Selection Differential Calculator

Calculator Inputs

Use direct means for summary statistics or raw mode for comma-separated trait values.

Input Mode

Raw mode estimates means and population SD from trait lists.

Trait Name

Units

Generation Label

Heritability (h²)

Population SD

Used in direct mode. Raw mode estimates it automatically.

Population Mean

Selected Mean

Population Count

Selected Count

Population Trait Values

Comma, space, or semicolon separated values.

Selected Trait Values

These values define the selected group in raw mode.

Example Data Table

This example models a trait under artificial selection. The selected group has a higher mean than the whole population, producing a positive selection differential.

Trait	Population Mean	Selected Mean	Population SD	Heritability	Selection Differential	Predicted Response
Beak depth	12.40 mm	14.10 mm	2.30 mm	0.42	1.70 mm	0.7140 mm
Plant height	48.00 cm	53.50 cm	5.40 cm	0.35	5.50 cm	1.9250 cm
Body mass	21.80 g	24.20 g	3.10 g	0.51	2.40 g	1.2240 g

Formula Used

Selection differential: S = X̄_selected − X̄_population

Standardized differential: S / SD_population

Predicted response: R = h² × S

Predicted offspring mean: X̄_population + R

In raw mode, the calculator first computes the population mean, selected mean, and sample standard deviation from the entered trait lists. In direct mode, it uses your supplied summary statistics.

How to Use This Calculator

Select Direct means and parameters or Raw trait values.
Enter a trait name, units, and generation label for cleaner reporting.
Provide population mean, selected mean, and population SD in direct mode.
Or paste comma-separated population and selected trait values in raw mode.
Add heritability if you want predicted response and offspring mean.
Enter counts to estimate selection proportion and selection ratio.
Press the calculate button to show results above the form.
Use the CSV and PDF buttons to save the result summary.

FAQs

1. What does selection differential measure?

It measures how far the selected group mean differs from the original population mean. A positive value means selected individuals have a higher average trait value than the population.

2. Why is heritability included?

Heritability helps estimate the expected response to selection. The calculator uses the breeder’s equation, where response equals heritability multiplied by the selection differential.

3. What is the difference between direct and raw mode?

Direct mode uses summary inputs you already know. Raw mode calculates means and population variation from entered trait values, which is useful for classroom or field datasets.

4. What does a negative selection differential mean?

A negative value means the selected individuals have a lower average trait value than the original population. This indicates selection favored smaller or reduced trait values.

5. What is standardized differential?

It scales the selection differential by population standard deviation. This makes trait shifts easier to compare across studies, traits, or units with different magnitudes.

6. Can I use this for natural and artificial selection?

Yes. The math works for both settings, provided your selected group and baseline population are clearly defined and measured using the same trait scale.

7. Why do I need population standard deviation?

Population standard deviation is needed for the standardized differential. It expresses selection strength relative to population variability rather than raw trait units alone.

8. Are the predicted offspring values exact?

No. They are model-based estimates from the breeder’s equation. Real populations may deviate because of environment, nonadditive genetics, sampling error, or changing selection pressure.