True, but was my point clear about this thought experiment?
Yes. If you consider natural selection over a long time period then it could be described as random. Just as the earth's climate could be described as random. However, because over the time period organisms adapt to their environment the selection criteria (such as the climate) are pretty stable, "random" is misleading. Sure, some DNA from one generation to the next will be lost due to trees falling on heads, tornadoes and lucky preditors, but this is just noise on top of the general trend that dominates. If this noise was bigger than the general selection criteria then there could be no adaptation by organisms.
I was trying to put forward my view that the selection is truely random, and the precice course of evolution is truely random (probabilistic) and not pseudorandom, unlike the excel random number generator, for example...
Many individuals that would otherwise breed are just unlucky, due to random events. This affects the selection, starting from which sperm actually fertilises the egg in the first place.
Add in random behaviour of predators, then acts of Zeus, and one can only make short-term predictions about the course of evolution of any particular species descendants, other than to say it is highly likely that most will not reproduce sucessful offspring.
For the purpose of this thread are you considering meteorites, and volcanoes as random, or pseudorandom, or something else?
That's a hard question to answer. If there are rules that every particle in the universe has to obey then nothing is truly random. I prefer to think of random as a word to express qualatively the amount of ignorance an observer has about a process or the inputs to the process.
E.g., someone getting lung cancer is random. Someone who smokes 30-a-day getting lung cancer is less random to an informed observer than a non-smoker getting lung cancer.
Meteorites and volcanoes could be considered random. The effect of a large meteorite strike or volcanic eruption would be a step-change in the selection criteria. Either side of this step change the selection criteria would be pretty stable or simple functions over time. If there was insufficient variance in a particular population to cope with the new environment, that population would die out.
"That will not model the trend in evolution, which tends to reduce variance."
Speciation?
The sum total distributions of the genomes of every organism would show multiple distributions, (could one treat each DNA letter as part of a base4 number?- I am more than a bit unsure of this). Two separate sepcies would show different means and standard deviations.... arrgh. I hope that you can follow this as I am thinking after typing, but not deleting...
True this would be less than if every mutation survived and reproduces, which would be truely disordered.
Jim
Isn’t an environment with species less random than one with ponds full of goo?
A random process that reduces variance is best modeled as a random process that reduces variances.
If each year, we pick, deterministicly, one person who died childless, and somehow recover their genome (assuming we had some technology to do so) and pass it on, we would increase the variance in the population through a determistic method.
If I have the set of N random numbers (listed in order): 1, 2, 4, 4, 7, 8, 9 so N = 7. The mean and standard deviation are 5 and 3.055 respectively.
If I add a number to the set, say 7, the mean and standard deviation are 5.25 and 2.915. I.e. the standard deviation goes down, not up. If I repeatedly add the number 7, the standard deviation tends to zero and the mean to 7. So you’re statement is wrong.
If each year we selected one person in the population to die, using a random number generator to do so, we would reduce the variance in the population through a random method.
If I have the set of N random numbers (listed in order): 1, 2, 4, 4, 7, 8, 9 so N = 7. The mean and standard deviation are 5 and 3.055 respectively.
If I delete one of the numbers from the set, say 7, the mean and standard deviation are 4.667 and 3.204. I.e. the standard deviation goes up, not down. So you’re statement is wrong.
Increased variance should not be confused with random, and reduced variance should not be confused with non-random. You can't equate one with the other.
Walt
I don’t. What I think is that a distribution with a narrower variance is
less random than one with a wider variance.
Useful selection functions are stable or simple functions over time, with less variance than the population being chosen from. Randomness in the selection function limits how well adapted an organism can be. I.e. it puts a lower limit on the variance of the population selected for the next round.
NB: All values were calculated using Microsoft Excel average() and stdev() functions.