Open AccessRelationships Between Disease Incidence at Two Levels in a Spatial Hierarchy
Author(s) -
G. Hughes,
Neil McRoberts,
L. V. Madden,
Gottwald Tr
Publication year - 1997
Publication title -
phytopathology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.264
H-Index - 131
eISSN - 1943-7684
pISSN - 0031-949X
DOI - 10.1094/phyto.1997.87.5.542
Subject(s) - incidence (geometry) , negative binomial distribution , statistics , mathematics , scale (ratio) , biology , spatial ecology , multinomial distribution , poisson distribution , ecology , geography , cartography , geometry
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 that relates observed variance to theoretical binomial variance 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 estimating an approximate variance of disease 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 increase of disease incidence at the higher scale.