Before I reply, it should be noted that I am actually a physics student and that my understanding of biology and population genetics is limited to what I had learned back in the days when I was a biology major.
1. Different species has different chromosomal karyotypes
Different species in sexual animals almost all have karyotic changes, which means chromosomal differences detected under microscope. They are deletion, amplification, duplication, insertion, and inversion, even chromosomal number changes. Neo-Darwinism is based on change of allele frequencies, which cannot provide explanation how allele change lead to addition, deletion of pieces of chromosome, or change of chromosomal numbers.
It is not entirely true that speciation can only result from an immediate change in allele frequency. At least in plants, polyploidy is a very common phenomenon that leads to new plant species.
2. Against all scientific evidences so far available
For example, lateral transfer in bacteria, polyploids in plants, generation of asexuals from sexual animals (virgin births), generation of SARS or HIV and many virus, incorporation of mitochondria by symbiosis, etc. they all fall into instantaneous biodiversity, not gradual one by RMNS mechanism.
Can anybody give me an example of speciation by RMNS? (do not just tell difference allele frequencies in different groups of same species).
Tarantulas.
3. Lack of explanatory power
Beside lack of transitional fossils, there are more examples, such as chicken-egg paradox, atavisms, innovative organ, bottleneck effect, mosaic evolution, Cambrian explosion, rate of evolutionary change, few speciation in big mammals, RMNS mechanism poorly explains these phenomena.
I'm not sure how to interpret what you stated above. Could you be more specific?
4. Un-falsification
Because RMNS model has no predictory power, there is no way falsifying it, and you cannot prove it wrong by scientific methods. In other words, it stands in any outcomes. By Popperian criteria, Neo-Darwinism is a pseudo-science.
Actually, Darwin said it himself in
Origin of Species that if a true altruistic species ever be found, it would falsify his theory.
5. Too complicated
According Neo-Darwinists, there are several mechanisms of speciation (biodiversity): genetic drifting, natural selection, geographical isolation, sexual selection and instantaneous speciation. Among geographical isolation, there is vicariant speciation, peripatric speciation, also parapatric speciation. Each mechanism has own myths and assumptions. Worse than that,
nobody can tell which organisms come into beings by which mechanism; they are just intensive exercise of your imagination.
Aside from the "too complicated" claim, which I'm not sure that it has anything to do with what we are talking about, I don't think the underlined statement is true.
Off the top of my head, I can name several examples of species that came from geographical isolation. But just for kicks, you can fly to any of the islands in South America to find examples of such species.
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