1. Characterization of mating systems Stevan J. Arnold Oregon State University

2. 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

3. INTRODUCTION

4. 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

5. 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

6. Determination vs characterization of mating systems Spatial distribution of resources System of mating “Intensity of sexual selection” Temporal availability of the limiting sex OSR Emlen & Oring 1977 Variation in reproductive success

7. 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?

8. Two obsessions Sexual selection (animals) Inbreeding (plants)

9. 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

10. PERSPECTIVES ON ANIMAL MATING SYSTEMS

11. Alternative characterizations Selection theory measures Indices of resource monopolization Potential reproductive rates

12. Fundamental information about the mating system is captured in the parental table Arnold & Duvall 1994

13. 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 I s, I s ; I, I; β ss, β ss Bateman 1948, Crow 1958, Wade 1979, Wade & Arnold 1980, Arnold & Duvall 1994, Shuster & Wade 2003

14. 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

15. 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

16. The relationship between β ss, I s, and I β ss =slope= 1.46 offspring/mate I s =0.21 I=0.18

17. A parental table and Bateman plots derived from it

18. The Bateman gradient as a part of selection on a trait Arnold & Duvall 1994

19. Indices of resource monopolization Based on a random, null distribution of resources Complex functions of mean and variance Q, Q = Index of resource monopolization I δ,I δ = Morisita’s index No known connection to evolutionary theory Koko et al. 1999, Fairbairn & Wilby 2001

20. 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

21. 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 ?

22. PERSPECTIVES ON PLANT MATING SYSTEMS

23. 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

24. Parental table and Bateman plots for a population with partial selfing

25. Theoretical perspective: connections to evolutionary theory Inbreeding depression Inbreeding coefficient Selection on selfing rate Inheritance Evolution of selfing rate Selfing rate Lande & Schemske 1985

26. INSIGHTS FROM THE EMPIRICAL PERSPECTIVE

27. Summary of insights from the empirical perspective DATAEVOLUTIONARY PARAMETERS THAT CAN BE ESTIMATED Mating successOpportunity for sexual selection Reproductive successOpportunity for fecundity selection, Bateman gradients Traits in males and females Sexual and fecundity selection gradients Traits in offspringHeritabilities (G-matrix), response to selection Fitness of offspringHeritability of mating and reproductive success, parental selection Inbreeding coefficients or pedigree Inbreeding depression, coefficients of inbreeding

28. 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).

29. COLLABORATORS M. J. Wade (Indiana University) R. Lande (Imperial College) D. Duvall (Oklahoma State University) A. G. Jones (Texas A&M University)