Transcript Characterization of mating systems

Characterization of mating
systems
Stevan J. Arnold
Oregon State University
OVERVIEW
1. 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 measures
3. PERSPECTIVES ON PLANT MATING SYSTEMS
• Inbreeding theory measures
• The parental table
4. INSIGHTS FROM THE EMPIRICAL PERSPECTIVE
5. 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
OSR
Spatial
distribution of
resources
Temporal
availability of
the limiting sex
Variation in reproductive success
“Intensity of sexual selection”
System of mating
Emlen & Oring 1977
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 theory
Fundamental
General
SECONDARY CONSIDERATIONS.Simplicity
Intuitive
Gender neutral
Desirable 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 + POLYANDRY
Males
1
2
3
4
5
6
7
8
no. mates
no. offspring
1
5
2
6
3
2
3
Females
4
8
5
6
7
8
2
2
2
6
3
2
6
6
2
9
2
8
1
6
1
2
2
2
6
1
6
3
7
1
8
4
8
no. mates
3
3
3
4
1
1
1
0
no. offspring
13
13
10
17
1
2
2
0
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 sexuallyselected traits and fitness
• When this gradient is zero, there can be
no sexual selection
Arnold & Duvall 1994
The relationship between βss, Is,
and I
βss=slope= 1.46 offspring/mate
Male Bateman Gradient
14
I=0.18
2
12
1
Number of offspring
3
10
8
6
4
2
0
0
1
2
3
4
Number of mates
1
2
Is=0.21
5
6
7
A parental table and Bateman plots
derived from it
POLYGYNY + POLYANDRY
Males
1
2
3
4
5
6
7
8
1
5
2
6
Females
4
3
2
3
8
5
6
7
8
2
2
2
6
3
2
6
6
2
9
2
8
1
6
1
2
2
no. mates
no. offspring
2
6
1
6
3
7
1
8
4
8
no. offspring
13
13
10
17
1
2
2
0
Female Bateman Gradient
Male Bateman Gradient
10
Number of offspring
20
Number of offspring
no. mates
3
3
3
4
1
1
1
0
15
10
5
0
0
1
2
3
-5
Number of mates
4
5
8
6
4
2
0
0
1
2
3
Number of mates
4
5
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
Potential reprod.
rates
Sex ratio
Opportunitities for selection
Bateman gradients
Intensity of sexual selection
Indices of
resource
monopolization
?
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
PARTIAL SELFING
Females
Males
1
2
3
4
1
1
1
2
4
2
1
1
3
4
1
4
5
1
3
5
1
2
1
6
6
1
7
2
8
no. mates
no. offspring
3
6
5
14
5
10
4
7
= selfed progeny
=outcross progeny
5
6
7
no. mates no. offspring
2
2
5
10
3
6
4
11
6
11
3
10
4
11
1
5
2
1
4
2
4
3
1
3
7
4
10
2
1
4
5
4
12
0
0
Female Bateman Gradient
Ovule parentage
Male Bateman Gradient
Pollen parentage
16
14
12
10
8
6
4
2
0
0
2
4
Number of mates
6
8
Number of offspring
Number of offspring
8
14
12
10
8
6
4
2
0
-2 0
1
2
3
4
Num ber of m ates
5
6
Theoretical perspective: connections to
evolutionary theory
Inbreeding coefficient
Selfing rate
Inbreeding depression
Selection on
selfing rate
Inheritance
Evolution of 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)