Mathematical Ecology of Spatial Pattern of Biological Population

Some methods allowing for aggregated patterns of disease incidence in the analysis of data from designed experiments

“…The statistical analysis of disease incidence data based on the beta-binomial model is closely related to the use of the beta-binomial distribution to describe aggregation of disease incidence, as discussed by Shiyomi & Takai (1979), Shiyomi (1981), Qu et ai (1990) and Hughes & Madden (1993). In fact, if one were describing aggregation of disease incidence by fitting a separate betabinomial distribution to each of a series of frequency distributions of, say, diseased plants per quadrat, the procedures would be essentially identical.…”

Comment-Using spatial and temporal patterns of Armillaria root disease to formulate management recommendations for Ontario's black spruce (Picea mariana) seed orchards

“…The first application of the β-binomial distribution in plant disease epidemiology seems to have been in the description of the frequency distribution of rice plants infected with yellow dwarf disease (caused by a mycoplasma-like organism) (Shiyomi and Takai 1979;Takai and Shiyomi 1980). Unfortunately, it is clear that neither of these articles, both published in Japanese, nor a subsequent one published in English (Shiyomi 1981), made much impact on the mainstream epidemiological literature. Subsequently, Qu et al (1990) fitted the β-binomial to the TSWV data originally published by Cochran (1936).…”

Spatial pattern indices based on distances between individuals on a line‐segment with finite length

“…The spatial pattern is determined by many factors, such as reproduction, death, migration, reaction to the natural enemies, and environmental heterogeneity which strongly influence the fitness of species within the habitat. Typical spatial patterns of populations have been calssified as follows: (1) random spatial pattern, (2) aggregated spatial pattern, and (3) even (or regular) spatial pattern (for example, Greig-Smith, 1964;Pielou, 1974;Shiyomi, 1981;Begon et al, 1990).…”