# Geometric Models of Speciation in Minimally Monophyletic Genera Using High-Resolution Phylogenetics

## TL;DR

This paper uses geometric models to explain how species in a genus survive and evolve over time, combining phylogenetics and physics principles.

## Contribution

Introduces geometric models using regular polygons to explain speciation and survival patterns in minimally monophyletic genera.

## Key findings

- Regular polygons inscribed in circles model balanced survival areas for new species in a genus.
- The model aligns with a physics meta-law and explains the 'rule of four' in vascular plant genera.
- High-resolution ancestor–descendant analysis outperforms traditional phylogenetic methods in modeling evolutionary results.

## Abstract

High-resolution phylogenetics using both morphology and molecular data reveal surfactant-like trait buffering of peripatric descendant species that facilitate resilience for supra-specific entities across geologic time. Regular polygons inscribed in circles model balanced areas of survival of various numbers of new species in one genus. This model maximizes the peripatric survival of descendant species, with populations partly in allopatric habitats and in sympatric areas. It extends the theory advanced with Willis’s Age and Area hypothesis. Hollow curves of the areas bounded between a series of inscribed regular polygons and their containing circles show a ranked progression governed by similar power laws of other phenomena, including Zipf’s law and a universal meta-law in physics. This model matches best the physics meta-law (law of laws) but is only one of several somewhat different curves generated by somewhat different processes. A rule of four can explain why most genera in vascular plants exhibit a hollow curve of optimally one to five species per genus. It implies a constraint on variation that enhances survival and provides a physics explanation for the monophyletic skeleton of macrogenera. A high-resolution form of ancestor–descendant analysis is compared to traditional phylogenetic analysis to best modeling of the demonstrable results of evolutionary processes. Arguments are advanced for the preservation of scientific concepts of taxa over cladistic clades.