Theoretical Ecology

, Volume 9, Issue 2, pp 149–161 | Cite as

Dealing with stochastic environmental variation in space and time: bet hedging by generalist, specialist, and diversified strategies

  • Philip H. CrowleyEmail author
  • Sean M. EhlmanEmail author
  • Evelyn Korn
  • Andrew Sih


Building on previous work, we derive an optimization model for a two-state stochastic environment and evaluate the fitnesses of five reproductive strategies across generations. To do this, we characterize spatiotemporal variation and define grain (=patch) size as the scale of fitness autocorrelation. Fitness functions of environmental condition are Gaussian. The strategies include two specialists on each of the environmental conditions; two generalists that each fare equally well under both conditions, but one (a conservative bet hedger) optimizes the shape of the fitness function; and a diversified bet hedger producing an optimal mix of the two specialists within individual broods. When the environment is primarily in one of the two states, the specialist on that state achieves the highest fitness. In the more interesting situation where the two environments are equally prevalent in the long term, with low-moderate environmental variation, a generalist strategy (that copes with both states well) does best. Higher variation favors diversified bet hedgers, or surprisingly, specialists, depending mainly on whether spatial or temporal variation predominates. These strategies reduce variance in fitness and optimize the distribution of offspring among patches differently: specialists by spreading offspring among many independently varying patches, while diversified bet hedgers put all offspring into a few patches or a single patch. We distinguish features consistent with strategies like diversified bet hedgers that spread risk in time from features linked to strategies like specialists that spread risk in space. Finally, we present testable hypotheses arising from this study and suggest directions for future work.


Grain size Lineage fitness Optimization Spatiotemporal variation Trade-off 



We thank Aviv Brokman, Vincent Calgagno, Éric Wajnberg, Jon Wright, and the Crowley and Sih lab groups for comments on the project and manuscript. PHC thanks EK and AS, and EK thanks AS, for hospitality during sabbatical visits when many of these ideas were developed. SME acknowledges support from a National Science Foundation Graduate Research Fellowship; no other extramural funding supported this work. Contributions by author are as follows: PHC developed the models and wrote the draft manuscript; SME wrote most of the computer code in MATLAB and conducted the runs that generated the figures and Appendix C (supplementary materials); EK checked all of the mathematics; all four authors helped develop the ideas and approach and edited the manuscript.

Supplementary material

12080_2015_272_MOESM1_ESM.docx (148 kb)
ESM 1 (DOCX 148 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Biology and Center for Ecology, Evolution and BehaviorUniversity of KentuckyLexingtonUSA
  2. 2.Department of Environmental Science and PolicyUniversity of CaliforniaDavisUSA
  3. 3.School of Business and EconomicsUniversity of MarburgMarburgGermany

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