The rate of facultative sex governs the number of expected mating types in isogamous species


It is unclear why sexually reproducing isogamous species frequently contain just two self-incompatible mating types. Deterministic theory suggests that since rare novel mating types experience a selective advantage (by virtue of their many potential partners), the number of mating types should consistently grow. However, in nature, species with thousands of mating types are exceedingly rare. Several competing theories for the predominance of species with two mating types exist, yet they lack an explanation for how many are possible and in which species to expect high numbers. Here, we present a theoretical null model that explains the distribution of mating type numbers using just three biological parameters: mutation rate, population size and the rate of sex. If the number of mating types results from a mutation–extinction balance, the rate of sexual reproduction plays a crucial role. If sex is facultative and rare (a very common combination in isogamous species), mating type diversity will remain low. In this rare sex regime, small fitness differences between the mating types lead to more frequent extinctions, further lowering mating type diversity. We also show that the empirical literature supports the role of drift and facultativeness of sex as a determinant of mating type dynamics.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Visualization of the model illustrating three types of potential event: sexual reproduction, asexual reproduction and mutation.
Fig. 2: Dynamics of mating type frequency with three initial mating types (M0 = 3).
Fig. 3: Dynamics of the mating type number, M, with M0 = 2 for various parameters under different modelling assumptions.
Fig. 4: Bounds on the expected number of mating types predicted by the model as a function of the population size, N, and the per-generation mutation rate, mg, when there are no selective differences between the mating types (σ = 0).


  1. 1.

    Billiard, S. et al. Having sex, yes, but with whom? Inferences from fungi on the evolution of anisogamy and mating types. Biol. Rev. 86, 421–442 (2011).

    PubMed  Google Scholar 

  2. 2.

    Iwasa, Y. & Sasaki, A. Evolution of the number of sexes. Evolution 41, 49–65 (1987).

    PubMed  Google Scholar 

  3. 3.

    Nagylaki, T. The deterministic behavior of self-incompatibility alleles. Genetics 79, 545–550 (1975).

    CAS  PubMed  PubMed Central  Google Scholar 

  4. 4.

    Kothe, E. Tetrapolar fungal mating types: sexes by the thousands. FEMS Microbiol. Rev. 18, 65–87 (1996).

    CAS  PubMed  Google Scholar 

  5. 5.

    Lehtonen, J., Kokko, H. & Parker, G. A. What do isogamous organisms teach us about sex and the two sexes? Phil. Trans. R. Soc. B 371, 20150532 (2016).

    PubMed  Google Scholar 

  6. 6.

    Beukeboom, L. & Perrin, N. The Evolution of Sex Determination (Oxford Univ. Press, Oxford, 2014).

  7. 7.

    Geng, S., De Hoff, P. & Umen, J. G. Evolution of sexes from an ancestral mating-type specification pathway. PLoS Biol. 12, e1001904 (2014).

    PubMed  PubMed Central  Google Scholar 

  8. 8.

    Hamaji, T. et al. Sequence of the gonium pectorale mating locus reveals a complex and dynamic history of changes in volvocine algal mating haplotypes. G3 6, 1179–1189 (2016).

  9. 9.

    Togashi, T. & Cox, P. A. The Evolution of Anisogamy (Cambridge Univ. Press, Cambridge, 2011).

  10. 10.

    Lehtonen, J. & Kokko, H. Two roads to two sexes: unifying gamete competition and gamete limitation in a single model of anisogamy evolution. Behav. Ecol. Sociobiol. 65, 445–459 (2011).

    Google Scholar 

  11. 11.

    Parker, G. A., Baker, R. R. & Smith, V. G. The origin and evolution of gamete dimorphism and the male–female phenomenon. J. Theor. Biol. 36, 529–553 (1972).

    CAS  PubMed  Google Scholar 

  12. 12.

    Togashi, T., Bartelt, J. L., Yoshimura, J., Tainaka, K. & Cox, P. A. Evolutionary trajectories explain the diversified evolution of isogamy and anisogamy in marine green algae. Proc. Natl Acad. Sci. USA 109, 13692–13697 (2012).

    CAS  PubMed  Google Scholar 

  13. 13.

    Hoekstra, R. F. in The Evolution of Sex and its Consequences (ed. Stearns, S. C.) 59–91 (Birkhaeuser, Basel, 1987).

  14. 14.

    Nozaki, H., Mori, T., Misumi, O., Matsunaga, S. & Kuroiwa, T. Males evolved from the dominant isogametic mating type. Curr. Biol. 16, R1018–R1020 (2006).

    CAS  PubMed  Google Scholar 

  15. 15.

    Hadjivasiliou, Z., Iwasa, Y. & Pomiankowski, A. Cell–cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes. J. R. Soc. Interface 12, 20150342 (2015).

    PubMed  PubMed Central  Google Scholar 

  16. 16.

    James, T. Y. Why mushrooms have evolved to be so promiscuous: insights from evolutionary and ecological patterns. Fungal Biol. Rev. 29, 167–178 (2015).

    Google Scholar 

  17. 17.

    Hoekstra, R. F. On the asymmetry of sex: evolution of mating types in isogamous populations. J. Theor. Biol. 98, 427–451 (1982).

    Google Scholar 

  18. 18.

    Hadjivasiliou, Z. & Pomiankowski, A. Gamete signalling underlies the evolution of mating types and their number. Phil. Trans. R. Soc. B 371, 20150531 (2016).

    PubMed  Google Scholar 

  19. 19.

    Phadke, S. S. & Zufall, R. A. Rapid diversification of mating systems in ciliates. Biol. J. Linn. Soc. 98, 187–197 (2009).

    Google Scholar 

  20. 20.

    Hurst, L. D. Why are there only two sexes? Proc. R. Soc. B 263, 415–422 (1996).

    Google Scholar 

  21. 21.

    Hurst, L. D. & Hamilton, W. D. Cytoplasmic fusion and the nature of sexes. Proc. R. Soc. B 247, 189–194 (1992).

    Google Scholar 

  22. 22.

    Hutson, V. & Law, R. Four steps to two sexes. Proc. R. Soc. Lond. B 253, 43–51 (1993).

    CAS  Google Scholar 

  23. 23.

    Hadjivasiliou, Z., Lane, N., Seymour, R. M. & Pomiankowski, A. Dynamics of mitochondrial inheritance in the evolution of binary mating types and two sexes. Proc. R. Soc. B 280, 20131920 (2013).

    PubMed  Google Scholar 

  24. 24.

    Nieuwenhuis, B. P. S. et al. Evolution of uni- and bifactorial sexual compatibility systems in fungi. Heredity 111, 445–455 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Vuilleumier, S., Alcala, N. & Niculita-Hirzel, H. Transitions from reproductive systems governed by two self-incompatible loci to one in fungi. Evolution 67, 501–516 (2013).

    PubMed  Google Scholar 

  26. 26.

    Umen, J. G. Evolution of sex and mating loci: an expanded view from volvocine algae. Curr. Opin. Microbiol. 14, 634–641 (2011).

    PubMed  PubMed Central  Google Scholar 

  27. 27.

    Nedelcu, A. M. & Michod, R. E. Sex as a response to oxidative stress: the effect of antioxidants on sexual induction in a facultatively sexual lineage. Proc. R. Soc. B 270, S136–S139 (2003).

    CAS  PubMed  Google Scholar 

  28. 28.

    Harris, E. H. The Chlamydomonas Sourcebook: A Comprehensive Guide to Biology and Laboratory Use (Academic Press, Cambridge, 1989).

  29. 29.

    Van den Hoek, C., Mann, D. & Jahns, H. M. Algae: An Introduction to Phycology (Cambridge Univ. Press, Cambridge, 1996).

  30. 30.

    Goodenough, U., Lin, H. & Lee, J. H. Sex determination in Chlamydomonas. Semin. Cell. Dev. Biol. 18, 350–361 (2007).

    CAS  PubMed  Google Scholar 

  31. 31.

    Hartl, D. L. & Clark, A. G. Principles of Population Genetics 4th edn (Sinauer Associates, Sunderland, 2007).

  32. 32.

    Hartfield, M. & Keightley, P. D. Current hypotheses for the evolution of sex and recombination. Integr. Zool. 7, 192–209 (2012).

    PubMed  Google Scholar 

  33. 33.

    Power, H. W. On forces of selection in the evolution of mating types. Am. Nat. 110, 937–944 (1976).

    Google Scholar 

  34. 34.

    Paixao, T., Phadke, S. S., Azevedo, R. B. & Zufall, R. A. Sex ratio evolution under probabilistic sex determination. Evolution 65, 2050–2060 (2011).

    PubMed  Google Scholar 

  35. 35.

    Abramowitz, M. & Stegun, I. A. Handbook of Mathematical Functions (Dover Publications, New York, 1965).

  36. 36.

    Wright, S. The distribution of self-sterility alleles in populations. Genetics 24, 538–552 (1939).

    CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Nunney, L. The effect of neighborhood size on effective population size in theory and in practice. Heredity 117, 224–232 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  38. 38.

    Charlesworth, B. Effective population size. Curr. Biol. 12, 716–717 (2002).

    Google Scholar 

  39. 39.

    Baranova, M. A. et al. Extraordinary genetic diversity in a wood decay mushroom. Mol. Biol. Evol. 32, 2775–2783 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  40. 40.

    Gossmann, T. I., Keightley, P. D. & Eyre-Walker, A. The effect of variation in the effective population size on the rate of adaptive molecular evolution in eukaryotes. Genome Biol. Evol. 4, 658–667 (2012).

    PubMed  PubMed Central  Google Scholar 

  41. 41.

    Tsai, I. J., Bensasson, D., Burt, A. & Koufopanou, V. Population genomics of the wild yeast Saccharomyces paradoxus: quantifying the life cycle. Proc. Natl Acad. Sci. USA 105, 4957–4962 (2008).

    CAS  PubMed  Google Scholar 

  42. 42.

    Nieuwenhuis, B. P. S. & James, T. Y. The frequency of sex in fungi. Phil. Trans. R. Soc. B 371, 20150540 (2016).

    PubMed  Google Scholar 

  43. 43.

    Doerder, F. P., Gates, M. A., Eberhardt, F. P. & Arslanyolu, M. High frequency of sex and equal frequencies of mating types in natural populations of the ciliate Tetrahymena thermophila. Proc. Natl Acad. Sci. USA 92, 8715–8718 (1995).

    CAS  PubMed  Google Scholar 

  44. 44.

    Lucchesi, P. & Santangelo, G. How often does conjugation in ciliates occur? Clues from a seven-year study on marine sandy shores. Aquat. Microb. Ecol. 36, 195–200 (2004).

    Google Scholar 

  45. 45.

    Lee, S. C., Ni, M., Li, W., Shertz, C. & Heitman, J. The evolution of sex: a perspective from the fungal kingdom. Microbiol. Mol. Biol. Rev. 74, 298–340 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  46. 46.

    Dunthorn, M. & Katz, L. A. Secretive ciliates and putative asexuality in microbial eukaryotes. Trends Microbiol. 18, 183–188 (2010).

    CAS  PubMed  Google Scholar 

  47. 47.

    Ruderfer, D. M., Pratt, S. C., Seidel, H. S. & Kruglyak, L.Population genomic analysis of outcrossing and recombination in yeast. Nat. Genet. 38, 1077–1081 (2006).

    CAS  PubMed  Google Scholar 

  48. 48.

    Jang, H. & Ehrenreich, I. M. Genome-wide characterization of genetic variation in the unicellular, green alga Chlamydomonas reinhardtii. PLoS ONE 7, e41307 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. 49.

    Hadjivasiliou, Z. Theoretical Studies on the Role and Evolution of Mating Types and Two Sexes. PhD thesis, Univ. College London (2014).

  50. 50.

    Nieuwenhuis, B. P. S. & Aanen, D. K. Sexual selection in fungi. J. Evol. Biol. 25, 2397–2411 (2012).

    CAS  PubMed  Google Scholar 

  51. 51.

    Bull, J. J. & Pease, C. M. Combinatorics and variety of mating-type systems. Evolution 43, 667–671 (1989).

    CAS  PubMed  Google Scholar 

  52. 52.

    Wilson, A. M. et al. Homothallism: an umbrella term for describing diverse sexual behaviours. IMA Fungus 6, 207–214 (2015).

    PubMed  PubMed Central  Google Scholar 

  53. 53.

    Bell, G. Experimental sexual selection in Chlamydomonas. J. Evol. Biol. 18, 722–734 (2005).

    CAS  PubMed  Google Scholar 

  54. 54.

    Milgroom, M. G. Recombination and the multilocus structure of fungal populations.Annu. Rev. Phytopathol. 34, 457–477 (1996).

    CAS  PubMed  Google Scholar 

  55. 55.

    Teixeira, M. et al. Asexual propagation of a virulent clone complex in a human and feline outbreak of sporotrichosis. Eukaryot. Cell 14, 158–169 (2015).

    PubMed Central  Google Scholar 

  56. 56.

    Brisse, S. et al. Uneven distribution of mating types among genotypes of Candida glabrata isolates from clinical samples. Eukaryot. Cell 8, 287–295 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. 57.

    Kwon-Chung, K. J., Edman, J. C. & Wickes, B. L. Genetic association of mating types and virulence in Cryptococcus neoformans. Infect. Immun. 60, 602–605 (1992).

    CAS  PubMed  PubMed Central  Google Scholar 

  58. 58.

    Narmani, A., Arzanlou, M. & Babai-Ahari, A. Uneven distribution of mating-type alleles among Togninia minima isolates, one of the causal agents of leaf stripe disease on grapevines in northwest iran. J. Phytopathol. 164, 441–447 (2016).

    CAS  Google Scholar 

  59. 59.

    Du, X.-H. et al. Mixed-reproductive strategies, competitive mating-type distribution and life cycle of fourteen black morel species. Sci. Rep. 7, 1493 (2017).

    PubMed  PubMed Central  Google Scholar 

  60. 60.

    West, S. Sex Allocation (Princeton Univ. Press, Princeton, 2009).

  61. 61.

    Mandel, M. A., Barker, S., Kroken, B. M., Rounsley, S. D. & Orbach, M. J. Genomic and population analyses of the mating type loci in Coccidioides species reveal evidence for sexual reproduction and gene acquisition. Eukaryot. Cell 6, 1189–1199 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  62. 62.

    Douglas, T. E., Strassmann, J. E. & Queller, D. C. Sex ratio and gamete size across eastern North America in Dictyostelium discoideum, a social amoeba with three sexes. J. Evol. Biol. 29, 1298–1306 (2016).

    CAS  PubMed  Google Scholar 

  63. 63.

    Gervais, C. E., Castric, V., Ressayre, S. & Billiard, A.Origin and diversification dynamics of self-incompatibility haplotypes. Genetics 188, 625–636 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. 64.

    Wright, S. On the number of self-incompatibility alleles maintained in equilibrium by a given mutation rate in a population of a given size: a re-examination. Biometrics 16, 61–85 (1960).

    Google Scholar 

  65. 65.

    Wright, S. The distribution of self-incompatibility alleles in populations. Evolution 18, 609–619 (1964).

    Google Scholar 

  66. 66.

    Hadjivasiliou, Z., Pomiankowski, A. & Kuijper, B. The evolution of mating type switching. Evolution 70, 1569–1581 (2016).

    PubMed  PubMed Central  Google Scholar 

  67. 67.

    Nieuwenhuis, B. P. S. & Immler, S. The evolution of mating-type switching for reproductive assurance. Bioessays 38, 1141–1149 (2016).

    PubMed  Google Scholar 

  68. 68.

    Becks, L. & Agrawal, A. F. Higher rates of sex evolve under K-selection. J. Evol. Biol. 26, 900–905 (2013).

    CAS  PubMed  Google Scholar 

  69. 69.

    Bengtsson, B. O. & Ceplitis, A. The balance between sexual and asexual reproduction in plants living in variable environments. J. Evol. Biol. 13, 415–422 (2000).

    Google Scholar 

  70. 70.

    Crow, J. F. & Kimura, M. An Introduction to Population Genetics Theory (Blackburn Press, Caldwell, 1970).

  71. 71.

    Yokoyama, S. & Hetherington, L. E. The expected number of self-incompatibility alleles in finite plant populations. Heredity 48, 299–303 (1982).

    Google Scholar 

  72. 72.

    McKane, A. J., Biancalani, T. & Rogers, T. Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond. Bull. Math. Biol. 76, 895–921 (2014).

    PubMed  Google Scholar 

  73. 73.

    Muirhead, C. A. & Wakeley, J. Modeling multiallelic selection using a Moran model. Genetics 182, 1141–1157 (2009).

    PubMed  PubMed Central  Google Scholar 

  74. 74.

    Gillespie, D. T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976).

    CAS  Google Scholar 

Download references


We thank J. Christie, L. Turner and the audience of the seminar series at the Milner Centre for Evolution for useful discussions and input. G.W.A.C. thanks the Finnish Center for Excellence in Biological Interactions and Leverhulme Early Career Fellowship provided by the Leverhulme Trust for funding. H.K. thanks the Swiss National Science Foundation and Academy of Finland for funding.

Author information




G.W.A.C. designed the project and conducted the mathematical analysis. G.W.A.C. and H.K. developed the model and wrote the paper.

Corresponding author

Correspondence to George W. A. Constable.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Mathematical theory, model analysis and simulations

Reporting Summary

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Constable, G.W.A., Kokko, H. The rate of facultative sex governs the number of expected mating types in isogamous species. Nat Ecol Evol 2, 1168–1175 (2018).

Download citation

Further reading


Quick links

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing