Sex Differences in Fitness Variance and the Evolution of Mating Systems II

Size: px

Start display at page:

Download "Sex Differences in Fitness Variance and the Evolution of Mating Systems II"

Mervin Russell Shields
5 years ago
Views:

1 Sex Differences in Fitness Variance and the Evolution of Mating Systems II Stephen M. Shuster Northern Arizona University Last Time, I mates = [1/(1 - p )][ (V harem ) / (H 2 )] + (p ) / (1 - p ) becomes I mates = (m) [ (V m ) / (m 2 )] (1/m) or more simply, I mates = (m) (P) = m* What Does This Mean? The mean spatial crowding of sexually receptive females, m*, provides a direct estimate of the opportunity for sexual selection, I mates, arising from the distribution of females in space.

2 A Model Population N males = N females = a b The Relationships Between M, mating, m and m* N mating a Nmating m m* M The Relationship Between M and H a H M

3 H The Relationship Between m and H b b H m m The Relationship Between 1/(1-p ) and H c H 1/(1-p) The Relationship Between M and V mates a Vmates M

4 The Relationship Between V m and V harem 6 b Vharem Vm The Relationship Between m*, H and V mates c m* H Vmates The Relationship Between m* and I mates a Imates m*

5 When Females are Clumped in Space, I mates = [1/(1 - p )][ (V harem ) / (H 2 )] + (p ) / (1 - p ) But it is not always possible to measure p. The Relationship Between P and I harem 3 c 2 Iharem P When the Sex Ratio Equals 1, I males = (1/R)I females + I mates When the Sex Ratio is Biased, I males - I females = (1-1/R) I females + I mates

A Worked Example: Part A Paracerceis sculpta The Distribution of Isopods in Spongocoels m transect sampled once/month over 2 years. 15,.25 m quadrats per sample.

6 A Worked Example: Part A Paracerceis sculpta The Distribution of Isopods in Spongocoels m transect sampled once/month over 2 years. 15,.25 m quadrats per sample. Each spongocoel represents a patch, defended by a male. Male Polymorphism in Paracerceis sculpta α-, β- and γ-male morphs exist. β- and γ-males prefer to invade large harems.

7 Uninvaded Spongocoels Large α-males can defend their spongocoels against other α-males. Uninvaded spongocoels (>8% of all spongocoels) can serve to illustrate the strength of sexual selection on α-males. Table 2.1: Calculation of m* and P from monthly distributions of P. sculpta females in L. losangelensis spongocoels with with males, Month Nfemales M m Vm m* P Oct Nov Dec Feb Mar Apr May Jun Jul Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Totals Paracerceis sculpta: V mates on m* r 2 =.94; F [1,23] =317.28, P= Vmates m*

8 Paracerceis sculpta: I harem on P r 2 =.92; F [1,23] =127.13, P= Iharem P 2 Paracerceis sculpta: I mates on m* r 2 =.84; F [1,23] =54.8, P=.1 1. a.8 Imates m* The Effect of Sex Ratio on I mates r 2 =.25, F [1,23] =7.5, P=.12 3 a 2 Imates(adj) R

9 Conclusion 1 We can measure the intensity of sexual selection from the spatial distribution of females. The spatial distribution of females is only one component of the sex difference in the opportunity for selection. Important Factors: I males = 1/R (I females ) + I mates Sex ratio (R = 1/OSR) Space (m*) Time (t*) A Model Population N males = N females = a Time b Time

The Mean Crowding of Females in Time The mean crowding of females within intervals during the breeding season can be expressed as, t* = t + [(V t / t) -1] t* = the number of other receptive females

10 The Mean Crowding of Females in Time The mean crowding of females within intervals during the breeding season can be expressed as, t* = t + [(V t / t) -1] t* = the number of other receptive females the average receptive female experiences within her period of receptivity. When Females are Clumped in Time Two components of variance in mating success exist: (1) the variance in mating success within the class of males that actually mate by defending individual females. (2) the variance in mating success among the mating and non-mating males. What Does This Mean? The mean temporal crowding of sexually receptive females, t*, provides a direct estimate of the opportunity for sexual selection, I mates, arising from the distribution of females in time.

11 However, The relationship between m* and I mates is proportional. At m* max one or a few males could defend and mate with all of the females in the population. Conversely, the relationship of between t* and I mates is reciprocal. At t* max, the ability of one or a few males to mate with multiple females is reduced. The Relationships Between m*, t* and I mates a b Imates Imates m* t* This is WHY: The effects of the spatial and temporal distributions of females on I mates, must be examined simultaneously. The behavior of males and females in response to these conditions must be considered as well.

12 A Model Population N males = N females = a b The I mates Surface (Shuster & Wade 3) Imates m* t*.5. Within Season Variation in m* and t* Will describe an ellipsoid on the I mates surface. Spatial Patchiness (m*) Temporal Patchiness (t*) Imates (m*obs) The slope of the ellipsoid will depend on how m* and t* interact within a single breeding season.

13 Among-Species Variation in m* and t* I mates (m*obs) Each species is expected to generate a unique cloud of points along the m*, t* and I mates axes. Spatial Patchiness (m*) Temporal Patchiness (t*) Divergence in m* and t* Ι Related species are expected to show similar mating systems. Also, divergent species within larger taxa should be predictably divergent. Spatial Crowding (m*) Temporal Crowding (t*) Other Factors Influencing the Intensity of Sexual Selection 3. Female life history. 4. Alternative mating strategies. 5. Genetic covariance between the sexes.

Iteroparity The duration of female reproductive competence: Uniseasonal vs.

14 Three Components of Female Life History: The number of times a female mates: Monandry vs. Polyandry The number of reproductive episodes in a female s lifetime: Semelparity vs. Iteroparity The duration of female reproductive competence: Uniseasonal vs. Multiseasonal Iteroparity The Effect of Monandry on I mates When a female mates once and produces only one clutch of offspring, she awards her entire reproductive output to a single male. The Effect of Polyandry on I mates When a female mates more than once, she partitions her clutch into several subclutches, equal in number to the number of sires.

$2 1 2 3 4 5 6 7 8 9 Female Mate Number Each mating male sires only a fraction of the offspring of each mate he secures.$ The variance in mate numbers among males is reduced.

The variance in mate numbers among males is reduced.

15 Overall Effects of Polyandry on I mates Offspring Sired Per Mate Female Mate Number Each mating male sires only a fraction of the offspring of each mate he secures. The variance in mate numbers among males is reduced. Mate Guarding Temporal ( t* ) mobile mobile sedentary Spatial ( m* ) males guard individual females males search for females males facultatively search or guard females males guard groups of females The Effect of Semelparity on I mates When a female produces only one clutch of offspring, no variance exists within females in the number of offspring produced. All of the variance exists among females.

$As clutch number increases, I mates becomes a smaller fraction of the total variance in offspring numbers.$

16 The Effect of Iteroparity on I mates When a female produces more than one clutch, the variance in offspring numbers can be partitioned into within- and among-female components. The Overall Effects of Iteroparity on I mates Multiple reproductive episodes by females erode I mates. As clutch number increases, I mates becomes a smaller fraction of the total variance in offspring numbers. This Means That: I mates is eroded least in monandrous, semelparous species; It is eroded most in polyandrous, iteroparous species.

17 The Meaning of I ( m*obs ) Imates (m*obs) The value of I mates is adjusted by multiple mating and multiple breeding episodes by females. Spatial Patchiness (m*) ( Isires + Iclutch size) I Temporal Patchiness (t*) The adjusted sex difference in the opportunity for sexual selection is I. The I mates Surface for the spatial distribution of α-males, I mates(avg) =3.31±1.67, N= Imates m* t*.

18 Male Polymorphism in Paracerceis sculpta α-, β- and γ- male morphs exist. β- and γ-males prefer to invade large harems. Calculating the Variance in Offspring Numbers for Females X females = 62.1 V Xfemales = I females = V Xfemales / X 2 =.14 Calculating the Variance in Mate Numbers Among All Males (N=555) 8 V total = V within + V among 6 = Frequency 4 α β γ Harem Size R 2 = (1.49) 2 = 2.21 I total = 1.39 I among =.1 I males /I females = 9.93

19 The I Surface for all males (N=555) Imates m* t*.5. Thus, High variance in mate numbers among males is unstable; it represents a functional bias in the population sex ratio. Thus, whenever I mates >, alternative mating strategies are expected to evolve. And, When N mating increases, H, V mates and I mates all must decrease. Thus, alternative mating strategies erode the sex difference in the opportunity for selection.

20 Dynamic Evolution of Mating Systems The mean spatial crowding of matings, m*, is low, and the mean temporal crowding of matings, t* is high. Sedentary Pairs If Females Become More Spatially Aggregated: Males are expected to continue to defend individual females, but breeding will occur in large aggregations. Mass Mating Slight Decreases in t* Can cause spatially aggregated singlepair mating systems to rapidly become more polygynous or polygynandrous, thereby rapidly increasing I.

If Male Traits Attract the Attention of Females Then the spatial

21 Polygamy Occurs When The mean spatial crowding of matings, m*, and the mean temporal crowding of matings, t* are both moderate. If Male Traits Attract the Attention of Females Then the spatial distribution of matings becomes more clumped and the temporal distribution of mating becomes more dispersed.

The Operational Sex Ratio, the Potential Reproductive Rate, and the Opportunity for Sexual Selection Stephen M. Shuster

The Operational Sex Ratio, the Potential Reproductive Rate, and the Opportunity for Sexual Selection Stephen M. Shuster Stephen M. Shuster Northern Arizona University Objectives. Definitions of OSR/PRR.