2.1: Environmental Sex Determination in Turtles

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It is a well known, but little understood fact that the sex of some reptiles depends on the environment in which the egg is incubated (temperature is important), and is not purely a genetic determination. A graph of some data on a species of fresh water turtles appears in Figure 2.1.1¹.

Explore 2.1.1 Examine the graph for Chrysemys picta and write a brief verbal description of the dependence of the percentage of females on incubation temperature for a clutch of Chrysemys picta eggs.

$2-1.JPG$

Figure $\PageIndex{1}$: Percent female hatchlings from incubation of Chrysemys picta eggs at various temperatures.

Your experience probably does not include a single analytic formula that describes the dependence of the percentage of females on incubation temperature for a clutch of turtle eggs. It is easiest to use a piecewise definition; use one formula for a range of temperatures and other formulas for other ranges of temperatures. Your verbal description in the case of Chrysemys picta could say that if the temperature is less than 28$^{\circ}$C, the percent of female is zero, and if the temperature is greater than or equal to 29$^{\circ}$C, the percent of female is 100. One could describe what happens between 28$^{\circ}$C and 29$^{\circ}$C, but the accuracy of the data probably does not warrant such a refinement. This piecewise procedure of describing data occurs often enough to have a special notation.

\[\text { Percent of hatchlings that are female }=\left\{\begin{array}{ll}
0 & \text { if } \operatorname{Temp}<28^{\circ} \mathrm{C} \\
\text {Uncertain } & \text { if } 28^{\circ} \mathrm{C} \leq \mathrm{Temp}<29^{\circ} \mathrm{C} \\
100 & \text { if } 29^{\circ} \mathrm{C} \leq \mathrm{Temp}
\end{array}\right. \label{2.1}\]

The designation Uncertain for $28^{\circ} \mathrm{C} \leq \mathrm{Temp}<29^{\circ} \mathrm{C}$ is a bit unsatisfactory but we hope the example sufficiently illustrates piecewise definition of dependence.

Exercises for Section 2.1 Environmental Sex Determination in Turtles.

Exercise 2.1.1 Data on the temperature determination of sex for the snapping turtle, Chelydra serpentina appears in Figure Ex. 2.1.1.

Write a verbal description of the dependence of the percentage of females on incubation temperature for a clutch of Chelydra serpentina eggs.
Write formulas similar to Formulas 2.1 to describe the dependence of the percentage of females on incubation temperature for a clutch of Chelydra serpentina eggs.

Figure for Exercise 2.1.1 Percent females from clutches of Chelydra serpentina (snapping turtle) eggs incubated at various temperatures.

$2-1-1.JPG$

¹This data was collected by Ralph Ackerman from a number of publications, most of which are referenced in, Fredric J. Janzen and Gary L. Paukstis, Environmental sex determination in reptiles: Ecology, evolution, and experimental design, The Quarterly Review of Biology 66 (1991) 149-179.