RufusAtticus

The Hardy-Weinberg Model

G.H Hardy (1877-1947)
Wilhelm Weinberg (1862-1937)

Initial assumptions about the population:

1. Diploid
2. Sexual
3. Nonoverlapping generations
4. Random mating
5. The size of the population is (effectively) infinite.
6. Migration can be ignored
7. Mutation can also be ignored
8. The gene under consideration is diallelic. (A and a)
9. Selection does not affect the alleles under consideration.
10. Identical allele frequencies in males and females.
11. Mendelian Inheritance

Allele Frequencies:

The frequency of the A allele is represented by p, and the frequency of the a allele is represented by q. Note: p+q=1.

Genotype Frequencies:

At Hardy-Weinberg equilibrium the frequency of the genotypes will be related to the allele frequencies as follows.

AA: p^2 Aa: 2pq aa: q^2

Rationale:
Let P, Q, and R represent the genotype frequencies (AA, Aa, aa) in the parental population. The allele frequencies are related to these genotype frequencies as follows.

p = (2P + Q)/2 = P + Q/2
q = (2R + Q)/2 = R + Q/2
p + q = P + Q + R = 1

The frequency of two AA individuals mating is P*P, with the frequency of AA, Aa, and aa offspring being 1, 0, and 0 respectively. Likewise:

Therefore:

P’ = P^2 + 2PQ/2 + (Q^2)/4 = (P + Q/2)^2 = p^2
Q’ = 2PQ/2 + 2PR + (Q^2)/2 + 2QR/2 = 2(P+Q/2)(R+Q/2) = 2pq
R’ = (Q^2)/4 + 2QR/2 + R^2 = (R+Q/2)^2 = q^2

Significance:

A population satisfying the initial assumptions does not evolve.

~~RvFvS~~

This followed the treatment in Principles of Population Genetics, Third Edition by Hartl and Clark.

RufusAtticus

Follow up:

In the population above, two types of assumptions were made: assumptions about the nature of the genes and assumptions about the nature of the population.

H-W equilibrium can still occur in loci with more than two alleles.

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RvFvS
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wdog

hey rufus,

thanks for the post, however you must treat me as a freshmen student of bio. The math is not a problem but the terminology and context are (such as what does diploid mean). So could you either supply it or give a link to the basics? thanks

RufusAtticus

Optics Guy,

A diploid is an organism that contains two sets of chromosomes. For humans, gametes (sperm and egg) are haploid (N), and somatic cells (body cells) are diploid (2N). Some common species are tetraploids (4N) or hexaploids (6N). I'm not quite sure what the record is though.

Talk.Origins has an article that might be worthwile to read if you haven't yet:

Introduction to Evolutionary Biology 2.0

Do you have anymore questions? It'll definately be easier for me to define any terms that you are unfamiliar with than try to figure out what you need. (Sorry about that.) I am completely willing to clarify anything.

~~RvFvS~~

Secular Pinoy

Added info:

Another good internet resource is found here. This page is part of a tutorial series on Physical and Cultural Anthropology here.

RufusAtticus

Reference Materials:

http://www.sciencekomm.at/advice/dict.html#chem
http://www.encyclopedia.com/
http://www.m-w.com

~~RvFvS~~

RufusAtticus

secularpinoy,

Thanx for the additional web info.

-RvFvS

wdog

Ok I'll check out some of these references, but to take you up on your offer please define the following:
diallelic
allele
Mendelian Inheritance

thanks

wehappyfew

Great topic, Rufus. Being a non-biologist, I often struggle with the application of this math to the evo-creto debate.


For example:

Let's suppose a Creationist proposes that the current genetic diversity found in humans is explainable by postulating that Adam and Eve's genomes contained the maximum possible diversity. This would allow, at most, 4 alleles per somatic gene, obviously.

Step two for the Creationist is to call upon recombination and exon shuffling to mix those 4 alleles into the currently observed 14 alleles/gene. At the nucleotide level, we would expect most of the coding genes to be mostly identical. But in the non-coding portion, almost any nucleotide sequence could be assumed for Adam and Eve, then shuffled since then. With such freedom in the inital conditions, it seems difficult to make a logical argument against this scenario.



OK. Now, can you evaluate the reasonableness of this scenario, mathematically. What predictions does the HW equation make about Adam and Eve's genome expressed in today's human population? Is there any data available that contradicts this scenario? And please discuss the expected differences between X, Y, and somatic genes in this process.

Thanks. :notworthy

RufusAtticus

Mendelian Inheritance: Inheritance following the rules discovered by Johann Gregor Mendel. Traits are determined by hereditary factors known as genes. Genes have different forms known as alleles. A gene with two alleles is a diallelic gene.

Mendel's Rule of Segregation (or first rule) is that alleles segregate from one another in the formation of gametes. For a diploid individual with two alleles (A and a) for one gene, 50% of its gametes will carry the A allele and the other 50% will carry the a allele.

Mendel's Rule of Independent Assortment (or second rule) is that alleles of separate genes segregate independently. We now know that this is only true when genes are on separate chromosomes or far apart on a single chromosome. The traits Mendel was observing in pea plants satisfied this requirement.

Source: The Science of Genetics by Atherly, Girton, and McDonald.

Additional resource (thanx sp):
http://anthro.palomar.edu/mendel/default.htm