The family tree part is mentioned in the Developer Journal: Scaling.
if you look after your animals well, you can witness ENTIRE GENERATIONS living out their lives, allowing you to TRACE A LINEAGE back to the FIRST RELATIVES ARRIVING in your zoo. The genetics of these FAMILY TREES also plays a factor in animal scaling with genes being passed from parent to child.
source: developer journal scaling
Just as a small example.
So, I have issue with using this statement as a confirmation that they "promised" that actual, physical, automatic, family trees would be available in game.
It seems that people are taking this statement and turning it in to more than it is.
Its just fluff words for saying that your animals breed and die and then breed again and if you take the time to look at them occasionally you can see this happening. No where have I ever seen them say that a Family Tree would be a confirmed in-game feature that you can look at in an in-game menu.
Would I like to have a family tree? Certainly! But taking this statement as some kind "promise" for a feature is just kind of nuts.
You can trace a lineage in any game that has breeding mechanics with enough patience and a notebook or skill in Excel or Photoshop.