Ecology and Epidemiology
The distribution of naturally occurring epiphytic populations of Xanthomonas campestris pv. phaseoli on individual leaves of dry beans was assessed by various graphical and statistical techniques. Population sizes of X. c. phaseoli were estimated from the number of characteristic colonies formed on MXP medium. Data sets that contained 20 or 100 leaves and supported detectable numbers of X. c. phaseoli departed significantly from normality. Logarithmic transformation failed to result in normal distribution of data. The flexible Weibull distribution was selected as a possible alternative to normal and lognormal distributions for fitting censored and uncensored data sets. Kolmogorov-Smirnov goodness-of-fit tests indicated that a Weibull distribution fit in all but five of 23 data sets. Bacterial counts of X. c. phaseoli were plotted as straight lines in Weibull but not in normal or lognormal cumulative probability plots. The ability of Weibull and lognormal distributions to fit data sets was compared by the ratio of the maximized likelihood test statistic (RML^{I/n}). In the majority of data sets that contained several (>50) data points and low levels of censoring, a lognormal distribution was rejected and a Weibull distribution was accepted regardless of the cultivar’s susceptibility to common blight. When data sets contained few uncensored data points, the distinction between Weibull and lognormal distributions for describing data was unclear. Explanations other than the general nature of the Weibull distribution may account for the superiority of Weibull for fitting data sets. The Weibull density function was derived from a model based on the assumption that bacterial numbers are related to the length of time bacteria have been on a leaf. However, further investigations are needed to elucidate the biological interpretation of Weibull parameters as they pertain to epiphytic population dynamics of X. c. phaseoli. |