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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 Gametes (Sperm and eggs) Mating System Generation Begins Zygotes (fertilized eggs) {GYY, GYy, Gyy} NO Natural Selection Generation Ends Reproducing Adults {GYY, GYy, Gyy} Life cycle Natural Selection Natural Selection Juveniles 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 150 YY 300 Y Alleles = 2 x 150 400 Y Alleles = 1 x 400 400 Yy 400 y Alleles = 1 x 400 90 yy 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 Can ALWAYS take individual genotypes apart into alleles 150 YY 300 Y Alleles = 2 x 150 400 Y Alleles = 1 x 400 400 Yy 400 y Alleles = 1 x 400 90 yy 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 Genotypes Always Unpackage Alleles Alleles Unique Genotypes Cannot Always REpackage Genes in Populations With NO Natural Selection Generation Ends Reproducing Adults Generation Begins Diploid Zygotes {GYY, GYy, Gyy} Parents {GYY, GYy, Gyy} (fertilized eggs) ?? 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 ??? Genotypes Always Unpackage Alleles When CAN we Repackage???? Alleles Unique Genotypes 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) Female Parents in Population YY M a l e s Gametes: 1 Y YY Yy yy Gametes: 1 Y Gametes: ½ Y, ½ y Gametes: 1 y Frequency: GYY Frequency: GYy Frequency: Gyy YY ½ YY, ½ Yy Yy (GYY)2 (GYY)(GYy) (GYY)(Gyy) Gametes: ½ Y, ½ y ½ YY, ½ Yy ½ Yy, ½ yy Frequency: GYy (GYY)(GYy) ¼ YY ½ Yy ¼ yy Frequency: GYY Yy (GYy)(Gyy) (GYy)2 yy Gametes: 1 y Yy ½ Yy, ½ yy yy Frequency: Gyy (GYY)(Gyy) (GYy)(Gyy) (Gyy)2 Adding up YY Offspring YY M a l e s Gametes: 1 Y Female Parents in Population YY Yy yy Gametes: 1 Y Gametes: ½ Y, ½ y Gametes: 1 y Frequency: GYY Frequency: GYy Frequency: Gyy YY ½ YY, ½ Yy Yy (GYY)2 (GYY)(GYy) (GYY)(Gyy) Gametes: ½ Y, ½ y ½ YY, ½ Yy ½ Yy, ½ yy Frequency: GYy (GYY)(GYy) ¼ YY ½ Yy ¼ yy Frequency: GYY Yy (GYy)(Gyy) (GYy)2 yy Gametes: 1 y Yy ½ Yy, ½ yy yy Frequency: Gyy (GYY)(Gyy) (GYy)(Gyy) (Gyy)2 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. Adding up Yy Offspring YY M a l e s Gametes: 1 Y Female Parents in Population YY Yy yy Gametes: 1 Y Gametes: ½ Y, ½ y Gametes: 1 y Frequency: GYY Frequency: GYy Frequency: Gyy YY ½ YY, ½ Yy Yy (GYY)2 (GYY)(GYy) (GYY)(Gyy) Gametes: ½ Y, ½ y ½ YY, ½ Yy ½ Yy, ½ yy Frequency: GYy (GYY)(GYy) ¼ YY ½ Yy ¼ yy Frequency: GYY Yy (GYy)(Gyy) (GYy)2 yy Gametes: 1 y Yy ½ Yy, ½ yy yy Frequency: Gyy (GYY)(Gyy) (GYy)(Gyy) (Gyy)2 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. 2 , 2P P , P 2 } {GYY, GYy, GFreq. } = { P yyof A Y y y Freq. ofY a allele allele and parents PY = offspring PY The Hardy – Weinberg Equilibrium is one of the Population 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 P = offspring P Y Y The Hardy – Weinberg Equilibrium is one of the Population 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, m, 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. = 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. Mechanism of Mutation μ A Allele in the Parent a Allele in the Parent u a Mutant Allele in the Gamete and then In the Offspring A Mutant Allele in the Gamete and then In the Offspring Change in allele frequency, DPa, as a result of mutation Mechanism of Mutation μ A Parent Frequencies: {PA, Pa} a u Reproduction With Mutation Offspring Frequencies: {PA’, Pa’} How similar are PA’ and PA? The change in allele frequency, DPa, caused by mutation Parent Frequencies: {PA, Pa} Freq of a allele in offspring after mutation Pa’ Reproduction With Mutation Offspring Frequencies: {PA’, Pa’} Mutation rate from A to a times the Freq of A before mutation Non-Mutation rate times the Freq of a before mutation = (1- v) Pa + μPA ΔPa = Pa’– Pa = μ – (u + m)Pa Change in allele frequency, DPa, as a result of mutation Parent Frequencies: {PA, Pa} Reproduction With Mutation 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.