Major advances in biology that relied on math (a biased list in-progress)
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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.
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!!!!)
1911 - Ross's epidemic model showing threshold-behavior in malaria transmission
1913 - Sturtevant maps genes to linear chromosomes based on linkage
1918 - Fisher introduces ANOVA to understand reconcile Mendel and Galton
1925 - Fisher's ultimate refinement of Analysis of Variance, based on plant data
1926 - Volterra's explanation of fisheries oscillations using Lotka's
independently proposed equations.
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
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 arithmias????????????????????
1988 - Murray on animal coat patterning (building on Turing, 1952)
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
Theoretical biology more broadly
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Paul Ehrlich realizes that if dyes can be made that tag
bacteria cells without tagging human cells, than there is
a chemical difference that might be exploited for treatment
purposes (magic bullets). Circa 1900
1953 - Watson and Crick identify the structure of DNA
("modelling without math")