Shapiro has published 3 papers on the subject in addition to his book.
I will link to one which is freely available.
He summarises how he views evolution happens as below:
Although there remain many gaps in our knowledge, we are now in a position to outline a distinctively 21st century scenario for evolutionary change. The scenario includes the following elements:
(1) hereditary variation arises from the non-random action of built-in biochemical systems that mobilize DNA and carry out natural genetic engineering;
(2) major disruptions of an organism’s ecology trigger cell and genome restructuring. The ecological disruptions can act directly, through stress on individuals, or indirectly, through changes in the biota that favour unusual interactions between individuals (cell fusions, interspecific hybridizations). Triggering events continue until a new ecology has emerged that is filled with organisms capable of utilizing the available resources;
(3) ecologically-triggered cell and genome restructurings produce organisms which, at some frequency, will possess novel adaptive features that suit the altered environment. Novel adaptive features can be complex from the beginning because they result from processes that operate on pre-existing functional systems, whose components can be amplified and rearranged in new combinations. Competition for resources (purifying selection) serves to eliminate those novel system architectures that are not functional in the new ecology;
(4) once ecological stability has been achieved, natural genetic engineering functions are silenced, the tempo of innovation abates, and microevolution can occur to fine-tune recent evolutionary inventions through successions of minor changes.
You will need to read the paper to understand where he is coming from. He has referenced 209 papers to support his claims. I have only read the paper. Haven’t looked up any of his references.