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From Gregor Mendel to Eric Davidson: Mathematical Models and Basic Principles in Biology.

Ute Deichmann1

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Summary

Mathematical models in biology, from heredity to gene networks, show that successful approaches integrate biological principles and inductive, hypothetico-deductive methods for lasting impact.

Keywords:
Alan TuringD'Arcy ThompsonEric Davidsonbiological specificitygene regulatory networksgenetic causality

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Area of Science:

  • Evolutionary biology
  • Developmental biology
  • Genetics

Background:

  • Mathematical modeling has been integral to biology since the 19th century.
  • This analysis focuses on models in heredity and developmental biology, tracing their evolution.
  • Key models range from Mendel's work to Eric Davidson's gene regulatory networks.

Observation:

  • Models vary in their epistemological underpinnings and incorporation of biological principles like specificity and causality.
  • Approaches neglecting these principles had limited long-term influence on research direction.
  • Even admired models like D'Arcy Thompson's or Turing's had varied impacts.

Findings:

  • Successful biological models are not solely mathematical descriptions but combine inductive and hypothetico-deductive methodologies.
  • While computational tools and big data facilitate pattern recognition, they don't replace core scientific methods.
  • Causal-mechanistic explanations remain crucial for understanding complex biological systems.

Implications:

  • Future biological modeling should prioritize integration of biological principles with robust experimental methodologies.
  • The enduring importance of inductive and hypothetico-deductive approaches is highlighted for advancing biological understanding.
  • This work provides a framework for evaluating the efficacy and impact of mathematical models in biological research.