Table 3. Open in new tab Summary of key...

Table 3.

Summary of key results of the two model frameworks.

Model version	Population genetic models	Quantitative genetic models
Stabilizing selection on the male trait	N/A	Equilibria are neutrally stable unless the trait that females prefer $\bar{y}$ ⁠, is extremely low or high.
Directional selection on the male trait	Two-locus model: Male trait is lost without sufficient preference strength; preference strength is then neutral Preference strength evolves in runaway fashion whenever the male trait can evolve Three-locus model: Male trait is lost without sufficient preference strength With high mutation rate and preference strength, male trait evolves and preference strength increases in runaway fashion With low mutation rate, male trait and preference strength initially increase but are ultimately lost	For some parameter values, there are stable equilibria when the average of log-preference strength $\bar{x}$ is within a range $[x_{1}, x_{2}]$ ⁠. Runaway may happen for equilibria with $\bar{x} < x_{1}$ or $\bar{x} > x_{2} .$ All equilibria will be unstable when the strength of viability selection, the genetic variance of the male trait, or female preference are too large.

Model version	Population genetic models	Quantitative genetic models
Stabilizing selection on the male trait	N/A	Equilibria are neutrally stable unless the trait that females prefer $\bar{y}$ ⁠, is extremely low or high.
Directional selection on the male trait	Two-locus model: Male trait is lost without sufficient preference strength; preference strength is then neutral Preference strength evolves in runaway fashion whenever the male trait can evolve Three-locus model: Male trait is lost without sufficient preference strength With high mutation rate and preference strength, male trait evolves and preference strength increases in runaway fashion With low mutation rate, male trait and preference strength initially increase but are ultimately lost	For some parameter values, there are stable equilibria when the average of log-preference strength $\bar{x}$ is within a range $[x_{1}, x_{2}]$ ⁠. Runaway may happen for equilibria with $\bar{x} < x_{1}$ or $\bar{x} > x_{2} .$ All equilibria will be unstable when the strength of viability selection, the genetic variance of the male trait, or female preference are too large.