The MF and FMF patterns
It is easy to envision how the FMF pattern aligns with Mighty Males (Fig. 3a). Recall that the FMF pattern is broadly found in turtles and crocodilians, as well as in some lizards, and is likely the ancestral condition (Fig. 1a). Under the FMF pattern, females are produced in hot and cold incubation environments, and males at intermediate temperatures. Assuming the physiology of the embryo evolves to match the average environment (e.g., Ewert 1985), then one would expect that an intermediate temperature would represent optimal incubation conditions, imparting a high-quality phenotype and high individual condition. Temperatures that deviate from the average environment, however, would produce phenotypes of a quality that is inversely proportional to the degree of deviation (e.g., Noble et al. 2018).
The framing of the MF pattern with respect to the focal hypothesis depends on the evolutionary origin of the MF pattern. In the simplest and perhaps most probable case, the FMF pattern and FM pattern are two sides of the same coin, and it suffices to explain the adaptive significance of the FMF pattern. Specifically, sex seems to be determined by the amount of development that occurs above and below the TPiv during the thermosensitive period (Georges et al. 1994), with high temperature resulting in a short thermosensitive period (Carter et al. 2018, 2019b; Massey et al. 2019). Temperatures below the lower TPiv have low developmental leverage and hence have a relatively weak influence on sex. Selection maintaining the lower TPiv is therefore relatively weak, and the lower TPiv may be lost (or functionally so (Schwarzkopf & Brooks 1985; Janzen 2008)) without a major influence on primary sex ratios, leaving the MF pattern of cool males and warm females.
However, if the MF pattern evolves through both the thermal limits of viability and changes in male-determining temperatures (e.g., Deeming and Ferguson 1989; Ewert and Nelson 1991; Ewert et al. 2004), then the MF pattern requires more thorough dissection. The alignment of the MF pattern with Mighty Males requires that assumptions be made with respect to the position of TPiv along the axis of performance. I suggest that TPiv should occur at a temperature that results in approximately average fitness for both sexes (Fig. 3b), but critically, fitness should decline with temperature at a faster rate above TPiv (i.e., female-producing temperatures) vs below TPiv. The reasoning is that male-producing temperatures should reflect the peak of the performance curve, where a unit change in temperature has little influences on fitness, whereas female-producing temperatures should represent the shoulder of the curve, where fitness changes rapidly with temperature. Therefore, performance metrics should be relatively invariant with respect to temperature in the range of male-producing temperatures (i.e, slightly cooler than TPiv), although male-producing temperatures that are far cooler than TPiv may result in a decrease in performance.