4.3: Hardy Weinberg - Biology

4.3: Hardy Weinberg - Biology

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Skills to Develop

  • Define population genetics and describe how population genetics is used in the study of the evolution of populations
  • Define the Hardy-Weinberg principle and discuss its importance

The mechanisms of inheritance, or genetics, were not understood at the time Charles Darwin and Alfred Russel Wallace were developing their idea of natural selection. This lack of understanding was a stumbling block to understanding many aspects of evolution. In fact, the predominant (and incorrect) genetic theory of the time, blending inheritance, made it difficult to understand how natural selection might operate. Darwin and Wallace were unaware of the genetics work by Austrian monk Gregor Mendel, which was published in 1866, not long after publication of Darwin's book, On the Origin of Species. Mendel’s work was rediscovered in the early twentieth century at which time geneticists were rapidly coming to an understanding of the basics of inheritance. Initially, the newly discovered particulate nature of genes made it difficult for biologists to understand how gradual evolution could occur. But over the next few decades genetics and evolution were integrated in what became known as the modern synthesis—the coherent understanding of the relationship between natural selection and genetics that took shape by the 1940s and is generally accepted today. In sum, the modern synthesis describes how evolutionary processes, such as natural selection, can affect a population’s genetic makeup, and, in turn, how this can result in the gradual evolution of populations and species. The theory also connects this change of a population over time, called microevolution, with the processes that gave rise to new species and higher taxonomic groups with widely divergent characters, called macroevolution.

Everyday Connection: Evolution and Flu Vaccines

Every fall, the media starts reporting on flu vaccinations and potential outbreaks. Scientists, health experts, and institutions determine recommendations for different parts of the population, predict optimal production and inoculation schedules, create vaccines, and set up clinics to provide inoculations. You may think of the annual flu shot as a lot of media hype, an important health protection, or just a briefly uncomfortable prick in your arm. But do you think of it in terms of evolution?

The media hype of annual flu shots is scientifically grounded in our understanding of evolution. Each year, scientists across the globe strive to predict the flu strains that they anticipate being most widespread and harmful in the coming year. This knowledge is based in how flu strains have evolved over time and over the past few flu seasons. Scientists then work to create the most effective vaccine to combat those selected strains. Hundreds of millions of doses are produced in a short period in order to provide vaccinations to key populations at the optimal time.

Because viruses, like the flu, evolve very quickly (especially in evolutionary time), this poses quite a challenge. Viruses mutate and replicate at a fast rate, so the vaccine developed to protect against last year’s flu strain may not provide the protection needed against the coming year’s strain. Evolution of these viruses means continued adaptions to ensure survival, including adaptations to survive previous vaccines.

​​​​​​Population Genetics

Recall that a gene for a particular character may have several alleles, or variants, that code for different traits associated with that character. For example, in the ABO blood type system in humans, three alleles determine the particular blood-type protein on the surface of red blood cells. Each individual in a population of diploid organisms can only carry two alleles for a particular gene, but more than two may be present in the individuals that make up the population. Mendel followed alleles as they were inherited from parent to offspring. In the early twentieth century, biologists in a field of study known as population genetics began to study how selective forces change a population through changes in allele and genotypic frequencies.

The allele frequency (or gene frequency) is the rate at which a specific allele appears within a population. Until now we have discussed evolution as a change in the characteristics of a population of organisms, but behind that phenotypic change is genetic change. In population genetics, the term evolution is defined as a change in the frequency of an allele in a population. Using the ABO blood type system as an example, the frequency of one of the alleles, IA, is the number of copies of that allele divided by all the copies of the ABO gene in the population. For example, a study in Jordan1 found a frequency of IA to be 26.1 percent. The IB and I0 alleles made up 13.4 percent and 60.5 percent of the alleles respectively, and all of the frequencies added up to 100 percent. A change in this frequency over time would constitute evolution in the population.

The allele frequency within a given population can change depending on environmental factors; therefore, certain alleles become more widespread than others during the process of natural selection. Natural selection can alter the population’s genetic makeup; for example, if a given allele confers a phenotype that allows an individual to better survive or have more offspring. Because many of those offspring will also carry the beneficial allele, and often the corresponding phenotype, they will have more offspring of their own that also carry the allele, thus, perpetuating the cycle. Over time, the allele will spread throughout the population. Some alleles will quickly become fixed in this way, meaning that every individual of the population will carry the allele, while detrimental mutations may be swiftly eliminated if derived from a dominant allele from the gene pool. The gene pool is the sum of all the alleles in a population.

Sometimes, allele frequencies within a population change randomly with no advantage to the population over existing allele frequencies. This phenomenon is called genetic drift. Natural selection and genetic drift usually occur simultaneously in populations and are not isolated events. It is hard to determine which process dominates because it is often nearly impossible to determine the cause of change in allele frequencies at each occurrence. An event that initiates an allele frequency change in an isolated part of the population, which is not typical of the original population, is called the founder effect. Natural selection, random drift, and founder effects can lead to significant changes in the genome of a population.

Hardy-Weinberg Principle of Equilibrium

In the early twentiethcentury, English mathematician Godfrey Hardy and German physician Wilhelm Weinberg stated the principle of equilibrium to describe the genetic makeup of a population. The theory, which later became known as the Hardy-Weinberg principle of equilibrium, states that a population’s allele and genotype frequencies are inherently stable— unless some kind of evolutionary force is acting upon the population, neither the allele nor the genotypic frequencies would change. The Hardy-Weinberg principle assumes conditions with no mutations, migration, emigration, or selective pressure for or against genotype, plus an infinite population; while no population can satisfy those conditions, the principle offers a useful model against which to compare real population changes.

Working under this theory, population geneticists represent different alleles as different variables in their mathematical models. The variable p, for example, often represents the frequency of a particular allele, say Y for the trait of yellow in Mendel’s peas, while the variable q represents the frequency of y alleles that confer the color green. If these are the only two possible alleles for a given locus in the population, p + q = 1. In other words, all the p alleles and all the q alleles make up all of the alleles for that locus that are found in the population.

But what ultimately interests most biologists is not the frequencies of different alleles, but the frequencies of the resulting genotypes, known as the population’s genetic structure, from which scientists can surmise the distribution of phenotypes. If the phenotype is observed, only the genotype of the homozygous recessive alleles can be known; the calculations provide an estimate of the remaining genotypes. Since each individual carries two alleles per gene, if the allele frequencies (p and q) are known, predicting the frequencies of these genotypes is a simple mathematical calculation to determine the probability of getting these genotypes if two alleles are drawn at random from the gene pool. So in the above scenario, an individual pea plant could be pp (YY), and thus produce yellow peas; pq (Yy), also yellow; or qq (yy), and thus producing green peas (Figure (PageIndex{1})). In other words, the frequency of pp individuals is simply p2; the frequency of pq individuals is 2pq; and the frequency of qq individuals is q2. And, again, if p and q are the only two possible alleles for a given trait in the population, these genotypes frequencies will sum to one: p2 + 2pq + q2 = 1.

Art Connection

In plants, violet flower color (V) is dominant over white (v). If p = 0.8 and q = 0.2 in a population of 500 plants, how many individuals would you expect to be homozygous dominant (VV), heterozygous (Vv), and homozygous recessive (vv)? How many plants would you expect to have violet flowers, and how many would have white flowers?

In theory, if a population is at equilibrium—that is, there are no evolutionary forces acting upon it—generation after generation would have the same gene pool and genetic structure, and these equations would all hold true all of the time. Of course, even Hardy and Weinberg recognized that no natural population is immune to evolution. Populations in nature are constantly changing in genetic makeup due to drift, mutation, possibly migration, and selection. As a result, the only way to determine the exact distribution of phenotypes in a population is to go out and count them. But the Hardy-Weinberg principle gives scientists a mathematical baseline of a non-evolving population to which they can compare evolving populations and thereby infer what evolutionary forces might be at play. If the frequencies of alleles or genotypes deviate from the value expected from the Hardy-Weinberg equation, then the population is evolving.


The modern synthesis of evolutionary theory grew out of the cohesion of Darwin’s, Wallace’s, and Mendel’s thoughts on evolution and heredity, along with the more modern study of population genetics. It describes the evolution of populations and species, from small-scale changes among individuals to large-scale changes over paleontological time periods. To understand how organisms evolve, scientists can track populations’ allele frequencies over time. If they differ from generation to generation, scientists can conclude that the population is not in Hardy-Weinberg equilibrium, and is thus evolving.

Art Connections

[link] In plants, violet flower color (V) is dominant over white (v). If p=.8 and q = 0.2 in a population of 500 plants, how many individuals would you expect to be homozygous dominant (VV), heterozygous (Vv), and homozygous recessive (vv)? How many plants would you expect to have violet flowers, and how many would have white flowers?

[link] The expected distribution is 320 VV, 160Vv, and 20 vv plants. Plants with VV or Vv genotypes would have violet flowers, and plants with the vv genotype would have white flowers, so a total of 480 plants would be expected to have violet flowers, and 20 plants would have white flowers.

  1. 1 Sahar S. Hanania, Dhia S. Hassawi, and Nidal M. Irshaid, “Allele Frequency and Molecular Genotypes of ABO Blood Group System in a Jordanian Population,” Journal of Medical Sciences 7 (2007): 51-58, doi:10.3923/jms.2007.51.58.


allele frequency
(also, gene frequency) rate at which a specific allele appears within a population
founder effect
event that initiates an allele frequency change in part of the population, which is not typical of the original population
gene pool
all of the alleles carried by all of the individuals in the population
genetic structure
distribution of the different possible genotypes in a population
broader scale evolutionary changes seen over paleontological time
changes in a population’s genetic structure
modern synthesis
overarching evolutionary paradigm that took shape by the 1940s and is generally accepted today
population genetics
study of how selective forces change the allele frequencies in a population over time

Teaching Hardy-Weinberg Equilibrium using Population-Level Punnett Squares: Facilitating Calculation for Students with Math Anxiety

Hardy-Weinberg (HW) equilibrium and its accompanying equations are widely taught in introductory biology courses, but high math anxiety and low math proficiency have been suggested as two barriers to student success. Population-level Punnett squares have been presented as a potential tool for HW equilibrium, but actual data from classrooms have not yet validated their use. We used a quasi-experimental design to test the effectiveness of Punnett squares over 2 days of instruction in an introductory biology course. After 1 day of instruction, students who used Punnett squares outperformed those who learned the equations. After learning both methods, high math anxiety was predictive of Punnett square use, but only for students who learned equations first. Using Punnett squares also predicted increased calculation proficiency for high-anxiety students. Thus, teaching population Punnett squares as a calculation aid is likely to trigger less math anxiety and help level the playing field for students with high math anxiety. Learning Punnett squares before the equations was predictive of correct derivation of equations for a three-allele system. Thus, regardless of math anxiety, using Punnett squares before learning the equations seems to increase student understanding of equation derivation, enabling them to derive more complex equations on their own.

4.3: Hardy Weinberg - Biology

Scarlet tiger moth (Callimorpha dominula). Photo credit: copyright Shane Farrell, England.

Consider a gene locus in a diploid population with two possible alleles, A and a. Let p and q represent the frequency of the A and a alleles in the population, respectively. As there are only two possible alleles, p and q, we know that

The three genotypes possible are AA, Aa, and aa. The Hardy-Weinberg Law states that after one generation of random mating, the frequencies of the three genotypes in the population are given by:

An individual has genotype AA if both parents contribute an A allele. Likewise, if both parents contribute an a allele then the individual has genotype aa. This can happen one way, and the probability that an individual is homozygous for allele A is the frequency of the A allele in the population squared, and the probability that an individual is homozygous for allele a is the frequency of the a allele in the population squared.

An individual has genotype Aa if either an A allele is inherited maternally and an a allele is inherited paternally, or if an a allele is inherited maternally and an A allele is inherited paternally. The probability of having an A and a allele is pq (the product of their frequencies in the population), and since a heterozygous genotype can arise two different ways, the frequency of genotype Aa is 2pq. Notice that because p+q = 1, we also know that (p+q) 2 = p 2 +2pq +q 2 = 1.

A note of caution

The Hardy-Weinberg Law assumes that the population mates randomly, is of infinite size, and that there is no mutation, no migration, and no natural selection.

4.3: Hardy Weinberg - Biology

What will happen in the next generation? To answer this question, we will use the Hardy-Weinberg principle, which applies basic rules of probability to a population to make predictions about the next generation. The Hardy-Weinberg principle predicts that allelic frequencies remain constant from one generation to the next, or remain in EQUILIBRIUM, if we assume certain conditions (which we will discuss below).

For example, if the allelic frequencies of alleles A and a in the initial population were p = 0.8 and q = 0.2, the allelic frequencies in the next generation will remain p = 0.8 and q = 0.2. The conditions for Hardy-Weinberg equilibrium are rarely (if ever) encountered in nature, but they are fundamental to understanding population genetics. When a population deviates from Hardy-Weinberg predictions, it is evidence that at least one of the conditions in not being met. Scientists can then determine why allelic frequencies are changing, and thus how evolution is acting on the population.

The conditions for Hardy-Weinberg equilibrium:

  1. Population is infinitely large -&ndash or large enough to minimize the effect of genetic drift, which is change in allele frequencies due entirely to random chance (and not selection).
  2. No selection occurs - so all the individuals in the population have an equal chance of surviving and reproducing.
  3. Mating is random &ndash so that an individual is equally likely to mate with any potential mate in the population, regardless of genotype or phenotype.
  4. No migration - so no alleles enter or leave the population.
  5. No mutation - so allelic characteristics do not change

Because mating is random (Condition 3, above), we can think of these diploid individuals as simply mixing their gametes. We do not need to consider the parental origin of a given gamete (i.e. if it comes from a heterozygous or homozygous parent), but simply the proportion of alleles in the population. For example, for the population mentioned previously with p value of 0.8 and q value of 0.2, we can think of a bag of mixed gametes with 80% of which are A and 20% are a .

Therefore, on the paternal side (the sperm) we have the given proportions of the two alleles (0.8 of allele A and 0.2 of allele a ) freely mixing with the eggs (the maternal contributions), which have the alleles in the same proportions (0.8 of A and 0.2 of a ).

The probability of an A sperm meeting an A egg is 0.8 x 0.8 = 0.64. The probability of an A sperm meeting an a egg is 0.8 x 0.2 = 0.16. The probability of an a sperm meeting an A egg is 0.8 x 0.2 = 0.16. The probability of an a sperm meeting an a egg is 0.2 x 0.2 = 0.04.

Therefore in the following generation, we would expect to have the following proportion of genotypes:

That is, if there were a thousand offspring, there would be:

This in turn translates to 1600 A alleles (640 + 640 + 320), and 400 a alleles (320 + 40 + 40). 1600/2000 = 0.8 and 400/2000 = 0.2 that is, the allele frequencies are the same as in the parental generation.

To generalize: if the allele frequencies are p and q, then at Hardy-Weinberg Equilibrium you will have (p + q) X (p + q) = p 2 + 2pq + q 2 as the distribution of the genotypes.

  • The frequency of AA individual will be p 2 .
  • The frequency of Aa individuals will be 2pq.
  • The frequency of aa individuals will be q 2 .

Furthermore, the frequency of A alleles will be p 2 + pq (equal to the frequency of AA individuals plus half the frequency of Aa individuals). Since p + q =1, then q = 1 - p. The frequency of A alleles is p 2 + pq, which equals p 2 + p (1 &mdash p) = p 2 + p &mdash p 2 = p that is, p stays the same from one generation to the next. The same can be shown for q.

So we see that with random mating, no selection, no migration or mutation, and a population large enough that the effects of random chance are negligible, the proportion of alleles in a population stays the same from generation to generation.

Let&rsquos test your knowledge of this topic:
In a population that is in Hardy-Weinberg equilibrium, the frequency of the dominant allele A is 0.40. What is the frequency of individuals with each of the three allele combinations, AA , Aa and aa ?

Frequency of AA individuals: _______
Frequency of Aa individuals: _______
Frequency of aa individuals: _______

Click here for an explanation:

Since the frequency of allele A is 0.4, the frequency of allele a is 1 &ndash 0.4 = 0.6.

When the population is in Hardy-Weinberg equilibrium:

The frequency of AA individuals is (0.4)(0.4) = 0.16
The frequency of Aa individuals is 2(0.6)(0.4) = 0.48
The frequency of aa individuals is (0.6)(0.6) = 0.36

(Note: a good way to check if your answers are correct is to verify that the values add up to 1.)

Hardy-Weinberg Equilibrium & Natural Selection

In this article we will discuss about the Hardy-Weinberg Equilibrium in Relation to Natural Selection:- 1. Meaning of Hardy-Weinberg Equilibrium 2. Elaboration of Hardy-Weinberg Equilibrium 3. A Case study of Natural Selection 4. Factors Effecting 5. Measurement of Fitness and Selection.

  1. Meaning of Hardy-Weinberg Equilibrium
  2. Elaboration of Hardy-Weinberg Equilibrium
  3. A Case study of Natural Selection
  4. Factors Effecting Hardy-Weinberg Equilibrium
  5. Measurement of Fitness and Selection in Hardy-Weinberg Equilibrium

1. Meaning of Hardy-Weinberg Equilibrium:

It is a theory of population genetics, separately deduced by G. H. Hardy (1908) and W. Weinberg (1908) based on Mendel’s law of heredity. In this theory they proposed that, “if all other factors remain constant, the frequencies of particular genes and geno­types will remain constant in a population, generation after generation”. This genetic stability of population is known as Hardy – Weinberg equilibrium or genetic inertia.

To understand this theory one have to be acquainted with following terminologies.

An ecological popula­tion is a group of organisms of the same species living together within a common area at the same time and interbreeding with each other. Among geneticists a population is usual­ly defined as a community of sexually inter­breeding or potentially interbreeding individuals.

Since Mendelian laws apply to the transmission of genes among these individu­als, such a community has been termed by Wright as a ‘Mendelian population’.

The size of the population may vary, but it is usu­ally considered to be a local group (also called deme), each member of which has an equal chance of mating with any other mem­ber of the opposite sex, i.e., random mating. As most of the theoretical discussions are made on the diploid organisms, we will con­sider here only diploid population.

These are simply the proportions of the different alleles of a gene in a population.

Let us consider a diploid organism has only two genes at any locus in a Mendelian population. For example, if we consider the human MN blood group of 100 member population, there are a total of 200 genes in the population that contain 50-MM individuals, 20-MN individuals and 30-NN individuals. What will be the frequencies of M and N genes?

200 genes are present in 100 persons, as humans are diploid. Among hun­dred people, there are 50MM, 20MN and 30NN individuals.’

50 MM people contain 50 x 2 = 100 M genes.

20 MN people contain 20 M genes and 20 N genes.

30 NN people contain 30 x 2 = 60 N genes.

Therefore, number of M genes in this population is 100 + 20 = 120 and that of N genes is 60 + 20 = 80.

Among 200 genes M is 120 in number

among 1 gene M is 120/200 = 0.6 and similarly, among 200 genes N is 80 in number

among 1 gene N is 80/200 = 0.4.

So, the gene frequency of M is 0.6 and N is 0.4 in this population.

(iii) Genotype Frequency:

This is the simple proportion of different genotypes of a gene and its alleles in a population.

If we consider the same popu­lation as described in gene frequency — what will be the genotype frequencies?

As per example, number of MM genotypic individuals are 50, MN indi­viduals are 20 and NN are 30. Total number of individuals are 100.

Again, using unitary system.

Among 100 individuals MM are 50

Similarly, among 100 individuals MN are 20

And among 100 individuals NN are 30

From this solution it is found that the fre­quency of MM genotype is 0.5, frequency of MN genotype is 0.2 and frequency of NN genotype is 0.3.

Calculation of Gene Frequency from Genotype Frequency:

The gene frequencies can be calculated from the genotype frequencies directly, using the following formula.

(as each heterozygote contains one such gene).

In our foregoing example of genotype frequency calculation, we find MM = 0.5, MN = 0.2 and NN = 0.3. Putting these values in the formula we can get the frequen­cies of M and N genes.

This result corresponds to the result of the previous calculation of gene frequencies.

It is the sum total of genes in the reproductive gametes of a popu­lation.

2. Elaboration of Hardy-Weinberg Equilibrium:

The general relationship between gene frequencies and genotype frequencies can be described in algebraic terms by means of Hardy-Weinberg principle as follows.

If p is the frequency of a certain gene in a panmictic population (suppose gene M) and q is the frequency of its allele (in this case N gene), so that p + q = 1 (i.e., there are no other alleles), the frequencies of the genotypes in the population in equilibrium will be p 2 for MM, 2 pq for MN and q 2 for NN and the sum of all these genotype frequencies will be equal to 1.

The same results are also produced by the expansion of the binomial (p + q) 2 = p 2 + 2pq + q 2 .

From our example of MN blood group of man we can see that p = M = 0.6 and q = N = 0.4 and p + q = 1. The genotype frequencies at equilibrium condition will be

MN = 2pq = 2 x 0.6 x 0.4 = 0.48

Then p 2 + 2pq + q 2 = 0.36 + 0.48 + 0.16 = 1

Therefore, it can be said that the popula­tion is in equilibrium state. If this popula­tion interbreeds, the next generation of this population will also show equilibrium. The proportion of the two genes will be same in the next generation.

But if selection pressure works on any genotype, then number of the particular genotype may change. Still the p 2 + 2pq + q 2 will show the value 1, gene­ration after generation. Natural Selection and Hardy-Weinberg

According to Neutrality concept of molecular evolution, selection forces act at gene level. In general, a gene locus is considered to be polymorphic if at least two alleles are present in the popula­tion, with a frequency of at least 1 percent for the second most frequent allele.

The mainte­nance of different genotypes in a population through heterozygote superiority is termed as ‘balanced polymorphism’, which is neces­sary to preserve genetic variability through selection. Different polymorphic forms may become established in different environment.

3. A Case study of Natural Selection:

The British pep­pered moth Bistort betularia was observed for a long period. They were nocturnal in habit and during day they used to rest on surfaces mainly on trunks. There were two types of moths, one with pale wings with minute black markings and is almost invisible on lichen covered tree trunks, and the other with black wings.

The number of different varie­ties of moth collected over a long period from Manchester is tabulated below:

(i) This change from predominant pale- coloured population of moths to black (melanic) population took only 50 years and corresponds with the most rapid increase in industrial development.

(ii) The difference between pale moth (variety typica) and melanic form (variety carbonaria) is the differential selection of polymorphic forms of genes.

(iii) The genes responsible for production of melanic forms were probably hidden in the population for many years. But they were not selected in the non-industrial areas, where they were easily predated by the birds during day time, as they were con­spicuous in the usual lichen-covered tree trunk.

(iv) With the advancement of indus­trialization and pollution, the situa­tion becomes opposite. Due to pollu­tion, lichens became absent on the tree trunks. The pale moths thus become conspicuous and were sub­jected to predation. Thus, nature gradually selected the melanic forms.

4. Factors Effecting Hardy-Weinberg Equilibrium:

The genetic properties of a population are influenced by the process of transmission of genes from one generation to the next by a number of agencies, irrespective of whether the population is in equilibrium or in non-equilibrium.

There are two types of processes by which we can describe the changes of gene and genotype frequencies. One is the ‘systematic process’, which tends to change the gene frequency in a manner predictable both in ‘amount’ and in ‘direc­tion’.

The other is the ‘dispersive process’, which arises in small populations from the effects of sampling, and is predictable in ‘amount’ but not in ‘direction’. There are three systematic processes — migration, mutation and selection.

The dispersive process includes four consequences, random drift, differentiation between sub-popula­tions, uniformity within sub-populations and increased homozygosity. Due to lack of scope we will discuss only systematic processes here.

The gene frequencies in the population may be changed by immigration or emigration of individuals from one population to the other. Therefore, number of individu­als will change from the existing condition. It may increase or decrease. In that case how we shall determine the gene frequency or genotype frequency?

Calculation of Gene Frequency in Case of Migration:

Suppose that a large population consists of a proportion x of new immigrants in each generation. Therefore, the remainder, 1 – x, will be natives.

Again, let the frequency of a gene (sup­pose m gene) be qx among immigrants and q0 among the natives. Then the frequency of the m gene in the mixed population (suppose qz) Will be

The change of gene frequency, ∆q, brought about by one generation of immi­gration will be the difference between the frequency before immigration and the fre­quency after immigration. Therefore, ∆q will be like this —

So, it can be said that the rate of change of gene frequency (here m gene) in a popula­tion depends on the immigration rate and on the difference of gene frequency between immigrants and natives.

In a population we can observe two types of mutations. One is ‘non-recurrent’ and the other is ‘recurrent’ mutation. In case of non-recurrent mutation, just one represen­tative of the mutated gene or chromosome appears in the whole population. This type of mutation is of very little importance in changing the gene frequency in a population.

In most of the cases this mutation product gets lost from the population, after one or- two generations. The recurrent mutation results in the appearance of mutant gene which is never so low so as to get completely lost from the population. Therefore, it exerts a ‘pressure’ on the gene frequency of the population.

How this Pressure can be Estimated?

Suppose that gene m, mutates to m2 with a frequency u per generation, (u is the pro­portion of all m1 genes that mutate to m2 between one generation and the next). Let the frequency of m, in one generation is q0, then the frequency of newly mutated m2 genes in the next generation is u times of q0, i.e., u.q0. So the new gene frequency of m, in this generation is q0-u.q0. Therefore, the change of gene frequency is – u.q0 or

All individuals of a population may not contribute equally their genetic materials to the next generation. This is because of the fact that individuals differ in viability and fertility. It is obvious that if individuals carrying gene a + are more successful in producing viable and fertile offspring than individuals carrying its allele a + , then the frequency of a + will tend to increase.

The wide variety of mechanisms that affect the reproductive success of a genotype is known collectively as ‘selection’, and the extent to which a genotype contributes to the offspring of the next generation is com­monly known as its ‘fitness, selective value or adaptive value’.

Therefore, if fitness is related with presence or absence of a particular gene (a – ) in the individual’s genotype, then it can be said that ‘selection’ operates on that gene. Thus, the gene which is under selection pressure will not be in same frequency as the parents and offspring. In this way, along with selection comes a change of gene frequency and consequently change in geno­type frequency.

5. Measurement of Fitness and Selection in Hardy-Weinberg Equilibrium:

It can be measured by the number of fertile offspring’s produced by one genotype compared to those produced by another. Suppose, if individuals of genotype a + produce an average 100 offspring’s that reach full reproductive maturity while genotype a + individuals produce only 90 in the same environment.

The adaptive value of a – relative to a + is reduced by ten offspring’s or the fraction 10/100 = 0.1. If we designate the adaptive value of a genotype as ‘w’ and the selective force acting to reduce its adaptive value as ‘s’ (the selection coefficient), then we can say that w = 1 and s = o for a + genotype and w = 0.9 and s = 0.1 for a + . The relationship between w and s is therefore, simply w = 1 – s or s = 1 – w.

Youreka Science

Youreka Science was created by Florie Mar, PhD, while she was a cancer researcher at UCSF. While teaching 5th graders about the structure of a cell, Mar realized the importance of incorporating scientific findings into classroom in an easy-to-understand way. From that she started creating whiteboard drawings that explained recent papers in the scientific literature… Continue Reading


The genesis of Hardy's letter to Science has been described by P unnett (1950), who in 1908 put the genetic problem to him. At that time R. C. Punnett was a Fellow of Gonville and Caius College and a Balfour Student in the Cambridge University Department of Zoology, and since 1903 had been assisting William Bateson with his Mendelian experiments. The circumstances can be described starting from Punnett's account, but with some significant variation where the written record differs from his recollection 41 years later.

On February 28, 1908, Punnett gave a lecture “Mendelism in relation to disease” to the Epidemiological Section of the Royal Society of Medicine in London (P unnett 1908). (In 1950 he mistakenly gave the title as “Mendelian heredity in man.”) It was a very full account of Mendelism as it was then understood, principally through the work of Bateson and his colleagues in Cambridge, suitably adjusted to appeal to a medical audience. In the Discussion, which is printed with the paper, M. Greenwood and Yule, associates of Karl Pearson, led the criticism of the “Mendelian school.” Yule said that if in man brachydactyly was determined by a dominant gene and random mating assumed, then “in the course of time one would then expect, in the absence of counteracting factors, to get three brachydactylous persons to one normal” but that this was not so.

Here Yule seems to have still been under the misapprehension that implicit in the Mendelian theory was the assumption that the gene frequency was one-half, for then indeed a 3:1 ratio would appear and be maintained.

Be that as it may, in his reply Punnett interpreted Yule as having asked “why the nation was not slowly becoming … brachydactylous.” (The example of brown and blue eyes was also mentioned, but because Hardy used brachydactyly as the sole example, we do so too.) This was not quite what Yule had suggested, as noted by C rew (1967) in his Royal Society obituary of Punnett, but from both P unnett 's (1950) later account and Hardy's letter it is clear that Punnett was perplexed as to why the dominant gene did not continually increase in frequency, and this is the problem he put to Hardy. Yule might easily have corrected him after the meeting, but presumably did not. P unnett (1950) later claimed that he answered that the heterozygotes must also contribute their “quota” of the recessives “and that somehow this must lead to equilibrium,” but there is no evidence of this in the printed record of the meeting.

4.3: Hardy Weinberg - Biology

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The Hardy-Weinberg Principle predicts allelic frequencies for a population that is not evolving.

When considering two alleles at a locus, like a red and brown coat allele in a squirrel population, the sum of the frequencies of each of the alleles represented by the letters p and q will equal one since there are only two alleles.

Additionally, the frequencies of each of the specific genotypes can be calculated. The frequency of red and brown coated individuals in the population, both of the homozygous types, will equal the square of the allelic frequency, or p squared and q squared. Since homozygous individuals have two of the same alleles.

Heterozygous individuals with red brown coats can arise two ways. If the egg provides the red allele and sperm the brown or vice versa. Therefore the frequency of the heterozygous individuals is two times the product of the allelic frequencies, Two times p times q.

The sum of all of these genotypic frequencies will be one. This principle is only true under specific, non-evolving conditions. There must be no selection, mating is random, and there is no selection for particular genotypes. There must be no gene flow from outside the population, and no mutations inside the population. Last, the population size must be very large because in small populations random events can substantially change allelic frequencies.

32.2: Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

In the early 20 th century, scientists wondered why the frequency of some rarely-observed dominant traits did not increase in randomly-mating populations with each generation. For example, why does the dominant polydactyly trait (E, extra fingers and/or toes) not become more common than the usual number of digits (e) in many animal species? In 1908, this phenomenon of unchanged genetic variation across generations was independently demonstrated by a German physician, Wilhelm Weinberg, and a British Mathematician, G. H. Hardy. The principle later became known as Hardy-Weinberg equilibrium.

Hardy-Weinberg Equation

The Hardy-Weinberg equation (p 2 + 2pq + q 2 = 1) elegantly relates allele frequencies to genotype frequencies. For instance, in a population with polydactyly cases, the gene pool contains E and e alleles with relative frequencies of p and q, respectively. Since the relative frequency of an allele is a proportion of the total population, p and q add up to 1 (p + q = 1).

The genotype of individuals in this population is either EE, Ee, or ee. Hence, the proportion of individuals with the EE genotype is p × p, or p 2 , and the proportion of individuals with the ee genotype is q × q, or q 2 . The proportion of heterozygotes (Ee) is 2pq (p × q and q × p) since there are two possible crosses that produce the heterozygous genotype (i.e., the dominant allele can come from either parent). Similar to allele frequencies, genotype frequencies also add up to 1 therefore, p 2 + 2pq + q 2 = 1, which is known as the Hardy-Weinberg equation.

Hardy-Weinberg Conditions

Hardy-Weinberg equilibrium states that, under certain conditions, allele frequencies in a population will remain constant over time. Such populations meet five conditions: infinite population size, random mating of individuals, and an absence of genetic mutations, natural selection, and gene flow. Since evolution can simply be defined as the change in allele frequencies in a gene pool, a population that fits Hardy-Weinberg criteria does not evolve. Most natural populations violate at least one of these assumptions and therefore are seldom in equilibrium. Nevertheless, the Hardy-Weinberg principle is a useful starting point or null model for the study of evolution, and can also be applied to population genetics studies to determine genetic associations and detect genotyping errors.

Edwards, A. W. F. &ldquoG. H. Hardy (1908) and Hardy&ndashWeinberg Equilibrium.&rdquo Genetics 179, no. 3 (July 1, 2008): 1143&ndash50. [Source]

Douhovnikoff, Vladimir, and Matthew Leventhal. &ldquoThe Use of Hardy&ndashWeinberg Equilibrium in Clonal Plant Systems.&rdquo Ecology and Evolution 6, no. 4 (January 25, 2016): 1173&ndash80. [Source]

Salanti, Georgia, Georgia Amountza, Evangelia E. Ntzani, and John P. A. Ioannidis. &ldquoHardy&ndashWeinberg Equilibrium in Genetic Association Studies: An Empirical Evaluation of Reporting, Deviations, and Power.&rdquo European Journal of Human Genetics 13, no. 7 (July 2005): 840&ndash48. [Source]

Hosking, Louise, Sheena Lumsden, Karen Lewis, Astrid Yeo, Linda McCarthy, Aruna Bansal, John Riley, Ian Purvis, and Chun-Fang Xu. &ldquoDetection of Genotyping Errors by Hardy&ndashWeinberg Equilibrium Testing.&rdquo European Journal of Human Genetics 12, no. 5 (May 2004): 395&ndash99. [Source]

How to use chi-squared to test for Hardy-Weinberg equilibrium

This post demonstrates the use of chi-squared to test for Hardy-Weinberg equilibrium. There is a question on a recent (February 2020) AP Biology practice test that required this calculation. The question is a secure item, so the exact question will not be discussed here. There is a previous post on this blog explaining how to test for evolution using the null hypothesis and chi-squared.

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For our examples, we'll use the fictional species featured in many of the evolution simulations. The population demonstrates incomplete dominance for color. There are two alleles red and blue. Heterozygotes have a purple phenotype.

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Chi-squared is a statistical test used to determine if observed data (o) is equivalent to expected data (e). A population is at Hardy-Weinberg equilibrium for a gene if five conditions are met random mating, no mutation, no gene flow, no natural selection, and large population size. Under these circumstances, the allele frequencies for a population are expected to remain consistent (equilibrium) over time. The H-W equations are expected to estimate genotype and allele frequencies for a population that is at equilibrium. The equations may not accurately predict the frequencies if the population is not at equilibrium (for example, if selection is occurring). However, it is possible that, even with the presence of an evolutionary force, a population may still demonstrate the expected H-W data.

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In the case of a trait showing incomplete dominance, the heterozygotes are distinct from the homozygous dominant individuals, which allows the genotype and allele frequencies to be calculated directly (without the H-W equations). This direct calculation can be compared to values based on H-W calculations to determine if the population is at H-W equilibrium.

For the first example, we'll use a simple data set (not generated by a simulation). In this case, there are 50 total individuals in the population 10 are red, 10 are purple, and 30 are blue. These are the observed values for the chi-squared analysis.

Determining Genetic Risk

The Hardy-Weinberg Equation is useful for predicting the percent of a human population that may be heterozygous carriers of recessive alleles for certain genetic diseases. This law predicts how gene frequencies will be transmitted generation to generation. To estimate the frequency of alleles in a population one must understand the basics of the Hardy-Weinberg equation:

p = the frequency of the dominant allele (represented here by A)
q = the frequency of the recessive allele (represented here by a)

For a population in genetic equilibrium: p 2 + 2pq + q 2 = 1

p 2 = frequency of AA (homozygous dominant)
2pq= frequency of Aa (heterozygous)
q 2 = frequency of aa (homozygous recessive)

The following is an example of using the Hardy-Weinberg equation to predict carrier frequency:

Phenylketonuria (PKU) is an autosomal recessive metabolic disorder that results in mental retardation if untreated during the newborn period. In the United States, one out of 10,000 babies is born with PKU. Given this incidence, what percent of the population are heterozygous carriers of the recessive PKU allele?

q 2 = 1/10,000
q =&radic 1/10,00=1/100
p = 1 (does not change from "1" in most equations)
2pq = 2 (1) (1/100) = 1/50

Given the above calculations, 1/50 individuals in the general population are carriers of PKU. If you are counseling a couple where the woman has a previous child (with a different partner) who has PKU, her chance to be a carrier is100% (1). Her new husband's chance to be a carrier is the population risk of 1/50. The risk for the fetus to inherit the mutation from each parent is 25% (1/4). Therefore the formula to calculate the risk for the fetus to be affected is: 1 x 1/50 x 1/4 = 1/200.

Watch the video: Hardy-Weinberg Equilibrium (June 2022).