Ken Ham says, in The Lie, that evolution has not occurred. Really?

Ken Ham, leader of the Answers in Genesis (AiG) organization, doesn’t believe evolution occurred:

“Christians who say God used evolution to bring everything including man into being, have a real problem. If evolution is not occurring today (that is, if God is not ‘creating’ through evolution), there is no basis to extrapolate into the past to say that evolution has ever occurred, as there is now no mechanism for it.” - Ken Ham, “Twenty Reasons Why Genesis and Evolution Do Not mix,” which is excerpted from Ham’s book, The Lie. The book seems to have been published in 2012.

So evolution can’t occur, because “there is no mechanism for it?” Well, maybe there is. AiG understands that it wasn’t possible to house and care for all the types of animals on the ark, with only 8 people to handle this. So, AiG says, there were just a hundred or so types of animals, but, after the ark landed, these exploded into the variety we have today. (See here)

This statement contradicts Ham’s claim that evolution can't occur: “God placed the potential for tremendous variety within the original created kinds. This original variation, altered by genetic mutations and other mechanisms after the Fall (such as natural selection), led to the great diversity of living things we see today.” - “Variety Within Created Kinds,” from Answers in Genesis, probably published in 2010.

God used natural selection and genetic mutations, and probably other mechanisms, to make possible the variety we find in created organisms. Praise to Him! 

Psalm 104:24 Yahweh, how many are your works!
    In wisdom, you have made them all.
    The earth is full of your riches.
104:25 There is the sea, great and wide,
    in which are innumerable living things,
    both small and large animals. (World English Bible, public domain)

Thanks for reading.