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Formulating the components of the hardy-weinberg equation

The probability rule we used in another module to predict genotype frequencies in the offspring generation of a specific population:

If every individual in a population has an equal probability of surviving and producing surviving offspring, then a genotype is expected to appear in the offspring generation with a frequency (probability) equal to the mathematical product of the frequency with which each allele that forms the genotype occurs in the population producing it.

can be use to generate a general formula for doing the same thing. That is, we can create a formula that describes how frequently particular genotypes will appear in the offspring generation when a population is not subject to an agent of evolution. This formula is known as the Hardy-Weinberg equation.

To do this, we will first generate the individual elements of the Hardy-Weinberg equation.

As the boxed rule above says, offspring genotype frequencies are calculated using parental allele frequencies. So imagine a population that has only two alleles for a given locus, A and a , and that in this population

  • the A allele occurs with a frequency equal to p
  • the a allele occurs with a frequency equal to q

To make sure you understand these phrases, substitute a number for p or for q. For example, p might be 0.4 meaning that the A allele occurs in 40% of the population's loci for this gene.

Notice that, because only two alleles exist in the population for this locus, the frequencies of the A and a alleles, p and q respectively, must sum to 1, the equivalent of 100%. Or

  • p + q = 1

Also notice that, if we know the frequency of only one of the two alleles in a population, we can use simple algebra to work out the frequency of the second. For example, if we know p, the frequency of the A allele, then

  • q = 1 - p

And, of course, if we know q, the frequency of the a allele, then

  • p = 1 - q

To confirm your understanding of this relationship between the frequencies with which two alleles occur in a population when only two alleles exist for a given locus, answer the following questions.

Please explain in your own words why p + q must always equal 1 when only two alleles exist in a population for a given locus.

An example answer: I imagine a locus as slots for alleles. In diploid organisms, each individual will have two 'slots' or two loci for the particular gene of interest, one per chromosome. If only two alleles exist to fill every slot in this population, the slots that are not filled with one of those two alleles must be filled with the second. Consequently, if 50% of the slots are filled with A alleles, then the remaining 50% must be filled with a alleles to account for 100% of the population's loci. Because 50% is equivalent to a frequency of 0.5, then the frequency of the A allele or p equals 0.5 as does the frequency of the a allele or q so that p + q = 1.

Let’s consider a real example of this. In 2005, Stefasson et al. reported the fascinating discovery of an allele in humans whose presence is associated with increased fertility in Icelandic and European populations. Females with at least one copy of the allele have approximately 3.5%, and males 2.9%, more children on average than non-carriers. The exact mechanism by which the allele, known as H2, affects fertility is unknown.

If we know that 21% of European loci for this gene house the H2 allele, then how frequently must the single alternative allele, H1, for that locus occur in this population? Why?

If 21% of the loci (equivalent to a frequency of 0.21) in a population contain the H2 allele and H1 is the only other possible allele for this locus, then 79% of the remaining loci (equivalent to a frequency of 0.79) must have this allele. No other alleles exist for this locus consequently, if H2 does not occur at a locus then H1 must be there instead.

Questions & Answers

what's economic development and growth
Popoola Reply
what do you understand by Ceteris Paribus?
Gabriel Reply
explain the uses of microeconomics
Nikita Reply
uses of microeconomics
Nikita
Adam Smith's definition of economics
Sylvia Reply
what is economic deficit
Amjad
this is a situation whereby a nation's outcome or available resources are not enough to the people thereby causing scarcity
Ariel
prices of Quality demanded is equal to Quality supplied
NABUBOLO Reply
it's quantity demand and quantity supplied that's called equilibrium
Romy
no
NABUBOLO
they deal With prices
NABUBOLO
define the elasticity
NABUBOLO
explain different types of elasticity
NABUBOLO
oops 😬 you are right you talk about quality I tell about quantity
Romy
elasticity is the measurement of the percentage change of one economic variable in response to a change in another
Romy
Cross Elasticity of Demand (XED) Income Elasticity of Demand (YED) Price Elasticity of Supply (PES)
Romy
anything else?
Romy
I need to know everything about theory of consumer behavior
Grace
How does one analyze a market where both demand and supply shift?
Gabriel Reply
That's equilibrium market
Ramon
but an equlibrum can appear twice on the same market... both in Movement along the Demand/supply curve of shift in the Curve
Gabriel
I Mean on the same curve..
Gabriel
how can consumer surplus be calculated
Franklyn
How can we analyze the effect on demand or supply if multiple factors are changing at the same time—say price rises and income falls? 
Gabriel Reply
because of fall of income, less will be demanded and much will be supply as a result of price rises. Rise in price always motivate new supplier to enter into the system. But it only possible in the short run
Kweku
yeah.. I think Ceteris Paribus is applied in this case
Gabriel
that is the law of Demand is Inversely related to the law of Supply... so that mean a positive change in demand may produce a negative return to supply I think.
Gabriel
what are the difference between Wants and Needs
Gabriel Reply
When the price is above the equilibrium, explain how market forces move the market price to equilibrium. Do the same when the price is below the equilibrium.
Gabriel
economic problems
Manishankar
yeah please Explain
Gabriel
I don't know this is my question
Manishankar
no it was a mistake...😂😂 can you explain how Wants and needs differs 😌
Gabriel
wants is what human desire but might not need them, human want are mostly articles of ostentatious while need is what human must get to live e.g inferior goods
Ramon
what's equilibrium price
james
equilibrium prices is a situation whereby the price of goods supplied equates to the demand
Ariel
this whereby the prices of quality demanded is equivalent to quality demanded
NABUBOLO
wants are numerous desire man that man can do without if not purchased e.g. cosmetic while need are desires that you cannot do without e.g. food
Franklyn
equilibrium price is that level of output were quantity demanded is equal to quantity supplied
Arthur
what are the importance of studying economics
Bherla Reply
To know if the country is growing or not through the country's GDP
Ariel
to manage our resources
TOBI
compare base years GDP and the current years GDP
james
To tell whether a country is growing there are many factors to be considered not necessarily only the GDP due to weaknesses of GDP approach
james
What is the law of demand
Yaw Reply
price increase demand decrease...price decrease demand increase
Mujahid
ıf the price increase the demand decrease and if the demand increase the price decrease
MUBARAK
all other things being equal, an increase in demand causes a decrease in supply and vice versa
SETHUAH
yah
Johnson
how is the economy of usa now
Johnson
What is demand
jude Reply
Demand is the quantity of goods and services a consumer is willing and able to purchase at various prices over a given period of time.
Yaw
yea
SETHUAH
Okay congratulations I'll join you guys later .
Aj
yes
MUBARAK
demand is the quantity and quality of goods and services a consumer is willingly and able to purchase at a particular price over a given period of time.
TOBI
calculate elasticity of income exercises
HABANABAKIZE Reply
If potatoes cost Jane $1 per kilogram and she has $5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth $0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend?
Susan Reply
cause of poverty in urban
DAVY Reply
QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of $56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
Falak Reply
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Source:  OpenStax, Understanding the hardy-weinberg equation. OpenStax CNX. Oct 22, 2007 Download for free at http://cnx.org/content/col10472/1.1
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