I came upon this post after having read a number of mostly interesting posts that strangely enough relieved most of the stresses of the day. I dove into this post expecting to experience more of the cathartic release provided by previous posts.
After I stopped pounding my head against the wall I decided to try to straighten out your misapprehensions of the process of speciation.
First we need to realize that of the millions of species that have lived on earth in the millions of possible different environments, there is room for a number of different speciation paths for a few to deviate from any 'norm' we may have evidence of. Each species path is contingent on what variations the species has experienced, is experiencing, and what limitations the current phenotype is constrained by. Physics, the environment and genotype determine which subset of the set of all possible changes a given species can experience. As the environment and genotype evolve, the 'variation subset' is guided through the full 'variation space'. This in effect removes the possibility of saltation from the set of possibilities.
Variation occurs in any population at speeds contingent on the same factors as mentioned above. There is no hard and fast rule, based on physics or environment that will regulate the speed of variation. Because the environment is essentially a complex system the speed of variation can proceed at a rate, given our short observation timeframe, that would be considered static or, at another timeframe within the species life, at an extremely fast, but gradual (morphologically speaking) rate.
Now back to speciation. The origin population, the 'parent', species 'A' lives in an environment that will only support a limited number of organisms. Because of this a small portion of the population heads off in search of greener pastures creating a 'daughter' population. These two populations never meet again. Over time the parent population experiences variation, going through a number of incarnations, A A1 A2 A3...An and the other population, the daughter, also experiences variation, A A-1 A-2 A-3...A-n. Each variation is based on previous variations in both populations for a cumulative effect. An and A-n are far enough apart in morphology to class as different species. At the same time, A and An are far enough apart that if a member of the A population were transported in time to the An population that member would have no desire or capability to interbreed with any member of An. They will be classed as different species. As you can see it is not a matter of either/or as you stipulate in:
"I am further aware that some evolutionists believe that new species evolve through divergence and yet other claim that interbreeding leads to new species.
Now lets look at Gould and Punk Ek.
For a while, scientists have been puzzled by the paucity of inter-species fossils while many transitional fossils have been found that span the higher taxa. If you take a look at Gould's response to the creationist quote-mining of his words you will see he was concerned by the inter-species fossils, not the transitionals of the higher taxa.
If evolution proceeded at a specific pace with a specific variation 'size' we should find fossils that show the gradual change from one species to another, for example, a sequence of fossil changes between an ocelot and a jaguar. We do not find that.
Gould proposed that speciation occurs at varied rates, many times with one species changing into another species too quickly for intermediate fossils to be preserved.
For example:
Species A gradually changes into species B over a time of one million years. If the generation cut off for species A is 20 years, there will be 50,000 generations, meaning that each generation is .002% different than the previous generation. (BTW - This is too small to observe in 150 years.) If one fossil is preserved in such a way that we are able to uncover it every 100,000 years, the difference between any two neighbouring fossils will be 10% different, enabling us to see, once we find all 10 fossils, a gradual and extremely smooth transition between the two species. However if the rate of evolution varies such that during the first 500,000 years each generation varies by .0006%, then goes through 90,000 years of rapid evolution say .018% per generation then 410,000 years of .0005% change per generation, those fossils will tell a very different story. The first 5 fossils found would look static, as if there was no change at all, especially if the changes were mostly of soft tissue which is not preserved. The next fossil found would be after the cumulative changes classified a new species, and would be different enough to appear as though the species appeared suddenly and 'fully formed'. All later fossils would reinforce this view. That's it for tonight. I still have a heck of a headache.
First we need to realize that of the millions of species that have lived on earth in the millions of possible different environments, there is room for a number of different speciation paths for a few to deviate from any 'norm' we may have evidence of. Each species path is contingent on what variations the species has experienced, is experiencing, and what limitations the current phenotype is constrained by. Physics, the environment and genotype determine which subset of the set of all possible changes a given species can experience. As the environment and genotype evolve, the 'variation subset' is guided through the full 'variation space'. This in effect removes the possibility of saltation from the set of possibilities.
This is really a lot of speculation.
If evolution proceeded at a specific pace with a specific variation 'size' we should find fossils that show the gradual change from one species to another, for example, a sequence of fossil changes between an ocelot and a jaguar. We do not find that.
Given that you acknowledge that these fossils haven't been found, you must consider the real likelihood that they simply do not exist and never existed. Isn't the absence of such fossils a big part of the 'gaps' in the ToE. To claim that they exist is speculation.
Gould proposed that speciation occurs at varied rates, many times with one species changing into another species too quickly for intermediate fossils to be preserved.
Proposed? Again, this is mere speculation and an attempt to explain away the absence of the fossil record that should exist if speciation was true. Wasn't that the primary reason for Gould's proposal?
You examples are not based on real world evidence. They are speculative; and you should really understand that while it may be an explanation, there is no evidence that it is based in reality.
It is frustrating when the evolutionists are reduced to using 'examples' which are not based on the real world or trying use irrelevant illustrations to support evolution. The worst abuse of this little 'trick' was the one about the amount of gas it takes to get from point 'A' to 'D' via 'B' and 'C'. Even you ought to admit that is a stretch far beyond all reason.