"'As far as you know, is there a compelling mathematical argument in support of macro-evolution?'
Yes. (1 + µ)n ~ 1 only if µ=0 (micorevolution does not exist) and/or n is small (young Earth). If you accept microevolution and an old Earth, macroevolution is inescapable."
Random formation of even a single protein is mathematically highly improbable even if n is ridiculously large (one billion years). Spontaneous generation is much, much less probable. Faith in the highly improbable is inescapable for those with the presupposition of "matter is all there is".
c) Calculations of Bradley and Thaxton for random production of a single protein.
Walter L. Bradley and Charles B. Thaxton calculated the probability of a random formation of amino acids into a protein to be 4.9 x 10-191. They began with the assumption that the probability of starting with an L-amino acid was .5, and the probability of starting with an L-amino acid was .5, and the probability of two L-amino acids joining with a peptide bond was also .5. They assumed that the twenty necessary amino acids existed in equal concentration in the prebiotic soup so that the probability of the right amino acid in the required position was .05.
Bradley and Thaxton were also generous towards the proponents of random processes when they also assumed that all of the chemical reactions would be with amino acids, ignoring the high probability of reactions with non-amino acid chemicals. They calculated the probability of the necessary placement of one amino acid to be .5 x .5 x .05 or .125. This, of coarse, meant that the probability of assembling N such amino acids would be .0125 x .0125 for N terms. Assuming a protein with 100 amino acids (.0125 x .0125 for 100 terms ), the mathematically impossible probability would be 4.9 x 10-191.
Bradley and Thaxton noted their agreement with Hubert P. Yockey and concluded that even assuming that all the carbon on earth existed in the form of amino acids and reacted at the greatest possible rate of 1012/s for one billion years (when actually only 130 million years were available), the mathematically impossible probability for the formation of one functional protein would be 10^-65.
other probability models posted here:
http://www.freerepublic.com/focus/f-news/1689062/posts?page=185#185
a) Calculations of Sir Fred Hoyle and Chandra Wickramasinghe for random generation of a simple enzyme and calculations for a single celled bacterium
b) Calculations of Hubert Yockey for random generation of a single molecule of iso-1-cytochrome c protein.
c) Calculations of Bradley and Thaxton for random production of a single protein.
d) Calculations of Harold Morowitz for single celled bacterium developing from accidental or chance processes.
e) Calculations of Bernd-Olaf Kuppers for the random generation of the sequence of a bacterium.