ThruLines at AncestryDNA is meant to be a tool to help analyze matches that have at least a partial family tree attached to their DNA results. The purported tree connecting you to the DNA match may or may not be correct.
The white boxes (John G, John M, and Theodore Trautvetter) in the illustration are names and relationships that are in the tree I have attached to my test results. The gray boxes (with “evaluate”) in the corner are names and relationships that have been pulled using AncestryDNA’s automated “tree stitching” based on one or more user submitted trees.
The tree of the match may only go back so far as the parent of the match. The names and relations may have been pulled from one or more trees others have submitted to AncestryDNA and those trees may or may not be connected to any DNA results. Each name and relationship in the gray boxes will have to be evaluated manually.
The white boxes are from your tree. The others are not and, like a therapist, you’ll have to evaluate those relationships for viability.