This is a very interesting topic in Population Genetics. A mathematics and biology combo of Hardy-Weinberg equilibrium is explained. The history, derivation, condition, merits and demerits of Hardy-Weinberg equilibrium is explained. Hope you all enjoy!!!!

1. Hardy-Weinberg Equilibrium
p2+ 2pq+ q2= 1 or (p+q)2 = 1

2. Gene: Unit of heredity
Allele: Alternating forms of the same gene
Phenotype: Observable characters
Genotype: Genetic makeup

3. History
• How is a dominant allele, responsible for 3:1 phenotype ratio in F2
generation, does not gradually replace all other types of alleles, if we
assume that all alleles confer equal fitness??
• For example, if a gene pool in one generation consists of 70% R alleles
and 30% r alleles, what stops proportion of R from increasing
dramatically??
• What proportion of alleles will be in the next generation??

4. • This very question was posed and independently answered by British
Mathematician Godfrey Hardy and German Physician Wilhelm Weinberg,
who first demonstrated it mathematically in 1908.
• The Hardy-Weinberg equilibrium states that the genetic variation in a
population will remain constant from one generation to the next in the
absence of disturbing factors.
• This predicts unchanging allele and genotype frequencies in a
population, a situation referred to as equilibrium.

5. Allele and Genotype Frequency
Allele frequency=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑝𝑖𝑒𝑠 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑎𝑙𝑙𝑒𝑙𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑎𝑙𝑙𝑒𝑙𝑒𝑠 𝑓𝑜𝑟 𝑡ℎ𝑎𝑡 𝑔𝑒𝑛𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Genotype frequency=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑤𝑖𝑡ℎ 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑔𝑒𝑛𝑜𝑡𝑦𝑝𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛

6. Question
• Let us consider a population of 100 pea plants with the following
genotypes:
49 purple flowered plants with genotype RR
42 purple flowered plants with genotype Rr
9 white flowered plants with genotype rr
• Calculate allele frequency of r and R?

7. Answer
Allele frequency=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑝𝑖𝑒𝑠 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑎𝑙𝑙𝑒𝑙𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑙𝑙 𝑎𝑙𝑙𝑒𝑙𝑒𝑠 𝑓𝑜𝑟 𝑡ℎ𝑎𝑡 𝑔𝑒𝑛𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Frequency of r =
(𝑅𝑟)+2(𝑟𝑟)
2(𝑅𝑅)+2(𝑅𝑟)+2(𝑟𝑟)
Frequency of r =
(42)+2(9)
2(49)+2(42)+2(9)
=
60
200
= 0.3 or 30%
49 = RR
42 = Rr
9 = rr

8. • Frequency of R =
(𝑅𝑟)+2(𝑅𝑅)
2(𝑅𝑅)+2(𝑅𝑟)+2(𝑟𝑟)
=
(42)+2(49)
2(49)+2(42)+2(9)
=
(42)+2(49)
2(49)+2(42)+2(9)
=
140
200
= 0.7 or 70%
As, total allele frequencies are always equal to 1 or 100%.
We can conclude when, r = 0.3, R= 1-0.3 = 0.7
49 = RR
42 = Rr
9 = rr

9. • Now we can find frequency of rr also called genotype frequency
Genotype frequency=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑤𝑖𝑡ℎ 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑔𝑒𝑛𝑜𝑡𝑦𝑝𝑒 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙𝑠 𝑖𝑛 𝑎 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Frequency of rr =
𝑟𝑟
𝑅𝑅+𝑅𝑟+𝑟𝑟
=
9
49+42+9
=
9
100
= 0.09 or 9%
49 = RR
42 = Rr
9 = rr

10. Relationship between allele and gene
frequency
• As R=0.7, the frequency of gamete carrying R allele, called p= 0.7 and
that of r is denoted by q, then p+q= 1
• Therefore, if p= 0.7 then q= 1-0.7= 0.3
• Consider Punnet square (chart showing all possible allele combination
of a particular cross)

11. Genotypes RR Rr rr
Genotype
frequencies
0.49 0.42 0.09
Allele frequencies R=0.7, r= 0.3
Generation 1
RR (p2)
(0.7)2 =0.49
Rr (pq)
(0.7)(0.3)= 0.21
Rr (pq)
(0.7)(0.3)= 0.21
rr (q2)
(0.3)2 = 0.09
R
r
R r Frequency of RR = (0.7)2 = 0.49
Frequency of Rr= 2(0.7)(0.3)= 0.42
Frequency of rr= (0.3)2 = 0.09
p2+ 2pq+ q2= 1 or (p+q) 2 = 1
0.49+ 2 (0.21)+ 0.09 = 1
Generation 2

12. Conditions for Hardy-Weinberg Equilibrium
The Hardy-Weinberg equilibrium states that the genetic variation in a
population will remain constant from one generation to the next in the
absence of disturbing factors.
1. The population should be large
2. Random mating
3. No migration between populations
4. No natural selection should operate
5. No new mutations

13. Reality
• No population satisfies Hardy-Weinberg equilibrium as;
• Organisms do not mate randomly
• Males contribute larger number of genes to the gene pool
• Migration rates are high
• Nevertheless, in large population with little migration and negligible
natural selection and mutation, Hardy-Weinberg is approximated for
certain genes.

14. • If a population does not obey Hardy-Weinberg equilibrium, we can
say that evolutionary mechanisms are affecting the population.
• When this occurs, researchers may wish to identify the reason(s)
why this disequilibrium has occurred, because this may provide
insight into factors affecting the future survival of the species.

15. Summary
• Definition of Hardy-Weinberg equilibrium
• Allele and Genotype Frequency
• Relationship between them
• Conditions for Hardy Weinberg equilibrium
• Real case: Not exists
• Scope of Hardy-Weinberg equilibrium

16. Thank you