Relationships between disease incidence at two levels in a spatial hierarchy

Area of Science:

• Plant pathology
• Spatial statistics
• Epidemiology

Background:

• Understanding disease incidence across hierarchical spatial scales is crucial for effective disease management and sampling strategies.
• Existing models often simplify spatial relationships, potentially overlooking the impact of aggregation on disease spread.
• The binomial and beta-binomial distributions provide frameworks for analyzing count data, but their application to hierarchical spatial disease incidence requires further investigation.

Purpose of the Study:

• To derive and test relationships between disease incidence measured at two levels of a spatial hierarchy.
• To investigate the influence of aggregation and sampling unit size on disease incidence across scales.
• To develop methods for estimating disease variance at a lower spatial scale from higher-scale measurements.

Main Methods:

• Utilized properties of the binomial distribution and beta-binomial distribution.
• Applied an empirical power-law relationship linking observed and theoretical binomial variance of disease incidence.
• Tested relationships using observational data for grape downy mildew, citrus tristeza, and citrus scab.

Main Results:

• Disease incidence at a higher spatial scale demonstrated an asymptotic relationship with incidence at the lower scale, degree of aggregation, and sampling unit size.
• For random disease patterns, the cross-scale incidence relationship was parameter-independent.
• Derived an equation to estimate lower-scale disease variance from higher-scale incidence measurements for sampling purposes.

Conclusions:

• Aggregation of disease at a lower spatial scale reduces the rate of incidence increase at a higher spatial scale.
• The derived relationships offer a more nuanced understanding of spatial disease dynamics.
• The findings support improved disease sampling and modeling by accounting for spatial hierarchy and aggregation.