Development time - temperature relationship of some physiological processes in the phytopathogenic fungi and pests

The duration of the physiological processes in the phytopathogenic fungi and pests can be estimated at constant and changing temperatures by the three parametric temperature x=p/t**n(1-t)**m and Sum(from z=1 to x) t**n(1-t)**mno.dz=p respectively, where x = the duration of the development time, t=(T-Tmin)/(Tmax-Tmin) the temperature equivalents, no.dz the development time unit and n, m, p parameters. The second model form is derived from the first one and is appropriate to describe the biological response, when the temperature of the development period remains constant. The equivalence between these two model forms is valid under some assumptions. The model is based on the hypothesis that the temperature effect on the rate of change in the duration of development time is controlled by the resultant of two opposite but simultaneously acting phenomena from which the first is favored by the low temperatures whereas the second is accelerated by high ones. The model x=p/t**n(1-t)**m has a higher precision concerning the forecasting of the duration of the development time than the sum of effective temperature rule, the Belehradek or the Janisch temperature model on account of the possibility of the former to describe mathematically the biological response at supra optimal temperatures and forecast in correctly next to the extreme temperatures of the temperature range. Parameters n, m, p have biological meaning and mathematical properties suitable for accessing the thermal requirements of the organism on the base of arithmetic values of these parameters and insuring the flexibility of fitting the corresponding temperature-duration curve on a large series of experimental data. Model x=p/t**n(1-t)**m gives a biologically acceptable prognosis of the development time in the range of the effective temperature. The estimation of the parameters can be achieved from the experimental data by a weighted least square method. The estimation of parameters in the model of changing temperatures is attainable in the same manner on the assumption that the frequency of temperatures hi in some temperature classes ki is linearly related to the response xi, with the bi's as xi and the class middles as ti can parameters n, m, p be estimated as in the model constant temperatures