You asserted this, but I do not believe this is true:
1. Your code so far has bugs that I pointed out that you did not address.
2. My corrected version shows no advantage as you'd intuitively expect.
> It's not an assumption, it addresses the fact that cicadas and predators sometimes do hatch out in synchrony.
You can't assume that because something sometimes happens it always happens. You need to take all possibilities into account evenly.
Anyway, I do not think that further discussion is useful. I have explained my point enough times that repeating it one more time is not going to cause you to see what I mean...so I'm out of this discussion for now.
I updated the code. This was not something I remembered to mention, since it didn't change the results for the zero synchrony case -- but it certainly proved your point that a difference in starting year wiped out the advantage, something I then discussed at length.
The current code (the old links should still work for this same version):
https://www.dropbox.com/s/7m8hq9yzcu5nztx/prime_reproduction...
The result:
3 = 1963 **************************************************************
4 = 1730 *******************************************************
5 = 1169 *************************************
6 = 1373 *******************************************
7 = 831 **************************
8 = 983 *******************************
9 = 799 *************************
10 = 814 **************************
11 = 499 ***************
12 = 842 **************************
13 = 424 *************
14 = 584 ******************
15 = 563 ******************
16 = 529 ****************
17 = 302 *********
18 = 553 *****************
19 = 273 ********
20 = 495 ***************
21 = 400 ************
22 = 353 ***********
23 = 227 *******
Not so for the case my simulation models, and other assumptions produce no advantage or disadvantage (they're neutral).
> You can't assume that because something sometimes happens it always happens.
We already covered this. My simulation doesn't make that assumption, it shows the advantage that is present when that happens, however rare that might be.
> You need to take all possibilities into account evenly.
I did. That was the point of my last post. The synchronous hatch-out produces an advantage, no other circumstance does. Therefore the overall advantage is equal to the synchronous advantage multiplied by its probability. This doesn't take into account the fact that natural selection can amplify small fitness advantages, it only describes its genesis -- no feedback effects are considered.
> I have explained my point enough times that repeating it one more time is not going to cause you to see what I mean
I do see what you mean, as I explained at length in my last post. The effect being described is a factor that may explain the two cicada reproduction cycles seen in nature, as my article points out.
I'm not sure if you're saying here that now that you've been made aware of the problem you're just going to say that it's intentional, and that you're introducing this arbitrary assumption because that's what your simulation is supposed to investigate. If that's the case then fine, but the results of your simulation are still meaningless. The reason the prime numbers come out is still a purely synthetic artifact.
I can understand that you're bummed that your article is misleading and don't want to admit it. Just let the article be. I'm probably the first and the last person to ever notice that it's wrong. Has been very effective for psychologists ;-)
Best wishes!
1. No, not even years necessarily, but any scenario in which cicadas and predators hatch out in synchrony, regardless of the numbering of the years (as long as both cicadas and predators have the same year number applied).
2. Did you miss that I tried adding one more loop that tested all the relationships between cicadas and predators WRT year differential, and that shows only a tiny advantage for prime-numbered years? The size of the effect being discussed only works if predators and cicadas hatch out in synchrony, so my having set both to zero ends up emphasizing this specific case to a perhaps absurd degree. If it weren't for the fact that natural selection tends to amplify small fitness advantages, this relatively small effect might not be be worth discussing.
> The primary reason why cicada all hatch together is because then the predators cannot catch them all because there are simply too many cicada.
Yes, true, but this doesn't address the timing of the synchronous hatch-out. Why 13 and 17 years, and no other cycles in nature? My paper only addresses the timing of the hatch-out, not the fact of it.
> you can't a priori assume that predators that share a prime factor are always synchronized with the cicada as you have done here.
But I don't do that. My simulation addresses the case in which cicadas and predators hatch out in synchrony (advantage goes to the cicada), versus times when they don't (no advantage or disadvantage). It's not an assumption, it addresses the fact that cicadas and predators sometimes do hatch out in synchrony. There is no "always" assumption at work, only that, when there is a synchronous hatch-out, this works to the advantage of prime-numbered reproduction cycles. Other year relationships between cicadas and predators show no advantage or disadvantage.
It's true that my simulation greatly exaggerates the effect, since such a synchronous hatch-out is rare in nature. But I already discussed why designing as full-on natural selection simulation would probably produce nothing more than an exhibition of confirmation bias.
The effect being discussed is real, it is much smaller than my simulation would lead one to believe, but natural selection often amplifies small differences in fitness.