The first assumption is the one that I have mentioned in the other thread, and it is also the one that Darwin made in his time. That the small changes in today's species from generation to generation can accumulate, with enough time, as to produce major changes such as new organs, new proteins, etc. This was very much an assumption in his time, and it was what permitted him to construct his famous 'tree of life'. I think it is still an assumption today, and here is why. When is the last time someone asked a question like this: can the small changes that we observe today be extrapolated to big changes with enough time ?
The question was asked, and studied in depth both experimentally and mathematically through much of the middle part of the last century. The findings of the biologists working at that time form the basis for much of modern evolutionary theory. So, no, you don't find much discussion about it in the current literature, but that's because the issue was settled decades ago not because it's being assumed by modern evolutionists.
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