  Time evolution of number of species (genera, families, and others),
population of them, and size distribution of present ones and life times are
studied in terms of a new model, where population of each genetic taxon
increases by a (random) rate and decreases by (random) division
(fragmentation). Each of log-normal, exponential and power law distributions in
various empirical data about mentioned events are considered for gradual,
intermittent and abrupt evolution cases. Results come out in good agreement
with several theoretical literatures and with available empirical data. Sum of
exponential functions with independent random amplitude and exponent are shown
to be useful to express many aspects of the present competition, and they are
shown here to involve power law with power -1.
