Coalescence Time Calculator
Calculate expected time to most recent common ancestor (TMRCA) for gene copies in a population. E[T] = 4Ne generations for diploid populations. Foundation of coalescent theory.
🧬 Population Genetics📐 E[T] = 4Ne (diploid)🧬 Biology
Effective population size Ne
Generation time (years)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Coalescence Time Calculator | — | E[T] = 4Ne (diploid) | generations |
Step-by-Step Examples
Example 1
Human Nuclear DNA
Human Ne~10,000.
- E[T] = 4x10000 = 40,000 generations
- At 25yr/gen: 1,000,000 years
- Most human allele pairs coalesce within ~1 Ma
✓ E[T] = 40k gen ≈ 1 Ma
Example 2
Human mtDNA
mtDNA Ne~5000 (haploid: 2Ne).
- E[T] = 2x5000 = 10,000 gen
- At 25yr: 250,000 years — mitochondrial Eve
- Consistent with African origin ~200kya
✓ E[T] = 10k gen ≈ 250 ka
Example 3
Drosophila
Ne~10^6.
- E[T] = 4 million generations
- Much deeper coalescence than humans
- Large Ne means more ancestral diversity maintained
✓ E[T] = 4M gen (very deep)
Real-World Applications
Phylogenetics
Expected gene tree depth within populations.
Ancestral Inference
TMRCA estimation from genomic data.
Demographic History
Variation in coalescence reveals population size changes.
Neutral Theory
Coalescence connects neutral variation to Ne.
Common Mistakes to Avoid
⚠️
Ne ≠ census size
Real Ne typically 0.1-0.5 of census N due to variance in reproduction and sex ratio.
⚠️
High variance around E[T]
Coalescence time is exponentially distributed — actual values span 0 to many multiples of E[T].
⚠️
Population structure changes pattern
Substructure slows between-group coalescence, speeds within-group.
Frequently Asked Questions
What is coalescence? ▾
Two gene copies sharing a single common ancestral copy going backwards in time.
What is mitochondrial Eve? ▾
MRCA of all human mtDNA ~150-200 kya in Africa. Every living human traces mtDNA to her.
Why is human Ne ~10,000? ▾
Historical estimate from neutral diversity pi ≈ 4Ne*mu ≈ 1e-3. Despite 8 billion people today, this reflects long-term historical population size.
What is PSMC? ▾
Pairwise Sequentially Markovian Coalescent — method to reconstruct historical Ne changes from a single diploid genome sequence.
How is Ne estimated? ▾
From neutral diversity: Ne = pi/(4*mu). Or from linkage disequilibrium patterns or coalescent-based demographic inference.