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In general, cellular phenotypes, as measured by concentrations of cellularcomponents, involve large degrees of freedom. However, recent measurement hasdemonstrated that phenotypic changes resulting from adaptation and evolution inresponse to environmental changes are effectively restricted to alow-dimensional subspace. Thus, uncovering the origin and nature of such adrastic dimension reduction is crucial to understanding the generalcharacteristics of biological adaptation and evolution. Herein, we firstformulated the dimension reduction in terms of dynamical systems theory:considering the steady growth state of cells, the reduction is represented bythe separation of a few large singular values of the inverse Jacobian matrixaround a fixed point. We then examined this dimension reduction by numericalevolution of cells consisting of thousands of chemicals whose concentrationsdetermine phenotype. As a result of the evolution, phenotypic changes due tomutations and external perturbations were found to be mainly restricted to aone-dimensional subspace. One singular value of the inverse Jacobian matrix ata fixed point of concentrations was significantly larger than the others. Themajor phenotypic changes due to mutations and external perturbations occuralong the corresponding left-singular vector, which leads to phenotypicconstraint, and fitness dominantly changes in the same direction. Once suchphenotypic constraint is acquired, phenotypic evolution to a novel environmenttakes advantage of this restricted phenotypic direction. This results in theconvergence of phenotypic pathways across genetically different strains, as isexperimentally observed, while accelerating further evolution.

Evolutionary dimension reduction in phenotypic space