Harmonics, evolutionary generators, DANCE, and HEAR—functional dimensions [Erratum: December 2021, v.28(45), p.64191-64192]

Evolution of the major kingdoms of life has spanned over the last 4 billion years on Earth. Studies of the process comprise different fields of study with alternative perspectives. This paper focuses on mathematic unification of the subject area; enriching an engineering based structure to advance our understanding of pathways which lead to distinct constructs in life, furthering geographic bordering processes with biological context. Application of logistic regression requires partitioning of variance within cellular and molecular systems; use of higher mathematic technique (multi-objective genetic algorithm) generates variance within the different scales of evolution, the result of which is analogous with the Fisher equation model of gene distribution within populations. Laboratory and field studies were integrated to illustrate emergence in evolutionary processes in the terrestrial/soil environment. Nematological field and laboratory trials validate the existence of triangular relationships within biological communities; further harmonic constants between interacting species may be found with emergent consequence. We distinguish different strategical groupings in the soil community, with the core groupings recognized with Meloidogyne spp. illustrating positive (emergent) growth; Radopholus similis (neutral growth), and Helicotylenchus pseudorobustus (negative growth). The patterns of emergent systems are shown in the extremes of Morocco’s dynamic soil environment. Fuzzy classification methods: Mamdani, Takugi-Sugeno-Kang; additional novel DANCE (Differential Algorithmic Network Centered Emergence) and functional expressions HEAR (Harmonic Evolutionary Algorithmic Resilience), are recommended to give a basis for development of constructs covering different categories of life.