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Meiosis and variation Lesson 10 Population genetics Learning objectives You should be able to: Use the Hardy–Weinberg principle to calculate allele frequencies in populations Write a definition of the terms population and gene pool A population is a group of individuals of the same species that can interbreed A gene pool is the set of genetic information carried by a population What is population genetics? Population genetics is the study of the entire pool of genetic diversity within a population. This is greater than the genetic diversity shown by one individual In population genetics, scientists measure and predict changes in allele and genotype frequency from generation to generation Studying it allows us to answer questions such as ‘how many children born in the UK in the next 10 years, are likely to develop cystic fibrosis?’ The birth of population genetics As we discussed in the last lesson, Mendel’s ideas about how inheritance operated did not catch on because noone knew of a mechanism by which they could work i.e. genes. Even Charles Darwin didn’t know a mechanism by which his inheritance of desirable characteristics could occur. As work in the late nineteenth and early twentieth century showed Mendel’s ideas to have been correct, scientists realised that it was important to consider the genetic diversity of the entire population when studying evolution Scientists in the early twentieth century, such as Godfrey Harvey and Wilhelm Weinberg (of whom more later) thus developed the study of population genetics How does population genetics work? One of the main challenges in population genetics is to work out the frequency of an allele within the population This is easy enough if the allele we want to know about is codominant but a bit harder if it is recessive or dominant In order to measure the frequency of an allele within a population we therefore need to know how the trait that it confers is inherited, in other words if it is dominant, codominant or recessive Working out the frequency of a codominant allele within a population Imagine a population of aliens in which skin colour is conferred by one gene locus The alleles that may be found at this locus are SR coding for red pigment and SY coding for yellow pigment, in other words they are codominant. If an allele is present then the pigment that it codes for is always produced in the alien’s skin cells. If both alleles are present then both of the pigments that they code for are present The possible genotypes for this locus are SR SR Red pigment only – the aliens have red skin SR SY Both red and yellow pigments – the aliens have orange skin SY SY Yellow pigment only – the aliens have yellow skin Working out the allele frequency In a population of 100 aliens: 41 have red skin genotyope 46 have orange skin genotype 13 have yellow skin genotype = = = SR SR SR SY SY SY The 41 red aliens represent 82 SR alleles (41 x 2) The 46 orange aliens represent another 46 SR alleles So of the 200 alleles for this trait within the population, 128 are SR The frequency of SR within the population is therefore 128/200 = 0.64 The frequency of SR + SY = 1 So the frequency of the SY allele = 1 - 0.64 = 0.36 But what if the alleles we are looking at are dominant or recessive? Imagine that the allele for red pigment was dominant so that any alien with it had red skin We could not therefore tell if a red alien was homozygous or heterozygous This makes calculating the frequency of either allele more problematic We have to use something called the Hardy-Weinberg equation Godfrey Hardy A British mathematician Wilhelm Weinberg A German doctor These two scientists developed the Hardy-Weinberg principle This states that the allele frequency in a population is distributed according to a mathematical model known as the Hardy-Weinberg equation The following assumptions are made for this to be correct: • The population is very large • Mating is random • No selective advantage exists for a particular genotype • There is no mutation, migration or genetic drift The Hardy-Weinberg equation p2 + 2pq + q2 = 1 p and q represent the frequency of two alleles in a population p2 = the frequency of individuals with two p alleles 2pq = the frequency of individuals who are heterozygous q2 = the frequency of individuals homozygous for the q allele An example Lets take cystic fibrosis as an example Remember, this is conferred by as recessive allele Possible genotypes are: CFCF where the person is entirely healthy CF cf where the person carries the allele but does not develop the disease cfcf where the person develops cystic fibrosis We know if someone has cystic fibrosis because they need medical treatment but how could we tell how many symptomless carriers there were in a population of 2000 in which only one person had cystic fibrosis? Calculating the frequency of heterozygotes Lets say: p represents the frequency of the dominant allele CF q represents the frequency of the recessive allele cf Therefore: p2 = frequency of genotype CFCF q2 = frequency of genotype cfcf 2pq = frequency of CFcf We know that p2 + 2pq + q2 = 1 We also know that q2 = 1/2000 = 0.0005 The maths bit (it’s not hard) If q2 = 0.0005 then q is the square route of this So q = 0.022 We know that p + q must = 1 Therefore p = 1 – 0.022 = 0.978 The frequency of carriers = 2pq 2pq = 2 x 0.978 x 0.022 = 0.043 This means that 4.3% of the population are carriers Our population was 2000 4.3% of 2000 = 0.043 2000 = 86