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Mathematical Model for Spore Germination at Changing Temperature. Paul E. Waggoner, The Connecticut Agricultural Experiment Station, New Haven, Connecticut 06504; J.-Y. Parlange, The Connecticut Agricultural Experiment Station, New Haven, Connecticut 06504. Phytopathology 64:605-610. Accepted for publication 29 October 1973. DOI: 10.1094/Phyto-64-605.

In the field, organisms develop in temp, radiation, and moisture conditions that are variable rather than steady, and that are often detrimental rather than temperate. A mathematical model is presented for predicting one aspect of development, the germination of spores, under variations of temp. The model predicts the failures in germination of Alternaria solani spores and the average and variability in the germination time among individual spores when temp varied from 25 to 45 C. In the model, it is conceived that developing spores either progress through, or die in, a series of stages between dormancy and the appearance of germ tubes; and that temp affects the number of stages successfully completed and the rates of progress or death. The rates and number of stages could be calculated at any instant from the current environment and currently attained development stage, and the calculation did not require information about the often complex changes in temp that the spore had encountered previously. In principle, the model can be generalized to other development criteria, to other organisms, and to other environmental variations in the field.