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2010 ; 81
(1 Pt 1
): 011902
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Quasispecies theory for finite populations
#MMPMID20365394
Park JM
; Muņoz E
; Deem MW
Phys Rev E Stat Nonlin Soft Matter Phys
2010[Jan]; 81
(1 Pt 1
): 011902
PMID20365394
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We present stochastic, finite-population formulations of the Crow-Kimura and
Eigen models of quasispecies theory, for fitness functions that depend in an
arbitrary way on the number of mutations from the wild type. We include back
mutations in our description. We show that the fluctuation of the population
numbers about the average values is exceedingly large in these physical models of
evolution. We further show that horizontal gene transfer reduces by orders of
magnitude the fluctuations in the population numbers and reduces the accumulation
of deleterious mutations in the finite population due to Muller's ratchet.
Indeed, the population sizes needed to converge to the infinite population limit
are often larger than those found in nature for smooth fitness functions in the
absence of horizontal gene transfer. These analytical results are derived for the
steady state by means of a field-theoretic representation. Numerical results are
presented that indicate horizontal gene transfer speeds up the dynamics of
evolution as well.
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