= Weak selection
<Weak selection> is a regime of an evolutionary model in which the focal trait or interaction changes <biological fitness> only slightly relative to a baseline. It permits calculations close to <neutral evolution>. In one common <evolutionary game theory> convention, a payoff $P$ changes <biological fitness> according to
$$
f=1-w+wP,
$$
where $w$ controls the contribution of the game. <Weak selection> requires the payoff-dependent change to be small on the scale of baseline <biological fitness>.<A simple rule for the evolution of cooperation on graphs and social networks by Hisashi Ohtsuki and others>[Nature 441, p. 502 and Figure 1; fitness map and definition of weak selection]{ref}
For example, take $w=0.01$ and two competitors with payoffs $P_1=2$ and $P_2=3$. Their fitnesses are $f_1=1.01$ and $f_2=1.02$. If their chances to fill a vacancy are proportional to <biological fitness>, the second competitor wins with <probability>
$$
\frac{f_2}{f_1+f_2}=\frac{1.02}{2.03}\approx0.50246,
$$
only slightly above the neutral value $1/2$. This invented calculation shows the meaning of a small selective bias. A small numerical $w$ would not ensure the same approximation if the payoffs were made enormously larger. <Weak selection> is also distinct from small <biological population> size: the strength of <genetic drift> and the cumulative effect of selection depend on additional features of the model.
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