Hardy-Weinberg Principle

12 Key excerpts on "Hardy-Weinberg Principle"

• 

  eBook - ePub

  Forest Conservation Genetics

  Principles and Practice

  • Andrew Young, David Boshier, Timothy Boyle(Authors)
  • 2000(Publication Date)
  • CSIRO PUBLISHING

    (Publisher)

  k(k + 1) number of different possible genotypes. The estimate of allele frequencies at a locus from knowledge of genotype frequencies is forthright under the assumptions of the Hardy-Weinberg Principle (Hardy 1908; Weinberg 1908). The principle states that in a large random-mating population with non-overlapping generations, the allele and genotype frequencies will remain constant from generation to generation when there is no mutation, migration and natural selection. The Hardy-Weinberg Principle provides the foundation for all population genetic investigation. It is the single, most important theorem for the genetic analysis of natural populations.

  3.1.1 Hardy-Weinberg equilibrium

  To illustrate the Hardy-Weinberg Principle, let the genotype frequencies of AA, Aa, and aa at a diallelic locus in the parental population be P, Q, and R respectively, where P + Q + R = 1. Alleles A and a at respective frequencies p and q can be estimated in the next generation as in Table 3.1 .

  The constancy of allele and genotype frequencies indicates that in the absence of mutation, migration and natural selection, Mendelian inheritance by itself will preserve genetic diversity in large randomly-mating diploid populations and attain Hardy-Weinberg equilibrium (HWE). The Hardy-Weinberg proportions are attained in one generation of random mating only if allele frequencies are the same in females and males. This prerequisite is true only for populations with non-overlapping generations. In populations with more complex life histories, the Hardy-Weinberg proportions are attained gradually over several generations.

  TABLE 3.1 Illustration of the Hardy-Weinberg Principle

  The level of genetic diversity in a population is affected by an array of genetic, life history and ecological characteristics that collectively define the population genetic structure. It is desirable to summarize the allele data at all loci in a simple way that expresses the level of genetic diversity in each sampled population and that would permit comparison with other sampled populations. Two sets of measurable parameters have been used to characterize population genetic structure (Brown 1989). The first set is geographical parameters that describe and quantify the geographical variation patterns of populations at the single-locus level. Four genetic diversity measures are commonly used:

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Human Population Genetics

  • John H. Relethford(Author)
  • 2012(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  a allele. Both Hardy and Weinberg independently showed that the expected genotype frequencies in the next generation are

  2.4

  These equations are often familiar to the introductory student in biological anthropology and biology classes. Following the initial math fear experienced by some students, just about everyone soon learns these simple equations. For example, if we know that p = 0.7 and q = 0.3 in the parental gene pool, we can quickly figure out the expected distribution of genotypes in the next generation as

  The utility of predicting outcomes in the next generation can be illustrated with a more specific type of question. For example, let us imagine that the frequency of a harmful recessive allele is 0.01 and we want to know how many children will be born having two recessives, and hence a genetic disease. In this case, Hardy–Weinberg allows a quick answer: q 2 = (0.01)2 = 0.0001, which is 1 in 10,000 offspring. Likewise, we could compute the expected proportion of heterozygotes that would not get the disease but would be carriers: 2pq = 2(0.99)(0.01) = 0.0198, which is 198 in 10,000 offspring.

  Using the Hardy–Weinberg equations is straightforward. It is a second aspect of the Hardy–Weinberg law that causes more confusion. Both Hardy and Weinberg independently showed that, under certain conditions, the genotype and allele frequencies would remain constant from one generation to the next. In other words, Hardy–Weinberg equilibrium states that nothing changes (the very definition of equilibrium ). Another way of saying that nothing changes is saying that there is no evolution! At this point in a typical lecture, everyone becomes rightfully perplexed. It is obvious from lab experiments, field studies, and the fossil record that organisms evolve all the time, which makes it difficult to understand why valuable lecture time (and textbook space) is being taken up by something that is clearly incorrect. The answer, which we then give in lecture, is that Hardy–Weinberg equilibrium gives us a baseline

  Sign up to read

  Learn more about book
• 

  Available until 20 Nov |Learn more

  An Introduction to Molecular Anthropology

  • Mark Stoneking(Author)
  • 2016(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  CHAPTER 4 A Simple Model: Hardy–Weinberg Equilibrium

  The previous chapter introduced some important concepts about populations, such as ideal populations and the effective population size. The emphasis throughout was on what happens to the gene pool, namely, the kinds of different alleles in a population and their frequencies. We now want to see how various evolutionary forces influence the gene pool. To do so, we will first set up a very simple—and therefore highly unrealistic—model of a population, without any evolutionary forces involved, and see how the gene pool changes over time. In the next chapter, we will make the model more realistic by adding the various evolutionary forces and then see what happens to the gene pool.

  Population genetics gets very mathematical very quickly; for those of you who found the math in the last chapter challenging, be forewarned, that was just a taste of what's to come. Still, we can get by with fairly simple algebra, and it is sometimes useful to try to understand the math behind the concepts. Therefore, I will continue to present the equations and urge you to work with them, while also focusing on what we learn from the equations—much of which (hopefully) does make sense, once you think about it.

  The Gene Pool With No Evolution: The Hardy–Weinberg Principle

  Let's start by assuming the following for our population:

  • discrete, nonoverlapping generations
  • random mating (all matings equally likely to occur)
  • infinite population size
  • no migration into or out of the population
  • no new mutations occur
  • everyone has the same viability (chance of surviving to the age when reproduction ends) and fertility

  This is a pretty boring model! But let's see what happens to the gene pool each generation with such a model. Consider a gene with two alleles, A and B. Let the frequency of A = p and the frequency of B = q, then hopefully it is clear that p + q = 1. Since humans are diploid, there are three genotypes for the two alleles at this gene: AA, AB, and BB. But in the gene pool model, we don't worry about genotypes; when it comes to producing the next generation, we just consider the alleles. The above assumptions about the population mean that we can think of the production of new offspring as occurring by everyone shedding their gametes (eggs and sperm) into one big pool and then gametes meeting randomly to produce offspring. There are two types of gametes in the pool: A gametes, which have a frequency of p, and B gametes, which have a frequency of q. The chance that two A gametes come together is just p × p = p2 , and this will be the frequency of AA genotypes in the next generation. Similarly, the frequency of BB genotypes corresponds to the chance that two B gametes come together, which is q × q = q2 . The AB heterozygote can come about by either an A gamete from the father and a B gamete from the mother, with frequency p × q = pq, or the other way around, also with frequency pq, so the frequency of AB heterozygotes is 2pq. And if we add up the frequency of all three genotypes in the next generation, it will be p2 +2pq + q2 , which can be factored into (p + q) (p + q), which equals 1 (since p + q

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Emery and Rimoin's Principles and Practice of Medical Genetics and Genomics

  Foundations

  • Reed E. Pyeritz, Bruce R. Korf, Wayne W. Grody(Authors)
  • 2018(Publication Date)
  • Academic Press

    (Publisher)

  With the monumental scientific advances that have resulted from the Human Genome Project, the genetic composition of populations can now be examined in detail. Thousands of rare alleles are known to be disease-causing variants and for most of these diseases [e.g., cystic fibrosis, Tay–Sachs, phenylketonuria (PKU), hemophilia A, and familial hypercholesterolemia], many different pathogenic variants are found within the same gene. In general, the frequencies of these rare disease alleles differ among populations, as do the frequencies of common alleles (>1%), many of which are associated with common diseases such as Crohn’s disease, diabetes, coronary disease, celiac disease, multiple sclerosis, and macular degeneration. The principles of population genetics attempt to explain the genetic diversity in present populations and the changes in allele and genotype frequencies over time. Population genetic studies facilitate the identification of alleles associated with disease risk and provide insight into the effect of medical intervention on the population frequency of a disease. Allele and genotype frequencies depend on factors such as mating patterns, population size and distribution, mutation, migration, and selection. By making specific assumptions about these factors, the Hardy–Weinberg law, a fundamental principle of population genetics, provides a model for calculating genotype frequencies from allele frequencies for a random mating population in equilibrium.

  12.2. Hardy–Weinberg Law

  The allele frequencies at a locus can always be calculated from the genotype frequencies, but the converse is not necessarily true. The Hardy–Weinberg law states that for a single autosomal locus in a large population in which (1) mating takes place at random with respect to genotype, (2) allele frequencies are the same in males and females, and (3) mutation, selection, and migration are negligible, genotype frequencies can be calculated from allele frequencies after one generation, regardless of the allele and genotype frequencies in the initial population. This is not true for a single X-linked locus or for any set of loci considered jointly; for these loci, the establishment of this relationship between allele and genotype frequencies takes more than one generation.

  12.2.1. Autosomal Locus

  Consider a locus with two alleles, A 1 and A 2 , and suppose the population frequencies of the three genotypes A 1 A 1 , A 1 A 2 , A 2 A 2 are p 11 , p 12 , p 22 , respectively, where p 11   +  p 12   +  p 22   =  1, then, in this initial population, the frequency of A 1 is p 11   +  ½p 12 and the frequency of A 2 is p 22   +  ½p 12

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Quantitative Genetics

  • Armando Caballero(Author)
  • 2020(Publication Date)
  • Cambridge University Press

    (Publisher)

  The Hardy–Weinberg principle can refer not only to a locus but to other elements, such as a chromosomal organization (for example, an inversion or a translocation). The extension to multiallelic loci is immediate. Suppose that locus A has n alleles, A 1 , A 2 , . . . A n , with frequencies p 1 , p 2 , . . . p n , respectively. The frequency of the homozygous A a A a Aa pq Aa pq aa q 2 AA p 2 Figure 2.1 Calculation of the expected genotype frequencies from the allele or gametic frequencies in a scenario under panmixia. The frequency of the gamete carrying allele A is p and that of allele a is q in both sexes. 2.2 Hardy–Weinberg Equilibrium 17 genotype A i A i is p 2 i , and that of heterozygote A i A j is 2p i p j , being n homozygotes and n(n − 1)/2 heterozygotes, and the expected global frequency of heterozygotes is H ¼ 1  X n i¼1 p 2 i ; ð2:2Þ which is called expected heterozygosity or gene diversity, and is a measure of the genetic variation present in the population for the locus in question. Another measure of genetic diversity in the case of multiallelic loci is the so-called allelic diversity or allelic richness, which is defined as the average number of alleles per locus that segregate in the population. The composition of genotype frequencies determined by the Hardy–Weinberg prin- ciple could remain unchanged throughout generations if there are no forces of change acting on the locus considered. For this, a series of conditions must be met, in addition to the aforementioned random pairing of gametes, which are the following: 1 The population census size must be infinite, so that changes in frequencies in successive generations would not be expected as a result of chance. 2 The Mendelian segregation of the locus should be correct, so that the heterozygotes produce an equal number of gametes carrying alleles A and a. 3 For a species with separate sexes, there should be equal allele frequencies in both of them.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Principles of Plant Genetics and Breeding

  • George Acquaah(Author)
  • 2012(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Hardy–Weinberg equilibrium . Hardy, from England, and Weinberg, from Germany, discovered that equilibrium between genes and genotypes is achieved in large populations. They showed that the frequency of genotypes in a population depends on the frequency of genes in the preceding generation, not on the frequency of the genotypes.

  Considering the previous example, the genotypic frequencies for the next generation following random mating can be calculated as follows: The Hardy–Weinberg equilibrium is hence summarized as:

  This means that in a population of 80 plants as before, about three plants will have a genotype of AA , 26 will be Aa , and 51, aa . Using the previous formula, the frequencies of the genes in the next generation may be calculated as:

  and q = 1 − p = 0.8

  The allele frequencies have remained unchanged, while the genotypic frequencies have changed from 4, 24, and 52, to 3, 26, and 51, for AA, Aa , and aa , respectively. However, in subsequent generations, both the genotype and gene frequencies will remain unchanged, provided that:

  1. random mating occurs in a very large diploid population;

  2. allele A and allele a are equally fit (one does not confer a superior trait than the other);

  3. there is no differential migration of one allele into or out of the population;

  4. the mutation rate of allele A is equal to that of allele a .

  In other words, the variability does not change from one generation to another in a random mating population. The maximum frequency of the heterozygote (H) cannot exceed 0.5 (Figure 3.1 ). The Hardy–Weinberg law states that equilibrium is established at any locus after one generation of random mating. From the standpoint of plant breeding, two states of variability are present – two homozygotes (AA, aa ), called “free variability”, that can be fixed by selection and the intermediate heterozygous (Aa

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Philosophy of Biology

  A Contemporary Introduction

  • Alex Rosenberg, Daniel W. McShea(Authors)
  • 2007(Publication Date)
  • Routledge

    (Publisher)

  Some philosophers of biology and some biologists have argued, in the light of considerations like these, that biological laws are really quite different from laws in physical science, and therefore biological theories and explanations must be quite different from those in chemistry or physics. These philosophers and biologists note that principles such as the Hardy–Weinberg “law” or Fisher’s “sex ratio model” play important roles in biological explanation, indeed they play many of the same roles that laws play in physical science. But for well-understood reasons, these models are quite different from the causal laws of chemistry or physics. From this it is inferred that biological laws are fundamentally different from physical laws, and that therefore biological explanation and biological theories are different as well.

  Recall the statement of the Hardy–Weinberg law: If four conditions obtain, in an infinitely large population, given an initial set of allele frequencies, then genotype frequencies remain constant. The four conditions are: no immigration or emigration, random mating, no mutation, and no natural selection. Given these conditions, it only takes a bit of elementary algebra to deduce that if in generation 1 the proportion of allele P in the population is p, and the proportion of allele Q is q, then in the ratio of genotypes PP, QQ, PQ in the next generation will be p2 , q2 , and 2pq . Weinberg was a physician, a biologist of a sort. But Hardy was a mathematician and he always claimed to be embarrassed that the “law” should bear his name, because it is nothing more than a trivial mathematical deduction. Hardy was right. The Hardy–Weinberg “law” has no more empirical content than, say, 2 + 2 = 4 or a definitional truth such as “All bachelors are unmarried males.”

  Now in the previous section we noted that such definitionally necessary truths cannot report contingent causal connections, have no explanatory power, cannot support counter-factuals, and therefore cannot be laws, at least not of the sort we are familiar with in other natural sciences. If biology is different, if the Hardy–Weinberg law really is a biological law, if it will really do explanatory work for biology in spite of its status as a definition or a “tautology,” then a great deal of philosophy of science will have to be overturned. To begin with, it will turn out that a priori,

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Thompson & Thompson Genetics in Medicine E-Book

  Thompson & Thompson Genetics in Medicine E-Book

  • Robert L. Nussbaum, Roderick R. McInnes, Huntington F Willard(Authors)
  • 2015(Publication Date)
  • Elsevier

    (Publisher)

  The Hardy-Weinberg law states that the frequency of the three genotypes AA, Aa, and aa is given by the terms of the binomial expansion of (p + q) 2 = p 2 + 2pq + q 2 . This law applies to all autosomal loci and to the X chromosome in females, but not to X-linked loci in males who have only a single X chromosome.

  The Hardy-Weinberg Law The Hardy-Weinberg law rests on these assumptions:

  • The population under study is large, and matings are random with respect to the locus in question. • Allele frequencies remain constant over time because of the following: • There is no appreciable rate of new mutation. • Individuals with all genotypes are equally capable of mating and passing on their genes; that is, there is no selection against any particular genotype. • There has been no significant immigration of individuals from a population with allele frequencies very different from the endogenous population.

  A population that reasonably appears to meet these assumptions is considered to be in Hardy-Weinberg equilibrium .

  The law can be adapted for genes with more than two alleles. For example, if a locus has three alleles, with frequencies p, q, and r, the genotypic distribution can be determined from (p + q + r )2 . In general terms, the genotype frequencies for any known number of alleles a n with allele frequencies p 1 , p 2 , … p n can be derived from the terms of the expansion of (p 1 + p 2 + … p n )2

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Introducing Genetics

  From Mendel to Molecules

  • Alison Thomas(Author)
  • 2014(Publication Date)
  • Garland Science

    (Publisher)

  163 Mutation 10.6 Disturbances of the Hardy–Weinberg equilibrium The Hardy–Weinberg equation enables us to predict allele and genotype fre-quencies in populations that are stable and unchanging. It is difficult, however, to find natural populations where all the assumptions required of the Hardy– Weinberg law rigorously exist. Rarely do we find large and randomly mating populations where no mutation, migration, or differential reproduction are occurring. Populations are dynamic – changes in size and structure are a natural part of their being. The final part of this chapter briefly considers the various factors that disturb equilibrium and how they might contribute to evolutionary change. We can think in terms of: 1. Factors that produce new variation (i.e. introduce new alleles into a popu-lation). Mutation is the main means of generating new alleles, although migration plays a subsidiary role. 2. Factors that change the profile of existing variation by altering allele frequen-cies within a population. Migration can have a major influence here along with genetic drift and differential reproduction. 10.7 Mutation Within a diploid, sexually reproducing population the gene pool is reshuffled each generation to produce new combinations of genotypes among offspring. These new genotype combinations are the result of the processes of meiosis and the random fusion of gametes. They ensure variability among individuals. Genotype Observed numbers ( O ) Expected numbers ( E ) O – E ( O – E ) 2 ( O – E ) 2 / E LL 133 118 15 225 1.91 LM 135 166 –31 961 5.79 MM 72 57 15 225 3.94 Total 340 340 11.67 • Null hypothesis: there is no difference between observed and expected genotype frequencies. • Significance level = 0.05; degrees of freedom = 2 (number of possible genotypes – 1); calculated χ 2 value = 11.67; critical χ 2 value = 5.99 As the calculated χ 2 value is greater than the critical χ 2 value, the null hypoth-esis is rejected.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Molecular Breeding of Crop Plants

  • Rajesh Singh(Author)
  • 2019(Publication Date)
  • Delve Publishing

    (Publisher)

  4.3. PROBLEMS ASCENDING FROM THE HARDY WEINBERG EQUILIBRIUM For the Hardy Weinberg equilibrium condition to be true, various conditions should be met. Though, some circumstances provide estimated conditions to fulfill the requirements. 4.3.1. The Problem of Population Size The Hardy Weinberg equilibrium needs the large random breeding population to be true. Though, practically, this law has been discovered to be roughly true for a majority of the genes in cross-pollinated species, apart from when the non-random mating occurs. Whereas inbreeding is the natural characteristic of the self-pollinated species, assortative breeding can Introduction to Concepts of Population Genetics 107 take place when the cross-pollinated species are nearly spread out in the field (Avise et al., 1987; Excoffier et al., 1992). 4.3.2. The Problem of Multiple Loci Research has displayed that it is likely for alleles at 2 loci to be in casual mating frequencies and not in the state of equilibrium with respect to one another. Additionally, equilibrium amongst 2 loci isn’t accomplished after a single generation of breeding as the Hardy Weinberg law determined but is accomplished slowly over numerous generations. Also, the existence of genetic association will slow down the attainment rate of equilibrium (Figure 4.2). If there isn’t any association (c=0.5), the differential amongst the actual and equilibrium frequency is decreased by 50% in each generation. At this rate, about seven generations would be needed to reach an estimated equilibrium. Conversely, at c =0.01 & c=0.001, about 69 & 693 generations would be taken, respectively, to attain equilibrium. The composite frequency of gene can be determined for the genes at the 2 loci (Weir & Cockerham, 1984). Figure 4.2: The methodology to association equilibrium under the random mat-ing of 2 loci considered together. Value of c provides the linkage frequency amongst 2 loci.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  An Introduction to Methods and Models in Ecology, Evolution, and Conservation Biology

  • Stanton Braude, Bobbi S. Low, Stanton Braude, Bobbi S. Low, Stanton Braude, Bobbi Low(Authors)
  • 2010(Publication Date)
  • Princeton University Press

    (Publisher)

  Section III Population Genetics This page intentionally left blank 10 Jason J. Kolbe Introduction and Background H uman modification of the environment fragments habitats around the world. Just as oceanic islands are isolated by water, terrestrial habitat islands become isolated by unsuit-able or inhospitable habitats (see chapter 9 for more). Habitats can become fragmented as roads and buildings are built, forests are clear-cut, or wetlands are drained. Habitat fragmentations and the consequential isolation of small populations are among the most critical contemporary conservation issues. Evolutionary processes at the genetic level (e.g., inbreeding, genetic drift, and gene flow) can lead to reduced genetic variation, which can further disrupt the potential for adaptive evolutionary change in small isolated populations. The Hardy-Weinberg equilibrium theory (H-W) is a fundamental concept in population genetics that provides the foundation for much of conservation genetics. Hardy-Weinberg establishes the null hypothesis for studies of allele frequency change, or microevolution, in populations. According to H-W, allele and genotype frequencies should remain constant over successive generations when the following circumstances are met: (1) large popu-lation size, (2) no migration across populations, (3) no net accumulation of mutations, (4) random mating, and (5) no natural selection. As you might guess, these are stringent conditions, rarely met. When we find departures from expected allele and genotype frequencies, we must reject the null hypothesis (see also chapter 15). If the null hypothesis is rejected, the population is in disequilibrium; we can look for the sources of change in allele or genotype frequencies. Five potential disequilibrium forces include: genetic drift, gene flow, mutation, nonran-dom mating, and natural selection (table 10.1). Compare these processes to the conditions required for H-W to predict equilibrium.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Population Genetics

  • Matthew Hamilton(Author)
  • 2011(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Table 2.2 , allowing you to calculate the odds ratio for a realistic example. In Chapter 4 we will reconsider the expected frequency of a DNA profile with the added complication of allele-frequency differentiation among human racial groups.

  Testing for Hardy–Weinberg

  A common use of Hardy–Weinberg expectations is to test for deviations from its null model. Populations with genotype frequencies that do not fit Hardy–Weinberg expectations are evidence that one or more of the evolutionary processes embodied in the assumptions of Hardy–Weinberg are acting to determine genotype frequencies. Our null hypothesis is that genotype frequencies meet Hardy–Weinberg expectations within some degree of estimation error. Genotype frequencies that are not close to Hardy–Weinberg expectations allow us to reject this null hypothesis. The processes in the list of assumptions then become possible alternative hypotheses to explain observed genotype frequencies. In this section we will work through a hypothesis test for Hardy–Weinberg equilibrium.

  The first example uses observed genotypes for the MN blood group, a single locus in humans that has two alleles (Table 2.4 ). First we need to estimate the frequency of the M allele, using the notation that the estimated frequency of M is and the frequency of N is . Note that the “hat” superscripts indicate that these are allele-frequency estimates (see Chapter 1). The total number of alleles is 2N given a sample of N diploid individuals. We can then count up all of the alleles of one type to estimate the frequency of that allele.

  Box 2.1 DNA profiling

  The loci used for human DNA profiling are a general class of DNA sequence marker known as simple tandem repeat (STR), simple sequence repeat (SSR), or microsatellite loci. These loci feature tandemly repeated DNA sequences of one to six base pairs (bp) and often exhibit many alleles per locus and high levels of heterozygosity. Allelic states are simply the number of repeats present at the locus, which can be determined by electrophoresis of PCR amplified DNA fragments. STR loci used in human DNA profiling generally exhibit Hardy–Weinberg expected genotype frequencies, there is evidence that the genotypes are selectively “neutral” (i.e. not affected by natural selection), and the loci meet the other assumptions of Hardy–Weinberg. STR loci are employed widely in population genetic studies and in genetic mapping (see reviews by Goldstein & Pollock 1997; McDonald & Potts 1997).

  Sign up to read

  Learn more about book