Friday’s Class 3 Extra Credit Questions

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 Mating System Generation Begins Zygotes (fertilized eggs) Gametes (Sperm and eggs) {GYY, GYy, Gyy} NO Natural Selection Natural Selection Life cycle Generation Ends Reproducing Adults Natural Selection Juveniles {GYY, GYy, Gyy}

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.

Can ALWAYS take individual genotypes apart into alleles YY 150 300 Y Alleles = 2 x 150 400 Y Alleles = 1 x 400 Yy 400 400 y Alleles = 1 x 400 yy 180 y Alleles = 2 x 90 90 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

Can ALWAYS take individual genotypes apart into alleles YY 150 300 Y Alleles = 2 x 150 400 Y Alleles = 1 x 400 Yy 400 400 y Alleles = 1 x 400 yy 90 180 y Alleles = 2 x 90 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

Alleles Unique Genotypes There is More than One Way to package alleles into genotypes. Knowing {PY, Py} CANNOT ALWAYS calculate the One and only, unique genotype frequency distribution: {GYY, GYy, Gyy}

The Two ways to genetically describe a Mendelian Population are only partially interchangeable Always Unpackage Genotypes Alleles Alleles Unique Genotypes Cannot Always REpackage

Genes in Populations With NO Natural Selection Generation Begins Diploid Zygotes (fertilized eggs) GenerationEnds Reproducing Adults {GYY, GYy, Gyy} {GYY, GYy, Gyy} ?? Parents Offspring How are these Genotype Frequency Distributions related to one another?

Under What Circumstances are the Two ways to genetically describe a Mendelian Population interchangeable ??? Always Unpackage Genotypes Alleles Alleles Unique Genotypes When CAN we Repackage???? THE ANSWER: is something you need to know

Random Matingis a mating system in which the frequency of a MatingType or Family Type equals the PRODUCT of the Genotype Frequencies of the Parents. Examples: Family TypeFamily Type Frequency Male x Female Parents YY x YY (GYY)(GYY) = (GYY)2 YY x Yy (GYY)(GYy) yy x Yy (Gyy)(GYy)

Female Parents in Population M a l e s

Female Parents in Population Adding up YY Offspring M a l e s

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: Genotypefrequencyin offspring, GYY, equals square of the gene frequency, pY, in the parents.

Female Parents in Population Adding up Yy Offspring M a l e s

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: Genotypefrequencyin 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. {GYY, GYy, Gyy} = { PY2 , 2PY Py, Py2} Freq. of A allele Freq. of a allele 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 • It occurs when errors are made in duplicating alleles in producing the gametes. • It is one of the weaker evolutionary forces, because errors are relatively rare. The error rate or mutation rate, m, in copying an allele of a nuclear gene is ~ 1 x 10-6 to 1 x 10-9. • 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.

= A alleles = a alleles Parent population Reproduction With Mutation Offspring population

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. μ Mechanism of Mutation a A Mutant Allele in the Gamete and then In the Offspring Allele in the Parent u a A Mutant Allele in the Gamete and then In the Offspring Allele in the Parent

Change in allele frequency, DPa, as a result of mutation μ Mechanism of Mutation a A u Reproduction With Mutation Offspring Frequencies: {PA’, Pa’} Parent Frequencies: {PA, Pa} How similar are PA’ and PA?

The change in allele frequency, DPa, caused by mutation Reproduction With Mutation Parent Frequencies: {PA, Pa} Offspring Frequencies: {PA’, Pa’} Freq of a allele in offspring after mutation Mutation rate from A to a times the Freq of A before mutation Non-Mutation rate times the Freq of a before mutation Pa’ = (1- v)Pa+ μPA ΔPa = Pa’– Pa = μ – (u + m)Pa

Change in allele frequency, DPa, as a result of mutation Reproduction With Mutation Parent Frequencies: {PA, Pa} Offspring Frequencies: {PA’, Pa’} ΔPa =Pa’– Pa = μ – (u + m)Pa At the Mutation Equilibrium, ΔPa = 0. 0 = μ – (u + m)P*a P*a = μ/(u + m) = The Equilibrium Allele Frequency = Rate at which A is wrongly copied as a, Relative to all errors at that gene.

Friday’s Class 3 Extra Credit Questions