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

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.