Table 1.

The biological parameters that drive the Red Queen and King effects in antagonistic and mutualistic symbioses

	Antagonistic symbiosis		Mutualism, $k$ small		Mutualism, $k$ large
	Short run	Long run	Short run	Long run	Short run	Long run
$1$/generation time	♕Q	♕Q	♕Q	No effect	♔K	No effect
Mutation rate	No effect	♕Q	No effect	No effect	No effect	No effect
Selection strength	♕Q	♕Q	♕Q	♔K	♔K	♕Q
Population size	♕Q	♕Q	♕Q	♔K	♔K	♕Q

For each of the parameters that determine evolutionary rate, we ask whether the population with the larger parameter value, which therefore evolves faster, is more successful (♕Q, a Red Queen effect) or less successful (♔K, a Red King effect) in the interaction, holding the other rate parameters constant and equal between the two populations. The short-run results are numerically computed for particular parameter values (Figs. 1–3). The long-run results are for the weak-mutation limit and are exact (see text for details). For selection strength and population size in the mutualisms, (i) we set one population’s selection strength to w (or both populations’, when studying the effect of population size) and assume that the larger parameter value is larger by a small amount, (ii) we define “k small” as k < 1/(1 + w) and “k large“ as k > 1/(1 + w), and (iii) we assume the populations to be sufficiently large