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I'm not sure this should have been moved to advice; if he wants a PFS specific answer, it differs from the generic answer.
You can either: choose a single animal from the MOST RESTRICTIVE list and the levels stack, or you can choose two different animals *BUT CAN ONLY USE ONE IN COMBAT.*
From the PRD Druid class: "If a character receives an animal companion from more than one source, her effective druid levels stack for the purposes of determining the statistics and abilities of the companion."
From Ranger: "This ability functions like the druid animal companion ability (which is part of the Nature Bond class feature), except that the ranger's effective druid level is equal to his ranger level – 3."
From Paladin: "This mount functions as a druid's animal companion, using the paladin's level as her effective druid level."
From Cavalier: "This mount functions as a druid's animal companion, using the cavalier's level as his effective druid level. The creature must be one that he is capable of riding and is suitable as a mount."
In other words: ask your GM if you're not playing PFS; many GM's would read the text above to say that the levels stack as long as (for instance) your TIGER is big enough to ride (one or more size categories larger than you).
I would also point out that PFS USED to just straight up have the levels stack under Joshua Frost's ruling on May 28, 2010 LINK; that ruling was subsequently changed by Mike Brock on November 29, 2012 Link, Link2 and Link3--that's 2 years of PFS during which the levels stacked just fine thanks and the world didn't end.