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Title: RELATIONSHIPS BETWEEN DISEASE INCIDENCE AT TWO LEVELS IN A SPATIAL HIERARCHY

Author
item HUGHES, G - UNIV. OF EDINBURGH
item MCROBERTS, N - SCOTISH AGR. COLLEGE
item MADDEN, L - OHIO STATE UNIV.
item Gottwald, Timothy

Submitted to: Phytopathology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/19/1997
Publication Date: N/A
Citation: N/A

Interpretive Summary: This is the first in a series of three papers that deals with sampling for plant diseases. This first paper deals with the statistical theory behind new sampling methods. Data used as model systems for the study came from three diverse plant diseases including grapevine downy mildew, a fungus disease of wine grapes, citrus scab, a fungus disease of citrus, and citrus tristeza, a virus disease of citrus. The theory involves sampling at one scale, i.e. groups of plants, and being able to predict the disease incidence at a lower scale, i.e. individual plants. The paper provides the equations and statistical theory to back up this sampling relationship. This theory makes surveys for plant disease much simpler. Using the suggested method, surveyors can take samples from fewer plants, not have to keep track of individual plant positions, and after analysis predict the disease incidence in an entire field or plantation with good accuracy at less expense of manpower and lab assays. Therefore, the method is applicable to scientific studies, to the conduct of surveys to determine the prevalence of pests by regulatory agencies, and to growers who might want to scout their own fields or plantations more easily to determine the prevalence of pests.

Technical Abstract: Relationships between disease incidence measured at two levels in a spatial hierarchy are derived. These relationships are based on the properties of the binomial distribution, the beta-binomial distribution and an empirical power-law relationship between the observed and binomial variances of disease incidence. Data sets for demonstrating and testing these relationships are based on observations of the incidence of grape downy mildew, citrus tristeza, and citrus scab. Disease incidence at the higher of the two scales is shown to be an asymptotic function of: incidence at the lower scale; the degree of aggregation at that scale; and the size of the sampling unit. For a random pattern, the relationship between incidence measured at two spatial scales does not depend on any unknown parameters. In that case, an equation for predicting an approximate variance of incidence at the lower of the two scales from incidence measurements made at the higher scale is derived, for use in the context of sampling. It is further shown that the effect of aggregation of incidence at the lower of the two scales is to reduce the rate of disease increase at the higher scale.