If these speculations are correct, human caused extinctions have two properties:
The result is a more homogeneous biotic environment, one in which many of the same plants and animals are found worldwide--English sparrows, starlings, dandelions, wild oats. Most of the grasses you see on the hills of California are native to the Mediterranean. Native Californian grasslands are largely confined to serpentine outcrops. Nearly all of the vegetation in lowland areas of Hawaii is introduced from other areas in the tropics. Of the roughly 1,700 plants native to Hawaii, almost half are introduced (see [11] for a more careful analysis of this issue).
Whether it is a good thing for the character of our natural world to be changed in this way is something we must decide on non-biological grounds. Life will continue on this planet whatever we decide, but what we decide will have an enormous impact on what kind of life does survive.