There is no way to increase it; and it is not of any real significance. The number is based upon the talents that manifest in your pet, and since the talents are predetermined there isn't any way to increase it for that particular pet. (although it does increase as each talent is revealed) If you hatch the pet with another pet, then the new pet may have a different pedigree.
Is there any way to increase the acquired pedgree, the second number? I have a sea dragon 72/22 is there a way I can increase the second number? Does it make any difference?
The second number is based on trained abilities learned.
example: Sea Dragon 72 train to teen .
category referring to talent/derby
1. it learns a common in each category result Sea Dragon 72(8) 2. it learns uncommon in each category result Sea Dragon 72(12) and so on these numbers are examples of how second number change is figured not exact amount.
so through breeding you can eliminate common/uncommon traits in your pets offspring to result in a higher pedigree pet.
example i bred my sprite(35) with my astral judge= new pet Sprite(47) not as many common/uncommon as my original sprite so i raised it to adult bred tha one with my astral judge new Sprite(53) now has vew few common/ uncommon a few rares/ultra rare and a epic where original only had common/ucommons.
And yes your pet will have maxed out every stat before you reach epic.
In answer to your question - no, once you have trained the pet, this number will not increase any further. You can hatch again to try and develop new talents, though - your next pet may obtain different talents and a higher number.