I think invites need to be reworked. As they are currently, only a couple of them have any good use while the others fill a very small niche as it is -- something that makes them worthless without needing them for that one specific purpose.
Case in point:
Reptile/Mammal/Bird catcher - each increase the chance of catching their respective groups.
Dragon/Cockatrice/Gryphon/Unicorn/Thunder(Roc)/Claw(Puma) Magician - each increases the chances of catching their respective pets.
Both of these provides a small boost, but each is less useful without each other. If they absorbed the catcher invites INTO the magician invites, so that it increased chance of den inhabitance AND chance of capture, then it'd really be useful. As it currently is they only fill a very small niche.
Trainer Invite - Really only useful when training a LOT of pets and/or high level pets (40+). To fix this, the trainer invite should also reduce the amount of time it takes to train a pet by 50% (so 2 hours instead of 4). Honestly the only thing stopping me from MASS training my pets is the fact that in the 4 hours it takes, I lose 4 energy, and with that 4 energy I could pretty much gain a level anyways.
Clairvoyant - Useless once you have the cartographer's guild. This one needs to just be gone or absorbed into a different invite - maybe captain of rangers? Either way Cartographers Guild > this useless invite.
Captain of Rangers - Not really useful because most of the time you'll only have 2-3 pets on your screen at a time anyways; besides the fact that you can't really 100% know where every pet is going to go. Only useful without knowing where the pets are/are going and even then, probably not too useful since you're better off just camping the watering holes with 2 catchers or the fields with 3 catchers. I think the Captain of Rangers should allow you to send out unlimited expeditions. If you think about it then you could cover the whole map if you wanted, which wouldn't be any more effective than only placing catchers exactly where you need them but at least this would be useful if you didn't know where a pet was going to go.
Geneticist - Really niche. Only very useful when looking for specific gene couplings, and even then isn't too useful unless you do a TON of catching/breeding. To fix this the geneticist should be able to research genes without either the vermillion or the money. Either way then this would be super useful. Imagine saving 2000 coins on researching a pet -- or saving 20 vermillion.
Dryad - only useful when you've caught all the pets on the map and you don't want to wait for more to appear naturally. This function may be better off left to the specific breed occurance invites instead. Also there have been complaints of this invite not doing ANYTHING so it probably needs its effectiveness increased.
Traveling Merchant - Usefulness debatable. Fills a small niche. You're probably better off spending your money at the magic shop. Should probably be limited to only selling magic items; which would then make it VERY useful since being able to buy premium items with coins is always nice.
Druid - One of the only REALLY useful invites. 10% permanent stat gain can make wild caught pets REALLY good; especially if you get some decent genes.
Traveling Magician - The other of the 2 really useful invites. Fog of War is so pointless and annoying and makes exploring a map take at LEAST twice as long as it should. I expect one they do the energy fix then it wont be so bad because you'll only be exploring twice with each pet so that fixes that.