Time course population growth rates

As noted in Section 2, Metz and Diekmann [MD, p. 237] describe a different size-structured model, one that reflects the cell-division process quite well. They assume that cell size x varies among the individual cells of the population, from a minimum value Xmin to a maximum value that is normalized to 1. A function b x) gives the per-unit time probability of a cell of size x dividing. Small cells are not allowed to divide (f>(Ar) = 0, xmother cell of size x is assumed to divide into two daughter cells, one of size px and one of size (1 -p)x, with probability d p), 0 < / < 1. Of course, d(p) = d l —p) and/o d(p) dp =. The unit of size x -whether length, area, or volume - is not specified in [MDj. This makes their assumption that the growth rate of a cell of size x is proportional to X (and to f(S)) subject to different interpretations. The reader is referred to [MD, p. 238] for the equations and hypotheses. Their model also can be reduced to the equations considered in Chapter 1. 

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