Drotar said:
I wouldn't quite say that about my teacher. If someone else had taught me, I NEVER would have learned that much in class. Any errors or flaws in my posts should be traced back to me alone.
BTW, did you help grade the AP exams for biology? I just received word that I got a 4, which is good news for me, but not something that's going to impress a scholar of your caliber. Just curious if you helped out with that.
No. My daughter also got a 4, however.
Not again! Equations! Drat!
Well, that looks like some aspect of the Hardy-Weinberg theorum.
It's not Hardy-Weinberg but simply elementary mathematics. Applies to proportions of ANYTHING. For instance, if you get a pizza half cheese and half pepperoni, you have N=2. Since C =1 and P =1, you have C/2 + P/2 = 1.
Hardy-Weinbery LAW is simply an extension of Mendelian genetics. If you have a trait P and p and mate the two, the offspring will be PP, 2Pp, pp witht the ratio of 1:2:1.
Now, if you have a population in which the frequency of allele P is "p" and the frequency of allele p is "q", then Hardy Weinberg says that, in the next generation, IN THE ABSENCE OF ANY OUTSIDE INFLUENCE, that p and q will not change.
Agreed, however you left out a vital assumption. That resources are so limited that animals are literally starving to death- BEFORE the reproductive age.
That's not an assumption, but a simplification.
[/QUOTE] Animals aren't the only ones reproducing. Plants are too. [/QUOTE]
But plants are up against a set if FINITE resources: space, nutrients, sunlight. Plants can't go on expanding their population forever. So there is a finite number of plants for herbivores to eat and therefore a finite number of herbivores for predators to eat.
The food chain, without man's interference, is relatively stable. At the rate which animals consume, the naturally dense forests reproduced to accomodate the life it held.
But that's NOT the amount of animals there COULD be if EVERY individual grew to adulthood. Each salmon, for instance, lays over 10,000 eggs, but of those only 2 survive to come back and reproduce. If all 10,000 salmon from all million salmon lived to reproduce, in one generation that would be 10 BILLION salmon. And the next generation there would be 10 TRILLION salmon and the next generation there would be 10 QUATRILLION salmon, and so on. So most are not surviving to adulthood.
Usually, if you really think about it, you really don't see animals lying on the floor or in trees starving to death.
Drotar, here you are not looking at the examples for what they are there for: to look at your "death rate has to be more than the birth rate for proportions to change" but have shifted the argument to "starving to death". I'll take it as accepted that your argument has been answered.
Fact: I never doubted the possibility for adaptation to function on a relatively small scale, WITHIN a species due to alleles. I did doubt speciation. And even if you DID prove it was possible, you can't prove that THAT was what actually happened. What, are you going to use carbon-dating?
That's the second time you have tried to divert the discussion to carbon dating. Tell you what, read these websites (all the pages) and then we can discuss it if you still have questions:
1.
http://www.c14dating.com/
2.
http://www.howstuffworks.com/carbon-14.htm
3.
http://www.don-lindsay-archive.org/creation/carbon.html
However, we have SEEN speciation happen before our eyes in both the lab and the wild and the fossil record. Also, looking at such things as biogeography, morphology, physiology, embryology, and genetics, the ONLY hypothesis to explain those that has not been falsified is speciation from a common ancestor. Special creation is falsified by data in those fields.
Didn't you just make the claim that atmospheric conditions are extremely unstable? (And I"m not just talking about the climate now- you gotta give me a little credit.)
No. I said climate could change.
That's where we differ. The claim that N is constant. If given time, the population expands. Now here's the issue: Is the difference between the death rates before the reproductive age of L-I GREATER than the expansion rate of the steadily growing population, which is N.
In most situations, N is constant. Documented. Populations do not expand, and they can't. There simply is not enough room on the planet for the population of every species to expand. Darwin calculated that, if left unchecked, in 10,000 years elephants could overrun the planet if the population was left unchecked.
Human populations in the last 300 years or so are an exception because we keep expanding our food source. But even here there are limits. There are finite resources, and the population can't expand forever.
To answer your question, YES! (But N is NOT the expansion rate. That would be N2-N1 were N2 is the number of individuals in generation 2 and N1 = the number of individuals in generation 1). I've given salmon as an example. Try your maple tree in your yard. How many seeds produced each year. How big an expansion of the number of maple trees in your neighborhood?
It's too simple- there are billions of factors in teh enviornment and diseases and genetics and whatever that can alter the results in a HEARTBEAT.
And those factors are all selection pressures, right? Drotar, we are trying to SIMPLIFY natural selection for you. Yes, there are at least hundreds and perhaps more selection pressures on each population. That is immensely complex. So we do what science does in ALL areas: we study situations that are representative of the system but are not as complex. If the hypothesis is right, then we can detect the action of the process -- natural selection in this case -- in the simple system. If natural selection is not operating, then we couldn't detect it in the simple system, could we?
I think it does. If we're still talking about the contribution of old alleles increasing, DESPITE the fact that they have the proper number of toes on each foot (hoof, sorry), then I maintain my old position. Change or not, the extra toe isn't going to be so substantial so as to wipe out group A. Forests, plains, swamp, whatever. It's a stinking toe man.
I have shown that the contribution of the old alleles in the population DECREASES. That is, the the number of individuals with alleles that make a small middle toe DECREASE with time, and the number of individuals with alleles for a larger middle toe INCREASE. Eventually, the alleles for a small toe disappear entirely and the population contains ONLY the alleles for a larger toe.
It doesn't matter that is is just a toe. As long as it gives some advantage in the competition, it will eventually replace the older trait.
Let's give you more equations. Sorry, but that's the way it is.
Remember that, in the absence of any outside influence, such as natural selection, the frequency of an allele does not change from generation to generation. That is, if you have a population and 100 and 10 individuals have allele A and 90 have allele a, the next generation will be exactly the same: 10 A and 90 a. This is called the Hardy-Weinberg Law. Frequencies are symbolized mathematically by p and q. W is the relative fitness value. So we have W(A), W(B), and W(AB). The last is the fitness of the heterozygote in a sexually reproducting population.
So, for the first generation the frequency p of A in the population is: p^2 +2pq + q^2. Straight Mendelian genetics.
The frequency of p in the next generation after selection is: p' = p^2W(A) + pq W(AB)/p^2W(A) + 2pq W(AB) + q^2 (WB).
Now, if W(A) and W(AB) are higher than W(B), it can be seen that p' will increase. Not chance, but pure determinism.
You can see all this and a lot more in Chapters 4 and 13 in Futuyma's Evolutionary Biology, 1999.
Remember Hardy-Weinberg. The frequency of an allele remains unchanged from generation to generation in the absence of outside influence. Therefore, the fitness of a new mutation is defined as the ratio of the number of progeny actually produced divided by the number of progeny expected by Mendelian genetics. This is going to be greater than one in the case of favorable mutations. From that we get a selection coefficient such that fitness = 1 - s.
Now, doing the math we find that the advantageous allele A increases in frequency, per generation, by the amount delta p = (1/2)spq/(1-q).
If you look at the equation, you see that delta p is positive as long as s is greater than 0, even if it is very small. Eventually p will equal 1, which means that every member of the population will have the allele. Thus, a characteristic with even a miniscule advantage will be fixed by natural selection. "Fixed" means every individual will have the allele.
So, as long as a trait is at all, even by the smallest degree, beneficial, then the odds that it will spread to become all the population is 100%.