly mates. while three out of seven represents an increase of 0.095. This asymrnetrical change in

the ratio translates into asymmetry in fitness gains and losses (Table 6.1). As a result. there is a cost-benefit ratio asymmetry associated with CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 191

Table 6.1: Asymmetric changes in ratio and relative fitness due to remating starting with either three out of six or two out of six costly mates. Fitness changes were calculated using Equation 6.1 (see text). The two changes in fitness for a given q must sum to 117.

Start Start

rn ratio 317 316 417 217 216 317 Change in 2 ratio Change in fitness with:

q = 0.5

remating for individual females that depends both on the ratio of + and on q (Table 6.1). This asymmetry could have important consequences for modeling female remating decisions. From the quantitative effects of q and m, we turn to the effects of S.

For the case of sterile males, the largest increases in average relative fitness from remating corne when the probability of mating with costly males

(s) is nearly 100% (see upper curve (a = O) in Figure 6.4). This means that when females cannot detect costly mates, the strength of selection on females increases with the frequency of sterile males in the population. If they can assess mate type, the strength of selection on females increases with the product of the frequency of sterile males and the proportion of Figure 6.4: Proportional advantage to remating (fitness advantage. WG;,+I/W,)as a Function of the proportion of costly males in the population for the case where females mate twice relative to single maters (m = 1). For both curves q = 2. The upper curve represents the case where the minimum relative fitness (a) is zero. and the lower curve is for a = 0.5. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 193 failed assessments a female is likely to make. Female remating is less likely to evolve when the costly male phenotype is rare or when female assessment abilities are good. However, when the proba.bility of mating with a sterile males is 100% (s = 1; for whatever reason). there is no advantage to remating.

For the case of mates that are less costly than sterile males (e.g.. males with sex-ratio distorters). setting the lower lirnit of f at some level a greater than zero does not change the main result-remating will increase relative fitness only when fitness functions are concave down. However. the extent to which remating increases relative fitness is no longer increasing across the whole range of the probability of mating with costly males

(s). Instead. remating increases relative fitness rnost when s is intermediate between zero ancl one (Figure 6.4). This means that. as was the case for sterility. female remating is less likely to evolve when costly males are rare (or when these males are rare and assessment is good). but it is also less likely to evolve in this case when costly males are common (or when these males are common and assessment is poor). This is because if a > 0. when s is above a certain threshold (- 0.59 in lower curve of Figure 6.4). the fitness gains that females get from remating begin to decrease. The threshold is determined by the fitness of females who mate only with the least fit males (a)and by the asymmetry between the gains and losses in CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. relative fitness resulting from remating (discussed above).

Discussion

In order for female multiple mating to evolve as a hedge against the costs of mating with costly males, females with intermediate proportions of costly mates must have relative fitnesses close to the fitness of females with only good mates (Le.. a female with one sterile mate and one normal mate must have an expected relative fitness of greater than 0.5). In other words the function relating female relative fitness to the proportion of costly mates (Figure 6.1) must be concave down. A linear or concave up relationship will not result in an advantage to multiple mating. This makes it interesting to speculate about what situations in nature would result in females having a concave down fitness function. It turns out that such a function is likely whenever costly male sperm are either less cornpetitive at fertilizing eggs, or are less preferred by females. First we consider two categories of mechanisms for producing male sterility and ask whether they are likely to produce concave down female fitness functions. Next we consider mates that carry smaller fitness costs. Finally. we consider the evolution of female assessrnent and consider some examples from nature. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

6.5.1 Fitness gains with sterile mates

Little is known about what produces male sterility [even hybrid sterility in matings between related species; Wu et al., 19961. Here. we distinguish two categories of mechanisms that are likely to have different consequences for female fitness: (1)males with no sperm or sperm that do not function properly, and (2) males with sperm that fertilize eggs which then fail to

develop. Type 1 males do not reduce the nimber of eggs available to the

sperm of a female's other mates. while type 2 males do essentially "kill" eggs, removing them from the pool of available eggs. The first type of

male sterility rnay result from parasites that prevent normal sperm for-

mat ion [parasitic cas t ration; Alvarez. 1993. Tagashira and Tanaka, 19981.

the depletion of sperm stores after repeated mating [Walker. 19801. or the

presence of some mutation that affects either sperm motility (e.g.. im-

mobile or sticky sperrn) or the ability of sperm to penetrate the outer

membranes of the egg [McIiee et al., 19981. Type 2 sterility may result from certain kinds of chromosome re-arrangements that can interfere with

meiosis. lead to nondisjunction and t hen interrupt development [McKee et al.. 19981. It may also result from cytoplasmic incompatibility induced

by mutually incompatible strains of Wolbachia bacteria in the male and

female [Werren. 19971. The well known phenomenon of sterility in the

offspring produced by hybrid matings may fa11 under either type 1 or type 2 sterility. The two categories of sterility are not equally likely to produce CHAPTER6. SELECTIONFOR MULTIPLE MATfNG IN FEMALES. 196 concave down fitness functions, and we will consider each type in turn.

If a female mates with one sterile and one normal male (in no particular order), is her fitness function likely to be concave down'? With type

1 sterility the answer is very likely to be yes. The fertile mate should provide a female with al1 (or nearly all) the sperm she needs to fertilize her eggs. so her fitness should be close to that of a female with only one normal mate. The sperm of males with type 1 sterility simply do not compete for fertilizations. provicled they do not mate last and clisplace 50% or more of the normal mate's sperm. This much displacement is unlikely when castrated or otherwise depleted males must use their onrn reduced supplies of sperm and seminal fluid to force out older ejaculates. Even when males use other mechanisms for sperm displacement [e.g.. the mocl- ified penis of rnany odonates: Waage. 198.11. it seems unlikely that sterile males will consistently be the last mate and therefore be in a position to displace the normal male's sperm. For this to occur, females who mate multiple times would have to have an unusually high probability of mating with sterile males (e.g.. s > 0.5). Alternatively. sterile males woiild need to be more cornpetitive for mates and get to mate last. or females would need to detect sterile males and choose to mate with them last. Al1 three of these scenarios seem unlikely. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 197

With type 2 sterility, the answer to whether the female fitness function will be concave down is essentially the same as for type 1 sterility. If sterile male sperm are less cornpetitive (or less preferred) a concave down fitness function is likely because sterile male sperm will fertilize less than half of

the available eggs, allowing the female to have a relative fitness that is > 0.5. When functional sperm are actually fertilizing eggs. if the sperm of the

two types of males are equally likely to fertilize eggs, a female that mates

once with each kind of mate will have, on average. a relative fitness that

is halfway between females who mate with either normal or sterile mates

only, resulting in a linear fitness function. For type 3 sterile-male sperm to

be less successful at fertilization. the genes underlying the post-fertilization

developmental failure would have to have negative pleiotropic affects on

sperm cornpetitive ability (or be less preferred by females). Something as

simple as type 2 sterile males producing fewer sperm would be enough to

allow a concave downward fitness funct ion.

6.5.2 Fitness gains with less costly mates

Thus far we have only discussed the effects on female fitness of having sterile mates. What about situations where females get some low level

of fitness from the lower quality mates (e.g., sex-ratio distorters or other

forms of intragenomic conflict with similar effects on female fitness)'? In

these cases. a concave down fitness function is again likely only when the CHAPTER6. SELECT~ONFOR MULTIPLE MATING IN FEMALES. 198 sperm of costly mates have lower cornpetitive ability (or are less preferred by females). Consider once more a female who mates with one normal and one costly mate in no particular order. If she does not prefer one male's sperm and there is no sperm cornpetition, on average her relative fitness will be halfway between the fitness of females who mate with either a costly mate only and a normal mate only, resulting in a linear fitness function: 0.5(a+ 1). On the other hand if sex-ratio distorter males are not as capable of displacing the sperm of previous mates. giving them lower fertilization success, a concave female fit ness function is espected.

In Drosophila pseudoobscura [Beckenbach. 1978. Wu. 1983al and in the stalk-eyed fly, Cyrtodiopszs whitei (Wilkinson. persona1 communication). the sperm of males with sex-ratio distorters fertilize less offspring than non-distorter males.

6.5.3 Assessrneut of males by females

The ability to assess whether males belong to one of the categories of costly mates described above may evolve if it allows females to either remate only when doing so will improve their fitness. or selectively use or remove the sperm of certain mates. There is growing evidence that females control sperm displacement (several chapters in both Smith, 1984: and Birkhead and iMQller, 1998). Fernales that remate after detecting a costly mate. for example, can use anatomical or physiological sperm-precedence adapta- CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 199 tions to prefer the sperm of last mates, effectively discriminating against the sperm of costly mates. Females can apparently also use the sperm of particular mates for fertilizing eggs [Ward. 1993. Werren, 1997, Arthur Jr. et al.. 19981. So a concave down fitness relationship will result either if good males mate last or if females manipulate their stored sperm to fa- vor good males. However. even if females cannot detect and discriminate against costly males. the average effect of last male sperm precedence woiild be expected to produce a concave down relative fitness function

whenever s < 0.5 because. due to their abundance. good males are more

likely to mate last.

Based on the potential strengt h of selection. assessment and cliscrimina-

tion by females seems most likely to evolve to detect type 2 sterility. where

costly male sperm are "killing" eggs: next most likely for less costly types

of mates (such as sex-ratio distorters). where fitness effects should be less

drastic: and least likely for type 1 sterility. where unless females mate only

with sterile males, fitness effects are expected to be small. CVe therefore

predict that when assessment occurs, it will most commonly involve female

assessrnent of mates (or their sperm) that will result in the developmental

death of eggs. Almost no data exist to test this prediction. however, we

will discuss evidence (in a stalk-eyed fly) of assessment that may involve

the detection of sex-ratio distorter mates using a morphological correlate CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

[Wilkinson et al., 1998bl.

6.5.4 Evidence from nature

Two species of Malaysian stalk-eyed flies provide a useful pair of esamples to consider the relevance of what we have discussed so far. In two species

( Cyrtodiopsis dalmanni ancl C. whitei ) females will mate multiple times in the lab [Lorch et al.. 1993, Wilkinson et al.. 1998a] and in the field [up to 20 times in 10 days: Wilkinson et al.. 1998al. Sex-ratio distorters in both species cause female-biasecl sex-ratios [Presgraves et al.. 19971 and bot11 species suffer high levels of male sterility [Wilkinson et al.. 1998al.

At least some of the instances of male sterility could be due to a lack of sperm transfer [31% of 83 lab-reared C. whitei males tested did not transfer sperm to a virgin female: Lorch et al.. 19931. and male C. dalmanni with the ses-ratio distorter produce fewer sperm [maybe as little as half: Presgraves et al.. 19971. Finally. Wilkinson et al. [1998b] have suggested that females may be using male eye-span to assess the presence of Y-linked modifier genes that will ameliorate the effects of X-linked sex- ratio distorter genes.

There is support in these species for the evolution of remating as a hedge against mating with costly males. As ment ioned earlier, when considering normal and sterile males. female fitness functions for mates that fail to CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 201 transfer sperm (type 1 sterility) are likely to be concave down. favoring the explanations we have been discussing. Males in these two species transfer sperm in a spermatophore [Kotrba, 19901, and these structures may make it difficult for females to detect the absence of sperm at least initially. If a fernale's normal mates transfer larger numbers of sperm, we would expect the female fitness functions to be concave down. Fernale C. whitei can ex- pel spermatophores afteï a variable amount of time [Iiotrba. 19911. which would give them a mechanism for discriminating against particular mates by not absorbing their sperm. though there is no evidence currently that they use this mechanism to prefer certain mates. The fitness function for normal males and males with sex-ratio distorters will also likely be concave down since distorter males will have half the sperm. reducing their ability to compete for fertilizations. Taken together. both of these types of costly mates are likely to result in a fitness function for females that is concave down. We also note that. to the extent that multiple mating reduces the deleterious effects of sex-ratio distorters, it can be implicated in esplaining the equilibrium levels of sex-ratio distorters in several species where it is found in the field [Presgraves et al.. 19971.

The evolution of multiple mating in stalk-eyed Aies is probably only partly explained by the benefits of reducing the effects of either sterile mates or mates carrying sex-ratio distorters. At least for C. whztei, female CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES. 202 sperm storage organs do not seem to fill up in as many as four matings [Lorch et al., 19931. Females may therefore be remating, at least in part, to insure that they have adequate numbers of stored sperm. Both C. white2 and C. dalmanni have higher remating rates and smaller spermatophores than a similar sized congener, C.quinqueguttata, supporting the hypothesis that remating niay be intended, in part, to increase sperm stores [Kotrba.

19961. However, both C. whitei and C. dalmanni mate up to 20 times in

10 days in the field [Wilkinson et al., 1998al-a seemingly large number of matings just to fill sperm storage organs or keep them full.

Are there other animals where we might expect to see concave down fitness functions'? The sand lizard. Lacerta agilis. seems a likely candi- date. As mentioned earlier. male sterility in the wild can be relatively high (4.5%). This example seems to fit into what we have called type

2 sterility because there is evidence that inviable eggs are the result of mating with sterile males [Olsson and Shine. 19971. If sterile male sand lizards transfer fewer sperm to females, if these sperm are less cornpetit ive or preferred. or if these males are less effective at sperm displacement. we would expect a concave down fitness function for females. Olsson and Shine [199'7] conclude that though multiple mating to avoid sterile males may have been involved in the origin of female remating, it is less likely to maintain remating t han sperm choice through cornpetition. PVe believe that sterile male avoidance could be involved in both the origin and maintenance of female remating in these lizards, but not unless sterile male sperrn are at a cornpetitive disadvantage. Without this sort of disadvantage, female fitness functions are not likely to be concave downward.

The same is true when the costly male is not sterile but has some less severe genetic incompatibility. There is evidence that the sperm of sex-ratio distorter males will also experience a competit ive disadvantage, allowing the negative effects of these kinds of mates on female fitness to drive the evolution of female remat ing. Sex-ratio distorter genes (and segregat ion distorters more generally in 5 species of Diptera) act by interfering with the production of non-distorter sperm. leading to reductions in the numbers of sperm transferred by distorter males [for review see Presgraves et al.. 19971. This reduction in sperm numbers has the effect of reducing sperm displacement [Wu. 1983al and reducing the ability of distorter males to win in numerical competitions for fertilizations. So we expect concave downward female fitness functions to commonly be associated with segregation distorters. It remains to be seen whether other forms of intragenomic conflict are likely to produce concave down fitness functions. and of course the generality of Our mode1 depends on whether or not this is true. CHAPTER6. SELECTIONFOR MULTIPLE MATING IN FEMALES.

6.6 Acknowledgments

We would like to thank Gerald Borgia for suggesting that females might remate to avoid having single-sex broods. Thanks are also due to Darryl

Gwynne. Luc Bussière, Locke Rowe, Nick Collins and Gerald Wilkinson for rornm~ntingon drafts of this papr and for disciission of netlails of the model. P.D.L. was supported by a grant from the National Science and

Engineering Research Council of Canada to D. Gwynne. Chapter 7

General discussion

The chapters of my thesis each represent a contribution to unifying life history theory and sexual selection theory. Three of the five chapters depend heavily on the idea that it is the correlation between fecundity and numbers of mates that causes sexual selection and that life history evolution can influence this correlation. The relationship between fecundity and number of mates (represented as the simple linear regression slope or

Bateman slope) is the key to understanding evolution of differences between the sexes. Considering either fecundity or number of mates alone leaves out something crucial. For example, if you measure only the number of mates and compare the variance in this measure between males and fernales, finding that there is no difference tells you nothing about the relative strength of sexual selection acting on the two sexes. Wit hout knowing the relationship between fecundity and numbers of mates. you would not know whether sexual selection is equally strong on both sexes CHAPTER7. GENERALDISCUSSION 206 or stronger on one than the other. Under many circumstances. even if the male and fernale variances in number of mates are indistinguishable, the male Bateman slope could be significantly greater (or less) than that seen for females, indicating that sexual selection is stronger on males (females) than on females (males). Since changes in life history allocation patterns affect both fecundity and mating success, using the Bateman slope approach also makes integrating life history theory and sexual selection theory more straightforward (as 1 demonstrated in Chapter 2). Using

Bateman slopes rather than one or the other of its components provides a convenient way to estimate sexual conflict oves mating frequency as well

(Chapter 4).

This thesis makes several useful contributions to the study of sexual selection. First among these is the concept of defining the upper limit on sexual selection as the maximum rate of gain in fecundity per additional mate. I believe that this concept is more useful in understanding the potential for sexual selection on the two sexes than previoiis concepts such as the opportunity for sexual selection [variance in number of mates standardized by the square of mean nuniber of mates; \Vade. 19871. Using the older standardized variance in the number of mates as a measure of the potential for sexual selection requires two assumptions. First, it requires the assumption that the sex with the highest variance in number of mates CHAPTER7. GENERALDISCUSSION '207' also has the highest variance in reproductive success. Second. it requires the assumption that this is due to a positive correlation between reproductive success and number of mates (without such a correlation. there would be no sexual selection of the kind 1 have described). My approach has been to actually measure the upper limit on this relationship and use its magnitude (the slope) to estimate the upper limit on sexual selection.

Defining the upper limit in the way 1 propose is a logical extension of using the fecundity by number of mates relationship rather than variance in number of mates to describe the strength of sesual selection. So the relationship between maximum fecundity and numbers of mates (the up-

per limit on sesual selection) determines the potential for sesual selection. and I extend this idea further by suggesting that that the ratio of male

to female upper limits is a useful index of the potential for sexual conflict over mat ing freyuency.

My other main contribution is in the form of a simulation model that

allows a fine grained understanding of how the relationship between fecun-

dity and numbers of mates is affected by relative nuptial gift value. This model is especially useful for understanding when sexual selection will be

stronger on one sex or the other. As more information on the distribution

of nurnbers of mates for males and females are reported, this model will be increasingly useful. CHGPTER7. GENERALDISCUSSION

7.1 Future directions

One of my goals for the near future is to push forward the idea of us in^

Bateman slopes to measure sexual selection while clarifying the pitfalls of using this technique. A large number of molecular parentage datasets now exist in a range of taxa that could be used to compare the intensity of sexual selection acting on males and females or to quantify sexual conflict over mating frequency To date, almost al1 of these datasets have been used to examine extra-pair copulation rates and to characterize mating systems. Only Iietterson and colleagues (1998) have esamined sexual differences in the intensity of sexual selection using the Bateman dope approach. Problems similar to those that arose in Chapter 4. where the male upper limit on sexual selection was underestimated and femaie upper limits may have been overestimated, may also arise when molecular parentage data are used to estimate actual sexual selection gradients. For example, if males are more likely than females to obtain matings outside the sampling area, what effect does this have on sexual selection gradient estimates [Ketterson et al., 1998]? Another vexing problem is how to decide whether increased numbers of matings occur because a female gains fitness by remating, or simply because her high fecundity makes her CHAPTER7. GENERALDISCUSSION 209 more attractive to males [Ketterson et al.. 19981. Would she have had the same fecundity if she mated only once? It may be possible to use multiple regression techniques (as in Chapter 4) to separate increases in fecundity due to remating from those due to larger female size. 1 have begun to try to raise interest in a mini-conference to work through some of these problems using existing molecular parentage datasets.

Very little is known about how matings are distributed among males.

Thoiigh females often retain evidence of past matings [e.g. **spermato- doses" in but terflies and decticine katydids: Gwynne. l98.lb], males bear no such signs. This shortage of information about males prevented me from more precisely modelling male mat ing distributions in simulations to examine the causes of sex role reversa1 (Chapter 2). 1 had to assume that male mating success depended in some arbitrary way on the value of a male trait. Clearly it would be interesting to know what the distribution of mates among males was. if only to test my assumptions about male mating success. The development of molecular techniques to determine paternity has allowed much more quantitative explorations of mating distributions for bot h male and females. However. t hese techniques only work if you can obtain DNA from a large sample of offspring and al1 (or at least most) of their putative parents. This is unlikely ever to happen for the katydids used as the bais of Chapter 2. For this reason. 1 plan to attempt to estimate mat ing frequency for groups of individually marked Mormon cricket males over a period of several weeks. By doing this in populations with and without sex role reversal, while at the same time collecting females, 1 should be able to estimate the distribution of mates among both males and females. This information coukl then be used in the mode1 described in Chapter 2. Rather than fixing female mating dis-

tributions and having males compete for mates in the simulations, what happens if I fix male distributions and allow females to compete for mates

based on their trait values (as might occur with sex role reversal)'? Does

this change any of the qualitative results*?

1 also have plans to use comparative phylogenetic techniques (like the

one explored in Chapter 3) to study relationships between life history

evolution and sexual selection across phylogene t ic trees. For example.

Hoglund and Sillén-Tullberg [1994] asked if lek mating systems in birds

made the evolution of male biased size-dimorphism more likely. They used

the concentrated changes test and found no support for this directional

hypothesis. However. they did not test the obvious alternative hypoth-

esis that evolution occurred in the opposite direction. In other words. does leking evolve more often than one would expect once male-biased

size dimorphism already exists? There is, in fact, strong support for the

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