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Sex Differences in Fitness Sex Differences in Fitness Variance and the Variance and the
Evolution of Mating Evolution of Mating SystemsSystems
Stephen M. ShusterNorthern Arizona University
Two Issues
1. The Source of Sexual Selection.2. The Intensity
of Sexual Selection.
Parental Investment and Sexual Selection
(Trivers 1972)
•The source of sexual selection is the
difference in initial parental investment between the sexes.
••“Females do all of the “Females do all of the investing; males do investing; males do
none of it.”none of it.”
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Problems with PIT
•The sex difference in initial parental investment is
difficult to compare within and among species.
•The correlation between sex differences in
gametic/parental investment and sexual dimorphism is
poor.•Measures of selection
intensity are indirect (e.g, PRR).
Measuring PRR
•Allow members of each sex unlimited
opportunities to mate in controlled setting.
•PRR=Xoffspring/unit time.
Mating Systems and Sexual Selection (Emlen & Oring 1977)
•Male reproduction is limited by the spatial
distribution of resources and by the temporal
distribution of sexually receptive females.
•The intensity of sexual selection on males depends
on the degree to which females are rare.
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The Operational Sex Ratio
OSR = Nmature males/Nreceptive
females
A reproductive competition coefficient.
OSR>1 = females are rare, competition for mates is
intense. OSR<1 = females are
abundant, competition for mates is relaxed.
The Environmental Potential for
Polygamy (EPP)
The degree to which the social and
ecological environment allows males to monopolize
females as mates.
Effects of the Spatial and Temporal
Distributions of Females
on EPP
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Problems with Estimating EPP
• The methods for measuring female distributions are not described.
•The scale for estimating EPP is undefined; selection intensity is not measured.
•Comparisons within and among species are imprecise.
Two Issues: Again
1. The Source of Sexual Selection.2. The Intensity
of Sexual Selection.
The Source of Sexual Selection
A sex difference in the variance in
fitness.(Wade 1979; Wade and
Arnold 1983; Shuster and Wade 2003)
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The Mean and The Mean and Variance in Variance in Offspring Offspring NumbersNumbers
NOtotal = 25
NOtotal = 25
O♀♀= 5; VO♀♀= 0; N=5.
O♂♂=5; VO♂♂= 0; N=5.
The Mean and The Mean and Variance in Variance in Offspring Offspring
Numbers, Numbers, by Sexby Sex
NOtotal = 25
O♀♀= 5; VO♀♀= 1010; N=5.
O♂♂=5; VO♂♂= 0; N=5.
If One Female If One Female Mates Twice...Mates Twice...
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NOtotal = 25
O♀♀= 5; VO♀♀= 2020; N=5.
O♂♂=5; VO♂♂= 0; N=5.
If One Female If One Female Mates Five Mates Five
Times...Times...
NOtotal = 25
O♀♀= 5; VO♀♀= 0; N=5.
O♂♂=5; VO♂♂= 2020; N=5.
If One Male If One Male Mates Five Mates Five
Times...Times...
When some individuals are excluded from mating, the
variance in offspring numbers is increased.
ThisThis is the source of sexual is the source of sexual selection.selection.
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The Intensity of Sexual SelectionThe variance in fitness
is proportional to the strength of selection.
A sex difference in the variance in fitness
determines whether and to what degree the
sexes will diverge.
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.
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0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
Average donuts per student w/ donuts (D)
Prop
ortio
n of
exc
lude
d st
uden
ts (p
0)Graphically,Graphically, pp00 = = 11--(1/(1/DD))
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
Harem Size (H)
Prop
ortio
n of
non
mat
ing
mal
es (p
0)
pp00 = = 11--(1/(1/HH))Shuster and Wade 2003Shuster and Wade 2003
Sexual Selection is a Sexual Selection is a Powerful Evolutionary Powerful Evolutionary
Force Because: Force Because: For every male who sires young with with several females, there
must be several males who fail to reproduce at all.
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Quantitative Analysis of
Mating Systems
•The Opportunity for Selection.•Analysis of
Variance.
The Opportunity for SelectionThe Opportunity for SelectionCrow (1958, 1962)
I = VI = VWW/W/W22
Compares the fitness of breeding parents relative to the population before selection.
The variance in fitness, VW, places an upper limit on the change in mean fitness from one generation to
the next.
An Upper Bound Because,
Heritability (h2) is usually less than 1.
The correlation between the variance in fitness and phenotypic change, i.e., the
relationship between Vw and ∆Z, is usually less than 1.
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How Can We Measure I = VW/W2
In a Natural Population?
Begin with:The Mean and Variance
in Offspring Numbers Among Females
X = Σ xj / Nfemaleswhere xj the brood size of the j-th
female
VX = Σ pj (X - xj)2
Where pj = the proportion of females with brood size j
Next:The Mean and Variance
in Offspring Numbers Among Males
Average Male Mating Success
= Nfemales / Nmales= the Sex Ratio (R)
X = Average Offspring/Female
RX = Average Offspring/Male
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The Distribution of Females with Males
A Key PointThe mean and variance in
offspring numbers for each mating class of males equals the
products, jX and jVfemalesrespectively,
wherej = harem size ; X = average offspring/female,
Vfemales = variance in offspring/female
This Means That:The mean and variance in offspring
numbers among mating males will far exceed the mean and variance in
offspring numbers among females.
Males with no mates will produce no offspring at all; thus unsuccessful
males produce fewer offspring than the average female.
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This Is Why:
Sexual selection is one of the most
powerful evolutionary
forces known,
It produces such rapid changes in
phenotype.
Darwin on Sexual SelectionDarwin on Sexual Selectionsexual 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).
The Quantitative Paradoxof Sexual Selection
Sexual selection CAN be much stronger than natural selection
because:
Males with no mates will produce no offspring at all.
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ANOVA:The Distribution of Females with Males
As in ANOVA,
VVtotaltotal = = VVwithinwithin + + VVamongamong
= The average of the variances in offspring numbers within the classes of males who mate
+The variance of the averages in offspring
numbers among the classes of mating and nonmating males
Vmales = Σ pj (jVfemales ) + Σ pj (jX-RX )2
= RVfemales + X 2Vmates
The Total Opportunity for Selection on Males and Females
(Wade 1979; Wade & Arnold 1980)
Recall that RX = average number of offspring/male;
dividing Vmales by [RX]2 gives
Vmales / [RX]2 = [RVfemales +X 2Vmates ] / [RX]2
which givesImales = (1/R)Ifemales + Imates
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Note That,
Imales = 1/R (Ifemales) + Imates
when R = 1,
Imales - Ifemales = Imates
In general, the sex difference in the opportunity for selection is due to differences in mate numbers
between the sexes.
The Opportunity for SelectionThe Opportunity for Selection•The sex difference in the variance in mate numbers causes sexual selection.
•Provides a direct measure of the intensity of sexual
selection.•Allows calculation of
confidence limits.•Provides an empirical
estimate of the degree to which the sexes will diverge.
How Can We Measure Imates
in a Natural Population?
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SyngnathusSyngnathus typhletyphle(Berglund et al. 1989)
0
5
10
15
20
0 0.5 1 1.5 2 2.5 3 3.5 4
N Filled Males
N F
emal
es
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6
N Matings
N M
ales
Males and females have multiple mates; sexual selection occurs in
both sexes.
Factors Influencing Factors Influencing the Intensity of the Intensity of Sexual SelectionSexual Selection 1. The spatial
distribution of mates.
2. The temporal distribution of
mates.
A Model PopulationNmales = Nfemales = 20
a b
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Mean CrowdingMean Crowding(Lloyd 1967)(Lloyd 1967)
m* = the number of other individuals the average
individual experiences as competitors.
m* = [Σ mi (mi - 1)]/ (Σ mi).
P = “Patchiness”; the ratio of the mean crowding to the
average number of individuals per patch (= m*/m).
Mean Crowding and Resource Based Mating Systems
(Wade 1995)
If we letM = the number of resource patches
containing at least 1 female;mi = the number of females in the i-th
patch; thenthe average density of females per
patch ism = Σ mi / M
The Mean Crowding of Femalesin Space
The mean crowding of females on resources defended by males can be expressed as,
m* = m + [(Vm / m) - 1]
In this context, m* represents the number of other females the average female experiences on
her resource patch.
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The Patchiness of Females in Space
Lloyd’s (1967) estimator of patchiness, P, measures the patchiness of females on resources
P = m*/mor by substitution,
P = 1 + [(Vm / m2) - (1/m)]Thus, P measures the degree to which females
are patchily distributed in space.
Average Male Mating Success
If p0 = the proportion of non-
mating males, (1 - p0) = the proportion of mating males,
and R = (Nfemales / Nmales), then
H = R / (1 - p0) 0 1 2 3 4 5 60
20
40; ; ; ; ;
Number of females (i)
Num
ber
of m
ales
RH
Variance in Male Mating Success
When females are clumped in space, two components of variance in male mating
success exist:(1) the variance in mating success within the class of males that actually mate by
defending resources. (2) the variance in mating success among
the mating and non-mating males.
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Total Fitness VarianceThe largest fraction
exists among mating and non-mating males.
Measures of selection that
exclude p0 (e.g., BSR, Q) under
estimate selection's intensity.
0 1 2 3 4 5 60
20
40; ; ; ; ;
Number of females (i)
Num
ber
of m
ales
RH
The Variance in Mating Success Within and Among Males
Vmates = Vwithin + Vamong
Vwithin = (p0 ) (0) + (1 - p0) Vharem
Vamong = (H - 0)2 (p0 ) (1 - p0)
Vmates = (1 - p0) Vharem + H2(p0 ) (1 - p0)
The Opportunity for Sexual Selection (Imates)
Recall that I = VW/W2,and that R (avg. mates/male) = H (1 - p0).
Dividing Vmates by R2 yields:
Imates = [1/(1 - p0)][ (Vharem) / (H2)]+ (p0 ) / (1 - p0)
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When Females Are Clumped in Space:
and R is assumed to equal 1, then H = 1/(1 - p0) = m,
and(Vharem) / (H2) = (Vm) / (m2)
Then by substitution,
Imates = [1/(1 - p0)][ (Vharem) / (H2)]+ (p0 ) / (1 - p0)
becomesImates = (m) [ (Vm) / (m2)] + 1 - (1/m)
or more simply,Imates = (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, Imates, arising from the
distribution of females in space.