characterization of mating systems stevan j. arnold oregon state university
TRANSCRIPT
Characterization of mating systems
Stevan J. ArnoldOregon State University
OVERVIEW1. INTRODUCTION• Qualitative vs quantitative characterization of mating systems• Determination vs characterization of mating systems• Two perspectives: theoretical & empirical• Two obsessions: sexual selection & inbreeding• What do we want?2. PERSPECTIVES ON ANIMAL MATING SYSTEMS• Alternatives • The parental table• Selection theory measures3. PERSPECTIVES ON PLANT MATING SYSTEMS• Inbreeding theory measures• The parental table4. INSIGHTS FROM THE EMPIRICAL PERSPECTIVE5. CONCLUSIONS
INTRODUCTION
Qualitative classification of mating systems
• Monogamy, polygamy, polyandry (Darwin 1871)
• Monogamy, resource defense polygyny, harem defense polygyny, explosive mating assemblage, leks, female access polyandry … (Emlen & Oring 1977)
• Etc
Limitations of qualitative classifications
• Progeny can be produced by matings that are difficult to observe.
• Difficult to specify how the categories grade into one another.
• Essential differences may masquerade under the same name.
• For all these reasons, we need quantitative characterizations
Determination vs characterization of mating systems
Spatial distribution of
resources
System of mating
“Intensity of sexual selection”
Temporal availability of
the limiting sexOSR
Emlen & Oring 1977
Variation in reproductive success
Two perspectives on quantitative characterization
• Theoretical.- Looking at the data from a theoretical perspective; what are the connections?
• Empirical.- Looking at theory from a data perspective; what can we do with the data in hand?
Two obsessions
• Sexual selection (animals)
• Inbreeding (plants)
What do we want in measures that characterize the mating
system?PRIMARY CONSIDERATIONS.-
Tangible connection to overarching theoryFundamentalGeneral
SECONDARY CONSIDERATIONS.-SimplicityIntuitiveGender neutralDesirable statistical properties
PERSPECTIVES ON ANIMAL MATING SYSTEMS
Alternative characterizations
• Selection theory measures
• Indices of resource monopolization
• Potential reproductive rates
Fundamental information about the mating system is captured in the
parental table
POLYGYNY + POLYANDRYFemales
Males 1 2 3 4 5 6 7 8 no. mates no. offspring1 5 6 2 3 132 3 8 2 3 133 2 6 2 3 104 2 3 6 6 4 175 1 1 16 2 1 27 2 1 28 0 0
no. mates 2 1 3 1 4 2 2 1no. offspring 6 6 7 8 8 9 8 6
Arnold & Duvall 1994
Selection theory measures
• Quantify Bateman’s three principles (variance in mating success, variance in offspring number, relationship between offspring number and mating success)
• Standardized variances, regression slopes
• Direct connection to theory for selection on quantitative traits
• Is, Is; I, I; βss, βss
Bateman 1948, Crow 1958, Wade 1979, Wade & Arnold 1980, Arnold & Duvall 1994, Shuster & Wade 2003
Properties of a selection opportunity, I
• Equals variance in relative fitness
• Equals squared coefficient of variation
• Sets upper limit on the magnitude of directional, stabilizing (disruptive), and correlational selection
• When this variance is zero, there can be no sexual selection
Properties of a Bateman gradient
• Equals the slope of the regression that relates reproductive success (offspring) to mating success (mates that bear progeny)
• Part of the selection that acts on every sexually-selected trait
• The final common path between sexually-selected traits and fitness
• When this gradient is zero, there can be no sexual selection
Arnold & Duvall 1994
The relationship between βss, Is, and I
3 2 1
12
Male Bateman Gradient
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7
Number of mates
Nu
mb
er o
f o
ffsp
rin
g
βss=slope= 1.46 offspring/mate
Is=0.21
I=0.18
A parental table and Bateman plots derived from it
POLYGYNY + POLYANDRYFemales
Males 1 2 3 4 5 6 7 8 no. mates no. offspring1 5 6 2 3 132 3 8 2 3 133 2 6 2 3 104 2 3 6 6 4 175 1 1 16 2 1 27 2 1 28 0 0
no. mates 2 1 3 1 4 2 2 1no. offspring 6 6 7 8 8 9 8 6
Male Bateman Gradient
-5
0
5
10
15
20
0 1 2 3 4 5
Number of mates
Nu
mb
er
of
off
sp
rin
g
Female Bateman Gradient
0
2
4
6
8
10
0 1 2 3 4 5
Number of mates
Nu
mb
er
of
off
sp
rin
g
The Bateman gradient as a part of selection on a trait
Arnold & Duvall 1994
Indices of resource monopolization
• Based on a random, null distribution of resources
• Complex functions of mean and variance
• Q, Q = Index of resource monopolization
• Iδ ,Iδ = Morisita’s index
• No known connection to evolutionary theory
Koko et al. 1999, Fairbairn & Wilby 2001
Potential reproductive rates
• Maximum possible production of offspring by males and females
• Maximum values in a sample or experimentally determined
• A determinant of OSR, rather than a characterization of the mating system
Clutton-Brock & Vincent 1991, Clutton-Brock & Parker 1992
Theoretical perspective: connections to evolutionary theory
Indices of resource
monopolization
Potential reprod.rates
Intensity of sexual selection
Opportunitities for selection
Bateman gradients
Sex ratio
Total selection Inheritance
Evolution of sexually-selected characters
?
PERSPECTIVES ON PLANT MATING SYSTEMS
Inbreeding theory measures
• Inbreeding depression measures the cost of inbreeding in populations with partial selfing.
• Equals the relative difference in fitness when offspring are produced by selfing versus outcrossing.
• Direct connection to theory for the evolution of selfing.
• Inbreeding depression (δ) is a function of selfing rate (s) and Wright’s inbreeding coefficient (f ).
Darwin 1876, Wright 1922, Charlesworth & Charlesworth 1984, Ritland 1990
Parental table and Bateman plots for a population with partial selfing
Parental Table with number of offspring as entries = selfed progenyPARTIAL SELFING =outcross progeny
FemalesMales 1 2 3 4 5 6 7 8 no. mates no. offspring
1 1 1 2 22 4 2 1 1 2 5 103 4 1 1 3 64 5 1 3 2 4 115 1 2 1 2 4 1 6 116 6 1 3 3 107 2 4 1 4 4 118 5 1 5
no. mates 3 5 5 4 3 4 4 0no. offspring 6 14 10 7 7 10 12 0
Male Bateman GradientPollen parentage
0
2
4
6
8
10
12
14
0 2 4 6 8
Number of mates
Nu
mb
er o
f o
ffsp
rin
g
Female Bateman GradientOvule parentage
-2
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
Number of mates
Nu
mb
er o
f o
ffsp
rin
g
Theoretical perspective: connections to evolutionary theory
Inbreeding depression
Inbreeding coefficient
Selection on selfing rate Inheritance
Evolution of selfing rate
Selfing rate
Lande & Schemske 1985
INSIGHTS FROM THE EMPIRICAL PERSPECTIVE
Summary of insights from the empirical perspective
DATA EVOLUTIONARY PARAMETERS THAT CAN BE ESTIMATED
Mating success Opportunity for sexual selection
Reproductive success Opportunity for fecundity selection, Bateman gradients
Traits in males and females
Sexual and fecundity selection gradients
Traits in offspring Heritabilities (G-matrix), response to selection
Fitness of offspring Heritability of mating and reproductive success, parental selection
Inbreeding coefficients or pedigree
Inbreeding depression, coefficients of inbreeding
CONCLUSIONS
• Characterization of mating systems using selection and inbreeding theory measures has advantages over other characterizations.
• The parental table offers a useful empirical perspective on mating systems.
• In some mating systems and for some purposes, the parental table needs to be supplemented with additional information (e.g., parental traits, offspring fitness).
COLLABORATORS
• M. J. Wade (Indiana University)
• R. Lande (Imperial College)
• D. Duvall (Oklahoma State University)
• A. G. Jones (Texas A&M University)