Quantitative genetics studies how traits influenced by multiple genes and environmental factors evolve within a population. To understand how a population changes over generations, scientists quantify the forces driving this change. The selection differential is a fundamental measure used in evolutionary biology and selective breeding programs to gauge the immediate impact of selection on a given trait. It provides a direct, measurable value for the strength of selection applied to a population.
Defining the Selection Differential
The selection differential, symbolized as \(S\), measures the difference between the mean trait value of the individuals chosen to breed and the mean trait value of the entire population from which they were selected. \(S\) quantifies the phenotypic advantage held by the selected parents compared to the average individual in the original group. For example, if a plant population averages 50 centimeters in height, and only plants averaging 65 centimeters are chosen to reproduce, the selection differential is the difference between these two means. This measure isolates the immediate impact of the selection process, whether driven by humans in a breeding program or by nature through differential survival.
The value of \(S\) represents how much the selected group deviates from the population average for a specific trait. A larger absolute value for the selection differential signifies a stronger intensity of selection. This measure is typically applied to the trait upon which selection is intentionally practiced.
The Mechanics of Calculation
Calculating the selection differential (\(S\)) requires determining two average trait values from the population under study. The fundamental formula is \(S = \mu_s – \mu_p\), where \(\mu_s\) is the mean trait value of the selected parents and \(\mu_p\) is the mean trait value of the entire initial population.
The first step involves measuring the trait for every individual to establish the overall population mean (\(\mu_p\)). This average serves as the baseline measurement against which the selected individuals will be compared. The second step is to identify and measure the mean trait value of the subset chosen to reproduce, establishing the selected mean (\(\mu_s\)).
\(S\) is calculated by subtracting \(\mu_p\) from \(\mu_s\). A positive value for \(S\) indicates selection favored individuals with a higher trait value, suggesting directional selection toward larger phenotypes. Conversely, a negative selection differential signifies that the chosen individuals had a trait value lower than the population average, representing selection for a smaller phenotype.
Connecting Selection Differential to Evolutionary Change
While \(S\) quantifies the strength of selection, it does not predict the evolutionary change in the next generation alone. For that prediction, \(S\) must be incorporated into the Breeder’s Equation: \(R = h^2S\). Here, \(R\) represents the Response to Selection—the actual change in the mean trait value observed in the offspring generation. The equation shows that the predicted evolutionary change is a product of the selection differential (\(S\)) and the heritability of the trait (\(h^2\)).
Heritability (\(h^2\)) describes the proportion of trait variation attributable to genetic differences. Heritability estimates range from zero to one. A value near one suggests variability is mostly due to genetics, while a value near zero suggests environmental factors are the primary cause. A large selection differential (\(S\)) will only result in a significant evolutionary response (\(R\)) if the trait has a sufficiently high heritability (\(h^2\)). If superior trait value is due to environmental factors rather than genetics, offspring will regress toward the original population mean, resulting in a small \(R\) despite a large \(S\).
A Worked Numerical Example
Researchers attempt to increase the average body weight in a population of laboratory mice. The initial population of 100 mice has an average body weight (\(\mu_p\)) of 30 grams. The heaviest 10 mice are selected as parents, and their average body weight (\(\mu_s\)) is 40 grams.
To calculate \(S\), the population mean is subtracted from the selected mean: \(S = 40 \text{ grams} – 30 \text{ grams} = 10 \text{ grams}\). This positive value of 10 grams indicates the strength and direction of the selection pressure applied to the trait. The heritability (\(h^2\)) of body weight in this mouse strain is 0.40, meaning 40% of the phenotypic variation is attributable to genetic factors.
The predicted evolutionary change (\(R\)) is calculated using the Breeder’s Equation: \(R = h^2S\). Substituting the values yields \(R = 0.40 \times 10 \text{ grams} = 4 \text{ grams}\). This predicts the next generation’s mean body weight will be 4 grams heavier than the original 30 grams, resulting in a new expected average of 34 grams.