  Motivated by empirical observations of algebraic duplicated sequence length
distributions in a broad range of natural genomes, we analytically formulate
and solve a class of simple discrete duplication/substitution models that
generate steady-states sharing this property. Continuum equations are derived
for arbitrary time-independent duplication length source distribution, a limit
that we show can be mapped directly onto certain fragmentation models that have
been intensively studied by physicists in recent years. Quantitative agreement
with simulation is demonstrated. These models account for the algebraic form
and exponent of naturally occuring duplication length distributions without the
need for fine-tuning of parameters.
