Mendelian Genetics: Independent Assortment and the Chi-Square Test

Vocabulary practice flashcards covering Gregor Mendel's Principle of Independent Assortment, multi-gene notation, dihybrid crosses, testcrosses, and statistical evaluation using the chi-square test.

Mendel’s Principle of Independent Assortment

Mendel's second principle stating that the inheritance of one trait is independent of the inheritance of another trait; during meiosis, alleles of different genes on different chromosomes segregate independently of one another.

Seven Phenotypic Pairs Studied by Mendel

The seven pairs of traits analyzed in pea plants: round or wrinkled ripe seeds, yellow or green seeds, purple or white petals, inflated or pinched ripe pods, green or yellow unripe pods, axial or terminal flowers, and long or short stems.

Monohybrid Cross

A genetic cross between two individuals involving one pair of contrasting traits, yielding a $3:1$ phenotypic ratio in the $F_2$ generation from heterozygous parents.

Dihybrid Cross

A genetic cross between parental organisms that differ in two distinct traits, producing an $F_2$ generation with a classic $9:3:3:1$ phenotypic ratio when alleles assort independently.

Dihybrid Cross Genotypic Ratio

The genotypic ratio of $1:2:1:2:4:2:1:2:1$ observed in the $F_2$ generation of a cross between two dihybrids ($Y/y \cdot R/r \times Y/y \cdot R/r$).

Slash Notation ($/$)

Genetic symbolism indicating alleles of a single gene located on different homologous chromosomes (e.g., $Y/y$).

Semicolon Notation ($;$)

Genetic symbolism indicating two genes located on different chromosomes, each with alleles on different homologs (e.g., $Y/y \,;\, R/r$).

Dot Notation ($\cdot$)

Genetic symbolism indicating two genes located on unknown chromosomes, each with alleles on different homologs (e.g., $Y/y \cdot R/r$).

Adjacent Notation without Separators ($YR/yr$)

Genetic symbolism indicating two genes situated on the same chromosome, each with alleles on different homologs.

Formula for Potential Gametes

The formula $2^n$, where $n$ is the number of heterozygous genes, used to calculate the total number of unique gamete genotypes produced by an organism.

FOIL Method (Gamete Determination)

A method using First, Outer, Inner, Last combinations to systematically derive all four potential gamete types (e.g., $Y \cdot R$, $Y \cdot r$, $y \cdot R$, $y \cdot r$) from a dihybrid organism ($Y/y \cdot R/r$).

Product Rule

A probability rule stating that the probability of two independent events occurring simultaneously is calculated by multiplying their individual probabilities.

Testcross (Multiple Genes)

A cross performed between an organism of unknown or presumed heterozygous genotype and an individual that is homozygous recessive for all traits examined (e.g., $e^+/e \,;\, wg^+/wg \times e/e \,;\, wg/wg$) to verify the unknown genotype.

Dihybrid Testcross Phenotypic Ratio

A phenotypic ratio of $1:1:1:1$ produced when a dihybrid individual is crossed to an individual that is homozygous recessive for both traits.

Hypothesis

A testable explanation formulated about an observed phenomenon.

Null Hypothesis ($H_0$)

The statistical proposition stating that the observed data does not deviate significantly from the expected data predicted by a genetic model.

Alternative Hypothesis ($H_1$)

The statistical proposition stating that the observed data significantly deviates from the expected data.

Chi-Square ($\chi^2$) Test

A statistical test employed to evaluate whether observed count data is significantly different from expected numbers based on a hypothesized genetic model.

Chi-Square ($\chi^2$) Statistic Formula

$$\chi^2 = \sum \frac{(\text{Observed} - \text{Expected})^2}{\text{Expected}}$$

Degrees of Freedom ($df$)

The number of independent variables in a statistical test, calculated as the number of possible outcomes (e.g., number of possible phenotypes) minus one ($df = n - 1$).

$p$-value

The probability of observing the experimental results (or more extreme results) if the null hypothesis ($H_0$) is true.

Critical Value ($p = 0.05$ Threshold)

The cutoff value from the $\chi^2$ distribution corresponding to a $5\%$ chance of observing the results by random error; if the calculated $\chi^2$ is less than this value, the researcher fails to reject $H_0$.

Causes for Rejection of Genetic Null Hypothesis

Factors that cause experimental results to significantly deviate from expectations, including sample size being too small, incorrect assumed mode of inheritance, gene linkage on the same chromosome, non-viable genotypes, or influences from other genes and the environment.