On evolution statistics [closed]

Question

This basic evolution theory question has been haunting me since childhood and I'm kind of embarrassed that I can't explain it yet:

Consider a butterfly. It's wings have evolved to look like the eyes of an owl, so to prevent it's predators who are themselves preys of the owl to attack it.

From what I've learned (and feel free to indulge me in the very basics if I get this wrong), natural selection suggests that the butterflies that didn't have the owl's eyes in their wings would be eaten, leaving the ones with the eyes to survive, right?

But that implies that this useful trait appeared in the butterfly's wings by chance. Now, I know trillions of butterflies have been born before this, but trying to figure out the possibility of this to happen by chance doesn't look like it's plausible. Let's go through the things that have to work right before this trait is passed over:

1. For a butterfly to be born in a different wing colour, it should be a genetic mutation which doesn't happen this often, for what I know.

2. The wings are composed of micro-scales. For every scale to compose an image so similar that confuses even us, the margin of error is very slim. It could be anything. It could be a picture of Tom Selleck for all we know. The scales must be in the correct spectrum of colour by a small margin of error. So that is already a very unlikely thing to happen.

3. Then, this butterfly cannot be eaten out of bad luck (mind you, the wings don't guarantee it will not be eaten, just enlarge her chances).

4. It has to mate, which also is not a guarantee to happen, since nature deals with competition. If this butterfly we are considering is a male, the female must find the wings hot, instead of being afraid of those creepy eyes.

5. The genes of this mutations must also be dominant, so when it mates and generates offspring, at least part of the new butterflies inherit this trait.

And this is a simple example. There are animals that evolved so smartly I can't even start to think of the possibilities.

My question is, more precisely, how likely is it for a species to evolve into complex solutions?

Answer 1

Remi.b's answer is great, but here's something less technical if that's what you're looking for:

1. Genetic mutations happen ALL THE TIME. Every time a cell divides, there is an error rate of about one per billion. That's a very low error rate per division, but when you multiply it by the number of divisions, times the number of cells, times the number of individuals, times the number of years the species has existed... well, that's a lot of mutations. Mind you, way fewer mutations will get passed along to offspring, because the vast majority of mutations are non-advantageous (because there a lot more ways to make a bad butterfly than a good one). But that's the job of selection, not mutation.

2. Evolution is a step-by-step process. There doesn't just have to be mutation and advantage, there has to be an advantage every step of the way. If big circles were selected for, that means intermediate forms (smaller circles, perhaps?) were selected for too. A blob that sort of looks like Tom Selleck will not confer as many fitness advantages as a blob that looks a lot like Tom Selleck (assuming the butterflies' predators hate Magnum P.I., which as far as I'm concerned is a perfectly reasonable assumption ;-)

3. Lots of butterflies get eaten by bad luck. But it's unlikely any trait was the result of one mutation in one individual (although it does happen sometimes). There are lots of mutations happening, and if one individual doesn't pass it along, another will. Think of this: maybe 100,000,000 years ago some butterfly developed a mutation that would be ten times more effective at discouraging predators than the owl-eye circles ... but then it got stepped on by a dinosaur. You'd never know it happened, and you're left eons later wondering how a way less impressive mutation happened.

4. There's natural selection, and there's sexual selection. Maybe the females don't like the owl-eye wings so those butterflies mate half as often as their more attractive brethren. But if the resulting offspring is four times more likely to survive, that ugly butterfly just won the gene pool lottery.

5. That's a common misconception, traits don't have to be dominant in order to be selected for. Think of this: lactose intolerance is dominant, but in many populations lactose intolerant people are in the minority, because after the domestication of the cow being lactose intolerant was enough of a disadvantage to make those people less likely to have offspring.

One of the concepts people most often lack when dealing with evolution is of scale. You're looking at a tiny, tiny, tiny fraction of all the mutations that could have possibly happened and thinking, "What are the odds that that happened, it seems so improbable!" But that's because you're not seeing the trillions and trillions and trillions of mutations that could have happened if random chance had taken things in an ever so slightly different direction. SOMETHING had to happen, it's the laws of physics. You're only able to see and be amazed by what did happen... well, because it's the thing that ended up happening. The more you think about it, the easier it is to wrap your mind around.

Answer 2

In your 5 points you basically cover several concepts of evolutionary biology.

1) The number of mutations depend on mutation rate. The mutation rate varies along genome sequences, species and individuals. According to the recent DECODE study (Kong et al., 2012) a human mother transmit on average 15 mutations to her offspring and a human father transmit on average $25 + 2(g-20)$ mutations to his offsprings, where $g$ is the age of the father and where the formula stands only for father older than 20 years old.

2) Mutations happen by chance and are not directed toward creating some specific feature. But it is much more likely to create a round of color on the wings of a butterfly than creating the picture of Tom Sellek. The reason has to do with the developmental and biochemical pathways linking the given mutation to its phenotypic effect. Looking at a given mutation, you can understand how it yield to the modification of some phenotypic trait by looking at the biochemical and devlopmental pathways.

3,4) The third point that you raise is called "genetic drift". Shortly speaking the concept of genetic drift may be called the good luck/bad luck effects. Stating differently genetic drift is the random sampling of alleles (gene variant) from a population. If some alleles are favored over some others at a given locus, then sampling is not 100% random but is not either 100% deterministic. The only case where genetic drift is absent is in infinite population (which is obviously an unrealistic case). Genetic drift is inversely propotional to population size and you'll understand it better by reading this post.

5) When the mutation is at very low frequency, the mutation needs to be dominant in order to be expressed, this is true. But an allele may increase in frequency due to genetic drift up to the point that some individuals are homozygous for this allele and therefore express the trait. Dominance and recessivity are just extreme case of a continuum and most often alleles have intermediate level of dominance. Pleiotropy is also something to consider. Note also thaat the frequency of the three possible genotypes $AA$, $AB$ and $BB$ are given by Hardy-Weinberg law (under some assumptions) $x^2$, $2x(1-x)$ and $(1-x)^2$ respectively, where $x$ is the frequency of the allele $A$.

Hope that helps!