Field of Science

Selection is random

ResearchBlogging.orgWhen is the effect of a mutation neutral?

A mutation (by this I mean any change to the genotype/genome of an organism) is neutral when it does not change the fitness of the organism. This can happen in different ways:

1) A mutation (SNP) that changes one nucleotide in the protein coding sequence, but does not change the amino acid. These are known as synonymous substitutions, and (mostly*) do not affect fitness.
2) When the mutation does not change fitness, just because the genomic change makes no difference for how well the cell/organism functions.
3) ... (See comments?)

Case number two can happen when the selection coefficient, s=w'/w-1, is zero (w is fitness before the mutation, w' is the fitness after). In this case the two organisms have equal fitness. However, if s is really small, then it will also not matter. The question is then how small s needs to be before the mutation will be neutral, and the answer is that it depends on the population size, N.

So why does neutrality of a mutation depend on the value of s compared to the population size? Because selection is random! Yes, I realize many will object to putting it like this. It goes against what "we" all learn, namely that mutations are random, but that selection weeds out the bad ones and promotes the good ones. Selection is indeed directional in this way, but it is also random.

The reason that selection is random is that fitness is not a value that determines with certainty who gets to reproduce. Fitness is a probability that describes the chance of reproducing. If two organisms have fitness 1.0 and 0.80, then the first has a 25% higher chance of reproducing than the second one does. And in a simulation, the way that is (properly, but not always) determined, is by selecting at random between these two organisms, but with a probability proportional to their fitness. This can for example be done by use of the acceptance-rejection method: choose any one organism at random (all equally probable), and then generate another random number between zero and the maximum fitness in the whole population. If this random number is less than the fitness of the chosen organism, then that organisms gets to reproduce. If not, reject this organism. Repeat the algorithm until you have selected as many organisms as you need (to reach carrying capacity, for example).

As you can see, done this way, selection is random, but - crucially - the probability distribution is not uniform (unless all organisms have the same fitness, in which case evolution of this population is completely neutral).

Now, in an infinitely large population any change in fitness, however small, can be "detected" by selection. If a mutation causes any change in fitness, it will make a difference for the evolution of an infinitely large population. But, in a finite population (slightly more realistic, and much easier to simulated when using agent-based** simulations), s might be too small for selection to detect the difference. The exact threshold depends on the mode of reproduction, but as a general rule (and for asexuals), if the selection coefficient is less than one over the population size, s<1/N, then the mutation is effectively neutral, and the mutation will drift in the population, either eventually going to fixation, or, more likely, disappear.

For example, if the population size is N=100, then mutations of effect s=0.001 are neutral.

A new paper in Evolution, Genome Structure and the Benefit of Sex, describes an evolutionary simulation that suggests that the benefit of sex is that recombination can change large blocks of the genome. The idea is a very well-known one, namely that because epistasis causes the fitness landscape to be rugged, i.e. having multiple peaks separated by valleys that must be crossed to reach a higher peak, point-mutations that change just one nucleotide (SNPs) may not do the trick. If crossing the valley causes a fitness decrease too detrimental, then the chance that the other higher peak is eventually located is too low. But, with recombination, larger parts of the genome can be reorganized in one fell swoop, and with some luck, one organism may find itself on another peak.

All very trivial, and easy to show with simulation, actually. One quibble I have is about a result stated in the caption of figure 2 of that paper. Here's what it says:

The highlighted portion says that (in a population of N=10,000 individuals) organisms with fitness one millionth higher than 1.02 goes to fixation much faster than the others. In other words, in a population of N=105, an organism with a mutation that increases its fitness by only 10-6 has a huge fitness advantage. And that just can't be true. It should be effectively neutral, the difference in fitness undetectable by selection.

Kick me if I can understand what's going on. My best guess is that this is an error, even though I checked with the authors, and they tell me it's not a typo, at least. Got another suggestion, dear reader? (Kudos for making it this far.)

* It actually can. Every codon has a specific tRNA that attaches to that codon, and if this tRNA is less abundant in the cell, then the new variant of the protein might be translated at a lower rate, which might affect the organism.

** Agent-based simulations retains information about each individual in the population, whereas infinitely large populations can only, and easily, be treated mathematically.

Watson, R., Weinreich, D., & Wakeley, J. (2011). GENOME STRUCTURE AND THE BENEFIT OF SEX Evolution, 65 (2), 523-536 DOI: 10.1111/j.1558-5646.2010.01144.x

Game theory applied to footballers

According to game theory, players (of any kind) should cheat when the benefits of doing so outweigh the costs. This theory has been applied for great effect in evolutionary biology (and many other fields), and results seem to explain how such strategies evolve.

I like (association*) football as much as the next guy (when the net guy isn't your local European fanatic), and play it myself, too. In fact, I got seriously injured yesterday when playing indoor. At least, seriously enough that i won't be playing for at least a week. But, I am hugely annoyed by professional footballers faking fouls. For those of you geeks who don't know what I'm talking about: Rather than actually fighting for the ball until they lose it, players will take a dive on purpose in the hopes of fooling the referee into awarding them a free kick. Everyone knows this, as it is blatantly obvious when watching the dives on TV. But it is apparently worth it, because they keep doing it.

As a side note, I don't personally understand why they think it's worth it. Imagine a footballer turned grampa having to explain his youtube savvy grandkids why he couldn't play it honestly like a decent person. No my choice of grandparenthood conversation.

At the annual SICB meeting**, three researchers from Australia presented results from a study of diving behavior in 60 games in six national leagues: Diving in soccer: When does it pay to be dishonest?

Dives were classified as legitimate, slightly deceptive (the player was touched by the opponent but exaggerated the consequences), or highly deceptive.

Science reports the results:
As game theory predicts, legitimate falls far outnumber fake falls, Wilson reported at the meeting. Only 6% of the 2800 falls were highly deceptive dives. Players were two to three times as likely to dive when close to the goal, where the payoff was huge: Statistics show that there is an 80% chance of scoring from penalty kicks. Almost none of the highly deceptive dives resulted in free kicks against the diver. And referees were most likely to reward dives that occurred close to the goals—perhaps because the players were farther away and the deception harder to detect, he noted.
"Only" 6%? That's till too many aged footballers who should not be giving wise advice to kids. And what about the slightly deceptive? Truth is, I can laugh about the blatant dives, but it annoys me to no end when a player with the ball (or as he is losing it) fails to normally jump over the legs of an opponent, but deliberately keeps his foot close to the ground until it hits the opponent, and then utterly fails to regain balance (and is subsequently awarded a free kick). I suspect the percentage of these "slightly" deceptive dives is significantly higher than 6%.

* Thus "soccer" (you better believe it).

** Society for Integrative and Comparative Biology, 2011 Meeting, Salt Lake City, UT, January 3-7, 2011.

Tenacious DNA

Just a quick promotion of this great little movie about our (life's) truly tenacious ability to survive (so far).

There'll be errors, but such is life. Errors are at the core or who we are, and why we are still here. Embrace, all.

Bad atheist billboard, you

Boy, the recent billboard put up by the American Atheists have gotten a huge amount a really bad criticism.

Massimo Pigliucci hates the message and the tone.
PZ Myers hates the design and thinks the message doesn't work.
Jerry Coyne thinks it's ugly and probably no very effective (but mainly has a problem with Pigliucci, as usual).
Rebecca Watson... hyperbole and cursing is always fun. And truthy.

Bill O'Reilly just hates atheists. (At least he admits that he's "not the smartest guy in town.")

My own thoughts are that the billboard probably works, and in the end that's all that matters. Yes, it could surely be better designed, and yes, the words could perhaps have been more carefully chosen. But at the end of the day, there are two considerations that most commentators ignore, but that I think must be taken into account. First off, and as Dave Silverman emphasizes, whether this billboard works is a matter of evidence. And it apparently does. People are coming out:
The good news is I do have facts. I have the fact that our membership is up 20% since November. I have the fact that we’ve seen a surge in purchases and donations. I have a nearly sold-out regional convention – in Alabama. I have more new members in the local Alabama group than they’ve gotten in the past 9 months combined. I have literally hundreds of emails to American Atheists from people who our message has reached, from all over the world, who truly appreciate our efforts. So, quite frankly, the assertion that we are “driving people into the closet” is simply an assumption Massimo uses to support his conclusion that the strategy is faulty. That’s not factual. We are succeeding quite well.
Silverman has more on the evidence in that post. And as he says in the interview, he wouldn't be on O'Reilly if it wasn't for the billboard, would he?

And that's the other consideration, namely that pretty much all that matters at this point in time is to let everyone know that we are atheists, and we are here. There are still people who don't really believe that we don't believe in their gods, and that it's not because we haven't read the Bible, or that we hate God. Religion is a scam, and the more people who know that we are many who think so, the more people will join us, because there are atheists in religious communities, sitting around in church every Sunday just because that's what one does.

Not anymore.

P.S. If you're wondering about the dearth of posts here lately, there are two reasons. Maybe three. I'm frightfully busy, working on 5+ different projects. I have recently experienced the feeling that myself and other bloggers are spinning our wheels, walking in each other's footsteps, wanking too much (figuratively speaking). But definitely also to finally have the opportunity to use the word 'dearth'.

Carnival of Evolution #31 at your service

Just click here.

Michael Barton is hosting this month, and there is a plethora of posts. Not least are several posts on NASAs arsenic-based life form flop, and a bunch on the Devosonians Devonians Devonans Desinovas Denosovans Denisovans.