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United States Department of Agriculture

Agricultural Research Service

Title: The Negative Binomial Distribution As a Model for Describing Counts of Greenbugs, Schizaphis Graminum, on Wheat

Authors
item Elliott, Norman
item Giles, Kris - OSU
item Royer, T - OSU
item Kindler, Dean
item Jones, D - OSU
item Tao, F - OSU

Submitted to: Southwestern Entomologist
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: February 1, 2003
Publication Date: June 1, 2003
Citation: ELLIOTT, N.C., GILES, K.L., ROYER, T.A., KINDLER, D., JONES, D.B., TAO, F.L. THE NEGATIVE BINOMIAL DISTRIBUTION AS A MODEL FOR DESCRIBING COUNTS OF GREENBUGS, SCHIZAPHIS GRAMINUM, ON WHEAT. SOUTHWESTERN ENTOMOLOGIST. 2003. v.23(2): p. 131-136.

Interpretive Summary: The greenbug is the most important pest insect in winter wheat in the Southern Great Plains. Improved methods for sampling this pest are needed to reduce the time required to make pest management decisions. Sequential sampling schemes used in managing pest insects involve sampling a variable number crop plants or parts of crop plants. The number of samples taken depends on the density of the pest insect in a field. If the density is close to that at which insecticide should be applied to protect the crop from economic loss, a large number of samples may need to be taken before a decision whether to spray the field or not can be made. However, when the density is much lower or much greater than that causing economic loss, very few samples may be required before a decision to spray is made. Thus sequential sampling saves considerable time compared to sampling schemes where a fixed number of samples are taken. Sequential sampling schemes based on theoretical probability distributions often require less time and resources for decision-making than those based on other mathematical formulas. Developing such a sampling scheme requires determining a probability distribution that adequately describes the frequency distribution of counts of the insects in samples. A theoretical probability distribution called the negative binomial distribution often provides a good fit to frequency distributions of insect counts. We obtained samples from 364 wheat fields to test whether the negative binomial distribution was a good fit to counts of greenbugs on wheat tillers (individual stems) in production fields. The negative binomial distribution proved to be a very good probability distribution for counts of greenbugs on tillers in winter wheat fields. The research indicated that it will be possible to develop a sequential sampling scheme for greenbugs in winter wheat derived from the negative binomial distribution. Such a sequential sampling scheme will require less time than sampling schemes currently in use with no reduction in the accuracy of decision making.

Technical Abstract: Sequential sampling schemes based on the sequential probability ratio test often perform very well for making control decisions in insect pest management. In order to develop a sampling scheme using the sequential probability ratio test, it must be known that the distribution of counts of the insect fits a particular probability distribution. For insects like the greenbug, Schizaphis graminum (Rondani), which have aggregated spatial distributions, the negative binomial distribution often provides an acceptable fit to sample data. The parameter, k, of the negative binomial distribution is considered to be an index of aggregation. Values of k near zero are indicative of a species for which individuals in a population are highly aggregated spatially, and large values of k indicate a species for which individuals are randomly distributed in space. The objectives of this study were to determine whether the negative binomial distribution provided a good fit to samples for greenbugs collected from winter wheat fields in Oklahoma, and to determine whether k varied over the range of values of the mean number of greenbugs per tiller (m) observed in a large number of samples from greenbug infested fields. Finally, if k did vary, we sought to develop a function to relate k to m. A total of 132 samples in which one or more tiller was infested with greenbugs were taken during the fall growing season, and 232 samples with one or more greenbugs were taken during spring. The frequency distribution of greenbug counts differed significantly from that expected for a negative binomial distribution for six of 132 fall samples (4.5%) and for 6 of 222 spring samples (2.7%). Estimates of k were highly variable and changed systematically as m increased. The parameters of a quadratic regression model fitted to samples with m > 0.25 did not differ significantly for fall and spring samples. The expected value of k from the quadratic regression model varied from approximately 0.3 to 0.7 as m varied from 2 to 12 greenbugs per tiller. Variation in estimates of k about the regression curve provided an indication of the extent to which k varied independently of m. The mean square error of the regression was equal to 0.043 and was relatively large compared to k. This indicates that a sequential sampling scheme based on the negative binomial distribution should be evaluated by simulation and/or direct validation to verify the utility of a sampling scheme prior to operational use in a pest management program.

Last Modified: 9/22/2014
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