Logistic、崔-Lawson种群增长模型理论及实例拟合比较

Comparison of theory and case fitting between Logistic and Cui-Lawson population increment models.

本文求出了Logistic方程、崔-Lawson方程的速度、加速度方程。Logistic方程在加速度等于零时的增长拐点只能在K/2处,此时的最大增长速度为μ_LK/4;崔-Lawson方程在加速度等于零时的增长拐点在处,此时的最大增长速度为。通过b的变化,在描述种群增长规律时,崔-Lawson方程可优于Logistic方程。本文还用变步长坐标轮换法对两个方程进行实例拟合比较,Logistic方程还比较了Gause、Andrewartha、May、Pearl、Krebs、万昌秀、王莽莽等人的方法与结果。拟合结果表明,崔-Lawson方程最优;在拟合Logistic方程的各种方法中,本文方法较优。

In this paper, equations of dt/dX and dX/dt^2 of Logistic and Cui-Lawson models are calculated. When d^2X/dt^2=0, the increment turning point of Logistic equation can only lies at the point of K/2 and then maximum value of dX/dt is μL K/4; under the same condition, the increment turning point of Cui-Lawson equation lies at the point of K/(b^(1/2)+1)and then the maximum value of dX/dt is μC K/(b^(1/2)+1)~2. Through the variation of b, the Cui-Lawson equation may be superior than the Logistic when they are used to describe the law of population increment. By adopting the method of rotating coordinate with changing length of pace, comparisons between case fittings of these two equations are made. Logistic equation is also compared with Gause's, Andrewartha's, May's, Kreb's, Wan Changxiou's and Wang Mangmang's methods and results. Fitting results show that Cui-Lawson equation is the best and among the methods of fitting Logistic equation, the one described here is better.