I appreciate your detailed reply. The attempt here was to really ask the question:
Has mathematical modeling been conducted of the amount of time it would take to generate the human genome?
For more recent human evolution, yes it has been done. Namely, scientists have modeled the evolution of the human genome since we split off from the chimp lineage. First, they compared human and chimp pseudogenes. These were chosen because mutations in pseudogenes tend to be neutral and neutral mutations accumulate at a more or less even pace. They then estimated the human mutation rate by measuring the occurence of deleterious mutations for known dominant Mendelian diseases like achondroplasia or hemophilia. What did they find?
quote:
Hum Mutat. 2003 Jan;21(1):12-27.
Direct estimates of human per nucleotide mutation rates at 20 loci causing Mendelian diseases.
Kondrashov AS.
SourceNational Center for Biotechnology Information, NIH, Bethesda, Maryland 20892, USA.
Abstract
I estimate per nucleotide rates of spontaneous mutations of different kinds in humans directly from the data on per locus mutation rates and on sequences of de novo nonsense nucleotide substitutions, deletions, insertions, and complex events at eight loci causing autosomal dominant diseases and 12 loci causing X-linked diseases. The results are in good agreement with indirect estimates, obtained by comparison of orthologous human and chimpanzee pseudogenes. The average direct estimate of the combined rate of all mutations is 1.8x10(-8) per nucleotide per generation, and the coefficient of variation of this rate across the 20 loci is 0.53. Single nucleotide substitutions are approximately 25 times more common than all other mutations, deletions are approximately three times more common than insertions, complex mutations are very rare, and CpG context increases substitution rates by an order of magnitude. There is only a moderate tendency for loci with high per locus mutation rates to also have higher per nucleotide substitution rates, and per nucleotide rates of deletions and insertions are statistically independent on the per locus mutation rate. Rates of different kinds of mutations are strongly correlated across loci. Mutational hot spots with per nucleotide rates above 5x10(-7) make only a minor contribution to human mutation. In the next decade, direct measurements will produce a rather precise, quantitative description of human spontaneous mutation at the DNA level.
[emphasis mine]
So we find that the observed human mutation rate is in the same ballpark as the rate needed to produce the differences seen between chimps and humans. Other scientists have found lower rates, but it is again in the same ballpark.
As to the larger picture and genome length, you are talking about a very volatile system. Yes, insertions can be the insertion of a single base. You can also have whole genome duplications where the genome doubles in size in a single generation. This makes it difficult to model because of the great disparity in the number of bases in each event, and the rare case of whole genome duplications.
More importantly, it would appear that 2 whole genome duplications (a 4 fold increase in the size of the genome in 2 distinct events) were vital in the evolution of the vertebrate genome.
quote:
PLoS Biol. 2005 Oct;3(10):e314. Epub 2005 Sep 6.
Two rounds of whole genome duplication in the ancestral vertebrate.
Dehal P, Boore JL.
SourceEvolutionary Genomics Department, Department of Energy Joint Genome Institute, Lawrence Berkeley National Laboratory, Walnut Creek, California, USA.
Abstract
The hypothesis that the relatively large and complex vertebrate genome was created by two ancient, whole genome duplications has been hotly debated, but remains unresolved. We reconstructed the evolutionary relationships of all gene families from the complete gene sets of a tunicate, fish, mouse, and human, and then determined when each gene duplicated relative to the evolutionary tree of the organisms. We confirmed the results of earlier studies that there remains little signal of these events in numbers of duplicated genes, gene tree topology, or the number of genes per multigene family. However, when we plotted the genomic map positions of only the subset of paralogous genes that were duplicated prior to the fish-tetrapod split, their global physical organization provides unmistakable evidence of two distinct genome duplication events early in vertebrate evolution indicated by clear patterns of four-way paralogous regions covering a large part of the human genome. Our results highlight the potential for these large-scale genomic events to have driven the evolutionary success of the vertebrate lineage.
emphasis mine
Does that help answer your questions?