What is the relationship of natural selection to the development of
bacterial resistance?

Aquired resistence of bacteria to antibiotics (which I assume your
question is directed towards) is natural selection at its simplest. In
a hostile environment, in this case, a bunch of bacteria living in a
body with antibodies, only the bacteria which have mutated and changed
to protect themselves will survive. This means that only the bacteria
which have built up a resistence will live on to have little bacteria
children of their own (of course by cell division). I've found a link
which explains this in more detail here:

http://lecturer.ukdw.ac.id/dhira/ControlGrowth/resistance.html

and the pertinent reading is quoted here:

"Vertical evolution is strictly a matter of Darwinian evolution driven
by principles of natural selection: a spontaneous mutation in the
bacterial chromosome imparts resistance to a member of the bacterial
population. In the selective environment of the antibiotic, the wild
type (non mutants) are killed and the resistant mutant is allowed to
grow and flourish. The mutation rate for most bacterial genes is
approximately 10-8. This means that if a bacterial population doubles
from 108 cells to 2 x 108 cells, there is likely to be a mutant
present for any given gene. Since bacteria grow to reach population
densities far in excess of 109 cells, such a mutant could develop from
a single generation during 15 minutes of growth."

Thank you for your question,

skermit-ga