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The world is covered is mana, the life force that flows through all things. In certain places, this mana is saturated to high levels. This affects the animals living in those areas, who absorb the high concentrations. Over many, many generations, these animals mutate away from their parent species, giving rise to unnatural creatures that are larger and more powerful. Ex: snakes evolve into hydras, lizards become great wymms, horses become unicorns, etc. Their changes get passed down to their offspring, and may continue to evolve in surprising ways.

The high concentration of mana in their genes have a number of various effects that give them advantages over other members of their parent species. Although they are not sapient like humans, they are more intelligent than average creatures. This makes them more efficient predators or prey animals.

Given how evolution works, these creatures would eventually out compete their cousins and drive them to extinction. This would eventually lead to the world being dominated by magical beasts, eliminating all other kinds of "regular" animals.

I want these places of highly concentrated mana to be rare but can occur anywhere, allowing these super charged creatures to interact with their less evolved brethren. At the same time, I don't want regular animals to be made extinct. How can I make this happen?

Make the super animals depend on mana to live, and move the mana around. As it passes through any given area it moves slowly enough that the animals change, but fast enough that the super animals don't have time to eradicate the normal animals.

This will cause the super animals to either migrate permanently to follow the mana (assuming they can adapt to new biomes), or die out. It's no problem if the supers die out because more will arise when mana passes through the same area again.

One way to move mana around is to make it depend on some pseudoscientific thing like astrology, so the ley lines are defined by where the projected paths of the planets on the surface of the Earth get closest. Maybe the mana spots cycle through the Earth's chackras (seriously, google it up, I couldn't come up with that on my own), but with the addition that the chackras move. Or maybe they form where mana flares from the sun strike the surface, because mana flares are invisible and not deflected by the planet's magnetic field.

Or, who knows? The gods do play dice with the universe. The world is a grid and mana spots are random events.

Hydras would not compete with snakes

Most snakes eat rodents, or other small animals. Even large constrictors don't generally eat adult-human-sized prey. Assuming that hydras would be interested in human-sized or larger prey, they are no longer in competition with their mundane snake forebears. The same holds true for lizards (often eating bugs) and great wyrms.

Now, the hydras and great wyrms might threaten to wipe out your horses, but that's another question.

Horses and unicorns could coexist, the same way elk and moose, or elephants and zebras, etc, coexist. As long as you've got a rich and varied ecosystem.

If it takes multiple generations for the mutations to take hold and change the animals into a new species, the local ecosystems have time to adjust. As others have pointed out, a new species can certainly change the prey/predator balance and result in problems in obtaining food or other resources, but it isn't necessarily the new species that came from one animal competing with (and winning over) that animal.

Intelligent animals can also work to increase available food, which helps other species as well. Behaviors that do this can come from evolution itself (like how ants can herd aphids) or can be from increased intelligence (primitive agriculture or creating habitats for food animals). Depending on how intelligent these new species are. You can build this skill into your evolutions if you choose.

Any animal that doesn't have enough food, water, or safe places to create and raise their young will migrate. If the new species are happy staying put, their cousins will find better pastures, as it were.

Even if one species reduces in population due to changes from the new species, there will be other communities elsewhere. So they won't go extinct.

Competition: The majority of evolutionary competition affecting predators is between the predator and its prey, not between competing predators. For example, there is an evolutionary pressure on cheetahs to run faster in order to catch their prey and a similar pressure on the prey to run faster in order to escape. A super-cheetah may find it easier to catch prey but won't compete directly with a standard cheetah so long as they don't deplete the prey animal too much. So both cheetah and super-cheetah could coexist in a similar manner to how two different predators with different hunting efficiencies often do exist in the same region.

As an alternative, perhaps super-predators naturally hunt super herbivores as they are larger (and tastier?). So normal prey animals are left for the normal predators.

Intelligence: If the super predators are smarter, they may voluntarily limit their populations to avoid killing all their normal prey - therefore there will be prey left over for normals (even if the normals find it a little harder to get a feed).

Fecundity: As an alternative, the mana might mess with ability to reproduce - or greatly increase time to reach maturity - in that case the supers population would always be small enough that they wouldn't compete for resources.

Competitive animals: There are some species that naturally compete amongst themselves, for mating privileges, leadership etc. Presumably supers would breed amongst themselves so there wouldn't be direct conflict with normals. Similarly, a super wont see a normal as a fitting opponent so wont bother fighting them for leadership - as a lion wouldn't bother fighting a cat.

In practice though, you might lose some normal species regardless of what rules you enforce. A super lion might find a normal elephant a better meal than an antelope or zebra, and they will be much easier to catch as elephants have not evolved with any defense from an extra-powerful predator. Consequences like that are the usual outcome when you add any new species to an ecosystem, and the supers are effectively equivalent to new species even in their normal environment.

Have the mana "settle" in isolated locations such as an inaccessible valley or island. Something which genetic exchange is either difficult or impossible.The species in this valley would then evolve isolated from the rest of its cousin species.