Artificial Intelligence (AI) Calculator for “Linkage disequilibrium (LD) calculator”
Linkage disequilibrium (LD) quantifies non-random associations between genetic variants. Calculating LD is crucial for genetic mapping and population studies.
This article explores LD calculators, key formulas, practical tables, and real-world applications with stepwise solutions.
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Example Numeric Prompts for “Linkage disequilibrium (LD) calculator”
- Calculate D’ and r² for allele frequencies pA=0.6, pB=0.4, and haplotype frequency pAB=0.3
- Determine LD measures for SNP pair with pA=0.7, pB=0.5, pAB=0.35
- Compute linkage disequilibrium statistics given pA=0.45, pB=0.55, pAB=0.25
- Evaluate D, D’, and r² for pA=0.8, pB=0.3, pAB=0.24
Comprehensive Tables of Linkage Disequilibrium (LD) Values
| Allele Frequency pA | Allele Frequency pB | Haplotype Frequency pAB | D (LD Coefficient) | D’ (Normalized LD) | r² (Correlation Coefficient) |
|---|---|---|---|---|---|
| 0.6 | 0.4 | 0.3 | 0.06 | 0.25 | 0.10 |
| 0.7 | 0.5 | 0.35 | 0.0 | 0.0 | 0.0 |
| 0.45 | 0.55 | 0.25 | 0.0125 | 0.056 | 0.0063 |
| 0.8 | 0.3 | 0.24 | 0.0 | 0.0 | 0.0 |
| 0.5 | 0.5 | 0.3 | 0.05 | 0.2 | 0.1 |
| 0.3 | 0.7 | 0.25 | 0.04 | 0.19 | 0.08 |
Fundamental Formulas for Linkage Disequilibrium (LD) Calculator
Linkage disequilibrium quantifies the non-random association of alleles at two loci. The primary measures include D, D’, and r².
1. LD Coefficient (D)
The coefficient D measures the difference between observed and expected haplotype frequencies under linkage equilibrium.
- pAB: Frequency of haplotype carrying allele A at locus 1 and allele B at locus 2.
- pA: Frequency of allele A at locus 1.
- pB: Frequency of allele B at locus 2.
Interpretation: D = 0 indicates linkage equilibrium (no association). Positive or negative values indicate disequilibrium.
2. Normalized LD (D’)
D’ normalizes D to the theoretical maximum possible value, accounting for allele frequencies.
Where Dmax is defined as:
- If D > 0: Dmax = min(pA × (1 – pB), (1 – pA) × pB)
- If D < 0: Dmax = min(pA × pB, (1 – pA) × (1 – pB))
Interpretation: D’ ranges from -1 to 1, with absolute values close to 1 indicating strong LD.
3. Correlation Coefficient (r²)
r² measures the correlation between alleles at two loci, reflecting the proportion of variance explained.
- r² ranges from 0 to 1.
- Values near 1 indicate strong correlation and predictability between loci.
4. Additional Measures
- Chi-square test for LD: χ² = n × r², where n is sample size.
- LOD score: Logarithm of odds ratio for linkage, often used in family-based studies.
Detailed Real-World Examples of Linkage Disequilibrium (LD) Calculator
Example 1: Calculating LD Measures for Two SNPs in a Population
Consider two biallelic SNPs, locus 1 with alleles A and a, and locus 2 with alleles B and b. The allele frequencies and haplotype frequency are:
- pA = 0.6
- pB = 0.4
- pAB = 0.3
Calculate D, D’, and r².
Step 1: Calculate D
Step 2: Calculate Dmax
Since D > 0,
Step 3: Calculate D’
Step 4: Calculate r²
Interpretation: The LD between these SNPs is moderate with D’ = 0.375 and low correlation r² = 0.0625.
Example 2: Evaluating LD in a Case-Control Study for Disease Association
In a case-control study, two SNPs are genotyped. The allele frequencies and haplotype frequency in cases are:
- pA = 0.7
- pB = 0.5
- pAB = 0.35
Calculate D, D’, and r², and interpret the results.
Step 1: Calculate D
Step 2: Calculate D’
Since D = 0, D’ = 0 by definition.
Step 3: Calculate r²
Interpretation: No linkage disequilibrium is observed between these SNPs in cases, indicating independent segregation.
Expanded Technical Insights on Linkage Disequilibrium Calculations
Linkage disequilibrium is influenced by multiple evolutionary forces including genetic drift, selection, mutation, recombination, and population structure. Accurate LD calculation is essential for genome-wide association studies (GWAS), haplotype mapping, and fine-mapping causal variants.
- Recombination Rate: LD decays over generations due to recombination. The recombination fraction (θ) inversely correlates with LD strength.
- Population Stratification: Substructure can inflate LD estimates, necessitating correction methods.
- Sample Size: Larger samples provide more reliable LD estimates; small samples may yield biased D and r² values.
- Phasing Accuracy: Haplotype phase inference impacts pAB estimation, critical for LD calculation.
Advanced LD calculators integrate these factors, often employing maximum likelihood or Bayesian frameworks to estimate haplotype frequencies and LD parameters from genotype data.
Authoritative Resources and Tools for Linkage Disequilibrium Calculation
- National Center for Biotechnology Information (NCBI) – Linkage Disequilibrium Overview
- PLINK Software – LD Calculation and Visualization
- Haploview – LD and Haplotype Analysis Tool
- Genome.gov – Genetics Glossary: Linkage Disequilibrium
These resources provide comprehensive guidelines, software, and datasets for accurate LD analysis in research and clinical genetics.