Exactly. Autosomal DNA testing will almost always show a match with one of your third cousins. But if you could test 100 of your proven fourth cousins, you probably would find matches with only 20 to 30 of them. And if you could test 100 of your proven fifth cousins, you'd be lucky to find matches with more than five or six.
On the other hand, Y-chromosome testing can give reliable results about your unbroken male-to-male line of ancestry going back thousands of years. And ditto for mitochondrial DNA testing, when it comes to your unbroken female-to-female line of ancestry.
Y is the way to go because only 14% of people in the UK share my Y Chromosome it is easy to eliminate all of the R1B’s with the same last name. It also helps to have a place to start, in my case I had seven generations in one town so that hitting the local Historical groups helps.
The upside is that they were prominent, in some cases, the down side is they bred like rats.
Thanks!
There’s also the out on the edge kinds of weird stuff:
Man who failed paternity test for his child is shocked to discover the DNA in his sperm came from his TWIN who was ‘lost’ in the womb in first-of-its-kind case
http://www.dailymail.co.uk/femail/article-3288976/Man-failed-paternity-test-child-shocked-discover-DNA-sperm-came-TWIN-lost-womb-kind-case.html
Woman Gives Birth to Children, Discovers Her Twin is Actually the Biological Mother, But She is Technically Her Own Twin
http://www.opposingviews.com/i/health/womens-health/woman-gives-birth-children-discovers-her-twin-actually-biological-mother-she
Weird: Kids’ DNA Tested, Parent Informed The DNA Is Not A Match
http://ace.mu.nu/archives/118606.php
Parent-Child Non-Matching Autosomal DNAÂ Segments
http://dna-explained.com/2015/05/14/parent-child-non-matching-autosomal-dna-segments/
Paternal mtDNA transmission
https://en.wikipedia.org/wiki/Paternal_mtDNA_transmission
Dental Calculus as an Alternate Source of Mitochondrial DNA
https://scahome.org/publications/proceedings/Proceedings.25Black.pdf