Parameter Estimability in the Dennis-Kemp Phenology Model

Dennis, Kemp, and Beckwith (1986) developed a model describing the stochastic, temperature-dependent development of insect life stages in the field. The model predicts the proportion of insects in a population that are in a given life stage at a given time. The model is based on a logistic probability distribution where maximum likelihood (ML) is used to compute parameter estimates. This paper explores the estimability of parameters within this model. Parametric bootstrap confidence intervals for parameters and functions of the parameters were studied for efficacy. Limitations due to low sample sizes were also studied. The ML parameter and function of the parameters bootstrap sampling distributions indicate can be described well with a large sample multivariate normal distribution. Confidence intervals also followed the prescribed coverage rate and are adequate with this model. Lower sample sizes had lower bootstrap confidence interval coverage rates, but converged quickly to 95% as sample size increased. Results from this paper should be of interest to insect-pest managers and researchers who model development of insects, plants, and animals. Examples of these techniques are presented using data from the western spruce budworm, Choristoneura occidentalis, rangeland grasshopper species M. sanguinipes and the almond tree P. dulcis.masters, M.S., Statistical Sciences -- University of Idaho - College of Graduate Studies, 2018-0