Measuring Sexual Selection

Transcription

1 Measuring Sexual Selection Stephen M. Shuster Northern Arizona University Sexual Selection Darwin s Two Questions: Why do males and females in the same species differ from one another, with male characters more exaggerated than those of females? Why do the males of related species exhibit greater differences in morphology than females of the same, related species? The First Question Is a micro-evolutionary one. The pattern is seen within species of most taxa. Indicates that selection acts to differentiate the sexes. Males are affected more than females.

2 The Second Question Is macro-evolutionary one. The pattern is observed across species, within genera or families of most taxa. Large differences in male phenotype among closely related taxa are the signature of a rapid and powerful evolutionary force. Phenotypic Differences Between the Sexes Are not associated with essential reproductive physiology. Are not associated with development of male and female gametes. Exaggerated plumage, coloration, behavior, and morphology of males are correlated with but are not necessary for reproduction. Yet These Differences Are So Marked That The Exaggerated Traits of Males Define Many Species.

3 Male-Female Differences Only male red-winged blackbirds (Aegelaius phonecius phonecius; Searcy 1979; Weatherhead & Robertson 1979), are black with red epaulets on the wings, females are inconspicuous and dull brown in color. Male-Female Differences In the bullfrog, Rana catesbania (Howard 1984), it is only the male, which makes the deep call from which the species gets its common name; female bullfrogs are silent. Male-Female Differences Only male bowerbirds (Borgia 1986) build elaborate bowers in which to court and mate with females.

4 Male-Female Differences In balloon flies (Hilara santor; Downes 197), only the males carry balloons of silk as nuptial gifts for females. Trivial Male Characters Darwin saw no obvious functional relationship between the exaggerated traits of males and the physical environment. In fact, Darwin considered sexual selection weak. Darwin on Sexual Selection sexual selection " depends, not on a struggle for existence, but on a struggle between males for possession of the females; the result is not death of the unsuccessful competitor, but few or no offspring. Sexual selection is, therefore, less rigorous than natural selection (1859, p. 88).

5 males Conflict How can sexual selection appear to be one of the most powerful evolutionary forces known, Yet Darwin himself considered sexual selection less rigorous than natural selection? The Micro-evolutionary Predictions Suggest that Darwin was right. Single-sex selection, sex-limited expression, age-limited expression and viability selection experiments all predict that sexual selection will be slow and weak. Selection on Both Sexes.3 Xmales X*males a.2 X*males - Xmales Frequency.1 = Smales Character.3 Xfemales X*females b X*females - Xfemales Frequency.2.1 females = Sfemales Character

6 males males Single Sex Selection.3 Xmales X*males a Frequency.2.1 X*males - Xmales = Smales Character.3 Xfemales = X*females b Frequency.2.1 X*females - Xfemales = Sfemales females = Breeders Character Disruptive Selection: Both Sexes.3 Xmales X*males a Frequency.2.1 X*males - Xmales = Smales > Character.3 Xfemales b X*females X*females - Xfemales Frequency.2.1 females = Sfemales < Breeders Character Sex-Limited Expression of Traits Sex-limited expression is an evolved property of a species developmental genetic system. In general, genetic correlations between the sexes must be modified for sex-limited expression to occur. This takes time.

7 males males Disruptive Selection: Within Males.3 X*males Xmales a X*males - Xmales.2 Frequency.1 = Smales(early) < Character.3 Xmales b X*males X*males - Xmales.2 Frequency.1 = Smales(late) > Character Viability Selection on Males Exaggerated male traits make males more conspicuous to predators. Calling male crickets expend much energy in calling and suffer increased predation by bats. Viability Selection on Males Male lampyrid beetles (Lloyd 1975) encounter a sex-specific risk of predation, often from heterospecific femmefatales that mimic the signals of receptive females and eat the responding males.

8 Viability Selection on Females In sage grouse, females may suffer increased predation in their attempts to mate with particular males (Höogland & Alatalo 1998). Viability Selection on Females In yellow dungflies (Scatophaga stercoraria) females may be injured or killed by the mating attempts of males (Parker 197) The Sex Specific Selection Differentials for an Exaggerated Male Trait Total Selection Viability Reproduction Differential Males Searly < Slate > Smales Females Searly < Slate < Sfemales < *A selection differential greater than zero indicates that the trait enhances this component of fitness and is favored by selection while a negative selection differential (< ) indicates the opposite.

9 A Poor Fit The macro-evolutionary pattern suggests that selection for exaggerated characters in males is rapid and strong. Darwin, micro-evolutionary theory, and studies of selection all predict that selection acting only on one sex will be slow and weak. The Quantitative Paradox of Sexual Selection How can sexual selection be strong enough to counter the opposing forces of male and female viability selection? Darwin s Two Components of Sexual Selection Male Combat Female Mate Choice

10 Male-Male Combat: winners mate, losers do not Female Choice: chosen males mate, not chosen do not. Current Approaches to the Study of Sexual Selection Identify the context of selection. Measure the degree to which traits are modified by selection. Speculate on the intensity of selection.

11 These Approaches Do Not Address the Quantitative Paradox Identifying the mechanism of sexual selection is not the same as identifying its evolutionary effect; To do this, we must measure the actual intensity of sexual selection Intensity of Sexual Selection If each male secures two or more females, many males would not be able to pair. C. Darwin, 1871, p. 266.

12 Instantaneous Calculation: N donuts = 1 N gradstudents = 1 R d = (1 donuts/1 students) = 1 Therefore, the average number of donuts per student eating donuts, D = R d = 1. When R d = D = 1 Number of grad students Donuts per grad student Each grad student is able to secure a donut. Life is good. Number of grad students But if One Student Takes Two Donuts per grad student One student must go without. D now equals the number of donuts, N donuts, divided by the number of students who secure donuts, or D = N donuts / (N students N students without donuts ).

13 Notice, N donuts = 1 N gradstudents = 1 R d = (1 donuts/1 students) = 1 But D increases from 1 per student, to per student [ = 1 donuts / (1-1) students]. If We Let, p d = fraction of students with donuts (= 9/1 =.9). (1 p d ) = p, the fraction of students without donuts (= 1/1 =.1). p d + p = = 1. Three Relationships 1. The distribution of donuts over all students, R d, can be expressed as, R d = N donuts /N students Or as, R d = p d (D) + p ()

14 It is Easy to See That R d = p d (D) + p () Because p () =, p d (D) =.9(1.111) = 1 as it should. Relationship #2 Because p d = (1 - p ), we can rewrite R d = p d (D) as, p = 1 (R d / D). This expression shows how the fraction of students without donuts, p, is related to R d and D. Relationship #3 If the ratio of donuts to students, R d, remains at 1, this equation simplifies to p = 1 (1 / D) What does this mean?

15 Graphically, p = 1-(1/D) Proportion of excluded students (p) Average donuts per student w/ donuts (D) Intensity of Sexual Selection If each male secures two or more females, many males would not be able to pair. C. Darwin, 1871, p Proportion of nonmating males (p) p = 1-(1/H) Shuster and Wade Harem Size (H)

16 Sexual Selection is a Powerful Evolutionary Force Because: For every male who sires young with with several females, there must be several males who fail to reproduce at all. What Do We Measure? The variance in fitness; is proportional to the strength of selection. The sex difference in the variance in fitness; its magnitude determines whether and to what degree the sexes will diverge. What Tools Do We Use? The Mean and Variance in Fitness The Opportunity for Selection Analysis of Variance

17 The Mean and Variance in Fitness Consider a population in which, N males = 1 N females = 1 Sex ratio = R = N females / N males = 1 Females mate once, males can mate more than once. Case 1: Monogamy The Classes of Mating Males, k i Males can be divided into a series of mating classes, k i. Thus, k males do not mate, k 1 males mate once, k 2 males mate twice, and so on. The Number Males in Each Mating Class, m i The value of each m i depends on how variable males are in their mating success. Here, m 1 = 1, all other mating classes =.

18 The Average Male Mating Success, M M = Σ [k i m i ] / Σ m i Or, [()() + (1)(1) + (2)() + (3)() + (4)() + (5)() + (6)()] / 1 = 1. The Average Mating Success of Mating Males, H H = Σ [k i m i ] / [Σ (m i ) m ] Or, [()() + (1)(1) + (2)() + (3)() + (4)() + (5)() + (6)()] / [1 ] = 1. The Variance in Male Mating Success, V M V M = [Σ(k i2 m i )/ Σm i ] -[Σ(k i m i )/ Σm i ] 2 Or, {[() 2 () + (1) 2 (1) + (2) 2 () + (3) 2 () + (4) 2 () + (5) 2 () + (6) 2 ()]/1} - {[()() + (1)(1) + (2)() + (3)() + (4)() + (5)() + (6)()]/1} 2 = 1 1 =

19 With Monogamy, All individuals have one mate. Thus, R = N females / N males = M = H = 1, and V M = Case 2: Random Mating The Classes of Mating Males, k i There are still 7 classes of mating males, but the distribution of males among mating classes has changed. The Number Males in Each Mating Class, m i With random mating, some males mate more than once; some do not mate at all. Thus, m =36, m 1 =38, m 2 =18, m 3 =6, m 4 =2, m 5 =, m 6 =.

20 The Average Male Mating Success, M 1 8 M = Σ [k i m i ] / Σ m i Or, [()(36) + (1)(38) + (2)(18) + (3)(6) + (4)(2) + (5)() + (6)()] / 1 = 1. The Average Mating Success of Mating Males, H 1 8 H = Σ [k i m i ] / [Σ (m i ) m ] Or, [()(36) + (1)(38) + (2)(18) + (3)(6) + (4)(2) + (5)() + (6)()] / [1 36] = The Variance in Male Mating Success, V M V M = [Σ(k 2 i m i )/ Σm i ] -[Σ(k i m i )/ Σm i ] Or, {[() 2 (36) + (1) 2 (38) + (2) 2 (18) + (3) 2 (6) + (4) 2 (2) + (5) 2 () + (6) 2 ()]/1} - {[()(36) + (1)(38) + (2)(18) + (3)(6) + (4)(2) + (5)() + (6)()]/1} 2 = 1.

21 With Random Mating, By chance, some males are excluded from mating. Thus, R = M = 1, but H > M. And because the distribution is wider, V M = 1. Case 3: Polygyny The Classes of Mating Males, k i Again, there are 7 classes of mating males, but the distribution of males in each class is even more extreme The Number Males in Each Mating Class, m i Now, each of the mating classes contains males, but, m =54, m 1 =22, m 2 =12, m 3 =4, m 4 =2, m 5 =2, m 6 =4. N males = N females = 1, so R = 1.

22 The Average Male Mating Success, M 1 8 M = Σ [k i m i ] / Σ m i Or, [()(54) + (1)(22) + (2)(12) + (3)(4) + (4)(2) + (5)(2) + (6)(4)] / 1 = 1. The Average Mating Success of Mating Males, H 1 8 H = Σ [k i m i ] / [Σ (m i ) m ] Or, [()(54) + (1)(22) + (2)(12) + (3)(4) + (4)(2) + (5)(2) + (6)(4)] / [1 54] = The Variance in Male Mating Success, V M V M = [Σ(k 2 i m i )/ Σm i ] -[Σ(k i m i )/ Σm i ] Or, {[() 2 (54) + (1) 2 (22) + (2) 2 (12) + (3) 2 (4) + (4) 2 (2) + (5) 2 (2) + (6) 2 (4)]/1} - {[()(54) + (1)(22) + (2)(12) + (3)(4) + (4)(2) + (5)(2) + (6)(4)]/1} = 2.32.

23 With Polygyny, Even more males are excluded from mating (m =54). Again, R = M = 1. But H >> M, and because the distribution of male mating success is wider, V M = M = M = 1 In General When N males = N females, R = M = 1, regardless of the distribution of females with males M = 1 This is true because the ratio, N females /N males equals the sex ratio, as well as the average number of mates per male N um ber of M ales H = H = H = 2.17 In General If some males mate more than once, other males will be excluded from mating. Thus, H > M, except with monogamy. This is true because average harem size equals N females divided by the number of mating males. As m gets larger, so does H because fewer males mate

24 V M = V M = 1 In General As H increases, so does the variance in mate numbers, V M. As m increases, fewer males contribute to the next generation V M = 2.32 Thus, the greater the variance in fitness, the stronger selection becomes