Sorry, this is going to be long. But come "end-game" and once people start to reach these major genes in large numbers I do see it being an issue

Lets be honest, some species have inherently better genes than others to breed for. They have an advantage over the other species, especially in battle and defeating bosses, when selectively bred.

Some examples of what I mean:
- Unicorns and pumas have no genes that, by themselves, do nothing. The roc and cockatrice have two genes that do nothing alone, and the dragon has three.
- The cockatrice has two genes which have a 50% chance to inflict a status effect which reduces health by 50% a turn, the dragon has one gene that has a 20% chance of causing a status effect that reduces health by 50% a turn and requires two other dominant genes to work.
- Cockatrice and unicorns have a gene that enables them to dodge 75% of attacks, taking no damage. Dragons have a gene that enables them to ignore damage on 30% of attacks.
- Additionally, the two dodge masters are also the only two pets who regenerate health.
- Berserk and Second Breath are a powerful abilities... if the battle lasts long enough they can come into play. In reality most of the PVP battles I've fought are over in no more than four turns. The only battles that run long are "regeneration" or "dodge" battles, both against cockatrice and unicorns which can also avoid many attacks. Strength and extra hits mean nothing if the opponent can dodge every attack and possibly heal while they are at it.

This means the best battlers, once people have bred for genes in certain combinations, will always be unicorns and cockatrice. Probably cockatrice if I'm honest, high dodge ability, regeneration, and high damage.
Rocs may do alright but are gimped a bit by do-nothing genes early on and relying on shared genes to avoid attacks and increase their HP.
Pumas are fairly middling, if silent pace bypasses their opponents' dodge bonus they are viable battlers and can possibly made "1 hit wonders" or able to deal an insane number of crits with the right genes.
Gryphons are fairly dull, they don't have as good of genes as a bird or cat (since they seem to pull their genes from roc and puma genes.) They have no unique genes and no combinations of genes that really stand out.
Dragons are pretty gimped in the long run; needing three different sets of dominant genes to get their most powerful attack that is still weaker than attacks that require one or two genes. Some of their other specials are dependent on long battles.

So, now that I've explained my reasoning, how about a suggestion?
Alter some gene's effects to help even the odds. This focuses more on increasing genetic potential rather than nerfing the OP species. I rather like that we can breed for ridiculously OP combinations of genes, I just feel all species should be able to have some fun.

Unicorns are cockatrice are fine. They don't need buffing, seriously.

Dragon:
Fire Gland/Spitting Muscle - Add a 30% chance of burning the opponent for 20% damage for 1-4 turns
Berserker - 75% chance to trigger and also boosts courage to increase attack damage (lets be honest, things in a blind rage tend to be pretty brave.)
Napalm Gland - Works without fire breathing and set opponents on fire with any bite attack. Still a 20% chance, still for 50%, stacks with fire breathing's bonus.
Boiling Blood - Up to 75% chance to trigger, stacks with berserk but not itself.

Why I think this is more balanced: This brings their damage dealing more on par with cockatrice at a base level, and able to surpass it if berserk and boiling blood activate. However they have no special increase to dodging or regeneration beyond their scales, the strategy would be to take them down fast before they wreck you or not be hit at all. Keep in mind they would be a "bite focused" species so even with the high damaging bite attacks with status effects they could be effectively countered if you have reason to believe they are spamming bite.

Gryphon:
Berserker -  Same as dragon's.
Second Breath - Replace it with a gene unique to them. "Battle Born," it would be similar to the unicorn's determination, but also makes them immune to the effects of stench and fragrance, removing the dodge bonus.

Why I think this is balanced: Their ability to deal damage or dodge isn't greater than any other species, but their resolve means they will land blows more often. They may be "average" blows, but they won't be missing turns or failing to connect as much.

Puma:
Silent Pace - I've not bred a puma with a dominant silent pace gene, so it may already do this, I dunno. But if the puma is the attacker their first attack should always connect. (in addition to being a critical.)
Second Breath - Increase to 30% so it has more of a chance to come into play.

Why I think this is balanced: Their genes seem normal until you notice that you can breed a puma with a very high crit chance. Add in lionheart and some of the shared genes like steel muscles they could hit extremely hard with every attack. With second breath, they can hit more often. They don't have any unique dodge or damage reducing abilities however and would very much be glass cannons. But if a puma gets the first strike, it may not need the second.

Roc:
Steel Beak/Electric Gland - Raise the damage increase to 65%
Electric Gland - Add a 20% to stun the opponent if hit with a physical attack. Stunned pets miss the next turn and cannot dodge.

Why I think It's Balanced: Sure lightning strike may not add a status effect like fire breath or acid strike... it just is the hardest hitting base attack in the game. Still, since it's a bite attack you can predict it's use if it's spammed in PVP and retaliate or resist it with another gene.
...Except the high damage of spurs and their rush-bonuses also make them potentially the most rounded out species for ruining your day. They can be left with a random attack pattern and still be deadly.
They have no special dodge or regeneration, so cannot recover from damage, but the ability to stun gives them a chance to retaliate against pets with high dodge. The downside is the roc must take damage to even have a chance of stunning their opponent, and stunned pets still regenerate/resist.

Or maybe cockatrice and Unicorn can just be heavily nerfed, but that seems boring. I'd rather make the rest of the species more awesome than two species less. >_>;

*"Special" genes can mean either "adds a bonus" or "unique to that species."

Ankokou, you're proposing a lot of big changes with no way to test them quickly... Some stepping stone is needed first. Maybe a minigame with no rewards, where you set genes and strategies for two fake pets and self-battle many times over to get results. 

On the topic of balance:

First of all, I mainly breed Rocs so my view is biased. However, I've always felt that they are really, really underpowered. All the other species get access to increased dodge, dragons get robust scales which is almost the same result. Dodge is great, because its virtually a free countermove. Cockatrices and unicorns have regeneration, which is only countered by high crit. Rocs, in exchange, get a huge stun chance which isn't shared by the other races, but only with Music beak and Massive wings, which ties up their beak and paw slots. This makes it so that to take advantage of the high stun, you already sacrifice lightning strike and counterstrike possibilities.  

Lightning strike is nice, but its not any better than fire strike or acid strike.  Also, both dragons and cockatrices get alternative organ choices in the case that they don't want to build elemental damage (Boiling blood, Regeneration). Rocs don't. We have Normal organs or electric gland... If you don't want lightning strike, that slot is wasted. None of the other species has a slot that is empty like this.

What also sucks as a Roc is that no matter how you build, you just can't break through countermove, unless you built counterstrike - but then you just gave up Massive wings and spurs, which are the Roc highlights, and you get no dodge increase. Adding to the fact that all the damage genes only target one of the moves, its really easy to choose countermoves for Rocs.

From experience, battling with good Rocs is like tossing a coin for everything. It's possible to beat level +5 pretty easily, it's also possible to lose level -5 due to countermove, countermove, countermove...

On the other hand, my counterstrike-focused and regeneration pets win more often around their level, and die more often level +3 to +5.

Hey, I'd be fine with testing it first. In fact every change should be carefully tested.
I can already tell you just based on the genes people have reached now there are major discrepancies in how well certain species do in PVP. If some changes are made, not all my ideas have to be used either.
Just balance is easily broken in PVP, it's as simple as that. It will only get more broken as time goes on and should probably be addressed before the game is released. (Meaning, not beta anymore.)

Fighting wild mobs is pretty easy in my experience and I don't care how OP anything is in what is basically a "single player" deal. The bosses are tough but random. My best "mob killer" is a gryphon with steel muscles and stats raised to slightly less than a GP1 pet. It's the PVP and trying to increase the empathsis on battle that is the issue.
(Also counterstrike isn't too good alone, but pretty nasty when paired with gracefulness or stench/fragrance. A unicorn with both grace and fragrance will almost always get two attacks if it stacks.)

The major weakness to roc's stun based PVP right now is it's entirely dependent on one attack, rush. If you are fighting a roc with those abilities you can usually assume the owner has biased the chance of using them and counter. In my own testing, I've not had a roc shriek/stun when the opponent dodged or used the countermove. Could be bad luck, but that's one of the reasons I want a stun chance when damaged, to make up for rocs lacking any special dodge or resist gene.
(And why a testing feature would be nice.)

As it stands right now, a regeneration + stench/fragrance pets are virtually impossible to beat, doubly so if you are defending, except maybe with a higher-damage regeneration/stench fragrance pet.
Which is why cockatrice will likely be the best, if they can land an attack their status effect poison will counter the regeneration and do extra damage while they try to land another blow.
The only possible way to counter this combo is if pumas with silent pace always hit with their first attack. A puma with that, an attack damage boost, lionheart, and steel muscles may have the strength to 1-shot most everything. (Unless it's a dragon with robust scales that resists that damage.) Again, testing would be great. :)

I agree that some species are a little bit weak but honestly I don't see anyone breeding a "perfect" pet any time soon. That and even bad pets with genetic power levels can beat pets with great genes but low stats -- so genes aren't everything.

If any changes are made, I feel like they HAVE to be made when the game pregresses to a point where there can be an adequate definition of the metagame. Anything prior to that will simply be conjecture.

If we could maybe have some sort of "testing" ground to see how balanced abilities are, then yeah. But I do feel like every gene has an adequate counter from some angle.

Regen pets are still 1-shot by critters. Critters are countered by damage blockers and dodgers. Dodgers can't be regeners even if they're only hit 1/10th of the time. Elemental users are countered by resistance and hard countered by mirror users. Everything in the game can be beaten by something, ya know?

Overall I feel like certain combos are lacking. Like, napalm strike is insanely hard to breed for, takes 3 slots, and does what cockatrices can do with ONE gene. But dragons also have some other really good moves.

So while each pet doesn't play every role equally, every pet has viable battle roles that give them definite strengths and weaknesses and I feel like making any change at this point would be jumping the gun.

TLDR; Don't support any changes but the game should be watched and once the metagame starts to form it should be balanced if/when neccessary.

And now, I need to just make this one point because your OP was deceptive and I'm not sure if you're just misinformed or what.

"- Cockatrice and unicorns have a gene that enables them to dodge 75% of attacks, taking no damage. Dragons have a gene that enables them to ignore damage on 30% of attacks."

This is wrong. The dodge simply increases their dodge chance (if any) by 75%, It's not a flat 75% chance to dodge. Dragons on the other hand have a FLAT 30% CHANCE to take ZERO DAMAGE. That's insane by itself. The dodge on the other hand is only great if you REALLY stack dodge (capping at 50% anyways). There was some confusion about this in another post but it got straightened out. In other words, if your opponent gives you a negative chance to dodge then that 75% increase amounts to nothing. The 30% ignore damage cannot be mitigated by anything, on the other hand.

So I've decided that I ought to go ahead and give this post a full rundown on my thoughts, so I'm going to break each suggestion down into sections and tell how I think it can be improved or changed to be more balanced or fair. 

- Unicorns and pumas have no genes that, by themselves, do nothing.

I feel like this is a fair point but not in the fact that all abilities that require 2 genes should be buffed to compensate. I just think maybe unicorns and pumas should be given 2-gene abilites other than quickmind/agile paws = counter. Admittedly I think also that maybe all genes that are part of 2-gene abilities should have solo effects just so they are never "useless".

- The cockatrice has two genes which have a 50% chance to inflict a status effect which reduces health by 50% a turn, the dragon has one gene that has a 20% chance of causing a status effect that reduces health by 50% a turn and requires two other dominant genes to work.

I agree here that  the 3-gene requirement for napalm is a lame requirement and is probably the most under-powered gene in the game because of it. Also, cockatrices have 3 genes which give them poison and they encompass all 3 of their attacks as well as being hit (you forgot the skin one).

- Cockatrice and unicorns have a gene that enables them to dodge 75% of attacks, taking no damage.

I already pointed out in a different post about how it's a 75% increase of their actual dodge ability (based on their stats vs opponent's hit) which means this is a lot less powerful if you don't specialize in dodge. EG if you have 4% chance to dodge (that'd be a 8 stat difference between your dodge and their hit) then 75% increase would only make it 7% chance to dodge. Also capped at 50% chance to dodge, although that IS a lot.

Dragons have a gene that enables them to ignore damage on 30% of attacks.

One of their best abilities. May be too powerful. Should probably be lowered to 20% like most other "the opponent did nothing" abilities like magic horn and musical larynx.

- Additionally, the two dodge masters are also the only two pets who regenerate health.

The only thing about this is both regen pets and dodgers can still be 1-shot by a heavy crit. Also regen just recently got nerfed down to 15% so it shouldn't be over-powered anymore.

- Berserk and Second Breath are a powerful abilities... if the battle lasts long enough they can come into play. In reality most of the PVP battles I've fought are over in no more than four turns. The only battles that run long are "regeneration" or "dodge" battles, both against cockatrice and unicorns which can also avoid many attacks. Strength and extra hits mean nothing if the opponent can dodge every attack and possibly heal while they are at it.

Again, you're making the same point about dodge and regen being over-powered but I've seen a rage pet 2-shot regen pets before. I've also never encountered a dodger that I couldn't beat with a pet with decent hitrate.

As for berserk and boiling blood, I don't really feel like either are over-powered or under-powered. I do feel like berseker and boiling blood should be on equal ground. Why is one cumulative and the other not?

This means the best battlers, once people have bred for genes in certain combinations, will always be unicorns and cockatrice. Probably cockatrice if I'm honest, high dodge ability, regeneration, and high damage.

This does seem like a somewhat generalized statement. As I've said before, a crit puma can 1-shot any other pet with a high enough attack and if their first attack lands. I've 1-shot so many pets with my silent pace puma that it's not even funny how powerful crit is when it connects.

Rocs may do alright but are gimped a bit by do-nothing genes early on and relying on shared genes to avoid attacks and increase their HP.

I agree that rocs are pretty underwhelming overall but I feel like they have a lot of un-tapped potential. They do seem to be one of the rarest breed on the site. Admittedly their massive wings ability is a 30% chance for the opponent to miss the turn AS WELL as the Musical Beak is a 40% chance for the opponent to miss the turn. Both abilities are stacked on RUSH which means you have a potential turn-deny pet. Admittedly I don't have enough rocs to really assess their turn battle potential but I feel like you're under-valuing them. I do agree they should probably give them some more unique abilities or something and maybe make it so that steel beak/electric gland give bonuses by themselves

Pumas are fairly middling, if silent pace bypasses their opponents' dodge bonus they are viable battlers and can possibly made "1 hit wonders" or able to deal an insane number of crits with the right genes.

I have a silent pace puma and they are already 1-hit-wonders. They can be very effective crit-mongers and easily sweep dodgers and regeners with 1 well-timed blow.

Gryphons are fairly dull, they don't have as good of genes as a bird or cat (since they seem to pull their genes from roc and puma genes.) They have no unique genes and no combinations of genes that really stand out.

Gryphons do seem a little middling but I don't think they are under or over powered. I feel like their combination between roc and puma genes gives them some good advantages and the ability to specialize in any stat/attack/tactic is what makes them unpredictable in battle. Other breeds only have one or two things they can really be good at but gryphons can be good at anything. IE Jack of all trades.

Dragons are pretty gimped in the long run; needing three different sets of dominant genes to get their most powerful attack that is still weaker than attacks that require one or two genes. Some of their other specials are dependent on long battles.

I don't think dragons are really that gimped. Robust scales is a very powerful ability and they have potential to be the best tanks in the game. I do think that their 3-gene napalm gland needs to be made independant so that it works by itself. Then I wouldn't really have any complaints. Fearsome look + robust scales would mean approximately 60% of the time the opponent is either letting you hit them or doing no damage to you. Then if you were tanky enough, any time they did hit you and do damage would just be ice cubes at the north pole, so to speak.

So, now that I've explained my reasoning, how about a suggestion?
Alter some gene's effects to help even the odds. This focuses more on increasing genetic potential rather than nerfing the OP species. I rather like that we can breed for ridiculously OP combinations of genes, I just feel all species should be able to have some fun.

Unicorns are cockatrice are fine. They don't need buffing, seriously.

Probably fair enough.

Dragon:
Fire Gland/Spitting Muscle - Add a 30% chance of burning the opponent for 20% damage for 1-4 turns

20% damage seems like, lower than cockatrice's poison but better than it currently is... Although I feel like all of the elemental 2-gene combos are at a distinct disadvantage. To compensate I suggest that all of the 2-gene combos have 1 gene that at least gives a stat boost or ability by itself.

Berserker - 75% chance to trigger and also boosts courage to increase attack damage (lets be honest, things in a blind rage tend to be pretty brave.)

With berserker being ancient now this is sort of moot.

Napalm Gland - Works without fire breathing and set opponents on fire with any bite attack. Still a 20% chance, still for 50%, stacks with fire breathing's bonus.

I support this suggestion because really that's only on-par with cockatrice's poison.

Boiling Blood - Up to 75% chance to trigger, stacks with berserk but not itself.

This has changed now. I think 50% chance to trigger is fine but it should stack with itself just like berseker does.

Why I think this is more balanced: This brings their damage dealing more on par with cockatrice at a base level, and able to surpass it if berserk and boiling blood activate. However they have no special increase to dodging or regeneration beyond their scales, the strategy would be to take them down fast before they wreck you or not be hit at all. Keep in mind they would be a "bite focused" species so even with the high damaging bite attacks with status effects they could be effectively countered if you have reason to believe they are spamming bite.

Their ability to be countered by rush-users is apparent. Although as I've said, fearsome look + robust scales is very powerful combo.

Gryphon:
Berserker -  Same as dragon's.

Isn't it already better, now? It does stack with itself according to the gene list.

Second Breath - Replace it with a gene unique to them. "Battle Born," it would be similar to the unicorn's determination, but also makes them immune to the effects of stench and fragrance, removing the dodge bonus.

I happen to like second breath. I've actually won a good deal of battles with it. I don't disagree that giving them some more unique genes wouldn't be too bad but I don't really feel like they NEED a buff.

Why I think this is balanced: Their ability to deal damage or dodge isn't greater than any other species, but their resolve means they will land blows more often. They may be "average" blows, but they won't be missing turns or failing to connect as much.

I don't feel like giving them an ability that makes them able to hit dodgers no matter what is really balanced because they'd hardly have to specialize then. It'd be a no-brainer because it'd just be 1 gene that'd nullify the usefulness of a number of other genes and make dodge-pets never want to face them at all.

I think instead it'd be interesting if they had an ability that made them not able to be ability countered. IE If they chose bite and you chose rush, they would still hit you. You could dodge the hit, or nullify the hit or whatever, but you can't hard-counter them. This would mean they hit more regardless of what move you used and would give them an interesting ability. I think this would be fair because they are swift, agile, flying creatures so they do have superior maneuverability. It'd be like a counter move that didn't rely on dodges.

Puma:
Silent Pace - I've not bred a puma with a dominant silent pace gene, so it may already do this, I dunno. But if the puma is the attacker their first attack should always connect. (in addition to being a critical.)

Silent pace doesn't need buffed. It's already a really good ability and can 1-shot lots of enemies.

Second Breath - Increase to 30% so it has more of a chance to come into play.

Second breath is also really powerful already. A free turn to attack an enemy can often be the difference between winning and losing, especially considered there is no counter for extra-turn abilities.

Why I think this is balanced: Their genes seem normal until you notice that you can breed a puma with a very high crit chance. Add in lionheart and some of the shared genes like steel muscles they could hit extremely hard with every attack. With second breath, they can hit more often. They don't have any unique dodge or damage reducing abilities however and would very much be glass cannons. But if a puma gets the first strike, it may not need the second.

Again, I don't feel like these abilities need a buff. I do think they could use some de-specialization though. I think it'd be cool if they had a "stalker" ability. How it'd work is every time they missed their opponent or were unable to act or whatever, their hitrate and damage would go up. Kind of like a wild beast stalking their prey, the longer the chase went on, the more powerful they would become. This would make them a very good counter against dodgers because then if they missed 5 times but hit the 6th time, it'd almost always be the killing blow.

Not only would this be a really interesting ability but it would also REALLY fit the whole image of Pumas.

Roc:
Steel Beak/Electric Gland - Raise the damage increase to 65%
Electric Gland - Add a 20% to stun the opponent if hit with a physical attack. Stunned pets miss the next turn and cannot dodge.

I don't think the damage should be raised but I do like the stun idea. Electricity does paralyze people, right?

Why I think It's Balanced: Sure lightning strike may not add a status effect like fire breath or acid strike... it just is the hardest hitting base attack in the game. Still, since it's a bite attack you can predict it's use if it's spammed in PVP and retaliate or resist it with another gene. 
...Except the high damage of spurs and their rush-bonuses also make them potentially the most rounded out species for ruining your day. They can be left with a random attack pattern and still be deadly.
They have no special dodge or regeneration, so cannot recover from damage, but the ability to stun gives them a chance to retaliate against pets with high dodge. The downside is the roc must take damage to even have a chance of stunning their opponent, and stunned pets still regenerate/resist.

 I still feel like you're under-valuing Rocs overall. Their insane turn-deny ability with Musical Beak + Massive Wings is a crazy combo. Add in Sharp Feathers for 45% damage boost (45% damage boost from ONE GENE! Seriously that's only 5% less than the breath-ability 2-gene combos!) and wow, rush is just crazy. Completely lock up an enemy while doing great damage? Yes please.

Or maybe cockatrice and Unicorn can just be heavily nerfed, but that seems boring. I'd rather make the rest of the species more awesome than two species less. >_>;

Yeah they just nerfed regen down to 15% so I feel like no more nerfs. I don't want all abilities to be watered down to the point where whoever has the higher genetic power will win because genetic power already can make a bad pet with no abilities beat a good pet with great genes.

*"Special" genes can mean either "adds a bonus" or "unique to that species."

So that was pretty much it. Overall I still feel like any sort of adjustments should be made slowly and evaluated thoroughly before any other changes. I really don't want to see them make 10 changes at once and completely throw the balance of the game out of whack. Just like bug-testing a program, you should only ever change 1 thing at a time, see if that fixes the problem, and if it doesn't then change something else.

Long story short, the more time it takes to adjust and balance the abilities, the more data we will have to evaluate any future changes.