Hiya, anonymous! :-) You'll have fun with your genetic genealogy experience. One of the first things you'll want to do when your (and your grandmother's, too) AncestryDNA data come back will be to upload it to a service--like GEDmatch.com or Family Tree DNA--that will allow you to dig into the detail of the matches and look at the specifics of segments along the chromosomes. Ancestry doesn't provide enough information to do the analyses you'll need to do.
Today's DNA Trivia: Ya know where most of our knowledge--and the math to compute it--about pedigree collapse and DNA originated? In the early 20th century from the breeding of farm animals. Kinda stands to reason, though, when you think about it. The generations are relatively short; breeders are trying for very particular traits; and they have to balance achieving those traits with organism frailty due to lack of genetic diversity.
It was a gentleman named Sewall Wright, employed by the USDA at the time, who wrote a brief but important paper in 1921 about inbreeding in animals called "Coefficients of Inbreeding and Relationship." You can view a copy of his paper in the resource archives of my one-name study, if you're curious. It works only for the amount of theoretical autosomal DNA sharing, but it's still a valid yardstick to this day. It can happily work out, for example, that half-1st cousins should be expected to share 66.6% of the amount of DNA that triple-2nd cousins do. <cough, cough>
But unless you get giddy working with summation symbols and superscript "to the power of" variables, a blog post by Jim Bartlett from a couple of years ago may be a good place to start, if you haven't already read it. Jim breaks things down into more genealogist-friendly terms and puts it into example tables. The tables may still take a little study to figure out how he's using them, but you can actually duplicate the format in a spreadsheet for your own use to look at expected, theoretical autosomal DNA sharing among two cousins with one or more shared ancestors, and the sharing in subsequent generations.
Pedigree collapse affects your genealogical use of autosomal DNA through four factors:
- The degree of the parent/child relationship (twins having children is the extreme, as Jaimie and Circe Lannister showed us)
- The distance in generations since the collapse (the original sharing gets more random and breaks up segments with each birth event)
- Whether the instance(s) of collapse are isolated or multiplicative (approaching actual endogamy)
- Whether the instance(s) of collapse affect a single family branch or spans across both your maternal and paternal lines
Your matches--certainly on that particular branch of your tree--will show a higher than average amount of total DNA sharing, as you suspect. Although we have to remember two things. First, that the expected shared total decreases by a factor of four at each generation after the pedigree collapse. For example, with no collapse the average sharing with a 2nd cousin is 3.13%, and with a 3rd cousin it's 3.13 divided by 4 = 0.78%. So the gap between the expected average sharing and sharing influenced by pedigree collapse shrinks very quickly. You can have three times more sharing with a 5th cousin than expected, and the total would still be less than 10cM.
Second is that while the shared total in centiMorgans will be higher with pedigree collapse, the length of the largest segments won't necessarily be...at least not significantly so. Your tripling of the total shared with that hypothetical 5th cousin won't result in a tripling of the length of the segments. (Jim points this out in his article, as well.) Segment length is driven mainly by the step during meiosis called crossover. Where the shared segment is located along the chromosome affects this, too. Segments nearer a chromosome's practical center--the spot where the pair of chromatids link together, called the centromere (creative, huh?)--are less likely to shuffle and recombine than are segments farther out toward the telomeres, the ends of the chromosomes. Bottom line, though, is that large segments are not "sticky"; they don't pass down from generation to generation unbroken. The end result here is that you probably won't be able to verify cousins much more, if any, distant than the rest of us since the collapse in your pedigree happened at your 8g- and 7g-grandparents, too far back for larger segments from them to be inherited.
The greater the degree of collapse, the more complex the task in matching the DNA evidence to the paper trail. This is why it's so difficult, if not impossible, to effectively use autosomal DNA to go reliably back more than a couple of generations in endogamous populations like the Ashkenazim or some Polynesian Islanders. The reason it's so complex is that once you suspect impact from pedigree collapse, it doesn't suffice to do what we would consider standard autosomal triangulation: finding multiple tested cousins who all share a meaningfully-sized segment and who also match the paper-trail. With pedigree collapse you can't just follow one trail to an MRCA couple: you have to investigate every possible pathway of genetic inheritance. Autosomal DNA triangulation to a single, shared, ancestral couple can be functionally impossible in truly endogamous populations. There are two reasons I believe the majority of autosomal triangulations I've seen are probably false: A) use of segment sizes that are too small without large numbers of individuals in the triangulation groups to substantiate them (and a corollary, not triangulating sufficiently to the actual MRCA but using shorter legs that stop at more recent generations); and B) use of shared DNA amounts that are far larger than predicted by the theoretical averages and that clearly indicate the likelihood of pedigree collapse, but without doing the hard work--and spending the time looking for and testing additional cousins--necessary to investigate all the possible pathways of the DNA inheritance.
Have fun! And join WikiTree! Most serious genealogists I know have some Sherlock Holmes in them: it isn't just the discoveries that they enjoy, but the detective work that goes into it. And genetic genealogy definitely adds a whole new set of sleuthing tools. :-)