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上一讲介绍多项式曲线及乘幂、指数、对数曲线的配合。本讲介绍Logistic生长曲线、概率单位回归曲线等。 一、Logistic生长曲线 它是比利时数学家Verhulst(1893年)首先在数学上推导出,但长期被湮没,直到本世纪的20年代才为生物学家及统计学家R.Pearl和L.J.Reed重新发现,在60年代后已广泛应用于动植物饲养、栽培、资源、生态等方面模拟研究中。假定生物在无限空间和无限营养来源等无约束的条件下,进行生长和繁殖,其量是以时间为指数的函数,但是实际上是在开始的瞬间以上关系是存在的,因为当生长或繁殖量增大后,环境恶化,营养不足,衰老加快,繁殖减慢,死亡增多,以及生物间反馈作用,约束条件必然跟随而来,因此生长曲线是一条“S”形曲线,对y轴是不对称的,而曲线上,下各有一条水平渐近线,当曲线上升到一定时间以后则很缓慢,但始终不与平行于x轴的渐近线相交。(日)
The last talk about polynomial curves and exponentiation, logarithmic curve with. This talk introduces Logistic growth curve, regression curve of probability units and so on. Logistic Growth Curve It was first mathematically derived by the Belgian mathematician Verhulst (1893) but was obliterated for a long time until the 1920s rediscovered biologists and statisticians R. Pearl and LJ Reed , Has been widely used in animal and plant breeding, cultivation, resources, ecology and other aspects of simulation studies since the 1960s. Assuming that the organism grows and reproduces under unconstrained conditions such as infinite space and unlimited nutrition, the amount is a function of time, but in fact the above relationship is present at the beginning of the moment because when growing or reproducing As the amount increases, environmental deterioration, undernutrition, accelerated aging, slowed reproduction, increased mortality, and biological feedback are bound to follow the constraints, so the growth curve is an “S” shaped curve, not the y-axis Symmetrical, with a horizontal asymptote at the top and bottom of the curve, which is slow when the curve rises for a certain amount of time, but never intersects an asymptote parallel to the x-axis. (day)