Here’s a critique of neo-Darwinism that, unusually for me, I express numerically.
Consider a species of elephants consisting of an average of one million inter-breeding individuals evolving into a new species over the course of one million years.
A female elephant has progeny over the course of 50 years. Call that a generation. Each generation is one opportunity per successive pair of elephants for the action of natural selection. Allotting 50 years to a generation, one million years per successive pair of elephants offers 20,000 potential opportunities for natural selection.
How efficient is natural selection at taking those potential opportunities? The ultimate expert Ronald Fisher in his equations used a figure for that of 1%. That would leave natural selection only 200 actual opportunities per pair of elephants in a million years. Spreading that over 500,000 pairs in the population gives a total for opportunities for selection of 100 million.
What must each act of selection involve? Female elephants have on average six progeny in their lifetimes, from which two must survive. So each opportunity is the culling of only two progeny for each one selected. That’s a very coarse selection tool.
How many items must that tool select for? All those involved in adaptive changes, of course, but also all those needed for continued survival. Independently-living creatures that become parasites over time lose functions they no longer need, so selection must act on our elephants to maintain all the assets they need for independent living. If natural selection is to be our primary mechanism of evolution we must come up with a figure for this. Making every amino acid in every protein in the body an asset to be maintained alone adds up to 50 million, half our total number of opportunities for selection. Maintaining all elephants’ genes would amount to three billion assets to be maintained, far in excess of the opportunities open for selection available to natural selection.
Also, if we are to make the action of genetic mutation plus natural selection our primary mechanism for maintaining a species' fitness, that mechanism must compensate for what's likely to happen in each generation when the blueprint of a successfully-working organism suffers the random damage needed to generate beneficial mutations. Suppose that, besides neutral changes and those harmful enough to forestall reproduction, for each mutation that's beneficial there are 100 that are merely harmful. Then with each generation there's a large decrease in fitness. Can the increase in fitness due to the occasional beneficial mutation offset the rapid loss of fitness resulting from that rapidly-growing preponderance of harmful mutations? Natural selection only 1% efficient would in each generation reduce each 100 harmful mutations only to 99. In his laying of the foundations for the modern synthesis Fisher omits an equation summing up the combination of fitness contributions of both beneficial and harfmful mutations that would have shown this. He tallies inheritances from only beneficial mutations.
From both these sets of figures it seems to me that random damage to genes plus a 1%-efficient selection for fitness can't account for how the evolved world appears.