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In this gene pool, the frequencies of each allele T and t is 50%.
Evolution and allele frequencies Gene pools are generally relatively stable over time. But not always. New alleles can be introduced as a result of mutation, and old alleles can disappear when the last organism carrying the allele dies. One result of evolution is that, after many generations of natural selection, some alleles prove to be advantageous and tend to be more frequent. Conversely, some alleles are disadvantageous to the survival of the organisms in the population, and are not passed on to as many offspring. From this it should be clear that, at any time an allele frequency is estimated, it is only a snapshot of the alleles at that time. Several generations later, the proportions of alleles may not be the same. In addition, if populations mix as a result of immigrations, there will probably be a change in allele frequencies. The same is true for emigrations, when one group with a particular allele leaves the population. Whatever the reason, if a gene pool is modifi ed and the allele frequencies change, we know that some degree of evolution has happened. No change in allele frequencies, however, means no evolution.
Individuals that are better adapted tend to survive and produce more offspring while the less well adapted tend to die or produce fewer offspring
Individuals that are better adapted tend to survive and produce more offspring while the less well adapted tend to die or produce fewer offspring
The variation that exists within a population is heritable (i.e. genetic) and determined by the presence of alleles
- These alleles may be passed from parent to offspring via sexual reproduction
Alleles encode for the phenotypic polymorphisms of a particular trait and may be beneficial, detrimental or neutral:
- Beneficial alleles will better equip the organism to survive and hence produce more offspring (encodes beneficial adaptations)
- Detrimental alleles will harm the survival prospects of an organism, leading to fewer viable offspring
- Neutral alleles will not affect the organisms survival prospects
Due to natural selection, the proportion of different alleles will change across generations (evolution)
- As beneficial alleles improve reproductive prospects (more offspring), they are more likely to be passed on to future generations
- Conversely, detrimental alleles result in fewer offspring and hence are less likely to be present in future generations
If environmental conditions change, what constitutes a beneficial or detrimental trait may change, and thus the allele frequencies in a population are constantly evolving
The Hardy–Weinberg equation
The Hardy–Weinberg equation
The Hardy-Weinberg equation is a means by which the frequency of two alternate alleles can be predicted within a population
For two alleles of a given genetic characteristic, three genotypes are possible (assuming Mendelian inheritance): AA, Aa and aa
- Dominant allele is A, with a frequency of p
- Recessive allele is a, with a frequency of q
The Hardy-Weinberg Equation
• The total frequency of both alleles will be 100% – in other words: p + q = 1
• Because genotypes consist of two alleles, this equation must be squared: ( p + q ) 2 = 1
• This gives the expanded Hardy-Weinberg equation:
p2 + 2pq + q2 = 1 (whereby p2 = AA ; 2pq = Aa ; q2 = aa)
You will recall from Section 3.4 that a Punnett grid shows the genotypes of the parents and offspring in a cross. For the Hardy–Weinberg equation, we need to look at the cross in a new way: as a model for the allele frequencies. To do this, we need the variables p and q:
• p = frequency of the dominant allele (allele T in the example below)
• p = frequency of the dominant allele (allele T in the example below)
• q = frequency of the recessive allele (allele t in the example below).
• q = frequency of the recessive allele (allele t in the example below).
When looked at individually, the frequencies of the alleles on chromosomes must add up to 1. So p + q = 1. For example, if p = 0.25 (or 25%) frequency, then q = 0.75 because whichever chromosomes do not have the dominant allele must carry the recessive one. What complicates things is the fact that we usually want to consider diploid organisms that carry two copies of any particular gene. As a result, the equation becomes (p + q)2 = 1.
If you remember your mathematics classes about polynomials, you’ll know that (p + q)2 can be expanded to p2 + 2pq + q2.
We can now deduce that p2 + 2pq + q2 = 1. This mathematical representation for the allele frequencies is known as the Hardy–Weinberg equilibrium and it is reached after only one generation of random interbreeding.
Looking again at the Punnett grid, in terms of the allele frequencies rather than genotypes, the following can be deduced:
• the frequency of TT = p2
• the frequency of Tt = 2pq
• the frequency of tt = q2.
By adding up all the possible proportions, we can see that 1/4 + 1/2 + 1/4 comes to a total of 1. Based on the frequencies, we can replace the proportions
Note that this equation gives mathematical support to the idea in Mendelian genetics that variation must be preserved from generation to generation. It is one of the characteristics of genetics that allows a population to be successful.
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