He included a line drawing of the Coalescence Process that I’ve included below.
I also heard from Bennett Greenspan, President and CEO of Familytree DNA, the testing company that we use. He concurs with this assessment although he says, "The quantity (total cM) is lower then I'd like for 3rd cousins, (referring to Paris ) but it's hard to believe that they just happen to show up 4th and 5th on your match list (referring to my match list) due to the size of their longest segment."
These men are scientists and thereby are drawing their conclusions based on science. I know that they don't necessarily have all of the cultural and historical information that I do regarding these families which lends credence to their assumption. This demonstrates that neither DNA testing and traditional genealogy testing are sufficient alone. They go hand-in-hand - each contributing to the overall understanding of our past.
The challenge for us is finding the missing link between these families.
Definition From Wikipedia: “In genetics, coalescent theory is a retrospective model of population genetics. It attempts to trace all alleles of a gene shared by all members of a population to a single ancestral copy, known as the most recent common ancestor (MRCA; sometimes also termed the coancestor to emphasize the coalescent relationship). The inheritance relationships between alleles are typically represented as a gene genealogy, similar in form to a phylogenetic tree. This gene genealogy is also known as the coalescent; understanding the statistical properties of the coalescent under different assumptions forms the basis of coalescent theory.
The coalescent runs models of genetic drift backward in time to investigate the genealogy of antecedents. In the most simple case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure. Advances in coalescent theory, however, allow extension to the basic coalescent, and can include recombination, selection, and virtually any arbitrarily complex evolutionary or demographic model in population genetic analysis. The mathematical theory of the coalescent was originally developed in the early 1980s by John Kingman.”