Harmonics, evolutionary generators, DANCE, and HEAR-functional dimensions.

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Systems engineering

Background:

• Life's evolution spans 4 billion years, studied across diverse fields.
• Existing research lacks a unified mathematical framework for evolutionary pathways.
• Engineering approaches can enrich biological understanding of life's development.

Purpose of the Study:

• To mathematically unify the study of life's evolution.
• To develop an engineering-based structure for understanding evolutionary pathways.
• To integrate biological context with geographic and environmental factors.

Main Methods:

• Application of logistic regression for variance partitioning in biological systems.
• Utilizing multi-objective genetic algorithms to model evolutionary variance across scales.
• Integrating laboratory and field studies, including nematological trials.
• Employing fuzzy classification methods (Mamdani, Takagi-Sugeno-Kang) and novel algorithms (DANCE, HEAR).

Main Results:

• Mathematical models analogous to the Fisher equation for gene distribution were generated.
• Triangular relationships and harmonic constants were validated in soil biological communities.
• Distinct growth strategies were identified in soil nematodes: Meloidogyne spp. (positive), Radopholus similis (neutral), and Helicotylenchus pseudorobustus (negative).
• Emergent system patterns were observed in Morocco's soil environment.

Conclusions:

• Mathematical unification provides a robust framework for studying evolution.
• Novel algorithms (DANCE, HEAR) offer a basis for developing constructs across life categories.
• Understanding species interactions and growth patterns is crucial for evolutionary studies.
• The study highlights the potential of engineering and mathematical approaches in evolutionary biology.