maximum variance unfolding
Weanalyze thepopulation dynamicsof abroadclass of tnessfunctions
that exhibit epochal evolution|a dynamical behavior, commonly observed in both
natural and articial evolutionary processes, in which long periods of stasis in an
evolving population are punctuated by sudden bursts of change. Our approach|
statistical dynamics
|combines methods from both statistical mechanics and dy-
namical systems theory in a way that oers an alternative to current landscape"
models of evolutionary optimization. We describe the population dynamics on the
macroscopic level of tness classes or phenotype subbasins, while averaging out
the genotypic variation that is consistent with a macroscopic state. Metastability
in epochal evolution occurs solely at the macroscopic level of the tness distribu-
tion. While a balance between selection and mutation maintains a quasistationary
distribution of tness, individuals diuse randomly through selectively neutral sub-
basins in genotype space. Sudden innovations occur when, through this diusion,
a genotypic portal is discovered that connects to a new subbasin of higher tness
genotypes. In this way, we identify innovations with the unfolding and stabilization
of a new dimension in the macroscopic state space. The architectural view of sub-
basins and portals in genotype space claries how frozen accidents and the resulting
phenotypic constraints guide the evolution to higher complexity.
that exhibit epochal evolution|a dynamical behavior, commonly observed in both
natural and articial evolutionary processes, in which long periods of stasis in an
evolving population are punctuated by sudden bursts of change. Our approach|
statistical dynamics
|combines methods from both statistical mechanics and dy-
namical systems theory in a way that oers an alternative to current landscape"
models of evolutionary optimization. We describe the population dynamics on the
macroscopic level of tness classes or phenotype subbasins, while averaging out
the genotypic variation that is consistent with a macroscopic state. Metastability
in epochal evolution occurs solely at the macroscopic level of the tness distribu-
tion. While a balance between selection and mutation maintains a quasistationary
distribution of tness, individuals diuse randomly through selectively neutral sub-
basins in genotype space. Sudden innovations occur when, through this diusion,
a genotypic portal is discovered that connects to a new subbasin of higher tness
genotypes. In this way, we identify innovations with the unfolding and stabilization
of a new dimension in the macroscopic state space. The architectural view of sub-
basins and portals in genotype space claries how frozen accidents and the resulting
phenotypic constraints guide the evolution to higher complexity.