摘要
本文首选讨论了经典的种群增长方程——指效方程Logistic方程。并基于营养学和化学吸附理论导出了方程 dx/xdt=u((x_m-x)/(x_m+(k-1)z))该方程有三个参数u,z_m和k。其次讨论了这些参数的生态意义和方程的一般性质。其中,u为内禀增长率,z_m为容纳量,k与种群利用资源的能力有关。当k=1时,该方程化为Logistic方程;k=0时,该方程化为指数方程。因此,该方程的推导过程给了Logistic方程一个理论解释,也给出了一个更适合于种群增长研究的方程。
Firstly, we give a summary of the classical equations which describe single population growth. Then using absorption theory of chemical kinetics and considering the relationship oetween population increment and the limting resources, we obtain d_x/d_t=u((x(x_m-x))/(x_m+(k-1)x)) and its integral form: ln(x/x_0)-kln((x_m-x)/(x_m-x_0))=u(t-t_0) The equations above have three parameters x_m, k and u, each of which has corresponding ecologi- cal significance, x_m sis referred as the earring capacity (the population density allowed by the limiting resource); k concerns the efficiency of nutrient (or resources)utilization by an organism; u is the intrin- sic growth rate. When k=0, the equation reduces to the exponential equation; when k=1, it reduces to the Logis- tic equation. This not only gives a theoritical explanation to the Logistic equation, but also presents a more suitable equation for the study of population growth.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
1993年第1期9-16,共8页
Journal of Inner Mongolia University：Natural Science Edition
关键词
单种群数学模型
种群增长方程
model of single population
ecological significance
population
