  The emergence of a predominant phenotype within a cell population is often
triggered by a rare accumulation of DNA mutations in a single cell. For
example, tumors may be initiated by a single cell in which multiple mutations
cooperate to bypass a cell's defense mechanisms. The risk of such an event is
thus determined by the extremal accumulation of mutations across tissue cells.
To address this risk, we study the statistics of the maximum mutation numbers
in a generic, but tested, model of a renewing cell population. By drawing an
analogy between the genealogy of a cell population and the theory of branching
random walks, we obtain analytical estimates for the probability of exceeding a
threshold number of mutations and determine how the statistical distribution of
maximum mutation numbers scales with age and cell population size.
