The Mathematics of Genetics and Evolution BY: MATT DEAN

Evolution: Requirements for Evolution—A change in the allele frequency of a population over time. Requirements: 1. Genetic Variability—may come from mutations and immigration. 2. More offspring are produced than can survive (due to limited resources, predation, etc…) 3. Some organisms must be better adapted than others. 4. There must be differential reproduction rates due to the adaptive characteristics of some members. Fitness Fecundity

Hardy Weinberg Video Part 1

Hardy Weinberg Video Part 2

Hardy-Weinberg Equilibrium Genetic Equilibrium Hardy-Weinberg Law Defined evolution by describing when it would not happen. There are 5 requirements that must be met for genetic equilibrium to occur. Requirements 1. No mutations. Germ cell mutations bring about evolution. Somatic cell mutations are not passed on to offspring. 2. No immigration or emigration. (No gene flow) 3. There must be a very large population in order to avoid genetic drift. Genetic Drift—unpredicted changes in allele frequencies due to chance. Usually occurs in small, isolated populations. 4. There must be no natural selection. 5. There must be no sexual selection. Mating must be random.

If you can take a square root, you can solve a Hardy Weinberg problem!!

Hardy Weinberg Problems 1. In humans, brown eyes are dominant over blue eyes. In a population of 1000 individuals, 750 have brown eyes. What are the frequencies of the dominant and recessive alleles? 2. How many individuals would you expect to be heterozygous (from #1)? 3. What is the expected frequency (percentage) of each possible genotype? 4. What is the frequency of the dominant allele? 5. What is the frequency of the recessive allele?

More Hardy Weinberg Problems 4. The ability to roll the tongue is dominant over the allele for the lack of the ability. If 64% of a population can roll their tongues, what are the frequencies of the dominant and recessive alleles? 5. Give the percentage of the population that would represent each possible genotype (from #4) 6. If the population consisted of 3000 individuals, how many individuals should be homozygous dominant for the trait?

More on Hardy Weinberg Suppose a teacher does a statistical analysis of the eye color in her school of mostly black students. She finds that of the 1000 students, 910 have brown eyes, while only 90 have blue eyes (the recessive trait). Five years later, she does her analysis again, since as an attempt at desegregation, some students are sent to other schools and new students from neighboring towns are brought in . She now finds that of the 1000 students, 840 have brown eyes and 160 have blue eyes.

More on Hardy Weinberg 1. In the original sample (1981) the frequency of the allele for brown eyes (B) was: 2. The number of students in the original sample that were expected to be heterozygous for brown eyes was: 3. Is the population in Hardy Weinberg equilibrium? Is evolution occurring? How do you know? What brought about the change, if there was change? 4. In the second sample, what was the frequency of the recessive allele? 5. Give the expected frequency of each possible genotype for samples 1 & 2.

More Hardy Weinberg 1. A recessive trait appears in 81% of the individuals in a population that is in Hardy-Weinberg equilibrium. What percent of the population in the next generation is expected to be homozygous dominant? 2. Nine percent of a population is homozygous recessive at a certain locus. Assuming the population is in Hardy Weinberg equilibrium, what the frequency of the recessive allele?

Trihybrid Crosses 1. What is the probability that parents with the genotypes TtWwMM and TTWwMm will produce an offspring with the genotype TTWWMM? 2. What is the probability that an offspring with the genotype NnRrDd will be produced from parents with the genotypes nnrrDd and NnRrDd?

Gene Mapping Video

Gene Mapping Questions Four genes, A, B, C, and D, occur on the same chromosome. Use the following crossover frequencies to determine the order of the genes on the chromosome. A—D—5% B—C—15% A—C—30% C—D—35% B—D—50% A. BCAD B. CBDA C. BACD D. CDAB E. CBAD

Genetics Problems Questions 1&2 refer to a female Drosophila heterozygous for ebony body color (recessive) and curly wings (recessive) that was mated to and ebony-bodied, curly-winged male resulting in the following offspring: 200 ebony body, normal wing 10 normal body, normal wing 5 ebony body, curly wing 150 normal body, curly wing

Genetics Problems 1. Choose the correct statement(s). The genes are linked. In the female, the alleles for normal body and normal wing are on the same chromosome. The genes are linked. In the female, the alleles for normal body and curly wing are on the same chromosome. The genes are unlinked. The genes are linked. In the female, alleles for ebony body and curly wing are on the same chromosome. The genes are linked. In the female, the alleles for ebony body and normal wing are on the same chromosome. A. I, II B. II, IV C. III D. II, V E. I, V

Genetics Problem 2. Which process must occur in order to obtain the ebony body, curly wing phenotype in the offspring? A. Nondisjunction during meiosis in the female. B. Crossing over during gamete formation in the female. C. Crossing over during gamete formation in the male. D. A mutation in the female. E. A mutation in the male.

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