Painting:  Le Moulin de la Galette

Le Moulin de la Galette (1887, van Gogh)

3   Digital Computing

3.1   Growing Degree-Days

Growing Degree-Days is a measure of temperature duration. Specifically it is the persistence of temperature in excess of a threshold amount that is necessary for daily biological processes such as insect development to begin. It is also the amount of average temperature over the threshold, which influences the speed of development. The threshold can be peculiar to a species of interest although most insect species have closely equivalent thresholds. Growing Degree-Days is calculated in such a way that, at any point in the year, its cumulative sum is proportional to development of insects up to that point in the year. Growing Degree-Days is capped by a temperature ceiling (the cutoff temperature), too, above which the amount of daily development does not depend on temperature.

The terminology is confusing. The term "Growing Degree-Days" as applied to phenology of insects (in this paper) is distinct from the terms "degree-days," "heating degree-days," and "cooling degree-days" common in heating, ventilation, and air-conditioning (HVAC) contexts such as laymen's summaries of architectural and construction engineering documents. "Degree-days" accounts for day-to-day differences in energy consumption for heating and cooling buildings, but the terms "degree-days" and "Growing Degree-Days" are used interchangeably in biological contexts, too. Please be aware that academic papers may and frequently do use their own terminology.

In 1969, Baskerville and Emin published refinements to the calculation of Growing Degree-Days based on high-speed digital computing, which adhere more closely to models of insect development than conventional cooling degree-days does. Theirs are the calculations that produce growing degree-day tables for controlling various species of insects.

3.2   Growing Degree-Day Table

Here is such a table for codling moth:

Growing Degree-Day (°F) Table

For Codling Moth (Cydia pomonella)
Threshold =  50°F
Cutoff =  88°F
Method:  gdd_single_sine_horizontal_cutoff

  \ Min Daily Temp
Max  44  46  48  50  52  54  56  58  60  62  64  66  68  70  72  74  76  78  80  82  84  86  88  90
 48   0   0   0 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 50   0   0   0   0 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 52   0   1   1   1   2 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 54   1   1   2   2   3   4 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 56   2   2   2   3   4   5   6 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 58   3   3   3   4   5   6   7   8 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 60   4   4   4   5   6   7   8   9  10 *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 62   5   5   5   6   7   8   9  10  11  12 *** *** *** *** *** *** *** *** *** *** *** *** *** ***
 64   5   6   6   7   8   9  10  11  12  13  14 *** *** *** *** *** *** *** *** *** *** *** *** ***
 66   6   7   7   8   9  10  11  12  13  14  15  16 *** *** *** *** *** *** *** *** *** *** *** ***
 68   7   8   8   9  10  11  12  13  14  15  16  17  18 *** *** *** *** *** *** *** *** *** *** ***
 70   8   9   9  10  11  12  13  14  15  16  17  18  19  20 *** *** *** *** *** *** *** *** *** ***
 72   9  10  10  11  12  13  14  15  16  17  18  19  20  21  22 *** *** *** *** *** *** *** *** ***
 74  10  11  11  12  13  14  15  16  17  18  19  20  21  22  23  24 *** *** *** *** *** *** *** ***
 76  11  12  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26 *** *** *** *** *** *** ***
 78  12  13  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28 *** *** *** *** *** ***
 80  13  14  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30 *** *** *** *** ***
 82  14  15  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32 *** *** *** ***
 84  15  16  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34 *** *** ***
 86  16  17  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36 *** ***
 88  17  18  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38 ***
 90  18  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  36  37  38  38
 92  18  19  20  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  37  38  38
 94  19  20  20  21  22  23  24  25  26  27  28  29  30  31  32  33  33  34  35  36  37  38  38  38
 96  20  20  21  22  23  23  24  25  26  27  28  29  30  31  32  33  34  35  35  36  37  38  38  38
 98  20  21  21  22  23  24  25  26  27  28  29  30  30  31  32  33  34  35  36  36  37  38  38  38
100  20  21  22  22  23  24  25  26  27  28  29  30  31  32  32  33  34  35  36  36  37  38  38  38
102  21  21  22  23  24  25  26  27  27  28  29  30  31  32  33  34  34  35  36  37  37  38  38  38
104  21  22  22  23  24  25  26  27  28  29  30  30  31  32  33  34  34  35  36  37  37  38  38  38
106  22  22  23  24  24  25  26  27  28  29  30  31  31  32  33  34  35  35  36  37  37  38  38  38
108  22  22  23  24  25  26  27  27  28  29  30  31  32  32  33  34  35  35  36  37  37  38  38  38
110  22  23  23  24  25  26  27  28  28  29  30  31  32  33  33  34  35  36  36  37  37  38  38  38
112  22  23  24  24  25  26  27  28  29  30  30  31  32  33  34  34  35  36  36  37  37  38  38  38
114  23  23  24  25  26  26  27  28  29  30  31  31  32  33  34  34  35  36  36  37  37  38  38  38
116  23  24  24  25  26  27  27  28  29  30  31  31  32  33  34  34  35  36  36  37  37  38  38  38
118  23  24  24  25  26  27  28  28  29  30  31  32  32  33  34  35  35  36  36  37  37  38  38  38

The asterisks fill cells representing the nonsense situation where minimum temperature would exceed the maximum.

Using the paper table requires a paper calendar. Each morning, the minimum and maximum temperature of the preceding day are recorded. The minimum temperature is located along the top of the table, the maximum temperature is located along the side, and the Growing Degree-Days where the column and row intersect are transcribed to yesterday's cell on the calendar. Cumulative Growing Degree-Days for today is the sum of Growing Degree-Days from all the previous cells on the calendar. Using the paper table is fairly simple even though the calculations that produce the table are arcane.

Predicting the developmental stage of an insect is then a straightforward matter of comparing today's cumulative Growing Degree-Days with published growing degree-day requirements for each developmental stage of the species of interest.

The published growing degree-day requirements for various species have been experimentally verified.

U. C. Agriculture and Natural Resources has a list of insect "Research Models" and the papers that purport to validate them, but see also Coop's "Library of Degree-Day Models."

Looking at the summaries of these papers, it is obvious that methods of approximating the actual Growing Degree-Days vary as do recommended threshold and cutoff temperatures for most species. The marvel is that insect-development models function well enough to be of real-world value in pest treatment, so do not be seduced by the precision of all the figures. It is not possible to practice the concepts without adopting one or another of the thresholds and cutoffs and explicit methods, of course; nevertheless, you should still feel free to make your own accommodation to the range of choice that the research presents.