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Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin

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Embedded Complexity of Evolutionary Sequences.

Jonathan D Phillips¹

¹Earth Surface Systems Program, University of Kentucky, Lexington, KY 40506, USA.

Entropy (Basel, Switzerland)

|June 26, 2024

Summary

This summary is machine-generated.

Evolutionary sequences possess inherent complexity. A new index, based on algebraic graph theory, quantifies this embedded complexity in historical ecological and environmental systems.

Keywords:

algebraic graph theory embedded complexity evolutionary sequence historical sequence spectral radius state-and-transition model

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Area of Science:

Ecology
Evolutionary Biology
Complex Systems

Background:

Biological and environmental systems exhibit multiple evolutionary pathways and outcomes due to nonlinear dynamics, historical contingency, and disturbances.
Understanding the single historical sequence that actually occurred from a multitude of possibilities is crucial for ecological and evolutionary studies.
Existing methods may not fully capture the complexity inherent in the temporal progression of system states.

Purpose of the Study:

To introduce a novel measure for quantifying the embedded complexity of historical sequences using algebraic graph theory.
To develop an index that reflects the information content and complexity of evolutionary and ecological sequences.
To apply this complexity index to ecological state-and-transition models (STM) and diverse case studies.

Main Methods:

Representing historical sequences as a series of system states S(t).
Utilizing algebraic graph theory to analyze sequences, focusing on the spectral radius (λ1) as a measure of complexity.
Calculating an embedded complexity index by comparing the complexity of the entire sequence to its constituent subsequences.

Main Results:

The embedded complexity index quantifies the information and complexity within historical sequences.
As sequences lengthen, overall complexity asymptotically approaches λ1 = 2, while embedded complexity increases significantly (N^2.6).
The method was successfully applied to four distinct case studies: benthic communities, glacial succession, pine woodlands, and delta habitats.

Conclusions:

The developed embedded complexity index provides a robust method for analyzing historical sequences in complex systems.
This approach offers new insights into the information dynamics and evolutionary trajectories of ecological and environmental systems.
The findings have implications for understanding system dynamics, predicting future states, and interpreting paleoecological and stratigraphic records.