Wilson D L
Department of Biology, University of Miami, Coral Gables, FL 33124.
Mech Ageing Dev. 1994 May;74(1-2):15-33. doi: 10.1016/0047-6374(94)90095-7.
Survival functions are fitted to survival data from several large populations. The Gompertz survival function corresponds to exponential mortality rate increases with time. The Weibull survival function corresponds to mortality rates that increase as a power function of time. A two-parameter, logistic survival function is introduced, and corresponds to mortality rates that increase, and then decrease, with time. A three-parameter logistic-mortality function also is examined. It reflects mortality rates that rise, and then plateau, with age. Data are from published studies of medflies, Drosophila, house flies, flour beetles, and humans. Some survival data are better fit by a logistic survival function than by the more traditionally used Gompertz or Weibull functions. Gompertz, Weibull, or logistic survival functions often fit the survival of 95+% of a population, and the 'tails' of the survival curves usually appear to fall between the values predicted by the three functions. For some populations, such 'tails' appear to be too complex to be fit well by any simple function. Survival data for males and females in some populations are best fit by different functions. Populations of 100 or more are needed to distinguish among the functions. When testing effects of environmental or genetic manipulations on survival, it has been common to determine the changes in parameter values for a given function, such as Gompertz. It may be equally important to determine whether the best-fit function has changed as well.
生存函数适用于来自几个大群体的生存数据。冈珀茨生存函数对应于死亡率随时间呈指数增长。威布尔生存函数对应于死亡率随时间呈幂函数增长。引入了一个双参数逻辑生存函数，它对应于死亡率随时间先上升后下降的情况。还研究了一个三参数逻辑死亡率函数。它反映了死亡率随年龄增长先上升然后趋于平稳的情况。数据来自关于地中海实蝇、果蝇、家蝇、面粉甲虫和人类的已发表研究。一些生存数据用逻辑生存函数拟合比用更传统的冈珀茨或威布尔函数拟合更好。冈珀茨、威布尔或逻辑生存函数通常能拟合95%以上群体的生存情况，生存曲线的“尾部”通常似乎落在这三个函数预测的值之间。对于一些群体，这样的“尾部”似乎过于复杂，无法用任何简单函数很好地拟合。一些群体中雄性和雌性的生存数据用不同函数拟合效果最佳。需要100个或更多个体的群体才能区分这些函数。在测试环境或基因操作对生存的影响时，通常是确定给定函数（如冈珀茨函数）参数值的变化。确定最佳拟合函数是否也发生了变化可能同样重要。
