Some properties of natural selection with single and multiple constraints

Abstract The properties of selection restricted by single and multiple constraints are examined by using the Lagrange and Kuhn-Tucker conditions of calculus. We show for a general set of fitness equations containing any number of strategy components and subject to any single differentiable equality constraint that the marginal fitnesses of any two strategy components are equal at the evolutionarily stable strategy (ESS) when expenditures are measured in the same units, those of a binding constraint. Equal marginal advantages are a necessary, though not usually a sufficient, condition for an interior ESS. When selection is operating under more than one constraint, the marginal fitnesses of any two strategy components are equal at the ESS whenever both components are affected by only one, and the same, binding constraint. The equalization of marginal fitnesses allows the positions of constrained fitness maxima to be explored in theoretical models or empirical tests and is a convenient heuristic for understanding selection.

[1]  P. Abrams.  Alternative Models of Character Displacement and Niche Shift. 2. Displacement when There is Competition for a Single Resource , 1987, The American Naturalist.

[2]  Joe C. Campbell,et al.  Developmental Constraints and Evolution: A Perspective from the Mountain Lake Conference on Development and Evolution , 1985, The Quarterly Review of Biology.

[3]  Gary E. Belovsky,et al.  Herbivore Optimal Foraging: A Comparative Test of Three Models , 1984, The American Naturalist.

[4]  P. Grubb,et al.  Towards a More Exact Ecology. , 1990 .

[5]  D. Tilman.  Plant Strategies and the Dynamics and Structure of Plant Communities. (MPB-26), Volume 26 , 1988 .

[6]  Thomas Caraco,et al.  Time Budgeting and Group Size: A Theory , 1979 .

[7]  D. J. Heath.  Brooding and the evolution of hermaphroditism. , 1979, Journal of theoretical biology.

[8]  E. Charnov.  Phenotypic evolution under Fisher's Fundamental Theorem of Natural Selection , 1989, Heredity.

[9]  D. J. Heath.  Simultaneous hermaphroditism; cost and benefit. , 1977, Journal of theoretical biology.

[10]  M. Ghiselin.  The Evolution of Hermaphroditism Among Animals , 1969, The Quarterly Review of Biology.

[11]  R. Lande.  NATURAL SELECTION AND RANDOM GENETIC DRIFT IN PHENOTYPIC EVOLUTION , 1976, Evolution; international journal of organic evolution.

[12]  D. L. Venable,et al.  Size-Number Trade-Offs and the Variation of Seed Size with Plant Resource Status , 1992, The American Naturalist.

[13]  D. Lewis,et al.  MALE STERILITY IN NATURAL POPULATIONS OF HERMAPHRODITE PLANTS THE EQUILIBRIUM BETWEEN FEMALES AND HERMAPHRODITES TO BE EXPECTED WITH DIFFERENT TYPES OF INHERITANCE , 1941 .

[14]  A. F. Mark,et al.  Floral initiation and development in New Zealand alpine plants , 1970 .

[15]  D. Lloyd,et al.  Genetic and phenotypic models of natural selection. , 1977, Journal of theoretical biology.

[16]  R. Levins.  Evolution in Changing Environments , 1968 .

[17]  R. McN. Alexander,et al.  The ideal and the feasible: physical constraints on evolution , 1985 .

[18]  H. Saiah,et al.  Why is the cladoceran Simocephalus vetulus (Müller) not a bang-bang strategist? A critique of the optimal-body-size model , 1987 .

[19]  Craig Loehle,et al.  Evolution: The Missing Ingredient in Systems Ecology , 1988, The American Naturalist.

[20]  S. Gould,et al.  The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[21]  B. Charlesworth,et al.  THE EFFECT OF INVESTMENT IN ATTRACTIVE STRUCTURES ON ALLOCATION TO MALE AND FEMALE FUNCTIONS IN PLANTS , 1987, Evolution; international journal of organic evolution.

[22]  J. M. Smith.  Will a Sexual Population Evolve to an Ess? , 1981, The American Naturalist.

[23]  Berger.  Handbuch der Vererbungswissenschaft , 1931 .

[24]  H. Pulliam,et al.  On the Theory of Optimal Diets , 1974, The American Naturalist.

[25]  R. Lande,et al.  A Quantitative Genetic Theory of Life History Evolution , 1982 .

[26]  D. Lloyd.  Variation strategies of plants in heterogeneous environments , 1984 .

[27]  B. Charlesworth,et al.  A Model for the Evolution of Dioecy and Gynodioecy , 1978, The American Naturalist.

[28]  Joel s. Brown,et al.  The Selective Interactions of Dispersal, Dormancy, and Seed Size as Adaptations for Reducing Risk in Variable Environments , 1988, The American Naturalist.

[29]  E. Charnov.  The theory of sex allocation. , 1984, Monographs in population biology.

[30]  P. K. Endress.  Evolutionary Trends in the Hamamelidales-Fagales-Group , 1977 .

[31]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[32]  J. Levinton.  Developmental Constraints and Evolutionary Saltations: A Discussion and Critique , 1986 .

[33]  Joel s. Brown,et al.  Evolutionary Ecology of Seed-Bank Annuals in Temporally Varying Environments , 1986, The American Naturalist.

[34]  Michael D. Intriligator,et al.  Mathematical optimization and economic theory , 1971 .

[35]  A. C. Chiang.  Fundamental methods of mathematical economics , 1974 .

[36]  David M. Raup,et al.  Patterns and Processes in the History of Life , 1986, Dahlem Workshop Reports.

[37]  T. Valone,et al.  The Optimization Research Program: Studying Adaptations by Their Function , 1990, The Quarterly Review of Biology.

[38]  J. Krebs,et al.  Behavioural Ecology: An Evolutionary Approach , 1978 .