3 ms·

> So there isn't a "starting point" in nature, only in these models. Exactly, that's my whole point. And your chosen simulation starting point highly influence

by jules 14y ago

> So there isn't a "starting point" in nature, only in these models. Exactly, that's my whole point. And your chosen simulation starting point highly influences the outcome of the simulation. The one you chose happened to give you the prime numbers, but another would give wildly different results. > And, because I model all the predator cycles between 1 and 30 in order to get a single result for one experimental cicada cycle, and because I model 1000 years, I have eliminated the starting point from consideration. Well, no, evidently not, but I don't feel like making this point once again, the posts above explain this sufficiently. > But to make sure we're on the same page, here's my latest algorithm: This algorithm is again unreadable and wrong: a % c == 0 and b % (((c+cr) % b)+1) == 0. Why is this doing a % c, i.e. the cicada cycle modulo the simulation year?? It SHOULD be doing it the other way around: the simulation year modulo the cicada cycle. Meaningful variable names help! The fix is simple: the expression should be c % a == 0 and (c+cr) % b == 0. (also already described in my previous post) > This version arbitrarily adds a random number 0 <= cr <= 99 to the starting year of the predator on each test That's the right idea (though wrong implementation -- see above).

lutusp 14y ago
> And your chosen simulation starting point highly influences the outcome of the simulation. Yes, it does. The effect I am describing is real, and I simply haven't thought it through in detail until now. 1. The starting point for my simulation has both the cicadas and the predators hatching out simultaneously, in year zero. This obviously happens in nature as well as in my simulation (but only rarely). 2. Given that starting condition, what is the likelihood that the predator, with a range of reproduction cycles, will succeed in synchronizing with the cicadas again, or (the best of all worlds) over and over in perpetuity? 3. The answer is that, if the cicadas adopt a prime-numbered reproduction cycle, the predators are handicapped by the fact that a typical prime number has fewer divisors than a composite number, and divisors are required for synchronization: http://en.wikipedia.org/wiki/Table_of_divisors http://en.wikipedia.org/wiki/Table_of_divisors 4. For cases in which the predators and the cicadas are out of synchronization, the outcome for a random difference in years is neutral -- not advantageous, not disadvantageous. I've shown this by adding a loop to my program that tests against a range of differences in years between cicadas and predators. When I do this, the difference between a prime and a composite nearly vanishes ("nearly" because the advantage of a prime numbered cycle is still present, but is almost completely buried by the much greater number of years where there's no advantage). 5. It is only when cicadas and predators hatch out in synchrony (for any one of a number of reasons) does this prime-number effect have any effect on the outcome. 6. In terms of natural selection, this leaves the prime-number effect, plus an initial synchronization between cicada and predator, as the only selection advantage, for which the prime-number effect works against the predators. 7. Nature, and natural selection, does something my simulation doesn't -- over time, by rewarding reproductive fitness, it amplifies the effect of small advantages, in some cases turning a chance, small fitness advantage into the entire population of a species in the future. 8. I could obviously write a more complex simulation that imitates natural selection, one in which a small advantage is eventually turned into a new species, but because of the complexity of such a simulation and the amount of tuning required, I don't think this would represent anything but confirmation bias. My simulation greatly exaggerates the advantage conferred by a prime number, and it assumes something that's almost never true in nature -- that cicadas and predators hatch out in synchrony at the outset. But that set of circumstances does represent a small fitness advantage, and it probably explains the two primary reproduction cycles of the cicada species my paper describes (i.e. 13 and 17 years).
- jules 14y ago
  Yes, I certainly did not disagree that the effect is real. But at the same time the effect shown by the simulation is due to an artifact of the simulation. Consider the two possible groups of predators with cycle 2: year 0123456789 ... predator1 X X X X X X ... predator2 X X X X X X ... In your simulation, you are only taking into account predator1, i.e. the predator that hatches at even years. You are not taking into account predator2, the one that hatches at odd years. This artificially punishes cicada that have cycles that are multiples of 2. Your argument is essentially that if you had a cicada with an even cycle length, then it would get eaten by predator 1. But one could equally validly say that an even cycle length is an advantage because predator 2 will never be able to eat it. For example the cicada cycle 4: year 0123456789 ... predator1 X X X X X X ... predator2 X X X X X X ... cicada X X X X This cicada gets eaten by predator1 but not by predator2. So by assuming that all predators with cycle length 2 are of type 1 you are artificially punishing cicada with cycle 4. If you do the simulation with equal amounts of predator1 and predator2 you would not see any difference between prime and non prime cicada. Now, it could still be that prime numbers have an evolutionary advantage; this kind of simulation is just insufficient to show it. For example I could think of a reason that has to do with natural selection of the predators. Because predators that are in exact dis-synchrony with the cicada have less food, they are less successful. So over time predators of type 1 will increase, and predators of type 2 will decrease. So predators naturally start to synchronize with cicada. That's why prime years are better for cicada, because there are fewer predator types that can synchronize with that. But the synchronization should be an emergent property of the simulation, you can't a priori assume that predators that share a prime factor are always synchronized with the cicada as you have done here. That's the theory, but in practice I can think of any number of reasons why in practice even this is a very flawed model. The primary reason why cicada all hatch together is because then the predators cannot catch them all because there are simply too many cicada. So if at one point in history the cicada had a cycle of 6 years, then they will not adapt to a cycle of 7 years through evolution. Because the lone cicada that evolves to hatch every 7 years will easily be eaten. This strategy only works when a bunch of them do it together. So it is very possible that 7 years is just a historical accident.
  - 14y ago
deleted 14y ago
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by jules 14y ago

lutusp 14y ago

> And your chosen simulation starting point highly influences the outcome of the simulation. Yes, it does. The effect I am describing is real, and I simply haven't thought it through in detail until now. 1. The starting point for my simulation has both the cicadas and the predators hatching out simultaneously, in year zero. This obviously happens in nature as well as in my simulation (but only rarely). 2. Given that starting condition, what is the likelihood that the predator, with a range of reproduction cycles, will succeed in synchronizing with the cicadas again, or (the best of all worlds) over and over in perpetuity? 3. The answer is that, if the cicadas adopt a prime-numbered reproduction cycle, the predators are handicapped by the fact that a typical prime number has fewer divisors than a composite number, and divisors are required for synchronization: http://en.wikipedia.org/wiki/Table_of_divisors http://en.wikipedia.org/wiki/Table_of_divisors 4. For cases in which the predators and the cicadas are out of synchronization, the outcome for a random difference in years is neutral -- not advantageous, not disadvantageous. I've shown this by adding a loop to my program that tests against a range of differences in years between cicadas and predators. When I do this, the difference between a prime and a composite nearly vanishes ("nearly" because the advantage of a prime numbered cycle is still present, but is almost completely buried by the much greater number of years where there's no advantage). 5. It is only when cicadas and predators hatch out in synchrony (for any one of a number of reasons) does this prime-number effect have any effect on the outcome. 6. In terms of natural selection, this leaves the prime-number effect, plus an initial synchronization between cicada and predator, as the only selection advantage, for which the prime-number effect works against the predators. 7. Nature, and natural selection, does something my simulation doesn't -- over time, by rewarding reproductive fitness, it amplifies the effect of small advantages, in some cases turning a chance, small fitness advantage into the entire population of a species in the future. 8. I could obviously write a more complex simulation that imitates natural selection, one in which a small advantage is eventually turned into a new species, but because of the complexity of such a simulation and the amount of tuning required, I don't think this would represent anything but confirmation bias. My simulation greatly exaggerates the advantage conferred by a prime number, and it assumes something that's almost never true in nature -- that cicadas and predators hatch out in synchrony at the outset. But that set of circumstances does represent a small fitness advantage, and it probably explains the two primary reproduction cycles of the cicada species my paper describes (i.e. 13 and 17 years).

jules 14y ago
Yes, I certainly did not disagree that the effect is real. But at the same time the effect shown by the simulation is due to an artifact of the simulation. Consider the two possible groups of predators with cycle 2: year 0123456789 ... predator1 X X X X X X ... predator2 X X X X X X ... In your simulation, you are only taking into account predator1, i.e. the predator that hatches at even years. You are not taking into account predator2, the one that hatches at odd years. This artificially punishes cicada that have cycles that are multiples of 2. Your argument is essentially that if you had a cicada with an even cycle length, then it would get eaten by predator 1. But one could equally validly say that an even cycle length is an advantage because predator 2 will never be able to eat it. For example the cicada cycle 4: year 0123456789 ... predator1 X X X X X X ... predator2 X X X X X X ... cicada X X X X This cicada gets eaten by predator1 but not by predator2. So by assuming that all predators with cycle length 2 are of type 1 you are artificially punishing cicada with cycle 4. If you do the simulation with equal amounts of predator1 and predator2 you would not see any difference between prime and non prime cicada. Now, it could still be that prime numbers have an evolutionary advantage; this kind of simulation is just insufficient to show it. For example I could think of a reason that has to do with natural selection of the predators. Because predators that are in exact dis-synchrony with the cicada have less food, they are less successful. So over time predators of type 1 will increase, and predators of type 2 will decrease. So predators naturally start to synchronize with cicada. That's why prime years are better for cicada, because there are fewer predator types that can synchronize with that. But the synchronization should be an emergent property of the simulation, you can't a priori assume that predators that share a prime factor are always synchronized with the cicada as you have done here. That's the theory, but in practice I can think of any number of reasons why in practice even this is a very flawed model. The primary reason why cicada all hatch together is because then the predators cannot catch them all because there are simply too many cicada. So if at one point in history the cicada had a cycle of 6 years, then they will not adapt to a cycle of 7 years through evolution. Because the lone cicada that evolves to hatch every 7 years will easily be eaten. This strategy only works when a bunch of them do it together. So it is very possible that 7 years is just a historical accident.
- 14y ago

deleted 14y ago

[deleted]