power_law {epiphy}

Taylor's and binary power laws.

Description

Assesses the overall degree of heterogeneity in a collection of data sets at the sampling-unit scale.

Usage

power_law(data, log_base = exp(1), ...)

Arguments

data

A list of intensity objects (count or incidence objects).

log_base

Logarithm base to be used.

...

Additional arguments to be passed to other methods.

Details

The power law describes the relationship between the observed variance of individuals within a data set (s^2) and the corresponding variance under the assumption of no aggregation (s\'^2). It can be expressed under its logarithmic form as: log(s^2) = log(a) + b log(Y), with:

• Y = p in the case of count data (Taylor's power law).

• Y = p(1 - p) in the case of incidence data (binary power law).

p corresponds to the mean proportion of recorded individuals in case of incidence data, and the absolute value in case of count data.

Value

A power_law object.

References

Taylor LR. 1961. Aggregation, variance and the mean. Nature 189: 732–35.

Hughes G, Madden LV. 1992. Aggregation and incidence of disease. Plant Pathology 41 (6): 657–660. doi:10.1111/j.1365-3059.1992.tb02549.x

Madden LV, Hughes G, van den Bosch F. 2007. Spatial aspects of epidemics - III: Patterns of plant disease. In: The study of plant disease epidemics, 235–278. American Phytopathological Society, St Paul, MN.

Examples

require(magrittr)
my_data <- do.call(c, lapply(citrus_ctv, function(citrus_field) {
   incidence(citrus_field) %>%
       clump(unit_size = c(x = 3, y = 3)) %>%
       split(by = "t")
}))
# my_data is a list of incidence object, each one corresponding to a given
# time at a given location.
my_power_law <- power_law(my_data)
my_power_law
summary(my_power_law)
plot(my_power_law) # Same as: plot(my_power_law, scale = "log")
plot(my_power_law, scale = "lin")