I have been doing a little bit of debating in the YEC community recently, and one of the people that I have taken on is Donny B from SFT.

I am also scheduling a follow-up debate with Donny, and it is in respect of that which I am seeking assistance.

Donny is fond of the analogy of a classroom, where even if one eliminates half of the students, if the students keep getting dumber every year, then eventually the whole class is going to fail.

We know that this is not the case, but I am thinking about an example with simple math that can show him how this is wrong.

I know that the math in the below example is not being done âcorrectlyâ in that I am not *doing* it, but what I do not know is whether the shortcuts that I am doing get close enough to the right answer to serve the purposes that I am trying to use it for.

If they arenât, would anybody like to help me massage this example so that it is valid, and or give me some pointers on the easiest way to do these calculations? I have watched a number of videos from Zach Hancock, and so I understand how to do the calculations by hand, but that is going to take a long time, and I do not know how to program a model to do them for me.

At any rate, here is the analogy:

*Donny, I have thought about how to tweak your classroom analogy to help explain to you whatâs going on. Iâm going to use fairly big, fairly round numbers for this example so that we can do the math in our heads, but weâll talk about what happens when you play with the values at the end.*

*I want you to imagine that there is a class at a very prestigious school, and it has 10 000 students. The students have different abilities to get different test scores on a scale from 1 to 100, and lets assume the class average is 55%, and that everybody below 50% fails the class. Thatâs our purifying selection.*

*For the sake of simplicity, lets just assume that the distribution of test scores for these students is a standard quintile distribution. So 20% of students score between 30% and 40%, 20% score between 40% and 50%, 20% score between 50% and 60%, 20% score between 60% and 70%, and 20% score between 70% and 80%.*

*They all take the test, and 40% of them fail. (thatâs our purifying event) They do not get to graduate. The others do.*

*Now this school has a strange rule. If you graduate, you get to pick a friend to attend the school the next year. If there are extra seats left in the class, then you can pick again, in order of your test scores until we have 10,000 students again for the next year. (that represents our relative fitness because the fittest individuals have the most offspring, up to the ecological carrying capacity of the environment)*

*Lets use the same Quintile distribution to determine how smart the friends each kid picks are. So each kid has 5 friends, one is 10% smarter than the kid, 1 is the same, one is 10% dumber, one is 20% dumber, and one is 30% dumber. (If the kid gets to pick twice, she chooses from a new set of 5 friends the second time)*

*So on average, each studentâs friends are 10% dumber than they are, and, as an average, the whole class is 10% dumber each year, and that represents our deleterious mutations,*

- so you would think the class is slowly going to get dumber over time, until eventually they all fail out, right?*

*But thatâs not what happens. *

*In the first year, everyone takes the test, and 40% fail. Then the class is going to choose their replacements to fill the class for the next year, but before they do, whatâs the class average? It was 55% before the test, but you have eliminated the bottom 40% of test takers, so the distribution now is 33% 50-60, 33% 60-70, 33% 70-80, so now the class average of those who get to pick a friend is actually 65%.*

*Then, everybody gets 10% dumber, bringing the class average down to 55%, right? Not so fast. We have to get back up to 10,000 students, so the top 2 quintiles get to pick again. Now the class average of the students making choices, per choice, looks like this: *

*20% 50-60, 40% 60-70, 40% 70-80. So the average of all the choosers is now about 70%. *

*Then the class gets 10% dumber, as we pick the crop of new students.*

*So 10% 40-50, 20% 50-60, 40% 60-70, 30% 70-80*

*The class average is now 60%.*

*This time, 10% are going to fail, *

*The top 10% are going to get to pick twice to fill the class, and the numbers are going to look about the same again, and they will stay that way, forever IN THIS EXAMPLE, using simplified quintiles.*

*If you want to get more complicated, and use precise mathematics, and model this, then the individual studentsâ scores are going to move around a little more inside their quintiles, and the point at which it stabilizes might be a bit lower, as we may need to have more kids picking more than one friend, but this gives you an idea of how this works and why it happens.*

*If you use different numbers, you are going to get different rates of change, and different balance points, and if you choose some numbers that are big enough or small enough for different values, of course you can hit a limit where class average is almost 100% all the time, or everybody fails out super fast, but in general, this is the pattern you would expect to see for most reasonable numbers.*

*And itâs the pattern that we DO see in nature.*

Thanks in advance for the help scientists!

Oh, also, in the original debate, I think that I did a fairly good job of beating Donny over the head with the fact that genetic entropy is going to be impossible for the simple reason that even if a deleterious mutation is individually unselectable, if they reach a point epistatically where they are going to have a selection effect, then the last piece of the puzzle is going to have an s coefficient that is sufficiently large to be âseenâ by evolution, if the population is large enough.

I would love any feedback the community cares to give about my performance