Just to be clear as Kevin writes " autosomal DNA tests (like AncestryDNA) are the wrong tests to investigate descendants of your 7th great-grandparents".
This refers only to your all male line 7th Grandparent (not plural because his wife cannot be determined by a Y-DNA test but only by an autosomal DNA test.
What is further confusing the less well informed readers is that Pauline writes about AncestryDNA.com which clearly doesn't offer a Y-DNA test in the first place. She explicitly writes:
"Although it's nice to think I might have Ancestry.com matches with all the living descendants of William Layton-9, Ancestry.com tends not to show cousins beyond about 8th cousins."
All the living descendants of William Layton-9 refers to male and female descendants, she doesn't write "all male living descendants".
I also don't want to split hair but technically this answer is actually wrong as Pauline is a female, so she can't use a Y-DNA test, it can be only used on her father or brothers (any direct male line descendant).
Here's a nice explanation including graphics as to which lines of your family tree are covered by autosomal, Y-DNA and mtDNA.