Harvey J. Gold

A simulation model of population dynamics of the codling moth, Cydia pomonella

A simulation model has been developed that predicts numbers and phenology of a population of codling moth, Cydia pomonella (L.), in an apple orchard. The model is a general insect population model based on the interative-cohort technique. It operates at two time scales: a fine time scale (1 h) for temperature-dependent physiological processes, and a coarse time scale (1 day) for population processes. The population is divided into a specifiable number of stages, and each stage is described by four process functions, which may be of any convenient mathematical form, and may differ among stages. Each stage is divided into cohorts of individuals born or emerged on the same day, and individuals within a cohort are considered probabilistically identical. The model simulates the processes of development, transition among stages, and mortality by using probability distributions representing these processes, and incorporates the effects of pesticides on mortality of the insect. Model output was evaluated by comparison with records of pheromone trap catches of codling moths in commercial apple orchards in North Carolina. The model predicts timing of the first spring flight well, depending on the initial age distribution used. Time between peaks of numbers of adults in the model is about 15 days longer than the observed period between flight peaks in orchards. Sensitivity analysis indicates that this discrepancy may be related to differences between measured ambient temperature and tree canopy temperature. The sensitivities of numbers of insects produced by the model, and timing of peaks in numbers present were determined for each of the parameters in the model. The parameters with greatest effect on the model output were those which control the locations of developmental rate functions and survival functions on the temperature scale. In the model, pesticides had a much larger effect on numbers of adults present than records of moths caught in pheromone traps indicate actually occurred, suggesting that moths caught in traps in commercial orchards where effective pesticides are applied may be largely immigrants.

Evaluation and calibration of three models for daily cycle of air temperature

Abstract Three simple empirical models for daily cycle of air temperature were parameterized and evaluated using one- to three-hourly temperature data from one to nine years at five locations in North Carolina. All three models calculate temperatures continuously from daily maximum and minimum temperatures. These models are the sine—exponential model and two versions of sinusoidal models. The sine—exponential model uses a truncated sine function for the day time and an exponential function in the night. The sinusoidal model has a cosine function for the period between times of minimum and maximum temperatures and another cosine function between times of maximum temperature and minimum temperature of the next day. A modified sinusoidal model uses a truncated sine function instead of cosine function for the interval between the times of minimum and maximum temperatures. The models were fitted to temperature data for each location and year by a nonlinear least-squares procedure. They were then evaluated for accuracy and stability in terms of the mean-square error and the variation in parameter estimates over year and location. The sine—exponential model gave the smallest mean-square error for the data tested and the sinusoidal model gave the largest. The least square estimates of parameters for the sine—exponential model had less variation among years than among locations. However, a set of averaged parameters can be used for all locations tested and all years without substantially increasing the error over the best fit model.

Value of information about weed distribution for improving postemergence control decisions

Abstract Weeds apparently occur in patches within fields. This spatial distribution has implications for choosing the most profitable postemergence control measure, because weed distribution influences the yield loss from competition, the design of the optimal scouting plan and the feasibility of patch spraying. Simulation models that use data on the distribution and composition of actual populations may be used to examine these implications for choosing between many potential treatments for postemergence control of a mixed species population. Simulation experiments were carried out to investigate the value of information about weed patchiness for improving the recommendations of a decision model (HERB) for postemergence weed control in soybean. Information about weed patchiness was more valuable when used to account for the possible error in the density estimates obtained by scouting than when used to increase the accuracy of the yield loss prediction. Accurate scouting was shown to be important for choosing treatments when control is required, as well as determining if control is necessary. Simulation results may be used to identify the optimal scouting plan once information about the cost of scouting becomes available.

Decision analysis as a tool for integrating simulation with expert systems when risk and uncertainty are important

Abstract Risk and uncertainty are important components of agricultural decision making. The methodology of applied decision analysis is especially useful in addressing such problems, but has not been widely integrated with expert systems. One problem has been the difficulty of handling uncertainty within the expert system framework in a way which is logically consistent with rational decision criteria. An additional problem in agriculture is the need to combine uncertain or incomplete information from simulations and statistical studies with the subjective knowledge of one or several experts. In this paper, it is argued that Bayesian probability theory provides a natural approach, and a methodology is developed for combining diverse sources of information within the framework of an expert system. The methodology is developed within the context of an expert system for protection of soybeans against corn earworm, using information from HELSIM, a heliothis population model (R. Stinner) and from the SOYGRO soybean crop model (G. Wilkerson).

A decision analytic model for chemical control of sooty blotch and flyspeck diseases of apple

Abstract A model is presented for the optimal timing of chemical sprays to control the diseases of apple, sooty blotch and flyspeck. The model accounts, at a simplified level, for dynamics of disease progress, chemical inhibition of disease spread, decay of fungistat, cost of control and market structure for apples. Computed sensitivities and estimated uncertainties for the key parameters are used to compute Bayes optimal control decisions, as well as expected value of improved accuracy. It is concluded that the decision as to chemical treatment is logically divided into two steps: (i) whether or not to treat; (ii) level of treatment. Crop quality is the most important determinant for the first step; fungistat decay rate for the second. Because of asymmetries in the economic loss curves, uncertainties lead to levels of treatment considerably above the deterministic optimum.

Kinetics of facilitated diffusion of oxygen in tissue slices

Abstract It has been reported by Longmuir and co-workers that respiration of certain tissue slices obeys Michaelis-Menten kinetics. To explain this and related results, Longmuir has postulated a carrier to transport oxygen through the tissue. In the present report the behavior of a mobile carrier and of a fixed site carrier are considered. Expressions for V max and K m are developed. In relation to these parameters, the following points are discussed: (a) dependence on tissue thickness; (b) dependence on carrier concentration; (c) dependence on non-uniformities in carrier concentration; (d) distinguishing between mobile and fixed-site carrier mechanisms.

An economic analysis of binomial sampling for weed scouting

Abstract Full-count random sampling has been the traditional method of obtaining weed densities. Currently it is the recommended scouting procedure when using HERB, a herbicide selection decision aid. However, alternative methods of scouting that are quicker and more economical need to be investigated. One possibility that has been considered is binomial sampling. Binomial sampling is the procedure by which density is estimated from the number of random quadrats in which the count of individuals is equal to or less than a specified cutoff value. This sampling method has been widely used for insect scouting. There has also been interest in using binomial sampling for weed scouting. However, an economic analysis of this sampling method for weeds has not been performed. In this paper, the results of an economic analysis using simulations with binomial sampling and the HERB model are presented. Full-count sampling was included in the simulations to provide a benchmark for comparison. The comparison was made in terms of economic losses incurred when the estimated weed density obtained from sampling was inaccurate and a herbicide treatment was selected that did not maximize profits. These types of losses are referred to as opportunity losses. The opportunity losses obtained from the simulations indicate that in some situations binomial sampling may be a viable economic alternative to full-count sampling for fields with weed populations that follow a negative binomial distribution, assuming no prior knowledge of weed densities or negative binomial k values. Nomenclature: Glycine max, soybeans.

A reference curve and space-time series analysis of the regional population dynamics of the southern pine beetle (Dendroctonus frontalis Zimmermann)

The southern pine beetle, Dendroctonus frontalis ZIMMERMANN, has done considerable damage to southeastern United States pines in the last 23 years of recorded information. During this interval the insect has undergone tremendous fluctuations in its population levels, ranging from near undetectability to the destruction of some 401004 cords of wood in 1975 (PRICE and DOGGETT, 1978). Because of its destructiveness this beetle has been the object of intense investigation by many researchers over the last decade (PAYNE, 1980). However, nearly all of this work falls into two categories, either stand-hazard rating (HicKs, 1980) or population dynamics on the local infestation (spot) level (CouLSON, 1980). These local infestations or spots are clusters of trees which are undergoing beetle colonization. Spots may contain one tree or thousands of trees and can grow over several years. New attacks within the spot are under pheromone control. However, information and analysis on the crucial aspects of inter-spot dispersal and large-scale population dynamics has remained virtually zero. Several authors have previously described the southern pine beetle (SPB) as possessing a multi-level population dynamics, i.e. several distinct levels of organization in behavior. COULSON (1979) discusses two dynamic levels, the single spot and the multiple spots situations. Each level is presumed to be a complex blend of site conditions, evnironmental stresses, and competitor/predator effects. GOLD, MAWBY and HAIN (1980) extend this two level system to a formal five-level hierarchy which includes tree, spot neighborhood, patch, subregion, and region. Furthermore this same set of authors ascribe a two phase dynamic structure to each of the five separate levels. Such two phase systems occur frequently in the dynamics of most organisms. Migratory behavior and feeding preference behavior are some common entomological examples. In particular many forest

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems I: One enzyme-one substrate systems

Abstract This paper presents the results of a study concerned with the development of stochastic models for certain prototype, structured one-enzyme systems and the comparisons of these models with their deterministic, i.e., solution chemistry analogs under steady state conditions. The comparisons are in the form of graphs of steady state reaction kinetics versus substrate concentration for each type of model. The lack of agreement between the deterministic and stochastic models is related to a measure of the non-linearity of the system, in accord with Jensens inequalities. Implications of these results, relative to experimental procedures are briefly discussed. A subsequent paper will present similar results for certain structured two-enzyme systems.

A method for the incorporation of parametric uncertainty in the weighted evaluation multi-attribute decision analysis model

We develop an extension of the classic Weighted Evaluation (WE) Multi-Attribute Decision Analysis (MADA) model that allows for uncertainty in the parameters of the model. Uncertainties in attribute importance weights and alternative evaluation ratings are represented by independent uniform, triangular or beta random variables; and an iterative multi-variate integration scheme is used to evaluate the mean, variance and skewness of the resulting Probabilistic Weighted Evaluation (PWE). These moments are used to compute two-term Edgeworth and normal approximations to the distribution of: (a) the PWE for each of several alternatives that are to be analysed separately; or (b) the difference between PWEs for selected alternatives that are to be analysed on a pairwise basis. The proposed methodology is used to compare probabilistically three alternative solutions to the Mexico City Airport Siting Problem of Keeney and Raiffa (Keeney, R. L. and Raiffa, H., Decisions with Multiple Objectives. Wiley, New York, 1976).