Box 6.2. Calculation of day-degrees
An outline of a simple method to estimate day-degrees (after Daly et al. 1978) is exemplified by data on the relationship between temperature and development in the yellow-fever mosquito, Aedes aegypti (Diptera: Culicidae) (after Bar-Zeev 1958).
- In the laboratory, establish the average time required for each stage to develop at different constant temperatures. The graph on the left shows the time in hours (H) for newly hatched larvae of Ae. aegypti to reach successive stages of development when incubated at various temperatures.
- Plot the reciprocal of development time (1/ H), the development rate, against temperature to obtain a sigmoid curve with the middle part of the curve approximately linear. The graph on the right shows the linear part of this relationship for the total development of Ae. aegypti from the newly hatched larva to the adult stage. A straight line would not be obtained if extreme development temperatures (e.g. higher than 32°C or lower than 16°C) had been included.
- Fit a linear regression line to the points and calculate the slope of this line. The slope represents the amount in hours by which development rates are increased for each 1 degree of increased temperature. Hence, the reciprocal of the slope gives the number of hour-degrees, above threshold, required to complete development.
- To estimate the developmental threshold, the regression line is projected to the x-axis (abscissa) to give the developmental zero, which in the case of Ae. aegypti is 13.3°C. This zero value may differ slightly from the actual developmental threshold determined experimentally, probably because at low (or high) temperatures the temperature — development relationship is rarely linear. For Ae. aegypti, the developmental thresh- old actually lies between 9 and 10°C.
- The equation of the regression line is 1/H = k(T° — Tt), where H = development period, T° = temperature, Tt = development threshold temperature, and k = slope of line.
Thus, the physiological time for development is H(T° — Tt) = 1/k hour-degrees, or H(T° — Tt)/24 = 1/k = K day-degrees, with K = thermal constant, or K-value. By inserting the values of H , T°, and T t for the data from Ae. aegypti in the equation given above, the value of K can be calculated for each of the experimental temperatures from 14 to 36°C:
Thus, the K-value for Ae. aegypti is approximately independent of temperature, except at extremes (14 and 34—36°C), and averages about 2740 hour-degrees or 114 day-degrees between 16 and 32°C.