## A Short History of Mathematical Population DynamicsAs 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

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 |

### Other editions - View all

A Short History of Mathematical Population Dynamics Nicolas Baca R,Nicolas Bacaer No preview available - 2011 |