The Canadian Entomologist · 1963 · 40 citations · 24 references
Life SciencesEcologyEntomologyInsect EcologyPopulation EcologySpatial EcologyInsect Population DynamicsPest DynamicsPest EcologyEgg Mass DistributionInsect Population EstimationNegative Binomial DistributionNegative Binomial ModelsNegative Binomial RegressionPest Population DynamicsPoisson Distribution
Abstract Counts of the Colorado potato beetle on potato did not conform to the Poisson distribution, there being an excess of uninfested and highly infested hills over the expected numbers. However, when observed distributions were fitted to the negative binomial series, the discrepancies were not significant when tested by chi-square. The negative binomial parameter k tended to increase with density. Using a common k , the distribution of the various stages may be described by expansion of ( q − px ) − k , when values of k are as follows: adult, 1.95; egg mass, 4.10; first instar, 0.68; second instar, 0.78; third instar, 1.04; fourth instar, 1.07. For all stages, the variance was proportional to a fractional power of the mean. Use of the individual potato stalk as a sample unit had little effect on the skewness of the distribution. Four transformations are offered for stabilizing the variance of field counts.
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Aggregation, Variance and the Mean
L. R. Taylor · Nature · 1961 · 2.5K citations
THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA
F. J. Anscombe · Biometrika · 1948 · 1.3K citations