So, in an alternate universe, Soviet Union never falls, and in 2068 a nuclear war happened. About 32,000 nukes were detonated in American, Soviet, EU, and Chinese cities. WW3 lasted about 5 hours or so, and hit every major American city. Anyway to the point, in post apocalyptic fiction, the wasteland is often filled with many mutant animals. I was skeptical of this, but I wondered if this could really happen. I am trying to make my story as realistic as possible so, my question is would animals mutate, or evolve, after the apocalypse? My question is, in about 20 human generations, would nay animals change or evolve to look different?
Simple answer is no, the hordes of mutant animals after nuclear war is just movie BS, just like the space fighters with wings so they can bank in vacuum.
Now there might be an increased rate of mutations, but most mutations are so detrimental that the creature is unlikely to even survive until birth, let alone to maturity. (It's also hard to distinguish any radiation-caused mutations from ordinary birth defects.)
Animals would continue to evolve, of course, just as they do now, in response to various pressures. Consider for instance how the coyote has evolved and expanded its range into eastern North America in response to the removal of other predators, becoming distinctly different from the western coyote in the process: https://en.wikipedia.org/wiki/Eastern_coyote
There's also the possibility of exotic animals escaping from game farms or private menageries and becoming endemic (as the Burmese python has in Florida), so you might have to deal with tigers and such.
Your best bet will be to give a look at the Chernobyl Zone, the animals and plants at the place have been living in a contaminated zone for many year now.
The result is... anticlimactic. Most mutations are detrimental and some will outright kill the animal before it can be born. You could have a couple of beneficial mutations, but they are rarely as impressive as Hollywood makes them to be.
What you can have is species adapting to fill in new niches, since humans are gone.
Any animals alive during the nuclear war will get a large dose of radiation. The only physical change is that they get blast injuries, acute radiation poisoning and/or cancer and die (just like humans).
Those which survive might encounter genetic damage. But most of these random mutations will be detrimental. You will see a lot of birth defects in the next generation. There will be lots of still-birth and those which survive will often have disabilities which just decrease their odds of survival and procreation.
There is a small chance that a radiation-induced mutation actually happens to be useful for survival. But only one specimen will have that mutation at first. When it is really that useful, then it might pass that mutation on to its offsprings. So it will take several generations until the animal with the unusual gene becomes a common sight in your world.
And radiation-induced mutation aside, the nuclear war will likely change the environment your animals live in a lot. Food becomes more scarce, but so do predators. Nuclear dust might change the climate. Humans don't affect the environment anymore. Resistance to radiation becomes a major survival factor. Some animal species become extinct, leaving ecologic niches for others to occupy. And these are just the most obvious changes.
When the environment changes, so do the evolutionary pressures. So after a few generations you might see some changes in the animal populations as they become more adapted to their changed environment.
tl;dr: If you want to see some interesting new animals, wait at least a few centuries.
Radiation is only one side of the coin.
I agree with most of the answers here. You should not expect in a few years a sudden outburst of "super-beasts" with exceptional properties1 due to the mutation.
That said, a nuclear war and the following climate changes could lead to a mass extinction, leaving lots of ecological niches open for colonization. So:
Radiation would increase mutations. But as explained in other answers, most of the changes will be negative to the individual. And even positive changes may be a dead end if they are too radical2). So, do not expect that after a few years there will appear a sudden outburst of very dangerous beasts just out of mutation.
Changed ecosystems will make some current species unviable while others will thrive. I think that this would be a more important factor than radiation. It will be a very unstable system (apex predators usually have few babies so malformations due to radioactivity would hurt them more, herbivores will thrive until they overeat because they no longer have predators, then some herbivores may complement their diet with some meat from dead animals...)
What I would expect:
Short term: massive death of everything, only a few species survive. Very bad time for predators and mammals, which are very energy-intensive, not so bad for small animals/insects.
Medium term (decades to centuries): plants and herbivores thrive. The overabundance of herbivores leads to defensive strategies for plants (poisonous trees/thorns/etc.) Scavengers also thrive, and some of them develop into carnivores.
Long term (even with radiation, tens or hundreds of thousands of years): Animals increase in size, specially predators.
Also, expect some mechanism to limit the spread of mutations/malformations. If too many of your offspring is unviable, you lose too many resources on them for the species to survive. So with increased mutation levels there is strong pressure to avoid mutations, either by changes at biological level (multiple DNA copies, mutant eggs killed in uterus) or at behavior level (killing or casting away "defective" offspring).
In any case, we already have a pretty good record of what evolution can lead up to, and radiation will not change that much. Current (and past) animals were already under a lot of pressure to be as effective as they could be3, so you can expect the results of evolution (radiation or not) to be in line with it. Maybe you get a vegetarian dog or a venomous rabbit, but you won't get a flying elephant.
1 The issues with some of their variations, like the "scaled up version of a current animal" have been discussed here to death.
2 So your are ten times bigger than the usual male of your species? Well, good look finding a female that will be able to carry on your offspring, if you have internal fecundation. Unless you are so lucky as to find a partner with a similar mutation, you are the last of your new species.
3 Although most of us may be not aware of it due to our capacity as a species to wipe out or keep away anything that could be dangerous to us.
Whether animals would evolve after such an extreme event is not known to science. It's simply something we haven't fully explored. As Aify links, the Chernobyl event lead to a great many mutations, may of which are graphically depicted at Chernobyl guide [Warning: disturbing images]. This site shows a great many people and creatures that are very clearly not fit in the evolutionary sense. But they're not the only creature at Chernobyl. Radiotropic Fungi have cropped up. They literally use melanin, the pigment that makes your skin dark and protects you from UV rays, to soak up gamma radiation and convert it into energy. To this day we are still trying to figure out exactly how the process works.
So we can see examples of both failures of animals due to mutation and success. As a general rule, the more complex the creature, the harder it is to find beneficial mutations. Complex creatures like deer and wolves and people tend to have growth patterns that are designed for very benign living conditions compared to your radioactive paradise. Generally speaking, it doesn't go well for them. Simple creatures have the advantage of being able to make a few million offspring and just see what happens. They also tend to have simpler growth patterns, so they are easier to adapt.
But there is an open question, and for that I turn to evolutionary science. The current understanding of the fossil record suggests evolution operates in a punctuated equilibrium, species remain rather stable until an event causes them to suddenly and dramatically change. This theory is relatively new, being only perhaps fifty years old. Scientists are still debating it, but it suggests that life can indeed evolve at a very very rapid rate, when called upon to do so. Whether a radioactive world is something which can cause such an event is not known, but if there's one thing we should have learned from Ian Malcom, "Nature finds a way."
One of the things you should consider, when thinking about the possibility of animals mutating in case of a WWIII is the timescale. While I see many people here noting Chernobyl and it's effects on the local wildlife, you should note that a meltdown of a nuclear plant is incredibly different from a nuclear bomb explosion. The Chernobyl will be a scar on the planet for the foreseeable millennia, due to most of the radioactive dirt-pile being in place. Nuclear weapons are relatively "clean". As the nuclear material gets separated into smaller chunks, even with the half-life of radiation for the elements staying the same, it will take far less time for most of the material to become harmless.
What you get is those five hours of initial hellfire, couple of days with radioactive fallout contaminating every place it can reach and in a month the survivors will have to battle the lack of food, uncontaminated water and lack of medicine. The chance of nuclear winter is debatable, so it's up to you to decide if you want to include the short-lived radioactive winter.
Most nukes will be targeted at military bases and other strategic locations first, as even in the "doomsday scenario" it makes zero sense to target some remote field in who-knows-where just to kill some animals. As the preferred method to nuke things is airburst (highest area of effect/lowest remaining radiation), most of the damage to outback places will be due to ensuing forest-fires and the like.
The currently-alive generation of living beings might get irradiated, which will most definitely lead to shortening their lifespan and likely negatively influence the next generation, but the most damage in the mid-term will come because radiation weakened the immunity of the organisms, so there will likely be far stronger infection/virulent outbursts than we're used to. Obviously, all of that will lead to massive changes in ecosystems, leading to a mass extinction event and major gaps in ecosystems.
However, where there are gaps, there are also possibilities. The surviving species will have to accommodate to a different world and that will lead to mutations and behavioral changes in two-three decades/century time-span. In twenty human generations the world would look incredibly different and the chances are incredibly high that even in three or four generations the humanity would be back as the dominant species, the big difference being that Australia and Oceania/Africa would likely become the cradle of the new civilizations (as you can't farm off the land, whichever country has an easiest access to food, e.g. fish, has the easiest time to bounce back).
As for the nuke count, 15k isn't that much. If the cold war would go as it went and Soviets with USA decided not to decrease nuke amount since 1960's, what the humanity would have to deal with comes closer to 50k - a count far more likely to wreak havoc in remote places than mere 15k.
The Mutually Assured Destruction isn't scary to the top players(USA, Russia, China etc.) because it would wipe out the entire humanity. It's scary that this war will, regardless of the result, make the ruling faction of any given side a loser, as new key players emerge on the ashes of the old world.
I'll go for a contrarian answer. The answer is "If you want", because it wasn't just a nuclear war. A Chinese general, cut off from his command structure, and knowing they were lost, decided to use a viral bio-weapon, considering it the only chance of saving Chinese citizens. Because they were a homogenous people, the scientists had engineered the virus so it would not affect Chinese.
But they got it wrong.
In the beginning, the virus made sterile all but a fraction of the world's non-Chinese population. Then it mutated, first infecting animals. While it did not seem to affect the animals' ability to reproduce, it did have other effects. Before long it jumped back to humans, and eventually found its first Chinese victim. But now they were not protected.
Now of course some random virus is extremely unlikely to cause meaningful change in animals, much less useful change. But it does give you a way to work around the 500 year time-scale.
You don't even need a nuclear war for this solution as nuclear winter and radiation are pretty rough. You just need an innocent "oops".
This all depends on how "real" this must be.
Just to give a different answer -- yes! But not because of the radiation.
This experiment for example showed that, via only selective breeding, evolution can be quite rapid:
Russian scientists achieved a population of domesticated foxes that are fundamentally different in temperament and behavior from their wild forebears. Some important changes in physiology and morphology became visible, such as mottled or spotted colored fur. Some scientists believe that these changes obtaining from selection for tameness are caused by lower adrenaline production in the new population, causing physiological changes within relatively few generations yielding genetic combinations not present in the original species. This indicates that selection for tameness, e.g. did not flee, produces changes that are related to the emergence of other dog-like traits, e.g. raised tail, coming into heat every six months rather than annually. These seemingly unrelated changes are a result of pleiotropy.[
Note the change in behaviour as well as shape.
So, existing species may change behaviour (dogs, cows, deer become more aggressive -- like aurochs, wild boar, wolves, and so on).
Climate change might also cause cross-breeding (grizzlies mating with polar bears, for example).
And a few hundred years seems to me plenty of time for long-distance migration -- for Siberian tigers to reach Germany, for example.
Yes, they will mutate. After 15,000 nukes on USA only, only bacterias will remain and they mutate already happily. And in the nuclear winter they will have to change to adapt to the low temperatures.
You new generation had forgotten all books about how dangerous the nuclear war really is. Let alone modern politicians.
Animals and plants mutate all the time, at a slow rate. You and everyone else are mutants, since each and everyone of your genes has been mutated as humans evolved. So radioactivity from a nuclear war might cause a slightly higher mutation rate in animal and plant species. Since most mutations are damaging, most mutated animals and plants would die fast and mutations would not accumulate very fast.
So people would notice a lot of plants and animal species going extinct from the effects of the nuclear war, but probably wouldn't notice an increase in mutations despite expecting to see it.
For fast reproducing animals like mice or insects you should see mutations after a few decades as radiation will increase mutation rates in case they survived the radioactive blast and begin to populate the contaminated lands. Slow reproducing animals will take way longer and get cancer in the process. Some kinds of animals will not be able to survive afterwards due to radiation, loss of habitat and food aswell as change in climate. This will cause the ecosystem to change a lot.
Where are the monsters?
Original stories on mutations were written when atomic/nuclear technology was new and there was no data, only fears. Since then we've had most of a century to study effects and to realize that the Earth and Sun have been emitting radiation all along and animals and plants have been dealing with it for billions of years. Species we have today are already, in part, the result of radiation. Natural selection will be the same force after the apocalypse as it has been all along.
Nothing new here but want to emphasize that even writing fiction about false mutation is quite irresponsible. Read Wikipedia on Chernobyl effects.
Studies do say that a meltdown is not equivalent to a bunch of bombs going off; those have much wider spread contamination so immediate effects would be significantly greater while long term effects are less.
But genetic resilience, or plasticity, has proven greater than nuclear radiation effects.
And if it was plausible, mutations over generations adding up to monsters, where are they? There's been bombs and meltdowns wind carried contamination from Japan all the way to Oregon and where are the monsters? Contamination from those and A bomb testing in the Pacific along with nuclear powered ships and who knows how many leaks, later high yield multi warhead testing... and so where are the 3 tailed whales with giant fangs?
I say again it's irresponsible to proliferate such misinformation while the known, documented negative health effects of current energy productions, chemical waste, and "conventional" weapons manufacture and use are contaminating our environment and destroying lives (and those to come) at a terrible rate that all nuclear power and weapons use hasn't come near.
Expanded use of nuclear energy is clearly most likely in the future and by non-fear based studies (and not those of oil company propaganda) much safer. We need to continue research and not encourage misinformation and deliberate bigotry. Authors that continue to do so profit from preying upon reinforcing ignorance.