Solving Problems on Hardy Weinberg Equilibrium

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Subject: Biology - Other

Field: Biology


“In a butterfly population, the color brown (B) is dominant over the color white (b). And, 30 % of all butterflies are white. Calculate the percentage of heterozygous butterflies in the population?”

Sounds familiar? Well, sure it does, for as students of evolutionary genetics, you are often faced with the task of computing variations in allele frequencies of populations under the Hardy Weinberg equilibrium since you sometimes fail to grasp the entire concept and its application. As students, we often wonder about the need or importance of this calculation and how to go about it becomes a dominant thought. This article is directed to empower you to solve problems on the Hardy Weinberg Equilibrium.

First, let a break apart the problem into fundamental steps. What do you need to know to solve such problems? 

  1. Concept of evolutionary genetics with regards to Hardy Weinberg equilibrium
  2. Application of that conceptual knowledge

Hardy Weinberg Equilibrium

Hardy Weinberg Equilibrium is an equation that states the changes in the genetic variation in a population and remains in equilibrium from one generation to another, provided certain conditions are maintained. It was discovered independently by Wilhelm Weinberg (Physician) and Thomas Hardy (Mathematician) in 1908.

So what does it mean?

Let P represent the dominant allele and q be the recessive allele expressing a certain population trait. According to Hardy Weinberg Equilibrium, in a stable population at equilibrium, allele frequencies for a particular locus involving the genotypic and allele frequencies remain constant from generation to generation. Hence for mating between two individuals in that population, we have 

             (P +q)2 =P2 +2Pq + q2 =1 

   or P+q=1, so P= 1-q 

This equation is a simple binomial expression that defines the allele frequencies of homozygous dominant, heterozygote, and homozygous recessives in the population. 

Remember the following points:

Frequency of homozygous dominant = P2Frequency of heterozygous 

  1. allele = Pq + Pq=2 Pq
  2. Frequency of homozygous recessive allele=q2
  3. ( P +q)2 =P2 +2Pq + q2 =1 , or P+q = 1 , 
  4. P= 1-q , or q = 1-P ( since P+q =1)

But it is imperative to understand that all populations are not Hardy Weinberg populations, and certain conditions must be maintained by the population to be recognized as in HW equilibrium.

Conditions of Hardy Weinberg Equilibrium 

  1. The population is large
  2. Mating is random in the population without any bias towards any trait (panmictic) 
  3. Migration of genes is absent through emigration or immigration 
  4. Random Genetic drive is absent 
  5. The meiotic drive is absent 

When your knowledge base is optimum, although it sometimes may appear tricky, the problem can be solved easily 

1) Understand the data given in the problem

The initial difficulty arises in the misinterpretation of the problem. The language must be followed correctly, and the salient points of data are identified for further analysis. Hardy Weinberg problems can come in different variations; identification of equilibrium condition, or finding out the heterozygote frequency and its associations, a component like the expression in frequency or number of individuals or certain diseases, even blood grouping in populations.

Let us consider the initial problem: 

The color brown (B) is dominant over the color white (b) in the population. And, 30% of all butterflies are white.

 Going through the problem, it is evident that

  • B is the dominant allele
  • b is the recessive allele

30% of the population is white.  This data provides valuable information.   

2) Use the given information to find out the frequency of the recessive allele 

In the given problem, when gone through properly, there are always details present that can provide crucial information regarding the allele under consideration.

Hence, according to the problem, 30% of the population is white, and since white is a recessive color, all whites are homozygous recessives.

So, according to the HW equilibrium, the q2 =30% or 0.3 so q= √ 0.3=0.547

3) Find out the frequency of the dominant allele

The next stage of the exercise is to calculate the other allele's frequency, usually the dominant allele. According to the Hardy Weinberg equilibrium, the recessive homozygote or the recessives bear only the q allele; hence, it is convenient to calculate the recessive allele initially. It makes the calculation of the dominant allele extremely simple 

Thus with the help of the frequency of the recessive allele and the Hardy Weinberg Equation, one can easily find out the frequency of the dominant allele P

Hence P= 1-q= 1-0.547=0.453

4) Calculation of the required allele frequency according to the problem 

The next is the calculation of the required allele frequency or percentage or number of individuals as per the problem 

It would help if you calculated the frequency of Heterozygote according to the requirement of the problem.

So, heterozygous = 2 pq = 2x0.453x0.547=0.495 

5) Finally, you need to answer the problem according to the required parameter in the question 

Since the problem is given in percentage unit, the answer will be 49.5%. 

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