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)