Skip to main content
SpringerLink
Log in

Daniel Bernoulli (1738): evolution and economics under risk

  • Published:
Journal of Biosciences Aims and scope Submit manuscript

Conclusion

In this 300th anniversary of Daniel Bernoulli's birth, this essay traces the influence of one of his works usually regarded by mathematicians and physicists as too minor to mention. From this source has flowed much of our understanding of how to deal with risk in economics and evolution. The concepts introduced by Bernoulli help us to think about the evolution of reproductive lifespan, dormancy and diapause, sexual versus asexual reproduction, and population dynamics. In economics they form the foundation of portfolio and insurance theory. The 1738 paper was definitely not minor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bernoulli D 1954 Exposition of a new theory on the measurement of risk;Econometrica 22 23–36 (Translation of Bernoulli D 1738 Specimen theoriae novae de mensura sortis;Papers Imp. Acad. Sci. St. Petersburg 5 175–192)

    Article  Google Scholar 

  • Brieman L 1960 Investment policies for expanding business optimal in a long-term sense;Nav. Res. Logistics Q. 7 647–651

    Article  Google Scholar 

  • Bulmer M G 1985 Selection for iteroparity in a variable environment;Am. Nat. 126 63–71

    Article  Google Scholar 

  • Cohen D 1966 Optimizing reproduction in a randomly varying environment;J. Theor. Biol. 12 119–129

    Article  PubMed  CAS  Google Scholar 

  • Cohen D 1968 A general model of optimal reproduction in a randomly varying environment;J. Ecol. 56 219–228

    Article  Google Scholar 

  • Dempster E 1955 Maintenance of genetic heterogeneity;Cold Spring Harbor Symp. Quant. Biol. 20 25–32

    PubMed  CAS  Google Scholar 

  • Dieckmann U 1997 Can adaptive dynamics invade?;Trends Ecol. Evol. 12 128–131

    Article  Google Scholar 

  • Doebeli M 1998 Invasion of rare mutants does not imply their evolutionary success: a counterexample from metapopulation theory;J. Evol. Biol. 11 389–401

    Article  Google Scholar 

  • Doebeli M and Koella J 1994 Sex and population dynamics;Proc. R. Soc. London B257 17–23

    Article  Google Scholar 

  • Ekbohm G, Fagerström T and 228-01 G 1980 Natural selection for variation in offspring numbers: comments on a paper by J H Gillespie;Am. Nat. 115 445–447

    Article  Google Scholar 

  • Ellner S 1989 Convergence to stationary distributions in two-species stochastic competition models;J. Math. Biol. 27 451–462

    Article  PubMed  CAS  Google Scholar 

  • Ferriére R and Gatto M 1995 Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations;Theor. Popul. Biol. 48 126–171

    Article  Google Scholar 

  • Frank S A and Slatkin M 1990 Evolution in a variable environment;Am. Nat. 136 244–260

    Article  Google Scholar 

  • Gillespie J H 1974 Natural selection for within-generation variance in offspring numbers;Genetics 76 601–606

    PubMed  CAS  Google Scholar 

  • Haldane J B S and Jayakar S D 1963 Polymorphism due to selection of varying direction;J. Genet. 58 237–242

    Article  Google Scholar 

  • Halder O 1889 Ueber einen Mittelwertsatz;richten 38–47

  • Jensen J L 1906 Sur les fonctions convexes et les inégalités entre les valeurs moyennes;Acta Math. 30 175–193

    Article  Google Scholar 

  • Lacey E P, Real L A, Antonovics J and Heckel D G 1983 Variance models in the study of life histories;Am. Nat. 122 114–131

    Article  Google Scholar 

  • Leonard J L 1999 Modern portfolio theory and the prudent hermaphrodite;Invert. Reprod. Dev. 36 129–135

    Google Scholar 

  • Levins R 1967Evolution in changing environments (Princeton: Princeton University Press)

    Google Scholar 

  • Lewontin R and Cohen D 1969 On population growth in a randomly varying environment;Proc. Natl. Acad. Sci. USA 62 1056–1060

    Article  PubMed  CAS  Google Scholar 

  • Markowitz H 1952 Portfolio selection;J. Finance 7 77–91

    Article  Google Scholar 

  • Merian P 1860 Die mathematicker Bernoulli. Jubelschrift zur vierten säculärfier der Universität Basel;Schweighauser'sche-Buchdruckerei, Basel, p 61

  • Real L A 1980 Fitness uncertainty and the role of diversification in evolution and behavior;Am. Nat. 115 623–638

    Article  Google Scholar 

  • Real L A and Ellner S 1992 Life history evolution in stochastic environments: a graphical mean-variance approach;Ecology 73 1227–1236

    Article  Google Scholar 

  • Robson A J, Bergstrom C T and Pritchard J K 1999 Risky business: sexual and asexual reproduction in variable environments;J. Theor. Biol. 197 541–556

    Article  PubMed  CAS  Google Scholar 

  • Ruel J J and Ayres M P 1999 Jensen's inequality predicts effects of environmental variation;Trends Ecol. Evol. 14 361–366

    Article  PubMed  Google Scholar 

  • Samuelson P 1971 The “fallacy” of maximizing the geometric mean in long sequences of investing or gambling;Proc. Natl. Acad. Sci. USA 68 2493–2496

    Article  PubMed  Google Scholar 

  • Sasaki A and Ellner S 1995 The evolutionarily stable phenotype distribution in a random environment;Evolution 49 337–350

    Article  Google Scholar 

  • Schaffer W M 1974 Optimal reproductive effort in fluctuating environments;Am Nat 108 783–790

    Article  Google Scholar 

  • Speiser A 1939Die Basler Mathematiker. 117.Neujahrsblatt Gesellschaft zur Beförderung des Guten und Gemeinnützigen (Basel: Helbing and Lichtenhahn) pp 51

    Google Scholar 

  • Stephens D and Krebs J 1986 Foraging theory (Princeton: Princeton University Press)

    Google Scholar 

  • Stuart A and Ord J K 1994Kendall's advanced theory of statistics, Vol. 1.Distribution theory (New York: John Wiley and Sons)

    Google Scholar 

  • Tobin J 1958 Liquidity preference as behavior toward risk;Rev. Economic Stud. 25 65–86

    Article  Google Scholar 

  • Young W E and Trent R H 1969 Geometric mean approximation of individual security and portfolio performance;J. Finan. Quant. Anal. 4 179–199

    Article  Google Scholar 

  • Yule G U and Kendall M G 1950Introduction to the theory of statistics (London: Charles Griffin)

    Google Scholar 

Download references

Author information

Author notes

  1. Stephen C. Stearns

    Present address: Department of Ecology and Evolutionary Biology, Osborn Memorial Laboratories, Yale University, P.O. Box 208106, 06520-8106, New Haven, CT, USA

Authors and Affiliations

  1. University of Basel, Zoology Institute, Rheinsprung 9, CH-4051, Basel, Switzerland

    Stephen C. Stearns

Authors
  1. Stephen C. Stearns
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stearns, S.C. Daniel Bernoulli (1738): evolution and economics under risk. J Biosci 25, 221–228 (2000). https://doi.org/10.1007/BF02703928

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02703928

Keywords

Search

Navigation