A Short History of Mathematical Population Dynamics

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Springer Science & Business Media, Feb 1, 2011 - Mathematics - 160 pages

As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.

This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy; the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine.

The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.

 

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Contents

The Fibonacci sequence 1202
2
Halleys life table 1693
5
Euler and the geometric growth of populations 17481761
11
Daniel Bernoulli dAlembertand the inoculation of smallpox 1760
21
Malthus and the obstacles to geometric growth 1798
31
Verhulst and the logistic equation 1838
35
Bienaymé Cournot and the extinction of family names 18451847
41
Mendel and heredity 1865
45
McKendrick and Kermack on epidemic modelling 19261927
89
Haldane and mutations 1927
97
Erlang and Steffensen on the extinction problem 19291933
101
Wright and random genetic drift 1931
105
The diffusion of genes 1937
111
The Leslie matrix 1945
117
Percolation and epidemics 1957
121
Game theory and evolution 1973
127

Galton Watson and the extinction problem 18731875
49
Lotka and stable population theory 19071911
55
The HardyWeinberg law 1908
59
Ross and malaria 1911
65
Lotka Volterra and the predatorprey system 19201926
71
Fisher and natural selection 1922
77
Yule and evolution 1924
81
Chaotic populations 1974
133
Chinas onechild policy 1980
141
Some contemporary problems
149
Figures
155
Index
157
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