How Mathematics Revolutionized Modern Biology: From Models to Ecology

Before the mid‑20th century, biological research relied mainly on qualitative methods such as observation, experimentation, and induction. Since the mid‑20th century, the injection of mathematical knowledge into biology has dramatically accelerated its modernization.

The rapid development of electronic computers provided powerful tools for large‑scale computation of multivariate, multifactorial mathematical models, overcoming previous limitations and, together with advances in control theory, information theory, and systems theory, spurred rapid progress in biological observation, reasoning, analysis, and imaging, ushering in an era of extensive use of mathematical models in biology.

Researchers began applying mathematical theory and methods to quantitatively describe real ecological processes and system dynamics, giving rise to mathematical ecology. The development of multivariate analysis and clustering methods laid the foundation for incorporating mathematics into biological classification, and the proliferation of computer technology fostered the emergence of numerical taxonomy. The deeper penetration of probability and statistics into genetics led to sub‑fields such as quantitative genetics and statistical genetics, where mathematical models play a crucial role. Examples include using stochastic process models to simulate moth phototaxis, control‑theoretic models for ecosystem regulation and animal navigation, information‑theoretic models for community diversity and stability, game‑theoretic models for pest‑control strategies, multivariate clustering, discriminant, and factor analysis for ecological‑geographic classification, optimization models for resource management, Monte Carlo simulations of population dynamics, set‑theoretic and fuzzy‑logic models for environmental classification, and topological models for mechanisms of inheritance, death, sensory perception, and biological clocks.

The application of mathematical modeling tools has opened new research topics and produced distinctive theoretical results, revitalizing the life sciences.

Shen Wenxuan, Yang Qingtiao. “Mathematical Modeling Attempts”.