Artificial Intelligence (AI) Calculator for “Expected and observed heterozygosity calculator”

Understanding genetic diversity requires precise calculations of heterozygosity metrics. Expected and observed heterozygosity are fundamental in population genetics.

This article explores the calculation methods, formulas, real-world applications, and provides extensive data tables for heterozygosity analysis.

Example Numeric Prompts for Expected and Observed Heterozygosity Calculator

• Allele frequencies: p = 0.6, q = 0.4; observed heterozygotes = 45; sample size = 100
• Genotype counts: AA = 30, Aa = 50, aa = 20; calculate expected and observed heterozygosity
• Allele frequencies: p = 0.7, q = 0.3; observed heterozygotes = 40; sample size = 90
• Genotype frequencies: AA = 0.36, Aa = 0.48, aa = 0.16; compute heterozygosity values

Comprehensive Tables of Expected and Observed Heterozygosity Values

Below are detailed tables illustrating typical allele frequencies, genotype distributions, and corresponding heterozygosity values from various species and populations. These tables serve as practical references for researchers and geneticists.

Fundamental Formulas for Expected and Observed Heterozygosity

Expected and observed heterozygosity are key metrics in population genetics, quantifying genetic variation within populations. Below are the essential formulas, variables, and interpretations.

1. Expected Heterozygosity (He)

Expected heterozygosity represents the probability that two randomly selected alleles from the population are different (heterozygous). It is calculated based on allele frequencies assuming Hardy-Weinberg equilibrium.

• He: Expected heterozygosity
• p_i: Frequency of the i-th allele in the population
• Σ: Summation over all alleles at the locus

For a biallelic locus (two alleles, p and q), the formula simplifies to:

• p: Frequency of allele A
• q: Frequency of allele a (q = 1 – p)

Interpretation:

• He ranges from 0 to 1, where 0 indicates no heterozygosity (fixed alleles), and 1 indicates maximum heterozygosity.
• Higher He values suggest greater genetic diversity.

2. Observed Heterozygosity (Ho)

Observed heterozygosity is the proportion of individuals in the population that are heterozygous at a given locus, based on genotype counts.

• Ho: Observed heterozygosity
• Numerator: Count of heterozygous genotypes (e.g., Aa)
• Denominator: Total sample size (N)

Interpretation:

• Ho is an empirical measure reflecting actual genetic variation in the sample.
• Comparing Ho to He can reveal deviations from Hardy-Weinberg equilibrium, indicating inbreeding, selection, or population structure.

3. Hardy-Weinberg Equilibrium (HWE) Genotype Frequencies

Under HWE, genotype frequencies are predicted from allele frequencies:

• These expected genotype frequencies are used to calculate expected heterozygosity.
• Deviations from these frequencies suggest evolutionary forces at work.

4. Fixation Index (F_IS)

The fixation index quantifies the reduction in heterozygosity due to inbreeding or population substructure:

• F_IS: Inbreeding coefficient
• Values range from -1 to 1
• Positive values indicate heterozygote deficiency (inbreeding)
• Negative values indicate heterozygote excess (outbreeding or selection)

Detailed Real-World Examples of Expected and Observed Heterozygosity Calculation

Example 1: Human Population Genotype Data

A sample of 100 individuals from a human population has the following genotype counts at a biallelic locus:

• AA = 30
• Aa = 50
• aa = 20

Calculate the expected heterozygosity (He), observed heterozygosity (Ho), and fixation index (F_IS).

Step 1: Calculate allele frequencies

Total alleles = 2 × 100 = 200

Number of A alleles = (2 × 30) + (1 × 50) = 60 + 50 = 110

Number of a alleles = (2 × 20) + (1 × 50) = 40 + 50 = 90

Allele frequencies:

Step 2: Calculate expected heterozygosity (He)

Step 3: Calculate observed heterozygosity (Ho)

Step 4: Calculate fixation index (F_IS)

Interpretation: The negative F_IS value indicates a slight excess of heterozygotes, suggesting no inbreeding.

Example 2: Maize Population Allele Frequencies

A maize population has allele frequencies p = 0.7 and q = 0.3. In a sample of 100 plants, 42 are heterozygous. Calculate He, Ho, and F_IS.

Step 1: Calculate expected heterozygosity (He)

Step 2: Calculate observed heterozygosity (Ho)

Step 3: Calculate fixation index (F_IS)

Interpretation: F_IS of zero indicates the population is in Hardy-Weinberg equilibrium at this locus.

Additional Technical Insights on Heterozygosity Calculations

Expected and observed heterozygosity calculations are foundational in assessing genetic variation, but several nuances affect their interpretation and application:

• Multiple Alleles: For loci with more than two alleles, He is calculated by subtracting the sum of squared allele frequencies from 1, capturing the complexity of multi-allelic systems.
• Sample Size Effects: Small sample sizes can bias Ho estimates; thus, confidence intervals or bootstrapping methods are recommended for robust inference.
• Population Structure: Subdivided populations may show heterozygote deficiencies (Wahlund effect), affecting Ho and He comparisons.
• Mutation and Selection: Both can alter allele frequencies, influencing heterozygosity metrics over time.
• Software Tools: Programs like GenAlEx, Arlequin, and PLINK automate these calculations, incorporating statistical tests for Hardy-Weinberg equilibrium and inbreeding coefficients.

For further reading and official guidelines, consult the National Center for Biotechnology Information (NCBI) and the Genetics Society of America.