Letter | Published:

Sex‐specific demography and generalization of the Trivers–Willard theory

Nature volume 526, pages 249252 (08 October 2015) | Download Citation


The Trivers–Willard theory1 proposes that the sex ratio of offspring should vary with maternal condition when it has sex‐specific influences on offspring fitness. In particular, mothers in good condition in polygynous and dimorphic species are predicted to produce an excess of sons, whereas mothers in poor condition should do the opposite. Despite the elegance of the theory, support for it has been limited2,3. Here we extend and generalize the Trivers–Willard theory to explain the disparity between predictions and observations of offspring sex ratio. In polygynous species, males typically have higher mortality rates4, different age‐specific reproductive schedules and more risk‐prone life history tactics than females; however, these differences are not currently incorporated into the Trivers–Willard theory. Using two‐sex models parameterized with data from free‐living mammal populations with contrasting levels of sex differences in demography, we demonstrate how sex differences in life history traits over the entire lifespan can lead to a wide range of sex allocation tactics, and show that correlations between maternal condition and offspring sex ratio alone are insufficient to conclude that mothers adaptively adjust offspring sex ratio.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    & Natural selection of parental ability to vary the sex ratio of offspring. Science 179, 90–92 (1973)

  2. 2.

    & Successful sons or advantaged daughters? The Trivers–Willard model and sex‐biased maternal investment in ungulates. Trends Ecol. Evol. 14, 229–234 (1999)

  3. 3.

    & Maternal dominance, maternal condition, and offspring sex ratio in ungulate mammals. Am. Nat. 163, 40–54 (2004)

  4. 4.

    & Sex differences in ageing in natural populations of vertebrates. Proc. Biol. Sci. 274, 3097–3104 (2007)

  5. 5.

    Question of adaptive sex‐ratio in outcrossed vertebrates. Proc. Biol. Sci. 205, 567–580 (1979)

  6. 6.

    , & Maternal condition and facultative sex ratios in populations with overlapping generations. Am. Nat. 168, 521–530 (2006)

  7. 7.

    & Facultative sex ratio manipulation in American kestrels. Behav. Ecol. Sociobiol. 30, 379–386 (1992)

  8. 8.

    , , & Mother’s occupation and sex ratio at birth. BMC Public Health 10, 269 (2010)

  9. 9.

    Sex‐biased investment in nonhuman primates: can Trivers & Willard’s theory be tested?. Anim. Behav. 61, 683–694 (2001)

  10. 10.

    , & in Sex Ratios: Concepts and Research Methods, (ed. ) Ch. 13, 266–286 (Cambridge Univ. Press, 2002)

  11. 11.

    Life‐history analysis of the Trivers and Willard sex‐ratio problem. Behav. Ecol. 7, 316–325 (1996)

  12. 12.

    Allele‐frequency change in a class‐structured population. Am. Nat. 135, 95–106 (1990)

  13. 13.

    The Genetical Theory of Natural Selection (Oxford University Press, 1930)

  14. 14.

    , , , & Age‐specific survival in five populations of ungulates: evidence of senescence. Ecology 80, 2539–2554 (1999)

  15. 15.

    & Advances in our understanding of mammalian sex‐biased dispersal. Mol. Ecol. 16, 1559–1578 (2007)

  16. 16.

    Verhaltensbiologie (Springer, 2006)

  17. 17.

    The Theory of Sex Allocation (Princeton Univ. Press, 1982)

  18. 18.

    , , & The influence of nonrandom mating on population growth. Am. Nat. 182, 28–41 (2013)

  19. 19.

    & Litter sex ratios in Richardsons ground squirrels: long‐term data support random sex allocation and homeostasis. Oecologia 174, 1225–1239 (2014)

  20. 20.

    , & Demography, not inheritance, drives phenotypic change in hunted bighorn sheep. Proc. Natl Acad. Sci. USA 111, 13223–13228 (2014)

  21. 21.

    , , & Maternal condition and offspring sex ratio in polygynous ungulates: a case study of bighorn sheep. Behav. Ecol. 16, 274–279 (2005)

  22. 22.

    & Sex ratio bias and reproductive strategies: what sex to produce when?. Ecology 92, 441–449 (2011)

  23. 23.

    The social system of bighorn sheep: grouping patterns, kinship and female dominance rank. Anim. Behav. 42, 71–82 (1991)

  24. 24.

    et al. Big mothers invest more in daughters – reversed sex allocation in a weakly polygynous mammal. Ecol. Lett. 8, 430–437 (2005)

  25. 25.

    & Birth‐sex ratios and local resource competition in roe deer, Capreolus capreolus. Behav. Ecol. 7, 461–464 (1996)

  26. 26.

    , & Variation in reproductive success of male and female Columbian ground squirrels (Urocitellus columbianus). Can. J. Zool. 90, 736–743 (2012)

  27. 27.

    Mating behavior of Columbian ground squirrels. I. Multiple mating by females and multiple paternity. Can. J. Zool. 73, 1819–1826 (1995)

  28. 28.

    & Mortality in relation to season, age, sex, and reproduction in Columbian ground squirrels (Spermophilus columbianus). Can. J. Zool. 79, 465–470 (2001)

  29. 29.

    , , & Age‐dependent sexual selection in bighorn rams. Proc. Biol. Sci. 269, 165–172 (2002)

  30. 30.

    Weight comparisons and litter size manipulation in Columbian ground squirrels (Spermophilus columbianus) show evidence of costs of reproduction. Behav. Ecol. Sociobiol. 48, 75–83 (2000)

  31. 31.

    et al. Patterns of body mass senescence and selective disappearance differ among three species of free‐living ungulates. Ecology 92, 1936–1947 (2011)

  32. 32.

    Altitudinal variation in the life history of the golden‐mantled ground squirrel (Spermophilus lateralis). Ecology 60, 272–279 (1979)

  33. 33.

    , & Mass‐ and density‐dependent reproductive success and reproductive costs in a capital breeder. Am. Nat. 152, 367–379 (1998)

  34. 34.

    , & Generation time, net reproductive rate, and growth in stage‐age‐structured populations. Am. Nat. 183, 771–783 (2014)

  35. 35.

    & Forgotten fathers: paternal influences on mammalian sex allocation. Trends Ecol. Evol. 29, 158–164 (2014)

  36. 36.

    & Estimation of individual fitness from life‐history data. Am. Nat. 147, 47–64 (1996)

Download references


We thank Y. Vindenes, S. Cubaynes, S. West, R. K. Kanda, J. A. Deere, J. Barthold, M. Brouard, R. A. Pozo, and E. G. Simmonds for comments. We thank M. Festa‐Bianchet and F. Pelletier for access to Bighorn sheep data and feedback. We acknowledge the use of the University of Oxford Advanced Research Computing facility. S.S. was funded by an ERC Advanced Grant to T.C., P.N. is funded by a Swiss National Science Foundation grant (SNF 3100AO‐109816), and L.T. was funded by grants from the European Commission (Marie Curie Fellowship 254442) and the Carnegie Corporation of New York (B8749.R01).

Author information


  1. University of Oxford, Department of Zoology, Oxford OX1 3PS, UK

    • Susanne Schindler
    •  & Tim Coulson
  2. Laboratoire de Biométrie et Biologie Evolutive (UMR 5558), Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

    • Jean‐Michel Gaillard
  3. Department of Computer Science, University of Surrey, Guildford GU2 7XH, UK

    • André Grüning
  4. Department of Biological Sciences, University of Calgary, Calgary, Alberta T2N 1N4, Canada

    • Peter Neuhaus
  5. School of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Wits 2050, South Africa

    • Lochran W. Traill
  6. Department of Biology, Stanford University, Stanford, California 94305, USA

    • Shripad Tuljapurkar


  1. Search for Susanne Schindler in:

  2. Search for Jean‐Michel Gaillard in:

  3. Search for André Grüning in:

  4. Search for Peter Neuhaus in:

  5. Search for Lochran W. Traill in:

  6. Search for Shripad Tuljapurkar in:

  7. Search for Tim Coulson in:


S.S., J.M.G. and T.C. conceived and designed the study. S.S. developed the models and, with S.T., derived the formulas. S.S. and T.C. wrote the manuscript. S.S., A.G. and S.T. contributed to the mathematical formulation of the model. P.N. collated data on Columbian ground squirrels. L.T. parameterized data for bighorn sheep. T.C. parameterized data for squirrels. All authors edited the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Susanne Schindler.

Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Tables 1-3, Supplementary Text and Data and additional references.

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.