  One of the most fundamental rules in metabolic ecology is the allometric
equation, which is a power-law scaling that describes the connection between
body measurements and body size. The biological dynamics of this essentially
empirical allometric equation, however, have yet to be properly addressed in
cell level. In order to fill the gap between biological process in cell level
and allometric scaling in metabolic ecology, we simply assumed a cell
bipartition without limitation, and then exponential cells increased during
their lifetime. Two synchronous exponential increasing could generate a
power-law scaling between body mass and an organ's weight. And the power-law
scaling between body mass and metabolic rate may also be obtained by
substituting an organ's weight with the weight of erythrocytes. Based on the
same assumption, the dynamic of cell proliferation reveal a complex exponential
scaling between body mass and longevity rather than the previously reported
power-law scaling. In other words, there is a quadratic relationship between
longevity and logarithmic form of body mass. In these relationships, all
parameters can be explained by indices in cell division and embryo.
