An evolutionary lineage may be analyzed as a complex adaptive system. It cycles through time from monothetic genus to monothetic realized niche, and forward again genus to niche. A genus is a set consisting of an ancestor species and its descendants each with the same ancestron traits. A niche is a physically coherent nexus of convergent species sharing the same novon of a virtual ancestor species (stochastic plus natural selection). Like speciation, nicheation is a complex, fractal process governed by non-linear processes. Superimposition of Turing patterns of separately evolved species may be a process that minimizes negetropic open space. The genus is here taken as the fundamental unit of evolution, tested and modified through interaction with environments oscillating across geological time. Four major modeling methods are used: radiate monothetic genera, NK-parallels of random Boolean networks, oscillations of the logistic map, and fractal dimensions. It is then possible to provide precise measures of resilience in species, genera and higher taxa, including survival-associated traits, changes in traits between and through periodic extinction events, and potential continuation of lineage and ecosystem niche complexity in the future. Systematics, evolution, and niche theory are linked by the same analytic modeling reflecting similar complex processes in speciation and "nicheation." The model organism is the bryophyte, particularly the moss family Pottiaceae.