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Von Foerster equation (ecology) : ウィキペディア英語版
Von Foerster equation (ecology)

The von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example, cell proliferation modeling; it is applied when age structure is an important feature in the mathematical model.〔MURRAY, J.D. Mathematical Biology: an introduction. third edition. Interdisciplinary Applied Mathematics. Mathematical Biology. Spring: 2002.〕
==Mathematical formula==
The mathematical formula can be derived from first principles. It reads:
:\frac + \frac = - m(a)n,
where: ''n'' = ''n''(''t'',''a''), ''t'' stands for time and ''a'' for age. ''m''(''a'') is the death in function of the population age; ''n''(''t'',''a'') is the population density in function of age.
When ''m''(''a'') = 0, we have:〔
:\frac = - \frac
It relates that a population ages, and that fact is the only one that influences change in population density; the negative sign shows that time flows in just one direction, that there is no birth and the population is going to die out.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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