The physiology of weak selection.

Reaction rates in metabolic pathways typically exhibit a kind of diminishing returns in which small variations in the activities of the individual enzymes have very little effect on overall flux. These effects are measured by the control coefficients of the enzymes, and most systems are governed by the summation theorem stating that all control coefficients must sum to unity. One implication is that complex systems will not usually contain single rate limiting steps, but rather be controlled to a greater or lesser extent by many enzymes, each exerting relatively small control. Wright understood this principle in 1934 and used it for his physiological theory of dominance. With respect to small variations in enzyme activity, the principle implies that many small variations should have only mild effects on fitness. Analysis of nucleotide polymorphisms in the genes for glucose-6-phosphate dehydrogenase and alkaline phosphatase in Escherichia coli implies that most amino acid replacements are harmful, and that the average selection coefficient against amino acid replacements that are polymorphic in natural populations is 1 x 10(-7) to 5 x 10(-7). In experiments to determine the a priori distribution of selection coefficients among random amino acid replacements, 25 replacements in beta-galactosidase were created by genetic means, and 22 of these produced selective effects too small to be detected in chemostat competition experiments (s less than 0.004 per generation).