taxon

And, loss of population of a taxon is independent of the (average) life time of its individuals.) Also, one new generated taxon may lose population in further time steps; and whenever any taxon has population less than one, and then we consider the situation as (gradual) extinction.
A physical model for competition between biological speciation and extinction

Yet, to study the effect of small sizes, we consider random initial populations, and assign Pri many (lower) taxa to the taxon under consideration, where P is some constant and ri is a random real number 0 ≤ ri < 1, with i ≤ M(0).
A physical model for competition between biological speciation and extinction

In Figure 1b, we display the ratio of extinction events to the number of current taxa, where it may be observed that, each taxon has the chance to give birth to an unsuccessful mutation, as time goes on; and, the inset is for the size distribution of extinction events, where linearity is clear.
A physical model for competition between biological speciation and extinction

Yet, this is valid for all taxa; namely, some lower taxa of each (higher) taxon become extinct quickly, and some others live long.
A physical model for competition between biological speciation and extinction

Ratio of extinction events to the number of current taxa, where it may be observed that, each taxon has a chance to give birth to an unsuccessful mutation, as time goes on; and, the inset is for the size distribution of extant, where linearity is clear.
A physical model for competition between biological speciation and extinction