"Darwinian evolution requires species to become extinct so that new species can replace them."

Tripe. Species change occurs whenever an opportunity arrives, and one or more existing populations has characteristics which allow them to exploit the opportunity. The opportunity can arrive in many ways, the most common probably being environmental change.

"Now...the Darwinian era is over. The epoch of species competition came to an end about 10 thousand years ago when... Homo sapiens, began to dominate and reorganize the biosphere. ..."

Also tripe. All species are constantly adapting to their environment. Human domination over the last five hundred years is merely another environmental factor from their evolutionary point of view - though perhaps as great a change as an ice age or an asteroid. Why should other species stop competing (to live) just because humans are cutting down the forests they live in?

10 thousand years? You probably couldn't even tell whether any evolutionary adaptations in that timescale were speciation or variation within a species.