Hexubiss
20-11-2004, 01:30
Evolution: Definitive Answer
The Hardy-Weinberg Equilibrium Law
The mutational theory of evolution proposed by DeVries, Bateson, and their contemporaries was accepted by most of the prominent geneticists at the turn of the century, and led to public testimonials that "Darwinism was dead."
But, like Mark Twain, reports of its death were greatly exaggerated. In the second decade of the 20th century, three other researchers, again working separately and mostly unbeknownst to each other, proposed a theory that would eventually lead to the re-establishment of natural selection as the prime mover of evolution.
As described in the reading, G. H. Hardy, Wilhelm Weinberg, and William Castle all proposed a mathematical theory that describes in detail the conditions that must be met for evolution to not occur. This theory, often called the Hardy-Weinberg Equilibrium Law, lays out the conditions that must be met for there to be no changes in the allele frequency in a population of interbreeding organisms over time.
Recall Mendel's definition of alleles: different gene forms that produce different forms of a trait. In the context of evolution, alleles are what code for the phenotypes that change over time in an evolving population.
Therefore, changes in the alleles present in a population will produce changes in the phenotypes present in that population. This, in a nutshell, is the genetic definition of evolution: changes in allele frequency in a population over time.
Conditions for Maintaining a Hardy-Weinberg Equilibrium:
What Hardy, Weinberg, and Castle all realized is that for allele frequencies to not change in a population, five conditions must be met:
There must be no mutations (i.e. alleles cannot change into other, different alleles)
There can be no gene flow (i.e. individuals cannot enter or leave the population)
The population must be very large (i.e. random changes cannot alter allele frequences)
Survival must be random (i.e. there can be no natural selection)
Reproduction must be random (i.e. there can be no sexual selection)
To visualize why these five conditions must be met for evolution to not occur, consider a population of 50 flowers in which there are two alleles for one gene controlling flower color:
R = red flowers
r = white flowers
Consider further a population in which 25 of the flowers are homozygous for red flowers (i.e. RR) and 25 of the flowers are homozygous for white flowers (i.e. rr). This means that the frequency of the two alleles in this population are equal:
R = red flowers = 0.5 = 50%
r = white flowers = 05. = 50%
Now, let's see what will happen if the flowers are allowed to randomly interbreed (i.e. exchange alleles with each other). We can model this by imaging that all of the alleles are thrown together into a pile, and then they are randomly drawn out two at a time to form the genotypes for 50 new flowers. What would the new distribution of allele frequencies and genotype frequencies be after this happens?
To figure out what will happen, consider the probabilities of drawing different combinations of red and white alleles (you can imagine them as red and white marbles if you wish). There are a total of 100 alleles in the population: 50 red and 50 white. Therefore, for each allele that is drawn, the probability of choosing a red is 50% and the probability of choosing a white is also 50%. These choices are independent of each other, so the probability of choosing pairs of alleles becomes:
RR = 0.5 X 0.5 = 0.25 red flowers
Rr = 0.5 X 0.5 = 0.25 red flowers
rR = 0.5 X 0.5 = 0.25 red flowers
rr = 0.5 X 0.5 = 0.25 white flowers
Notice what has happened: we have gone from a population in which one half of the flowers are red and one half are white, to a population in which three-fourths of the flowers are red and one-fourth are white. It looks like red flowers (i.e. the dominant phenotype) is becoming more common, while the white flowers (i.e. the recessive phenotype) is becoming less common, and therefore red flowers should eventually completely replace white flowers.
However, notice a crucial point: none of the alleles has disappeared; they have simply been redistributed. Therefore, if the five conditions list earlier for a Hardy-Weinberg equilibrium have been met (i.e. no mutations or gene flow, large population, and random survival and reproduction), then every time this exercise is repeated from now on, the same genotype frequencies (and therefore the same phenotype frequencies) will be obtained:
RR = 0.5 X 0.5 = 0.25 red flowers
Rr = 0.5 X 0.5 = 0.25 red flowers
rR = 0.5 X 0.5 = 0.25 red flowers
rr = 0.5 X 0.5 = 0.25 white flowers
Therefore, there will be no change in allele frequency in the population over time, and therefore evolution will not have occurred.
Therefore, there will be no change in allele frequency in the population over time, and therefore evolution will not have occurred.
Implications of the Hardy-Weinberg Equilibrium Law:
So what? All the Hardy-Weinberg Equilibrium Law seems to say is that there are conditions under which evolution can't happen? Aren't we interested in those conditions in which evolution can happen?
<b>Yes, but notice what the Hardy-Weinberg Equilibrium Law gives us: it outlines exactly what processes are essential to<i> </u>prevent evolution </i></u>, and therefore by negation shows us how evolution can happen.</b>
That is, if any of the five conditions for maintaining a Hardy-Weinberg equilibrium are not met, then evolution must be occurring. And, of course, virtually none of these conditions is never permanently met in any known natural population of organisms:
Mutations occur at a slow but steady rate in all known populations
Many organisms, especially animals, enter (immigration) and leave (emigration) populations
Most populations are not large enough to avoid random changes in allele frequencies
Survival is virtually never random
Reproduction in organisms that can choose their mates is also virtually never random
Therefore, according to the Hardy-Weinberg Equilibrium Law, evolution must be occurring in virtually every population of living organisms.
It is, in other words, as inescapable as gravity
The Hardy-Weinberg Equilibrium Law
The mutational theory of evolution proposed by DeVries, Bateson, and their contemporaries was accepted by most of the prominent geneticists at the turn of the century, and led to public testimonials that "Darwinism was dead."
But, like Mark Twain, reports of its death were greatly exaggerated. In the second decade of the 20th century, three other researchers, again working separately and mostly unbeknownst to each other, proposed a theory that would eventually lead to the re-establishment of natural selection as the prime mover of evolution.
As described in the reading, G. H. Hardy, Wilhelm Weinberg, and William Castle all proposed a mathematical theory that describes in detail the conditions that must be met for evolution to not occur. This theory, often called the Hardy-Weinberg Equilibrium Law, lays out the conditions that must be met for there to be no changes in the allele frequency in a population of interbreeding organisms over time.
Recall Mendel's definition of alleles: different gene forms that produce different forms of a trait. In the context of evolution, alleles are what code for the phenotypes that change over time in an evolving population.
Therefore, changes in the alleles present in a population will produce changes in the phenotypes present in that population. This, in a nutshell, is the genetic definition of evolution: changes in allele frequency in a population over time.
Conditions for Maintaining a Hardy-Weinberg Equilibrium:
What Hardy, Weinberg, and Castle all realized is that for allele frequencies to not change in a population, five conditions must be met:
There must be no mutations (i.e. alleles cannot change into other, different alleles)
There can be no gene flow (i.e. individuals cannot enter or leave the population)
The population must be very large (i.e. random changes cannot alter allele frequences)
Survival must be random (i.e. there can be no natural selection)
Reproduction must be random (i.e. there can be no sexual selection)
To visualize why these five conditions must be met for evolution to not occur, consider a population of 50 flowers in which there are two alleles for one gene controlling flower color:
R = red flowers
r = white flowers
Consider further a population in which 25 of the flowers are homozygous for red flowers (i.e. RR) and 25 of the flowers are homozygous for white flowers (i.e. rr). This means that the frequency of the two alleles in this population are equal:
R = red flowers = 0.5 = 50%
r = white flowers = 05. = 50%
Now, let's see what will happen if the flowers are allowed to randomly interbreed (i.e. exchange alleles with each other). We can model this by imaging that all of the alleles are thrown together into a pile, and then they are randomly drawn out two at a time to form the genotypes for 50 new flowers. What would the new distribution of allele frequencies and genotype frequencies be after this happens?
To figure out what will happen, consider the probabilities of drawing different combinations of red and white alleles (you can imagine them as red and white marbles if you wish). There are a total of 100 alleles in the population: 50 red and 50 white. Therefore, for each allele that is drawn, the probability of choosing a red is 50% and the probability of choosing a white is also 50%. These choices are independent of each other, so the probability of choosing pairs of alleles becomes:
RR = 0.5 X 0.5 = 0.25 red flowers
Rr = 0.5 X 0.5 = 0.25 red flowers
rR = 0.5 X 0.5 = 0.25 red flowers
rr = 0.5 X 0.5 = 0.25 white flowers
Notice what has happened: we have gone from a population in which one half of the flowers are red and one half are white, to a population in which three-fourths of the flowers are red and one-fourth are white. It looks like red flowers (i.e. the dominant phenotype) is becoming more common, while the white flowers (i.e. the recessive phenotype) is becoming less common, and therefore red flowers should eventually completely replace white flowers.
However, notice a crucial point: none of the alleles has disappeared; they have simply been redistributed. Therefore, if the five conditions list earlier for a Hardy-Weinberg equilibrium have been met (i.e. no mutations or gene flow, large population, and random survival and reproduction), then every time this exercise is repeated from now on, the same genotype frequencies (and therefore the same phenotype frequencies) will be obtained:
RR = 0.5 X 0.5 = 0.25 red flowers
Rr = 0.5 X 0.5 = 0.25 red flowers
rR = 0.5 X 0.5 = 0.25 red flowers
rr = 0.5 X 0.5 = 0.25 white flowers
Therefore, there will be no change in allele frequency in the population over time, and therefore evolution will not have occurred.
Therefore, there will be no change in allele frequency in the population over time, and therefore evolution will not have occurred.
Implications of the Hardy-Weinberg Equilibrium Law:
So what? All the Hardy-Weinberg Equilibrium Law seems to say is that there are conditions under which evolution can't happen? Aren't we interested in those conditions in which evolution can happen?
<b>Yes, but notice what the Hardy-Weinberg Equilibrium Law gives us: it outlines exactly what processes are essential to<i> </u>prevent evolution </i></u>, and therefore by negation shows us how evolution can happen.</b>
That is, if any of the five conditions for maintaining a Hardy-Weinberg equilibrium are not met, then evolution must be occurring. And, of course, virtually none of these conditions is never permanently met in any known natural population of organisms:
Mutations occur at a slow but steady rate in all known populations
Many organisms, especially animals, enter (immigration) and leave (emigration) populations
Most populations are not large enough to avoid random changes in allele frequencies
Survival is virtually never random
Reproduction in organisms that can choose their mates is also virtually never random
Therefore, according to the Hardy-Weinberg Equilibrium Law, evolution must be occurring in virtually every population of living organisms.
It is, in other words, as inescapable as gravity