We examine sources and dynamics of discontinuous changes in discrete m
ulti-level hierarchical ecological-economic systems. We hypothesize th
e anagenetic moment, the creation of a new level of hierarchy, as aris
ing from variable entrainment at some level. Bottom-up as well as top-
down dynamics are studied and competing theories of the sources of suc
h discontinuities are reviewed. Implications for the analysis of compl
ex ecological-economic systems are considered depending on whether the
y are characterized by single hierarchy, bi-hierarchy, or matrix hiera
rchy relationships.