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# BIO Analytic Methods

## Hardy–Weinberg Principle

The Hardy-Weinberg Principle describes the relationship between genotype ratios and allelic frequencies in a population, a relationship that can be used as a predictive tool if either genotypes ratios or allele frequencies for a population are known.

The principle is represented by two equations where `p` and `q` are allele frequencies:
`p2 + 2pq + q2 = 1`
`p + q = 1`

Thus, if the frequency `p` is known to be `0.4`, the frequency for `q` can be calculated from the second equation:
`q = 1 - 0.4 = 0.6`

Additionally, genotype ratios can be calculated from the parts of the first equation:
homozygous for p is `p2 = 0.42 = 0.16`
heterozygous is `2pq = 2(0.4)(0.6) = 0.48`
homozygous for q is `q2 = 0.62 = 0.36`
(Note that the calculated ratios add up `0.16 + 0.48 + 0.36 = 1`)

This method is limited by the assumption of the population existing in Hardy-Weinberg Equilibrium, a stable state that precludes evolution by maintaining the gene pool:

• no mutations
• no immigration or emigration
• no selection
• large population
• random mating

## Testcross (Backcross; concepts of parental, F1, and F2 generations)

A testcross is an analytic process that was developed alongside Mendelian genetics. It relies on the segregation of alleles from parent into progeny to identify the genotypes present across generations. As it requires the specific mating of individual organisms potentially including between siblings or, in the case of a backcross, the crossing of progeny with the parental generation, it can only be performed ethically and feasibly with certain types of organisms.

• Parental generation is the oldest generation being studied, the source of originating genotypes
• F1 generation is the progeny of the parental cross
• F2 generation is the progeny of a cross of the F1 generation

For a recessive allele only present in one heterozygous parent (the other parent being homozygous dominant), it will take until the F2 generation (cross of heterozygotes) before the recessive phenotype is displayed:

Parental cross

``` AA AAAAA aAaAa ```

F1 heterozygote cross

``` Aa AAAAa aAaaa ```

To use a testcross for analysis, an individual with the dominant phenotype but of unknown genotype (either homozygous dominant or heterozygous), is crossed with an individual with the recessive phenotype (necessarily homozygous recessive).

Progeny only displaying the dominant phenotype reveal the unknown genotype must have been homozygous dominant.

``` A?=A aAadomAadom aAadomAadom ```

Progeny displaying half the dominant phenotype half the recessive phenotype reveal the unknown genotype must have been heterozygous.

``` A?=a aAadomaarec aAadomaarec ```

## Gene mapping: crossover frequencies

Gene mapping determines the location of genes on a chromosome. Crossing over that occurs during meiosis is more likely to occur between genes that are located farther apart on a chromosome or less likely to occur between genes that are close together on a chromosome. Crossover frequencies (recombination frequency, r.f.), measured by comparing the combination of traits displayed in progeny, can then be used to estimate the distance between genes and ultimately their location on the chromosome.

The unit of measurement for recombination frequency is one recombination per 100 progeny (1% r.f.), called a centimorgan (c.m.) or map unit (m.u.). Progeny with the same combination of traits as the parents are called parental, while progeny displaying a combination different from the parents are called recombinant.

## Biometry: statistical methods

Biometry is the statistical analysis of biological data. Methods include probabilistic tools, Bayesian computations, and multivariate statistics.