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on unofficial and SP you can get high as you want.
The breed creatures inherit base stats of their parents (and those stats make up their level after tame, like 40 points in health, 31 in melee, etc.). Theoretically, you could have dinos with baselevel of 180 with all 180 points in one stat (needless to say that this is highly, highly improbable). If you'd breed those together, and the offspring inherits the correct stats, you have a higher level.
Example: For simplicity, lets say there are only two stats, melee and HP. Female with 31 HP and 40 Melee (Base level 71), and Male with 37 HP and 26 Melee (Base level 63) breed. The offspring randomly inherits their stats, so it could be 31 HP 26 Melee (Base level 57) or even 37 HP 40 Melee (Base level 77). To see how many points they actually have in each stat, you either need to calculate, or use a mod like super spyglass.
That's very interesting info, but I'm not sure if that answers my question if levels are limitless through breeding? Haha
You can breed past the maximum level one can achieve by taming, yes. Up to the level of having highests stat for each of the attributes that the parents have.
edit: Eminence explained it better/clearer so I'm just gonna edit this out, read below for more details :)
On official (or unofficial 'max difficulty') IE Max wild level of 150 you can theoretically get a level 1,640 I believe.
Level 150 + 75 (100% Taming effectiveness) = max level after tame of 225.
That's 224 points (level 1 does not have a point associated with it) distributed randomly by wild levels (the only ones transferrable to a baby during breeding)
There are a total of 7 stats
Health
Stamina
Oxygen
Food
Weight melee
Movement speed
Thus if you have 7 tames with all 224 points in one stat (there is a 1 in 2.00429186235E189 PER STAT. Assuming that each stat is given an equal chance to increase on every level) and you were to breed them until you got all seven of those stats on one Dino (7*224=1568) add in its one starting level (1569) and the seventy one level ups available after being born brings it to a Max level of 1,640.
I'm not sure if stat mutations add levels or not, if they do than this number would be a little higher, but never unlimited.
Dino level is based on stats spent, so in theory you could get an animal with enough stats up to around 450, at that point you can no longer use the cloning chamber to clear out the mutations needed to boost the stats beyond any sample you can find in the wild.
So, via the cloning chamber, 450 ish is max, baring of course really high extra difficulty settings.
It's quite a bit more complicated than I make it sound, but to my knowledge on an official server 450 is theoretical max-ish.
They do. But the steps are small (1-4 levels per mutation I believe) and you can get max 20 mutations per parent
^This is the correct answer.
https://ark.gamepedia.com/Breeding#Level_of_the_Offspring
I believe some time back they actually announced that 450 was a hard level cap. Meaning no matter what you can never get beyond that on official.