Abstract
Optimization models have been widely and successfully used in evolutionary ecology to predict the attributes of organisms1–8. Most such models maximize darwinian fitness in the face of tradeoffs and constraints; the numerical results usually depend on the exact form of the trade-offs or constraints. But not always9: for example, earlier work9 predicted that the optimal range in offspring size ought to show a – 1 scaling with small litter size, independent of most details of the underlying offspring-survival/offspring-size trade-off relation. Here I report that in non-growing (stationary), age-structured populations, three major life-history attributes (age at first breeding, size of an offspring in large litters, and reproductive effort) are likely to evolve to equilibrium values that satisfy a universal numerical rule; the underlying trade-off will have a slope of – 1 at the optimum, independent of most other aspects of the trade-off. Each of these three attributes can be viewed as an allocation problem between just two alternatives; the trade-off is then between having more of one alternative and less of the other. The slope of the trade-off is simply the slope of the curve of allowed combinations of the two alternatives. The theory predicts that natural selection will push to an equilibrium where the slope is always – 1. The economic structure is the same as that which underlies evolution of the sex ratio where the two alternatives are sons and daughters2,10.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Parker, G. A. & Maynard Smith, J. Optimality theory in evolutionary biology. Nature 348, 27–33 (1990).
Charnov, E. L. The Theory of Sex Allocation (Princeton Univ. Press, NJ, 1982).
Seger, J. & Stubblefield, J. W. in Adaptation 93–123 (Academic, New York, 1996)
Bulmer, M. G. Theoretical Evolutionary Ecology (Sinauer, Sunderland, MA, 1994.)
Godfray, H. C. J. Parasitoids (Princeton Univ. Press, NJ, 1994).
Charnov, E. L. Life History Invariants (Oxford Univ. Press, 1993).
Stearns, S. C. The Evolution of Life Histories (Oxford Univ. Press, 1992).
Charlesworth, B. Evolution in Age-Structured Populations. (Cambridge Univ. Press, 1994).
Charnov, E. L. & Downhower, J. F. A trade-off-invariant life-history rule for optimal offspring size. Nature 376, 418–419 (1995).
MacArthur, R. H. in Theoretical and Mathematical Biology (eds Waterman, T. H. & Morowitz, H.) 388–397 (Blaisdell, New York, 1965).
Williams, G. C. Natural selection, the cost of reproduction, and a refinement of Lack's principle. Am. Nat. 100, 687–690 (1966).
Charnov, E. L. Evolution of life history variation among female mammals. Proc. Natl Acad. Sci. USA 88, 1134–1137 (1991).
Lloyd, D. G. Selection of offspring size at independence and other size-versus-number strategies. Am. Nat. 129, 800–817 (1987).
Mock, D. W. & Parker, G. A. The Evolution of Sibling Rivalry (Oxford Univ. Press, 1997).
Stearns, S. C. Tradeoffs in life history evolution. Funct. Ecol. 3, 259–268 (1989).
Charnov, E. L. & Berrigan, D. Why do female primates have such long lifespans and so few babies? Evol. Anthropol. 1, 191–194 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Charnov, E. Trade-off-invariant rules for evolutionary stable life histories. Nature 387, 393–394 (1997). https://doi.org/10.1038/387393a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/387393a0
This article is cited by
-
Applying symmetries of elasticities in matrix population models
Theoretical Ecology (2021)
-
Reproduction elevates the corticosterone stress response in common fruit bats
Journal of Comparative Physiology A (2006)
-
Making life simpler
Nature (1997)
Comments
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.