Mendelian Genetics and Probability
Basic Principles of Heredity Introduction
Gregor Mendel: Discovered principles of heredity using experimental approach and mathematical analysis.
Peas: Good model system (short generation time, easy to hybridize, many phenotypes).
Genetic Terminology
Gene: Inherited DNA factor determining a characteristic.
Allele: Alternative form of a gene.
Locus: Specific place on a chromosome occupied by an allele.
Genotype: Set of alleles in an individual.
Heterozygote: Individual with two different alleles at a locus.
Homozygote: Individual with two of the same alleles at a locus.
Phenotype or trait: Appearance or manifestation of a characteristic.
Characteristic or character: Attribute or feature.
Monohybrid Crosses: Principle of Segregation and Dominance (Mendel's First Law)
Experiment: Crossed homozygous round (RR) and wrinkled (rr) peas.
F1 generation: All progeny round, exhibiting dominance (Rr).
F2 generation: Progeny from self-fertilized F1 showed a 3:1 phenotypic ratio (Round: Wrinkled).
Principle of Segregation (Mendel's First Law): Each diploid organism possesses two alleles for a characteristic. These alleles segregate equally during gamete formation, with one allele going into each gamete.
Dominance: When two different alleles are present, only the dominant allele's trait is expressed in the phenotype.
Meiosis: Segregation of alleles is caused by the separation of homologous chromosomes during meiosis.
Meiosis in Males vs. Females
Males: 1 spermatocyte produces 4 sperm (continuous after puberty).
Females: 1 oocyte produces 1 egg and 3 polar bodies (asymmetric divisions, pauses between stages).
Probability and Statistics
Multiplication Rule: Probability of two independent events both occurring is the product of their individual probabilities. P(A \text{ and } B) = P(A) \times P(B).
Addition Rule: Probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. P(A \text{ or } B) = P(A) + P(B).
Binomial Expansion: Used to determine the probability of a specific combination of outcomes in a series of events.
Number of orders: \frac{n!}{s!t!}
Probability of one specific order: p^s q^t
Total probability: \frac{n!}{s!t!} \times p^s q^t
Dihybrid Crosses: Principle of Independent Assortment (Mendel's Second Law)
Experiment: Crossed homozygous round, yellow (RRYY) and wrinkled, green (rryy) peas.
F1 generation: All progeny round, yellow (RrYy).
F2 generation: Progeny from self-fertilized F1 showed a 9:3:3:1 phenotypic ratio (Round, Yellow : Round, Green : Wrinkled, Yellow : Wrinkled, Green).
Principle of Independent Assortment (Mendel's Second Law): Different segregating pairs of alleles are transmitted independently of one another.
Meiosis: Independent assortment is caused by the independent behavior of different chromosome pairs during meiosis. Genes on different chromosomes assort independently.
Branch Diagram: An alternative method to Punnett squares for calculating expected phenotypic proportions in dihybrid crosses by multiplying probabilities of individual monohybrid crosses.
Chi-square Goodness of Fit Test
Purpose: Statistical test to determine the probability that observed deviations from expected results are due to random chance.
Steps:
Develop a hypothesis (expected ratio).
Convert expected ratios to expected counts.
Calculate the chi-squared (\chi^2) value: \chi^2 = \sum \frac{(observed - expected)^2}{expected}.
Determine degrees of freedom (Df): Df = \text{number of classes} - 1.
Determine the p-value: probability of observed data differing by chance if the hypothesis is true.
Interpretation: If p < 0.05, reject the hypothesis; if p > 0.05, fail to reject the hypothesis (deviations are likely due to chance).
Small p-value: Indicates that the observed values are significantly different from the expected values, suggesting the difference is not due to chance alone.