  The number of substitutions (of nucleotides, amino acids, ...) that take
place during the evolution of a sequence is a stochastic variable of
fundamental importance in the field of molecular evolution. Although the mean
number of substitutions during molecular evolution of a sequence can be
estimated for a given substitution model, no simple solution exists for the
variance of this random variable. We show in this article that the computation
of the variance is as simple as that of the mean number of substitutions for
both short and long times. Apart from its fundamental importance, this result
can be used to investigate the dispersion index R , i.e. the ratio of the
variance to the mean substitution number, which is of prime importance in the
neutral theory of molecular evolution. By investigating large classes of
substitution models, we demonstrate that although R\ge1 , to obtain R
significantly larger than unity necessitates in general additional hypotheses
on the structure of the substitution model.
