My question is this. Can a lack of genetic diversity accelerate snp mutations? ...
I've asked questions about this kind of thing and looked around. I can no scientific evidence or research that supports us. If someone has a research paper on this, please bring it forward?
On the other hand you might want to read the research on wave-surfing, particularly as it relates to R1b. Sometimes new alleles happen to ride on a wave of population growth, the result is lower STR diversity at least in terms of total breadth. At the same time, the large number of new, surviving births is increasing the total number of SNPs found.
Consider this - STR diversity requires more generations. The mutation of an absolute number of additional SNPs does not require more generations, just more births that survive to provide for more births. STR diversity does not necessarily grow because of larger, better surviving nuclear families. No matter how many sons a father has, for most ordinary STR mutations, the allele will only or increase or decrease by a value of one.
The absolute number of SNP mutations does grow with larger, better surviving familes as well as with more generations. The more sons a father has, the more likely new SNPs will occur. Every birth could result in an entirely different SNP that is unique in its own right.