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Modelling the longevity of complex living systems

Indrė Žliobaitė

TL;DR

The paper addresses macroevolutionary longevity by testing Van Valen's Law of Constant Extinction under Red Queen dynamics. It introduces a framework that classifies survivorship into Type I, II, and III by fitting linear models in plain, semi-log, and log-log coordinates, corresponding to $y = b - a x$, $N_t = N_0 e^{-\lambda t}$, and $N_t = g t^{-h}$, respectively, and uses Ordinary Least Squares to compare $R^2$ across fits. Applying the method to genera in the Artiodactyla order from the NOW fossil dataset reveals a best fit on semi-log coordinates consistent with Type II (memoryless) extinction, aligning with Red Queen predictions; other orders show similar memoryless patterns. The framework provides a simple, transformation-based test for the dominant survivorship regime and can be extended to analyze spatial patterns of species expansion and decline. Overall, the results support a macroevolutionary constant-extinction pattern in fossil records and offer a practical tool for testing survivorship types in macroevolutionary data.

Abstract

This extended abstract was presented at the Nectar Track of ECML PKDD 2024 in Vilnius, Lithuania. The content supplements a recently published paper "Laws of Macroevolutionary Expansion" in the Proceedings of the National Academy of Sciences (PNAS).

Modelling the longevity of complex living systems

TL;DR

The paper addresses macroevolutionary longevity by testing Van Valen's Law of Constant Extinction under Red Queen dynamics. It introduces a framework that classifies survivorship into Type I, II, and III by fitting linear models in plain, semi-log, and log-log coordinates, corresponding to , , and , respectively, and uses Ordinary Least Squares to compare across fits. Applying the method to genera in the Artiodactyla order from the NOW fossil dataset reveals a best fit on semi-log coordinates consistent with Type II (memoryless) extinction, aligning with Red Queen predictions; other orders show similar memoryless patterns. The framework provides a simple, transformation-based test for the dominant survivorship regime and can be extended to analyze spatial patterns of species expansion and decline. Overall, the results support a macroevolutionary constant-extinction pattern in fossil records and offer a practical tool for testing survivorship types in macroevolutionary data.

Abstract

This extended abstract was presented at the Nectar Track of ECML PKDD 2024 in Vilnius, Lithuania. The content supplements a recently published paper "Laws of Macroevolutionary Expansion" in the Proceedings of the National Academy of Sciences (PNAS).
Paper Structure (2 sections, 3 equations, 2 figures)

This paper contains 2 sections, 3 equations, 2 figures.

Table of Contents

  1. Acknowledgments.
  2. Disclosure of Interests.

Figures (2)

  • Figure 1: Survivorship curves (a) and their mathematical models under three coordinate transformations: plain (b), semi-log (c) and log-log (d).
  • Figure 2: Testing the type of survivorship for genera in the order Artiodactyla in the fossil record. The top right corner shows the coefficient of determination ($R^2$).