TY - JOUR
T1 - Some properties of natural selection with single and multiple constraints
AU - Lloyd, David G.
AU - Venable, D. Lawrence
N1 - Funding Information:
We are grateful to Peter Lloyd for assistance with the mathematics and parallels between biology and economics, and we thank him. Curt Lively. Joel S. Brown. and William A. Mitchell for critical comments on a draft of the manuscript. This work was supported in part by NSF grants BSR8516971 and BSR9107324.
PY - 1992/2
Y1 - 1992/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0027065226&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0027065226&partnerID=8YFLogxK
U2 - 10.1016/0040-5809(92)90051-T
DO - 10.1016/0040-5809(92)90051-T
M3 - Article
AN - SCOPUS:0027065226
SN - 0040-5809
VL - 41
SP - 90
EP - 110
JO - Theoretical Population Biology
JF - Theoretical Population Biology
IS - 1
ER -