  This paper develops a mathematical model describing the influence that
conjugation-mediated Horizontal Gene Transfer (HGT) has on the
mutation-selection balance in an asexually reproducing population of
unicellular, prokaryotic organisms. It is assumed that mutation-selection
balance is reached in the presence of a fixed background concentration of
antibiotic, to which the population must become resistant in order to survive.
We analyze the behavior of the model in the limit of low and high
antibiotic-induced first-order death rate constants, and find that the highest
mean fitness is obtained at low rates of bacterial conjugation. As the rate of
conjugation crosses a threshold, the mean fitness decreases to a minimum, and
then rises asymptotically to a limiting value as the rate of conjugation
becomes infinitely large. However, this limiting value is smaller than the mean
fitness obtained in the limit of low conjugation rate. This dependence of the
mean fitness on the conjugation rate is fairly small for the parameter ranges
we have considered, and disappears as the first-order death rate constant due
to the presence of antibiotic approaches zero. For large values of the
antibiotic death rate constant, we have obtained an analytical solution for the
behavior of the mean fitness that agrees well with the results of simulations.
The results of this paper suggest that conjugation-mediated HGT has a slightly
deleterious effect on the mean fitness of a population at mutation-selection
balance. Therefore, we argue that HGT confers a selective advantage by allowing
for faster adaptation to a new or changing environment. The results of this
paper are consistent with the observation that HGT can be promoted by
environmental stresses on a population.
