Evolution Calculator
Predict genotype distributions and allele frequency shifts under selection pressure.
Calculated using: p' = (p²w₁₁ + pqw₁₂) / w̄
Genotype Frequency Comparison
Visual representation of genotype distribution shifts after one generation of selection.
| Genotype | Relative Fitness (w) | Initial Frequency | New Frequency |
|---|
What is an Evolution Calculator?
An Evolution Calculator is a specialized computational tool used by biologists, researchers, and students to model how genetic structures change within a population over time. By applying mathematical principles like the Hardy-Weinberg equilibrium and fitness coefficients, this evolution calculator predicts how allele frequencies will shift in response to natural selection.
Who should use it? It is essential for population geneticists studying the spread of beneficial mutations, conservationists tracking genetic diversity, and educators explaining the mechanics of microevolution. A common misconception is that evolution takes millions of years; however, as this evolution calculator demonstrates, significant genetic shifts can occur in just a single generation under strong selective pressure.
Evolution Calculator Formula and Mathematical Explanation
The mathematical foundation of this tool rests on the selection model of population genetics. We assume a single locus with two alleles: Dominant (A) and Recessive (a).
Step-by-Step Derivation:
- Calculate initial genotype frequencies using p² + 2pq + q² = 1.
- Assign fitness values (w): wAA = 1, wAa = 1 – hs, waa = 1 – s.
- Calculate average population fitness: w̄ = p²wAA + 2pqwAa + q²waa.
- Determine the new allele frequency p' = (p²wAA + pqwAa) / w̄.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| p | Frequency of dominant allele | Decimal | 0.0 – 1.0 |
| s | Selection Coefficient | Decimal | 0.0 – 1.0 |
| h | Dominance Coefficient | Decimal | 0.0 – 1.0 |
| w̄ | Mean Population Fitness | Relative Value | 0.0 – 1.0 |
Practical Examples (Real-World Use Cases)
Example 1: Selection Against a Lethal Recessive Condition
Imagine a population where a recessive trait (aa) is lethal (s = 1.0) and the allele frequency p is 0.9. Inputting these into the evolution calculator shows that while the recessive genotype is eliminated each generation, the 'a' allele persists in heterozygotes (Aa), showing how slowly lethal recessives are purged.
Example 2: Antibiotic Resistance (Directional Selection)
In a bacterial colony, a new mutation provides resistance. If p (the resistant allele) starts at 0.01 with a high selection advantage (s = 0.5 against non-resistant), the evolution calculator will demonstrate a rapid "selective sweep" where the resistant allele frequency jumps significantly in the next generation.
How to Use This Evolution Calculator
Using this tool to model genetic changes is straightforward:
- Enter p: Input the starting frequency of your dominant allele.
- Define s: Adjust the selection coefficient to reflect how much disadvantage the recessive trait faces.
- Set h: Use the dominance coefficient to define if the heterozygote is affected by selection.
- Review Results: The primary display shows the new p frequency, while the chart visualizes the genotype shift.
Key Factors That Affect Evolution Calculator Results
While this evolution calculator provides accurate mathematical predictions, real-world biology involves additional complexities:
- Population Size: Genetic drift (random chance) has a massive impact on small populations, often overriding selection.
- Mutation Rate: New alleles are introduced via mutation, which this basic model assumes is zero.
- Gene Flow: Migration of individuals between populations can drastically alter allele frequencies.
- Non-Random Mating: Assortative mating or inbreeding disrupts the Hardy-Weinberg ratios.
- Environmental Stability: Selection coefficients (s) are rarely constant and change as environments shift.
- Linkage Disequilibrium: Alleles at different loci may be inherited together, affecting their individual evolutionary trajectories.
Frequently Asked Questions (FAQ)
What is a selection coefficient of 1.0?
This represents a lethal genotype or total sterility, meaning individuals with that genotype do not contribute to the next generation's gene pool.
Can the evolution calculator handle more than two alleles?
This specific version handles biallelic systems (A and a). Multi-allelic systems require more complex polynomial expansions.
Why does the chart show three bars?
The bars represent the three possible genotypes in a diploid organism: Homozygous Dominant (AA), Heterozygous (Aa), and Homozygous Recessive (aa).
What does a dominance coefficient (h) of 0 mean?
It means the trait is completely recessive; selection only acts on the 'aa' genotype, while 'Aa' has the same fitness as 'AA'.
How does this relate to Genetic Drift?
The evolution calculator models deterministic selection. Genetic drift is the stochastic (random) component not captured in this selection-only formula.
Is p + q always equal to 1?
Yes, in a two-allele system, the sum of frequencies must always equal 100% of the alleles at that locus.
Can I use this for human genetics?
Yes, for traits governed by simple Mendelian inheritance and clear selection pressures, like lactose persistence or sickle cell anemia.
Does it account for the bottleneck effect?
No, a bottleneck is a form of genetic drift. This tool focuses specifically on the "natural selection" component of evolution.
Related Tools and Internal Resources
- Hardy-Weinberg Solver – Check if your population is in genetic equilibrium.
- Genetic Drift Calculator – Model the impact of random chance on small populations.
- Natural Selection Simulator – Visualize long-term evolutionary trends.
- Allele Frequency Mapper – Track the geographic distribution of genes.
- Population Growth Model – Calculate exponential and logistic population increases.
- Mutation Rate Estimator – Calculate the frequency of new genetic variants.