Is there math behind that?

# Gauger and Mercer: Bifunctional Proteins and Protein Sequence Space

**T_aquaticus**#206

If you take any specific winner the chances of them winning with their winning ticket was 1 in 292 million. Therefore, according to the logic you are using, we would need hundreds of millions of drawings before we should have seen that person win. Since they won with relatively few attempts, does this mean the lottery was intelligently designed so that they would win? Can random drawings allow someone to win against such odds?

**Dan_Eastwood**(Dan Eastwood) #207

I intend to take a mathematical look at that in a new topic. I have limited time tho, so it won’t appear right away.

**Agauger**(Ann Gauger) #208

@T_aquaticus your lottery example is a good one but you missed something. The calculation is called the waiting times problem and it’s not trivial. Lotteries have varying amounts of money they are worth, depending on how long it’s been since the last win. The pot can be big or small or very big or not much more than the minimum. It’s a fallacy to say that because one bloke won early the average wait to a win is short. When the wait depends on multiple independent events it can be very long.

**T_aquaticus**#209

The lottery does depend on multiple independent events. Each number on the ticket is an independent event. You have to get 5 or 6 independent events in order to win.

The point is that the all of the average wait times to win FOR THE WINNERS is extremely short compared to the odds of winning. This is balanced out by the wait times of all the losers. The problem with your evolutionary models is that you don’t know how many losers there are. You don’t know how many possible beneficial mutations there are that didn’t win. [added in edit:] Heck, we don’t even know how many beneficial mutations there are in the human genome when we compare it to the chimp genome.

If we took one human genome, could we figure out how many substitutions would result in a beneficial change that also depended on a previous neutral mutation? No. We have no idea how many possible winners there are in a genome. Therefore, we can’t make any claims as to the improbability of there being a winner. It is really that simple.

**Agauger**(Ann Gauger) #210

Of course I agree that we don’t know how many cases there are where one or two neutral mutations combine epistatically to make a beneficial mutation in a protein, let alone a genome. That hasn’t stopped mathematicians from having a go at it. They build models and test different scenarios. It’s up to geneticists and molecular biologists to estimate the realism of the scenarios.

**Mercer**(John Mercer) #211

For diploids, I don’t see why. If a population is large enough, even a recessive lethal allele can’t be eliminated by selection. Why can’t such alleles random walk indefinitely?

**Agauger**(Ann Gauger) #212

Being diploid makes a difference, you are right. But the right alleles eventually have to co-occur.

**swamidass**(S. Joshua Swamidass) closed #213

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