The strategy of model building in population biology
The strategy of model building in population biology
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作者：
R. Levins
以前是独立的或多或少一致的理论。种群遗传学和种群生态学是种群生物学中最具数学性的两个领域，它们在不同的假设和技术下得到了发展，而数学生物地理学本质上是一个新的领域。对于群体遗传学，一个群体是由基因型的频率来指定的，而不参考年龄分布、反映过去历史的生理状态或群体密度。一次只对一个种群或物种进行研究，通常认为进化是在恒定的环境中发生的。另一方面，种群生态学承认多物种系统，根据它们的年龄分布、生理状态和密度来描述种群。环境允许变化，但物种被视为基因同质，因此进化被忽略了。但越来越多的证据表明，人口时间和进化时间是相称的。因此，种群生物学必须同时处理多物种系统中物种的遗传、生理和年龄异质性，这些系统在人口统计学上发生变化，并在异质环境中其他物种的波动影响下进化。问题是如何处理这样一个复杂的系统。简单粗暴的方法是建立一个数学模型，忠实地、一对一地反映这种复杂性。这可能需要使用大约100个带时间滞后的联立偏微分方程；测量数百个参数，求解方程得到数值预测，然后根据自然规律测量这些预测。然而：(a)需要测量的参数太多；有些仍然只是模糊的定义；许多人需要用一生的时间来测量。
what were previously independent clusters of more or less co herent theory. Population genetics and population ecology, the most mathematical areas of population biology, had developed with quite different assumptions and techniques, while mathematical biogeography is essentially a new field. For population genetics, a population is specified by the frequencies of genotypes without reference to the age distribution, physiological state as a reflection of past history, or population density. A single population or species is treated at a time, and evolution is usually as sumed to occur in a constant environment. Population ecology, on the other hand, recognizes multispecies sys tems, describes populations in terms of their age distributions, phys iological states, and densities. The environment is allowed to vary but the species are treated as genetically homogeneous, so that evolution is ignored. But there is increasing evidence that demographic time and evolu tionary time are commensurate. Thus population biology must deal simultaneously with genetic, physiological, and age heterogeneity within species of multispecies systems changing demographically and evolving under the fluctuating influences of other species in a heterogeneous environment. The problem is how to deal with such a complex system. The naive, brute force approach would be to set up a mathematical model which is a faithful, one-to-one reflection of this complexity. This would require using perhaps 100 simultaneous partial differential equa tions with time lags; measuring hundreds of parameters, solving the equations to get numerical predictions, and then measuring these pre dictions against nature. However: (a) there are too many parameters to measure; some are still only vaguely defined; many would require a lifetime each for their measurement.