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Mathematical Modeling of Extinction of Inhomogeneous Populations
1National Center for Biotechnology Information, National Institutes of Health - Bldg. 38A, 8600 Rockville Pike, Bethesda, MD, 20894, USA. karev@ncbi.nlm.nih.gov.
Bulletin of Mathematical Biology
|April 20, 2016
Summary
This study introduces novel sub-exponential population extinction models with finite lifespans. These models reveal that information loss principles govern extinction dynamics, offering insights into time perception.
Area of Science:
- Ecology
- Paleontology
- Conservation Biology
- Mathematical Biology
Background:
- Traditional exponential models for population extinction have limitations.
- Sub-exponential models offer a finite lifespan alternative, applicable in ecological and conservation contexts.
Purpose of the Study:
- To propose and investigate two novel sub-exponential population extinction models.
- To analyze unobserved heterogeneity and clone frequency distributions within these models.
- To explore the underlying principles governing population extinction dynamics.
Main Methods:
- Development of two distinct sub-exponential population extinction models.
- Investigation of independent clones versus a whole population decrease model.
- Calculation of clone frequency distributions and analysis of information loss principles.
Main Results:
- The first model (independent clones) dynamics are governed by Tsallis information loss.
- The second model (whole population) introduces 'internal population time' and is governed by Shannon information loss.
- Both models demonstrate that minimum information loss is a fundamental law for extinction evolution.
Conclusions:
- Sub-exponential models provide a more realistic framework for population extinction.
- The principle of minimum information loss is a unifying concept in extinction dynamics.
- The proposed framework may offer insights into the mechanisms of time perception.
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