Mathematical biology's biggest hits!
===============================================
(Major advances in biology that relied on math)
This is a biased list of examples I've found where
mathematics has been used to help researchers make important
contributions to biology. I'm always looking for more
things to add to the list, and biology is such a broad
field, I doubt I'll ever finish. If you see something
is missing or have suggestions for other improvements,
please let me know.
- - - - -
1638 - Galileo on the allometric scaling of bone sizes
1760 - Daniel Bernoulli showed smallpox inoculation would prolong life
expectancy. This was before doctors realized that cowpox infections
were also protective.
1798 - Thomas Robert Malthus on the growth of populations
and its consequences. While the manuscript does
not explicitly use algebra or other mathematical
devices, Malthus graduated from Cambridge with
honors in math, and the essay is, at heart, math.
1866 - Mendel uses conditional probability arguments to infer particulate
"Mendelian" inheritance.
1866 - William Farr predicts to time-course of Cattle plague
using auto-correlated differences.
1867 - Jenkin's attack on evolution via blending-inheritance reveals a large gap
in Darwin's theory.
1876 - Jorgen Gram publishes his first paper on forest management
1889 - Galton's "Natural Inheritance" popularizes his
observation of "regression towards mediocrity" - first use
of statistical arguments to understand patterns of heredity
for continuously varying traits.
1900 - Mendel's laws rediscovered by Correns and others (but see Mendel!!!!)
1907 - Boveri and Wien show that chromosomes have individual identities using Montecarlo simulation
1911 - Ross's epidemic model showing threshold-behavior in malaria transmission
1913 - Sturtevant maps genes to linear chromosomes based on linkage
1917 - D'Arcy Thompson publishes "On Growth and Form" connecting life and geometry
1918 - Fisher introduces ANOVA to understand reconcile Mendel and Galton
Subsequent work by Haldane, Wright, Dobzhansky, and others.
1925 - Fisher's ultimate refinement of Analysis of Variance, based on plant data
1925 - Lotka publishes "Elements of Physical Biology" connecting chemistry to population dynamics
1926 - Volterra's explanation of fisheries oscillations, independent of Lotka
1927 - Kermack and McKendrick's theory of disease
1937 - Fisher and Kolmogorov on invasion waves
Subsequent extension and applications, including
Kot on dispersal kernels, and Turrelli and Barton on Wolbachia
1937 - Torsten Teorell publishes the first modern pharmacokinetics theories
1952 - Hodgkin and Huxley action potentials in squid axon
1952 - Alan Turing, morphogenesis via reaction--diffusion
1954 - Schaefer and Gordon, maximum sustainable yield of fish.
1964 - Kimura published his monograph "Diffusion Models in
Population Genetics", the origin of modern stochastic
treatments of population genetics
1964 - Edwards and Cavalli-Sforza, first evolution-based algorithmic phylogeny
(likelihood + parsimony)
1964 - Zuckerkandl and Pauling 1964, Molecular clocks by Poisson model
(achieved fame with the genomics revolution in the 2000's)
1966 - Von Neumann universal constructor cellular automata
1970 - Conway's game of life
1971 - Knudson analyzes retinoblastoma data and develops
multi-hit carcinogenesis theory, leading to the discovery
of the first tumor suppressor genes.
1973 - John Maynard Smith's extension of game theory with ESS's
1975 - Arthur Winfree on the stability of biological clocks
1975 - John Kingman introduces the coalescent as a way to understand
samples of (neutral) genes (1982's paper culminated?)
1976 - May and Oster paper on chaos in ecology models
Subsequent experimental demonstration by Cushing et al in Tribolium
along with McCauley, Nelson, et al in Daphnia
1975 - Arthur Winfree and Cardiac arrhythmia
1988 - Murray on animal coat patterning (building on Turing, 1952)
1993 - Kepler-Perelson theory of affinity maturation in immunology
1996 - Perelson and Nowak theory of HIV viral dynamics
1997 - Stephen Hubbell's unified Neutral biodiversity theory
2000 - Elowitz and Leibler on the repressilator and synthetic biology