The mathematical technique of dimensional analysis is presented in the context of behavioral ecology. Dimensional analysis transforms the variables in a problem to a reduced set of unitfree variables. This transformation helps to reveal the nature of relationships among variables, simplifies modeling, and produces predictions that are readily compared across species and conditions. This paper illustrates the use of dimensional analysis by applying the technique to two well-known models from behavioral ecology: the marginal-value theorem and the cost-benefit model of territoriality. A dimensional analysis of the marginal-value theorem suggests the concept of standardized gain functions, which in turn allows us to present the first approximate analytical solution of the marginal-value theorem for an important class of gain functions. A dimensional analysis of the territoriality model reveals that some of the "cost functions" analyzed by earlier authors do not follow from their assumptions. This inconsistency is corrected in a "dimensionless" formulation of this classical model.
Bibliographical noteFunding Information:
We are grateful to E. Charnov, A. Joern, D. Kramer, and M. Mangel for their comments on earlier drafts of this manuscript. This work was supported by grant number BNS-8958228 from the National Science Foundation and by matching funds from Lincoln Telephone.
Copyright 2010 Elsevier B.V., All rights reserved.
- Dimensional analysis
- Marginal-value theorem
- Pure numbers
- Territorial behavior