How to Manage PestsDegree-Days
Temperature controls the developmental rate of many organisms. Plants and invertebrate animals, including insects and nematodes, require a certain amount of heat to develop from one point in their life cycles to another. This measure of accumulated heat is known as physiological time. Theoretically, physiological time provides a common reference for the development of organisms. The amount of heat required to complete a given organism's development does not vary—the combination of temperature (between thresholds) and time will always be the same. Physiological time is often expressed and approximated in units called degree-days (°D). Consult Baskerville & Emin (1969), Andrewartha & Birch (1973), Allen (1976), Zalom et al. (1983), and Wilson & Barnett (1983) if you are interested in the historical development of the degree-day concept. Developmental ThresholdsUpper and lower developmental thresholds have been determined for some organisms through carefully controlled laboratory and field experiments. For example, the lower developmental threshold is 51°F and the upper developmental threshold is 90°F for the San Jose scale (Quadraspidiotus perniciosus). Thresholds vary with different organisms. The lower developmental threshold for an organism is the temperature below which development stops. The lower threshold is determined by the organism's physiology. It is independent of the method used to calculate degree-days. The upper developmental threshold is the temperature above which the rate of growth or development begins to decrease or stop as determined by the cutoff method. The physiological interpretation of the upper threshold is dependent on the cutoff method. Degree-daysThe total amount of heat required, between the lower and upper thresholds, for an organism to develop from one point to another in its life cycle is calculated in units called degree-days (°D). Sometimes called heat units, degree-days are the accumulated product of time and temperature between the developmental thresholds for each day. Figure 1 illustrates the relationship between time and temperature, and the accumulation of degree-days. One degree-day is one day (24 hours) with the temperature above the lower developmental threshold by one degree. For instance, if the lower developmental threshold for an organism is 51°F and the temperature remains 52°F (or 1° above the lower developmental threshold) for 24 hours, one degree-day is accumulated.
A Celsius degree-day is not the same as a Fahrenheit degree-day because a Fahrenheit degree is smaller than a Celsius degree. It takes nine Fahrenheit degree-days to make five Celsius degree-days. DDc = 5/9 (DDf) and DDf = 9/5 (Ddc). Figure 2 shows that the areas under the temperature curve represented in Fahrenheit and Celsius units are equal, but the units differ. Each model in the UC IPM's phenology database gives degree-days for both scales. If you use other references, be sure to use the same scale as that used in the research.
Accumulated Degree-daysEach developmental stage of an organism has its own total heat requirement. Development can be estimated by accumulating degree-days between the temperature thresholds throughout the season. Each species requires a defined number of degree-days to complete its development. The accumulated degree-days from a starting point can help predict when a developmental stage will be reached. The date to begin accumulating degree-days, known as the biofix date, varies with the species. Biofix dates are usually based on specific biological events such as planting dates, first trap catch, or first occurrence of a pest. Accumulation of degree-days should be done regularly, especially when a control action decision is near.
Although it is simple to calculate the degree-days accumulated at a constant temperature in the laboratory, calculating degree-days for the daily temperature fluctuations that occur in nature is more difficult. Several methods are used to estimate degree-days through the use of daily minimum and maximum temperatures. All are approximations of the actual number of degree-days accumulated for a given set of daily temperatures and developmental thresholds, and therefore do not provide the exact degree-day values. However, most are adequate considering the accuracy of weather instruments used and the precision required for crop management decisions. (Some developmental relationships that require use of degree-hours have been determined. Accurate calculation of degree-hours requires a record of hourly temperatures rather than daily minimum and maximum temperatures. You can approximate degree-hours by multiplying the number of degree-days by 24.) The degree-day calculation methods differ somewhat in complexity. Season and climatic region also cause these methods to vary in how accurately they reflect actual degree-days. Whichever method is used, it is important to use the same method as that used in developing the organism's biological growth relationships. If the method is unknown, UC IPM recommends using the single sine method with a horizontal cutoff at the upper threshold, since it has been the most common method for many years in California. Degree-day calculations and accumulations are based on the area under the diurnal temperature curve and between the thresholds. Different methods for calculating degree-days are single sine, double sine, single triangle, and double triangle. Huber's method is a modification of the single sine method with a horizontal cutoff. From the simplest to the most mathematically complex, these are: single triangle, double triangle, single sine, double sine, and Huber's. All of these are linear methods because the rate of development is presumed to be a straight line directly related to temperature. There are nonlinear methods as well, but they are primarily used in research at this time. Note: Figures 3 through 6 illustrate the estimated accumulation of degree-days for a 3-day period. In the first half of the day, degree-days tend to be underestimated by an amount equal to area b. In the second half of the day, degree-days tend to be overestimated by an amount equal to area a. Over a 24-hour period, the overestimated area a helps to compensate for the underestimated area b. Triangle MethodsFigure 3 illustrates the single triangle method. The method draws a straight line between a day's minimum temperature and maximum temperature, assumes the next day's minimum temperature is the same, and draws another line to that point, forming two sides of a triangle. This method assumes the temperature curve is symmetrical around the maximum temperature. Degree-days are estimated by calculating the area within the triangle and between the thresholds.
The double triangle method is illustrated in Figure 4. Using two 12-hour or half-day calculations, the double triangle method draws a straight line between a daily minimum and maximum temperature, and another line vertically through the maximum temperature, forming two sides of a triangle. Degree-days are estimated by calculating the area within the triangle and between the thresholds. The second 12-hour period uses the same configuration with the minimum temperature of the following day. Degree-days for the day are the sum of the degree-days for the two half-days. See Note. Sine MethodsFigure 5 illustrates the single sine method. This technique uses a day's minimum and maximum temperatures to produce a sine curve over a 24-hour period, and then estimates degree-days for that day by calculating the area above the threshold and below the curve. This method assumes the temperature curve is symmetrical around the maximum temperature. See Note. Figure 6 illustrates the double sine method. This method fits a sine curve from the minimum temperature of the day to the maximum temperature of the day and then fits a separate sine curve from the maximum temperature of the day to the minimum temperature of the next day. Degree-days for the day are the sum of the degree-days for the two half-days. See Note. Huber's method. This method produces the same result as a single sine with a horizontal cutoff, except that 0.3 Fahrenheit degree-days are subtracted from a day's degree-day accumulation if the minimum and maximum temperatures for that day are between the upper and lower thresholds. This method has been used in the desert southwest in cotton pest management. Cutoff MethodsThe cutoff method refers to the manner in which the degree-day calculation area will be modified in relation to the upper threshold. UC IPM refers to the modification as a "method for cutoff at upper threshold." Other literature may refer to the upper developmental threshold cutoff, the upper cutoff, the upper developmental cutoff, or cutoff. The degree-day calculation method provides a choice of three cutoff methods - horizontal, vertical, and intermediate—to be used in conjunction with the sine and triangle calculation methods. (Huber's method automatically incorporates a horizontal cutoff method.) Figure 7 illustrates the modifications by each cutoff method to the single sine method of calculation. Horizontal cutoff method.The horizontal cutoff method assumes that development continues at a constant rate at temperatures in excess of the upper threshold. Mathematically, the area above the upper threshold is subtracted from the area above the lower threshold. Intermediate cutoff methodThe intermediate cutoff assumes that development slows, but does not stop, at temperatures above the upper threshold. Mathematically, the area above the upper threshold is subtracted twice from the area above the lower threshold. Vertical cutoff methodThe vertical cutoff method assumes that no development occurs when a temperature is above the upper threshold.
(max = maximum daily temperature, min = minimum daily temperature, U = upper threshold, L = lower threshold) |