[_ Old Earth _] A new start [Topic:Evolution]

[keebs]

I didn't mean to use the laughter as a personal attack, it was meant to show that I had been searching the internet for quantum algebra for about an hour after you had left your post, and I could not find anything. Then you turn up and reverberate the abstract of a paper I read nearly 6 months ago, I couldn't help but laugh...and what fun is laughter if you're only going to share it with yourself? As for you question on mutation, what else would you like to know? There is, quite literally, textbooks worth of information...

 

[Blazin Bones]

If you could provide any reliable source for this "quantum algebra", it would be helpful. As for your question on the probability of a beneficial mutation, around every 1 in 1000 mutations are beneficial. But, couple that with all of the mutations and our 6 billion population, add in the 50% chance of the mutation being passed down, and you have a fairly reasonable chance of the mutation being transmitted througout the population given enough generations.

Thank you for the explaination. I apologize for my conclusion, but I noted in the topic, a Formal Debate, that a disscusion on evolution had broken down to insults. An insulting enviroment is not a place where I would like to learn. On your statement involving mutation, if all this were true, each generation would need some method to sustain the mutation. That means, unless the mutation can be sustained on a wide scale basis, the mutation's population would decrease exponentually with each following generation. Then you must start from the original population of the mutating organism in question. When you start from there, the chance of a mutation surviving is not reasonable at all. Then you must add the possibility of having all of these mutations happening at the same time and then they still must meet the similar mutation while they are alive. This makes your possibility as close to zero as me becoming the president of the United States, exactly on my thirty-fifth birthday.

 

[keebs]

That means, unless the mutation can be sustained on a wide scale basis, the mutation's population would decrease exponentually with each following generation. Then you must start from the original population of the mutating organism in question.

One of the mechanisms of evolution is genetic drift. Genetic drift says that as we go through the generations, the allele frequency of an allele tends to either 1 or 0. Of course, this does not simultaneously happen, but it does happen (an example of genetic drift is the human mitochondria). Let's say that a man has a dominant allele mutation, and he produces two kids that that have an allele aA, where A is the dominant mutation. Now, suppose that he has three kids, and his three kids each have three kids...and so on...you can then work out the expected number of people in the population with his mutation (assuming it is neutral, a beneficial mutation would have a higher expectation, and the converse is true for a bad mutation) is (1.5)^x. That is an exponential increase, and if you are considering a small, closed (no migration) population, then the percent of people with this mutation with quickly converge to 1.

 

[Blazin Bones]

That means, unless the mutation can be sustained on a wide scale basis, the mutation's population would decrease exponentually with each following generation. Then you must start from the original population of the mutating organism in question.

One of the mechanisms of evolution is genetic drift. Genetic drift says that as we go through the generations, the allele frequency of an allele tends to either 1 or 0. Of course, this does not simultaneously happen, but it does happen (an example of genetic drift is the human mitochondria). Let's say that a man has a dominant allele mutation, and he produces two kids that that have an allele aA, where A is the dominant mutation. Now, suppose that he has three kids, and his three kids each have three kids...and so on...you can then work out the expected number of people in the population with his mutation (assuming it is neutral, a beneficial mutation would have a higher expectation, and the converse is true for a bad mutation) is (1.5)^x. That is an exponential increase, and if you are considering a small, closed (no migration) population, then the percent of people with this mutation with quickly converge to 1.

First, how is everyone today? I hope you are all well.

I believe that it is fair to suggest that, generally, genetic shift points to zero, for many of the same reasons in my last post. Even so, I will continue on your example. You have the man who has an aA allele frequency. First, unless he can find a mate with that same frequency(which the possibilities are exceedingly small), the chances of producing a "shifted" offspring is 1/4. Thus making the possibility of two "shifted" offspring, 1/8. Then, if both offspring contained the shifted gene, the possibility of both offspring producing three "shifted" children is 1/256, which is possible but not extremely likely.

 

[ThinkerMan]

I hope keebs doesn't mind me taking a stab at this...

Actually, if it is a dominant Allele mutation, it has a 50% chance of being passed on, assuming the mate is aa.

If you mate "Aa" with "aa", you get four possibile combos

25% of Aa
25% of aA
25% of aa
25% of aa

Thus, there is a 50% chance of passing the dominant trait to the next generation. This is the same equation with Brown Eyes. I actually know I am a Bb (dominant brown with recessive blue). My wife has blue eyes (bb)

Thus, we have a 50% chance of blue eyes and a 50% chance of brown eyed children.

If the population is generally isolated, over time (with unfortunately a little "downstream" cousin-lovin') the dominant trait will tend to increase in frequency. Place an equal number of blueyed people and brown eyed people in a small population, and over a few generations the percentage of blue eyed will tend to move towards zero.

I hope my memory of biology serves me here...please correct me if I made a mistake.

And I am doing quite well, for a Friday...thanks.

 

[Blazin Bones]

I hope keebs doesn't mind me taking a stab at this...

Actually, if it is a dominant Allele mutation, it has a 50% chance of being passed on, assuming the mate is aa.

If you mate "Aa" with "aa", you get four possibile combos

25% of Aa
25% of aA
25% of aa
25% of aa

Thus, there is a 50% chance of passing the dominant trait to the next generation. This is the same equation with Brown Eyes. I actually know I am a Bb (dominant brown with recessive blue). My wife has blue eyes (bb)

Thus, we have a 50% chance of blue eyes and a 50% chance of brown eyed children.

If the population is generally isolated, over time (with unfortunately a little "downstream" cousin-lovin') the dominant trait will tend to increase in frequency. Place an equal number of blueyed people and brown eyed people in a small population, and over a few generations the percentage of blue eyed will tend to move towards zero.

I hope my memory of biology serves me here...please correct me if I made a mistake.

And I am doing quite well, for a Friday...thanks.

I believe you are correct. The rate of genetic decay I stated would be slower, but still as constant. I note your points of isolation and "cousin lovin" but would you mind providing a source to support isolationism in early evolution. I only ask this because isolation of a geneticly shifted species is exetremly impossible in today's world, let alone a prehistoric society.

 

[keebs]

I hope keebs doesn't mind me taking a stab at this...

Actually, if it is a dominant Allele mutation, it has a 50% chance of being passed on, assuming the mate is aa.

If you mate "Aa" with "aa", you get four possibile combos

25% of Aa
25% of aA
25% of aa
25% of aa

Thus, there is a 50% chance of passing the dominant trait to the next generation. This is the same equation with Brown Eyes. I actually know I am a Bb (dominant brown with recessive blue). My wife has blue eyes (bb)

Thus, we have a 50% chance of blue eyes and a 50% chance of brown eyed children.

If the population is generally isolated, over time (with unfortunately a little "downstream" cousin-lovin') the dominant trait will tend to increase in frequency. Place an equal number of blueyed people and brown eyed people in a small population, and over a few generations the percentage of blue eyed will tend to move towards zero.

I hope my memory of biology serves me here...please correct me if I made a mistake.

And I am doing quite well, for a Friday...thanks.

Yes, what you have shown is quite right, but in my example I assumed that each carrier of the gene was going to have 3 kids, thus the expected number of kids with the gene would be 1.5 (because 3/2=1.5). And as each generation passes, these 1.5 (haha I know that sounds wierd) are going to increase the previous generation by 1.5 times the number in their generation, leading to the prospective number of people in the population with the given allele after x number of generations will be (1.5)^x. Sorry if I didn't word my post right, I was referring to the whole population and not just one family.

 

[keebs]

I believe you are correct. The rate of genetic decay I stated would be slower, but still as constant. I note your points of isolation and "cousin lovin" but would you mind providing a source to support isolationism in early evolution. I only ask this because isolation of a geneticly shifted species is exetremly impossible in today's world, let alone a prehistoric society.

My generation model does not make use of "cousin lovin'", in fact, I assumed they only mated with people without the dominant mutation. As for the source of isolationism, mountain ranges, the formation of the sahara dessert, or flood would have all provided the isolation needed for humans to evolve from chimps. And it is not extrememly impossible in today's society, as we find isolated populations all of the time in very dense rainforests such as the Amazon, and an amazing this is is that alot of these isolated populations exhibit many different features from normal people, such as lacking the necessary brain functions to learn how to read, or the necessary brain functions to determine interpret distance perspective.

 

[ThinkerMan]

keebs.

I was rather flippant with "cousin lovin'", but doesn't there have to be some downstream intereaction to move the allele frequency towards 1?

Now, of course, it could be many generations, but for the allele frequency to get high, say, where the great majority of any population is brown eyed, there has to be some converging of the gene pool, or am I wrong?

 

[Blazin Bones]

I would like to respond to you gentlemen, but I must go recieve my free, college dinner. I may return later tonight, since I have a football game I must attend. Enjoy your dinners, my friends.

 

[keebs]

Yes, there would have to be substantial "cousin lovin'" sometime within the population, but I excluded it for the sake of generality, as the chances of "cousin lovin'" happening within a population depends on the size of the population. And I also excluded it because if it did happen, then my expectation would just be an underestimate (if it would cause it to be an overestimate, then I would've added it in).

 

[ThinkerMan]

thanks keebs...

I assume "cousin lovin'" isn't the scientific word for it...haha.

Enjoying the thread....is your background in genetics?

 

[keebs]

Hahaha yes, I am enjoying the thread quite a bit...as for my background, I have none. I'm only a junior in high school, and the only classes I have taken at a college level (admitting AP courses, as I don't consider them at a college level) are Calc III and Diff. Equ. at the community college near my house.

 

[ThinkerMan]

Wow, Calc III and Diffy-Q in HS. That's great.

I made it through Calc II in HS, then decided to go in a different direction in college (liberal arts, if you can believe it).

Only since I've been out now a few years have I started getting back into math & science, but its been enjoyable relearning.

 

[Blazin Bones]

Let's say that a man has a dominant allele mutation, and he produces two kids that that have an allele aA, where A is the dominant mutation. Now, suppose that he has three kids, and his three kids each have three kids...and so on...you can then work out the expected number of people in the population with his mutation (assuming it is neutral, a beneficial mutation would have a higher expectation, and the converse is true for a bad mutation) is (1.5)^x. That is an exponential increase, and if you are considering a small, closed (no migration) population, then the percent of people with this mutation with quickly converge to 1.

This was your original example. As you can see, your first generation started with two offspring and continued into these two producing three offspring each of the following generations. Now, as to my starting with one family that is not isolated, to honestly discuss one specific genetic shift of mutation you must start from the begining.

Let me correct my math and restate the example statistically. I will allow for the passing of the mutation itself instead of just the mutation being dominant in the example offspring.

Begining:

Aa=male dominant, original mutation/ wife has aa allele
possibilites for offspring: 1/2 will possess the mutation
1/2 will not posses the mutation
Multiply the possibility by itself to represent two mutated offspring= 1/4

If this were to occur these offspring would each have 3 of their own.

These offspring each have a 1/8 chance of having three offspring with the mutation.

The chances of both of the second generation having three mutated offspring is 1/64

The third generation being six offspring, then attempt to bread three with the mutation

Each of these six has a 1/8 chance of producing three more offspring that possess the mutated gene.

The possibility of all six offspring of the third generation producing three more mutated offspring is 1/262144

As you can see, while the chance of producing a mutated offspring is still 1/2 the chances of the population increasing fast enough to sustain the mutation is very miniscule. This example even allows for the Isolation of the species. The chances of the of the successful survival of a mutation is just too small. Also If you allow the cousins to know(biblical term for intercourse) each other you decrease the rate of genetic decay, but dramatically increase the likelyhood of a negetive mutations and genetic side effects.

 

[Blazin Bones]

I shall look forward to your responses tommorrow. I to am enjoying this thread very much. As for now, I must go watch my friends at their high school football game. Good Night Gentlemen. Would you mind If I prayed for you men in my prayers? I realize that some of you are Atheist, so you most likely don't think it will do anything. Even so, I thought I should offer.

 

[Blazin Bones]

I shall look forward to your responses tommorrow. I to am enjoying this thread very much. As for now, I must go watch my friends at their high school football game. Good Night Gentlemen.

As you can tell by my posts I have returned early enough to visit the forums. I would continue the discussion, but I am currently catching up on some of the other topics and threads. Good Night.

 

[keebs]

Your math is write for the first sentence or two, but that is where it ends. Your math brakes down when you multiply the probabilities together.

Multiply the possibility by itself to represent two mutated offspring= 1/4

You do not do that. If I wanted to know how many of his two children are expected to have the mutation, I would multiply the probability by 2, to get the expected value of one kid with the mutation. In my example, you would multiply the probability by 3 (because it is assumed he will have three kids) to get an expected number of offspring with the mutation to be 1.5. As this goes through the generations, the current generation is expected to have 1.5 times the number of people with the mutation in the previous generation. This would give you an estimated number of people in the population with the mutation as 1.5^x, where x is the generation number (and setting the original generation to x=0).

 

[Blazin Bones]

Your math is write for the first sentence or two, but that is where it ends. Your math brakes down when you multiply the probabilities together.

Multiply the possibility by itself to represent two mutated offspring= 1/4

You do not do that. If I wanted to know how many of his two children are expected to have the mutation, I would multiply the probability by 2, to get the expected value of one kid with the mutation. In my example, you would multiply the probability by 3 (because it is assumed he will have three kids) to get an expected number of offspring with the mutation to be 1.5. As this goes through the generations, the current generation is expected to have 1.5 times the number of people with the mutation in the previous generation. This would give you an estimated number of people in the population with the mutation as 1.5^x, where x is the generation number (and setting the original generation to x=0).

First, Good morning and Good day. How are we all this morning? I'm well and I hope that you are too. [for ThinkerMan] Or as well as can be for a Saturday.

No, I do believe the math is correct. I even believe that the Thinkerman would agree with me as well. Allow me to clarify why this may be confusing you. I was not looking for the possibility of producing a single mutated offspring. Basic genetics will tell you when you start with a 1/2 chance you will end with a 1/2 chance. This does not allow for a strong enough population growth either. Even if you had three offspring, you argue that 1.5 may carry the mutation, but there is still a 1.5 that will not carry the mutation, which means its still 50/50. I put forth the probibilities for when all the children of a following generation will possess the shifted gene. I put forth this example because you would need this kind of rapid change to create a strong enough shift to survive through multiple generations. But, as you can see, the possibility of such a profound shift is fairly impossible.

 

[cubedbee]

There is only a 50/50 chance that each individual inherits the gene, but given the number of people who could possibly inherit, there is a very good chance that the prevalence of the gene will grow from generation to generation.

The mutated man in the first generation has 2 children. There is a 25% chance that neither inherit the mutation, and that's the end of the story. However, there is a 75% chance that at least 1 did inherit. We're also assuming that each subsequent generation has 3 children each. In this scenario, the 75% of the time that the mutation is passed on to the second generation, we have the following probabilities for the number of mutants in the third generation.

3rd Generation

0                       8.9%
1                       28.1%
2                       32.8%
3                       18.8%
4                       7.8%
5                       3.1%
6                       0.5%

63% of the time, the population has at least two mutants in the third generation. Going one further,

4th Generation

0                       12.9%	
1                       14.0%	
2                       18.6%	
3                       17.2%	
4                       13.4%	
5                       9.5%	
6                       5.9%	
7                       3.5%	
8                       2.0%	
9                       1.0%	
10+                       2.1%

Here, 55% of the time there is 3 or more mutants in the 4th generation. It can clearly be seen that there is a significant probability that the genetic mutation, which is dominant, is not going to be wiped out. For the 5th generation, you need to start taking into account the fact that it is becoming possible for two mutants to mate, especially in a smaller population.