  Ben-Ari and Schinazi (2016) introduced a stochastic model to study
`virus-like evolving population with high mutation rate'. This model is a birth
and death model with an individual at birth being either a mutant with a random
fitness parameter in $[0,1]$ or having one of the existing fitness parameters
with uniform probability; whereas a death event removes the entire population
of the least fit site. We change this to incorporate the notion of `survival of
the fittest', by requiring that a non-mutant individual, at birth, has a
fitness according to a preferential attachment mechanism, i.e., it has a
fitness $f$ with a probability proportional to the size of the population of
fitness $f$. Also death just removes one individual at the least fit site. This
preferential attachment rule leads to a power law behaviour in the asymptotics,
unlike the exponential behaviour obtained by Ben-Ari and Schinazi (2016).
