Natural selection
Natural selection changes the frequencies of heritable types when those types differ in reproductive success.
Relative fitness
If type \(i\) has frequency \(p_i\) and fitness \(w_i\), then after selection its frequency is
\[p_i'=\frac{p_iw_i}{\bar w},\qquad \bar w=\sum_jp_jw_j.\]Types with fitness above the population mean tend to increase in frequency, while those below it tend to decrease.
Interpretation
Fitness is context-dependent: it describes reproductive contribution under the particular biological and environmental conditions represented by the model.
Key idea. Selection is mathematically represented by differential reproductive success changing type frequencies across generations.