Many organisms, especially animals like insects, which depend on the environment for body heat, have growth stages and life cycles that are highly dependent on temperature. To better understand and model how insect life history events progress, for example in the emergence and initial growth of the biogeographical research subjects, we must first understand he relationship between temperature, heat accumulation, and subsequent development. The measure of the integration of heat over time, usually referred to as degree-days, is a widely used science-based method of forecasting, that quantifies heat accumulation based on measured ambient temperature. Some popular methods for calculation of degreedays are the traditional sinusoidal method and the average method. The average method uses only the average of the daily maximum and minimum temperature, and has the advantage that it is very easy to use. However, this simplest method can underestimate the amount of degree-day accumulation that is occurring in the environment of interest, and thus has a greater potential to reduce the accuracy of forecasting insect pest emergence. The sinusoidal method was popularized by Allen (1976, [1]), and gives a better approximation to the actual accumulation of degree-days. Both of these degree-day accumulators are independent of typical heating and cooling patterns during a typical day cycle. To address possible non-symmetrical effect, it was deemed prudent to construct degree-day accumulators to take into account phenomena like sunrise, sunset, and solar noon. Consideration of these temporal factors eliminated the assumption that heating and cooling in a typical day during the growth season is symmetric. In some tested cases, these newer degree-day integrators are more accurate than the traditional sinusoidal method, and in all tested cases, these integrators are more accurate than the average method. After developing the newer degree-day accumulators, we chose to investigate use of a logistic phenology model similar to one used by Onsager and Kemp (1986, [54]) when studying grasshopper development. One reason for studying this model is that it has parameters that are important when considering pest management tactics, such as the required degree-day accumulations needed for insects in immature stages (instars) to be completed, as well as a parameter related to the variability of the grasshopper population. Onsager and Kemp used a nonlinear regression algorithm to find parameters for the model. I constructed a simplex algorithm and studied the effectiveness when searching for parameters for a multi-stage insect population model. While investigating the simplex algorithm, it was found that initial values of parameters for constructing the simplex played a crucial role in obtaining realistic and biologically meaningful parameters from the nonlinear regression. Also, while analyzing this downhill simplex method for finding parameters, it was found there is the potential for the simplex to get trapped in many local minima, and thus produce extraneous or incorrectly fitted parameter estimates, although Onsager and Kemp did not mention this problem. In tests of my methods of fitting, I used an example of daily weather data from Onefour, AB, with a development threshold of 12 ±C and a biofix day of April 1st, as an example. The method could be applied to larger, more extensive datasets that include grasshopper population data on numbers per stage, by date, linked to degree accumulations based on the non-symmetrical method, to determine whether it would offer significant improvement in forecasting accuracy of spring insect pest events, over the long term. / xii, 106 leaves ; 29 cm