Neutral Theory Calculator
Calculate expected neutral nucleotide diversity (theta = 4Ne*mu) and compare with observed variation. Assess whether sequence data is consistent with neutral evolution or selection.
🧬 Molecular Evolution📐 theta = 4Ne x mu🧬 Biology
Effective population size Ne
Mutation rate mu (per site/generation)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Neutral Theory Calculator | — | theta = 4Ne x mu | per site |
Step-by-Step Examples
Example 1
Human Genome
Ne=10,000, mu=1.2e-8.
- theta=4x10000x1.2e-8=4.8e-4
- ~0.48 SNPs/kb expected
- Observed ~1/kb; slightly higher — may reflect expansion
✓ theta=4.8e-4, ~0.5 SNPs/kb
Example 2
Drosophila
Ne=10^6, mu=1.5e-9.
- theta=4x10^6x1.5e-9=6e-3
- ~6 SNPs/kb — consistent with observation
- Large Ne maintains high diversity
✓ theta=6e-3, ~6 SNPs/kb
Example 3
Bacteria
Ne=10^8, mu=5e-10.
- theta=4x10^8x5e-10=0.2
- 200 SNPs/kb if neutral
- Selective sweeps reduce observed diversity below this
✓ theta=0.2, selection reduces to ~10 SNPs/kb
Real-World Applications
Population Genomics
Baseline for detecting selection against neutral expectation.
Comparative Genomics
dN/dS uses neutral synonymous rate as reference.
Conservation
Low diversity vs theta reveals bottlenecks.
Pathogen Evolution
Identify immune-selected genes by excess variation vs neutral expectation.
Common Mistakes to Avoid
⚠️
Observed pi ≠ theta_W
Both estimate theta but differ: pi from pairwise comparisons, Watterson's from segregating sites. Tajima's D = (pi-theta_W)/stdev.
⚠️
Historical Ne, not current
theta reflects long-term Ne, not current census size. Human theta unchanged despite population explosion.
⚠️
Recombination ignored
Without recombination, selective sweeps deplete variation in large regions. Include recombination in realistic models.
Frequently Asked Questions
What is the neutral theory? ▾
Kimura 1968: most molecular variation is selectively neutral. Observed diversity = balance between neutral mutation and genetic drift.
What is Tajima's D? ▾
(pi - theta_W)/SE. D>0: excess common variants (balancing selection or bottleneck). D<0: excess rare variants (positive selection or expansion).
What is theta? ▾
theta = 4Ne*mu. Scales neutral diversity. Estimated from sequence data as pi or theta_W.
What is nearly neutral theory? ▾
Ohta: many mutations slightly deleterious. Their fate depends on Ne — neutral in small, selected in large populations.
What is dN/dS? ▾
Ratio of nonsynonymous to synonymous substitution rates. >1: positive selection. <1: purifying selection. Compares against neutral dS baseline.