friday’s class 3 extra credit questions
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Friday’s Class 3 Extra Credit Questions
• 3 Questions, Multiple Choice• 10 Minutes• 12 Extra Points Possible • Not Required to Participate; if you are
happy with your grade, come to class 10 minutes later at 9:15 on Friday.
Our Goal: To understand the “population consequences”Of Mendel’s Laws.
Question 1: How do we describe a Mendelian population?
Genes in Populations With NO Natural Selection
Generation EndsReproducing Adults
Gametes(Sperm and eggs)
Juveniles
Generation BeginsZygotes
(fertilized eggs)
Life cycle
MatingSystem
{GYY, GYy, Gyy}
{GYY, GYy, Gyy}
NaturalSelection
NaturalSelection
NO NaturalSelection
Answer: We describe a diploid Mendelian Population in two ways:
1. List all the different genetic kinds of individuals, i.e., all the genotypes.Calculate the genotype frequencies.
2. List all the different kinds of genes, i.e., all the alleles at all the genes. Calculate the allele frequencies.
PY = {(2)(#YY) + (1)(#Yy)}/{(2)(Total # Genotypes)}
PY = {(2)(#YY)}/{2N} + {(1)(#Yy)}/{2N} PY = (1){(#YY)}/{N} + (1/2){(#Yy)}/{N}
PY = GYY + (1/2)GYy
300 Y Alleles = 2 x 150150
Yy400400 y Alleles = 1 x 400
400 Y Alleles = 1 x 400
yy 90 180 y Alleles = 2 x 90
YY
Can ALWAYS take individual genotypes apart into alleles
Py = {(2)(#yy) + (1)(#Yy)}/{(2)(Total # Genotypes)}
Py = {(2)(#yy)}/{2N} + {(1)(#Yy)}/{2N} Py = (1){(#yy)}/{N} + (1/2){(#Yy)}/{N}
Py = Gyy + (1/2)GYy
300 Y Alleles = 2 x 150150
Yy400400 y Alleles = 1 x 400
400 Y Alleles = 1 x 400
yy 90 180 y Alleles = 2 x 90
YY
Can ALWAYS take individual genotypes apart into alleles
There is More than One Way to package alleles intogenotypes.
Knowing {PY, Py} CANNOT ALWAYS calculate theOne and only, unique genotype frequency distribution:
{GYY, GYy, Gyy}
UniqueGenotypes
Alleles
Genotypes Alleles
UniqueGenotypes
Alleles
Always Unpackage
The Two ways to genetically describe a Mendelian Population are only partially interchangeable
CannotAlways REpackage
Genes in Populations With NO Natural Selection
{GYY, GYy, Gyy}
Generation BeginsDiploid Zygotes
(fertilized eggs)
{GYY, GYy, Gyy}
Generation EndsReproducing Adults
??
How are these Genotype FrequencyDistributions related to one another?
Parents Offspring
Genotypes Alleles
UniqueGenotypes
Alleles
Always Unpackage
Under What Circumstances are the Two ways to genetically describe a Mendelian Population
interchangeable ???
When CAN weRepackage????
THE ANSWER: is something you need to know
Random Mating is a mating system in which the frequency of a Mating Type or Family Type
equals the PRODUCT of the Genotype Frequencies of the Parents.
Examples: Family Type Family Type Frequency
Male x Female Parents
YY x YY (GYY)(GYY) = (GYY)2
YY x Yy (GYY)(GYy)
yy x Yy (Gyy)(GYy)
YYGametes: 1 Y
Frequency: GYY
YyGametes: ½ Y, ½ y
Frequency: GYy
yyGametes: 1 y
Frequency: Gyy
YYGametes: 1 Y
Frequency: GYY
YY
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
Yy
(GYY)(Gyy)
YyGametes: ½ Y, ½ y
Frequency: GYy
½ YY, ½ Yy
(GYY)(GYy)
¼ YY ½ Yy ¼ yy(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
yyGametes: 1 y
Frequency: Gyy
Yy
(GYY)(Gyy)
½ Yy, ½ yy
(GYy)(Gyy)
yy
(Gyy)2
Female Parents in Population
Males
YYGametes: 1 Y
Frequency: GYY
YyGametes: ½ Y, ½ y
Frequency: GYy
yyGametes: 1 y
Frequency: Gyy
YYGametes: 1 Y
Frequency: GYY
YY
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
Yy
(GYY)(Gyy)
YyGametes: ½ Y, ½ y
Frequency: GYy
½ YY, ½ Yy
(GYY)(GYy)
¼ YY ½ Yy ¼ yy(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
yyGametes: 1 y
Frequency: Gyy
Yy
(GYY)(Gyy)
½ Yy, ½ yy
(GYy)(Gyy)
yy
(Gyy)2
Female Parents in Population
Males
Adding up YY Offspring
Parental Genotype Frequencies: GYY , GYy, Gyy
Parental Allele Frequencies: pY = GYY + (½)Gyy
Offspring Genotype Frequencies: GYY , GYy, Gyy
GYY = (1)(GYY)2 + (½)(GYY)(GYy) + (½)(GYY)(GYy) + (¼) (GYy)2
= (GYY +[½][GYy])2 = (pY)2
Note: Genotype frequency in offspring, GYY, equals square of the gene frequency, pY, in the parents.
YYGametes: 1 Y
Frequency: GYY
YyGametes: ½ Y, ½ y
Frequency: GYy
yyGametes: 1 y
Frequency: Gyy
YYGametes: 1 Y
Frequency: GYY
YY
(GYY)2
½ YY, ½ Yy
(GYY)(GYy)
Yy
(GYY)(Gyy)
YyGametes: ½ Y, ½ y
Frequency: GYy
½ YY, ½ Yy
(GYY)(GYy)
¼ YY ½ Yy ¼ yy(GYy)2
½ Yy, ½ yy
(GYy)(Gyy)
yyGametes: 1 y
Frequency: Gyy
Yy
(GYY)(Gyy)
½ Yy, ½ yy
(GYy)(Gyy)
yy
(Gyy)2
Female Parents in Population
Males
Adding up Yy Offspring
Parental Genotype Frequencies: GYY , GYy, Gyy
Parental Allele Frequencies: pY = GYY + (½)Gyy
Offspring Genotype Frequencies: GYY , GYy, Gyy
GYy = (½)(GYY)(GYy) + (½)(GYY)(GYy) + (½)(GYy)2
+ (½)(GYy)(Gyy) + (½)(GYy)(Gyy) + (2)(GYY)(Gyy)
= (2)(GYY +[½][GYy])(Gyy +[½][GYy])
GYy = (2)(pY)(py) Note: Genotype frequency in offspring, GYY, equals product of gene frequencies, pY and pY in the parents.
Hardy – Weinberg Equilibrium• Describes a population that is NOT evolving, because
there is NO Natural Selection or any other Evolutionary Force acting on the population.
• Allele frequencies do not change from parents to offspring under Hardy-Weinberg conditions!
• Genotype frequencies {GYY, GYy, Gyy} in the offspring population at fertilization are a simple function of the allele frequencies {p, q} in the parent generation.
Freq. of A allele
Freq. of a allele
= { PY 2 , 2PY Py, Py2 }{GYY, GYy, Gyy}
and parents PY = offspring PY
The Hardy – Weinberg Equilibrium is one of thePopulation consequences of Mendel’s Laws
NECESSARY ASSUMPTIONS for H-W• Large Mendelian population• Random mating• No mutation• No migration• No natural selection
Under these assumptions there is no change in allele frequency from one generation to the next (i.e. no evolution)! parents PY = offspring PY
The Hardy – Weinberg Equilibrium is one of thePopulation consequences of Mendel’s Laws
It is an Equilibrium that is achieved in one generation of random mating.
When a population deviates away from the Hardy-Weinberg Equilibrium it means EITHER:
(1) Mating is not random in the population;Or
(2) Some Evolutionary Force is acting in the population!
Mutation as an Evolutionary Force
1. It occurs when errors are made in duplicating alleles in producing the gametes.
2. It is one of the weaker evolutionary forces, because errors are relatively rare. The error rate or mutation rate, , in copying an allele of a nuclear gene is ~ 1 x 10-6 to 1 x 10-9.
3. It changes allele frequencies in a population and this change in the genetic composition of a population from parents to offspring is what we mean by evolution.
No Mutation
AA Parents produce only ‘A’ bearing gametes.
Aa Parents produce ½ ‘A’ and ½ ‘a’ bearing gametes
aa Parents produce only all ‘a’ bearing gametes.
With Mutation
AA Parents produce some ‘a’ bearing mutant gametes.
Aa Parents produce ½ ‘A’ and ½ ‘a’ gametes
aa Parent produce some ‘A’ bearing mutant gametes.
Offspringpopulation
= A alleles = a alleles
Parentpopulation
ReproductionWith Mutation
How strong is mutation as an evolutionary force?
Calculate how much the frequency of an allele changes in the population as a result
of mutation.
A aμMechanism of
MutationAllele in the
Parent
Mutant Allele in the Gamete and then
In the Offspring
Aa
Allele in the Parent
Mutant Allele in the Gamete and then
In the Offspring
Change in allele frequency, Pa, as a result of mutation
A aμMechanism of
Mutation
Parent Frequencies:{PA, Pa}
Offspring Frequencies:{PA’, Pa’}
ReproductionWith Mutation
How similar are PA’ and PA?
Pa’ = (1- v) Pa + μPA
The change in allele frequency, Pa, caused by mutation
Freq of a allele in offspring
after mutation
Non-Mutation rate times the
Freq of a before mutation
Mutation rate from A to a times
the Freq of A before mutation
ΔPa = Pa’– Pa = μ – ( + )Pa
Parent Frequencies:{PA, Pa}
Offspring Frequencies:{PA’, Pa’}
ReproductionWith Mutation
Change in allele frequency, Pa, as a result of mutation
ΔPa = Pa’– Pa = μ – ( + )Pa
At the Mutation Equilibrium, ΔPa = 0. 0 = μ – ( + )P*a
P*a = μ/( + ) =The Equilibrium Allele Frequency =
Rate at which A is wrongly copied as a,Relative to all errors at that gene.
Parent Frequencies:{PA, Pa}
Offspring Frequencies:{PA’, Pa’}
ReproductionWith Mutation
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