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Selection coefficient

Measure of disadvantage relative to the fittest genotype.

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Core idea

Overview

The selection coefficient quantifies the proportional reduction in the genetic contribution of a particular genotype to the next generation compared to a standard reference genotype. It measures the intensity of natural selection acting against a phenotype, where a higher value indicates a greater selective disadvantage.

When to use: Use this coefficient when modeling the rate of allele frequency changes within a population over time. It is essential in population genetics scenarios where you need to compare the reproductive success of different phenotypes against the most fit individual in the group.

Why it matters: This value allows biologists to predict how quickly beneficial traits will spread or deleterious traits will be eliminated from a gene pool. It is critical for understanding real-world phenomena like the development of antibiotic resistance in bacteria or the survival of endangered species in changing climates.

Symbols

Variables

w = Relative Fitness, s = Selection Coefficient

Relative Fitness
Variable
Selection Coefficient
Variable

Walkthrough

Derivation

Understanding the Selection Coefficient

Selection coefficient s measures how strongly a genotype/phenotype is selected against relative to the fittest type.

  • The fittest type has relative fitness W=1.
  • Fitness is based on survival and reproductive success in that environment.
1

Define Relative Fitness:

Relative fitness W compares reproductive success of a type to the most successful type.

2

Convert to Selection Coefficient:

If W is less than 1, then s is positive. Larger s means stronger selection against that type.

Result

Source: Standard curriculum — Population Genetics

Free formulas

Rearrangements

Solve for

Make w the subject

Start from the selection coefficient formula. Add w to both sides and subtract s from both sides to isolate w.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a downward-sloping straight line that crosses both the vertical selection coefficient axis and the horizontal relative fitness axis at a value of one. For a biology student, this means that as an organism becomes more fit relative to its peers, the measure of its disadvantage decreases proportionally. The most important feature of this linear relationship is that the selection coefficient and relative fitness always sum to one, meaning any increase in fitness results in an equal and constant reduction in the selection coefficient.

Graph type: linear

Why it behaves this way

Intuition

Imagine a population of different genotypes as runners in a race, where 'relative fitness' determines how fast each runner is, and 's' represents the handicap imposed on slower runners, preventing them from reaching the relevant quantity in the system.

The proportional reduction in the genetic contribution of a genotype to the next generation compared to the fittest genotype.
A higher 's' means the genotype is more severely disadvantaged and contributes less to the next generation's gene pool.
relative fitness
The reproductive success of a genotype compared to the most reproductively successful genotype in the population.
A higher relative fitness means the genotype is better at surviving and reproducing, contributing more offspring to the next generation.

Signs and relationships

  • 1 - relative fitness: The subtraction from 1 defines the selection coefficient 's' as the *disadvantage* or *reduction* in fitness. If a genotype has perfect relative fitness (1), its 's' is 0 (no disadvantage).

Free study cues

Insight

Canonical usage

The selection coefficient is used as a dimensionless quantity, typically expressed as a decimal value between 0 and 1, representing the proportional reduction in fitness of a genotype compared to the fittest genotype.

Common confusion

A common mistake is to confuse the selection coefficient (s) with absolute fitness or to assign units to it. Both the selection coefficient and relative fitness are dimensionless ratios.

Dimension note

The selection coefficient is inherently dimensionless as it represents a ratio or proportional difference in fitness. Fitness itself is often defined as the reproductive success or contribution to the next generation

Unit systems

dimensionless - The selection coefficient 's' quantifies the proportional disadvantage of a genotype, with values typically ranging from 0 (no disadvantage) to 1 (complete disadvantage or lethality).
relative fitnessdimensionless - Relative fitness is a ratio of the fitness of a particular genotype to the fitness of the most fit genotype in the population, making it a dimensionless quantity, typically between 0 and 1.

Ballpark figures

  • Quantity:

One free problem

Practice Problem

In a study of bird beak shapes, a specific genotype is found to have a relative fitness (w) of 0.85 compared to the most successful phenotype. Calculate the selection coefficient (s) acting against this genotype.

Relative Fitness0.85

Solve for:

Hint: Subtract the given relative fitness from the maximum possible fitness value of 1.0.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

When estimating fitness cost of a harmful allele, Selection coefficient is used to calculate the s value from Relative Fitness. The result matters because it helps compare biological conditions and decide what the measurement implies about the organism, cell, or ecosystem.

Study smarter

Tips

  • The fittest genotype in the population is always assigned a relative fitness (w) of 1.0.
  • A selection coefficient of 1.0 indicates that the genotype is lethal or sterile, contributing nothing to the next generation.
  • The value of s must range between 0 and 1 in standard directional selection models.

Avoid these traps

Common Mistakes

  • Mixing s and w.
  • Using percent instead of decimal.

Common questions

Frequently Asked Questions

Selection coefficient s measures how strongly a genotype/phenotype is selected against relative to the fittest type.

Use this coefficient when modeling the rate of allele frequency changes within a population over time. It is essential in population genetics scenarios where you need to compare the reproductive success of different phenotypes against the most fit individual in the group.

This value allows biologists to predict how quickly beneficial traits will spread or deleterious traits will be eliminated from a gene pool. It is critical for understanding real-world phenomena like the development of antibiotic resistance in bacteria or the survival of endangered species in changing climates.

Mixing s and w. Using percent instead of decimal.

When estimating fitness cost of a harmful allele, Selection coefficient is used to calculate the s value from Relative Fitness. The result matters because it helps compare biological conditions and decide what the measurement implies about the organism, cell, or ecosystem.

The fittest genotype in the population is always assigned a relative fitness (w) of 1.0. A selection coefficient of 1.0 indicates that the genotype is lethal or sterile, contributing nothing to the next generation. The value of s must range between 0 and 1 in standard directional selection models.

References

Sources

  1. Hartl, D. L., & Clark, A. G. (2007). Principles of Population Genetics. Sinauer Associates.
  2. Freeman, S., & Herron, J. C. (2007). Evolutionary Analysis. Pearson Prentice Hall.
  3. Wikipedia: Selection coefficient
  4. Evolution by Douglas J. Futuyma, 3rd Edition
  5. Hartl, D. L., & Clark, A. G. Principles of Population Genetics. Sinauer Associates.
  6. Futuyma, D. J., & Kirkpatrick, M. Evolution. Sinauer Associates.
  7. Crow, J. F., & Kimura, M. An Introduction to Population Genetics Theory. Harper & Row.
  8. Standard curriculum — Population Genetics