Ebook: A Short History of Mathematical Population Dynamics

<p>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.</p>

<p>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.</p>

<p>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.</p>

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<p>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.</p>

<p>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.</p>

<p>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.</p>

---

<p>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.</p>

<p>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.</p>

<p>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.</p>

Content:
Front Matter....Pages I-X
The Fibonacci sequence (1202)....Pages 1-3
Halley’s life table (1693)....Pages 5-10
Euler and the geometric growth of populations (1748–1761)....Pages 11-20
Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760)....Pages 21-30
Malthus and the obstacles to geometric growth (1798)....Pages 31-33
Verhulst and the logistic equation (1838)....Pages 35-39
Bienaym?, Cournot and the extinction of family names (1845–1847)....Pages 41-44
Mendel and heredity (1865)....Pages 45-48
Galton, Watson and the extinction problem (1873–1875)....Pages 49-54
Lotka and stable population theory (1907–1911)....Pages 55-58
The Hardy–Weinberg law (1908)....Pages 59-63
Ross and malaria (1911)....Pages 65-69
Lotka, Volterra and the predator–prey system (1920–1926)....Pages 71-76
Fisher and natural selection (1922)....Pages 77-80
Yule and evolution (1924)....Pages 81-88
McKendrick and Kermack on epidemic modelling (1926–1927)....Pages 89-96
Haldane and mutations (1927)....Pages 97-100
Erlang and Steffensen on the extinction problem (1929–1933)....Pages 101-104
Wright and random genetic drift (1931)....Pages 105-109
The diffusion of genes (1937)....Pages 111-116
The Leslie matrix (1945)....Pages 117-120
Percolation and epidemics (1957)....Pages 121-126
Game theory and evolution (1973)....Pages 127-131
Chaotic populations (1974)....Pages 133-140
China’s one-child policy (1980)....Pages 141-147
Some contemporary problems....Pages 149-153
Back Matter....Pages 155-160

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<p>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.</p>

<p>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.</p>

<p>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.</p>

Content:
Front Matter....Pages I-X
The Fibonacci sequence (1202)....Pages 1-3
Halley’s life table (1693)....Pages 5-10
Euler and the geometric growth of populations (1748–1761)....Pages 11-20
Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760)....Pages 21-30
Malthus and the obstacles to geometric growth (1798)....Pages 31-33
Verhulst and the logistic equation (1838)....Pages 35-39
Bienaym?, Cournot and the extinction of family names (1845–1847)....Pages 41-44
Mendel and heredity (1865)....Pages 45-48
Galton, Watson and the extinction problem (1873–1875)....Pages 49-54
Lotka and stable population theory (1907–1911)....Pages 55-58
The Hardy–Weinberg law (1908)....Pages 59-63
Ross and malaria (1911)....Pages 65-69
Lotka, Volterra and the predator–prey system (1920–1926)....Pages 71-76
Fisher and natural selection (1922)....Pages 77-80
Yule and evolution (1924)....Pages 81-88
McKendrick and Kermack on epidemic modelling (1926–1927)....Pages 89-96
Haldane and mutations (1927)....Pages 97-100
Erlang and Steffensen on the extinction problem (1929–1933)....Pages 101-104
Wright and random genetic drift (1931)....Pages 105-109
The diffusion of genes (1937)....Pages 111-116
The Leslie matrix (1945)....Pages 117-120
Percolation and epidemics (1957)....Pages 121-126
Game theory and evolution (1973)....Pages 127-131
Chaotic populations (1974)....Pages 133-140
China’s one-child policy (1980)....Pages 141-147
Some contemporary problems....Pages 149-153
Back Matter....Pages 155-160
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