This is a really sophisticated question. I had
to tap my friend the geneticist to help me out. I
have edited this a bit.
Let's take the second question first. The
short answer is "yes" for non-chromosomal DNAs and
"no" for the nuclear genome. In general, small
extranuclear genomes like mitochondrial DNA
replicate more rapidly as they decrease in size.
The more rapidly replicating a molecule, the
higher its relative frequency in the DNA
population, so over time selection favors
deletions of genes that aren't essential and the
extranuclear genome shrinks.
You can model this in bacteria with a strain
carrying a large plasmid that encodes resistance
to two antibiotics, and grow the cells in the
presence of only one drug. After several
generations, if you screen for the resistance to
the second drug, you'll find that a proportion of
the population is now sensitive and if you extract
the plasmid DNA, you'll verify the presence of
deletions. However, in higher eukaryotes unused
genes in the nuclear genome tend to persist and
accumulate in the course of evolution. In the
human genome, most of the DNA is non-coding and a
number of sequences are pseudogenes (code for a
protein but lack the regulatory regions that allow
them to be expressed. Look up "c-value paradox"
if you're interested in this phenomenon).
In the case of mitochondria, the nuclear
genome encodes mt-specific DNA and RNA polymerases
(enzymes needed for replication), so with the
evolution of those nuclear genes (or of the
specialization of the enzymes they encode),
replication genes on the organelle became
non-essential. At this point, deleting the
replication functions becomes advantageous due to
smaller genome size. There is also a selective
advantage for the host to control mt replication -
it can vary the number of mitochondria so that it
only invests in as many as it needs. The
combination of these pressures would be a
relatively strong selection for loss of self
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