> I may be misunderstanding what you're suggesting by this but it seems that we're suggesting that a population becoming more similar (stabilizing) doesn't involve a change in the population.

Of course not. My point is that evolution is not solely about change. Of course it's totally amazing how many different forms life takes, and this is the result of changes over billions of years. But just as amazing is how much has not changed. All the life forms contain DNA and have millions of sequences in common. Even if not identical, they are far too similar to be ignored. 

¶

Related sequences are designated as being homologous; however, the term
homology often leads to confusion. Homology is not a measure of similarity, but rather
signifies that sequences have a shared evolutionary history and, therefore, possess a
common ancestral sequence.

conserved regions contain important regulatory elements, non-protein-encoding genes,
and regions important for chromosome structure.

Many comparative studies of the genomes of humans and mice have shown that
their organization, to a large extent, is similar. This indicates that, since the last com-
mon ancestor, the structural organization has been conserved.

Homology 
A classification based on the phylogenetic
origin of structures. Characters that were
inherited either unchanged or changed from
common ancestors (e.g., specific kinases of mice
and humans, or extremities of mice and humans)
are considered homologous.

From
Applied Bioinformatics
https://doi.org/10.1007/978-3-319-68301-0

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