ForestGapR (version 0.0.2)

GapSizeFDist: Forest Canopy Gap-size Frequency Distributions

Description

This function quantifies the size frequency distribution of forest canopy gaps using Zeta distribution, which is a discrete power-law probability density.

Usage

GapSizeFDist(gaps_stats,...)

Arguments

gaps_stats

A data.frame containing basic statistics of forest gaps. Output of (GapStats) function.

...

Supplementary parameters for (plot).

Value

A log-log plot of gap-size Frequency Distributions and a vector containing the and minimum value of the likelihood. The parameter is the scaling exponent for the power-law Zeta distribution fitted to the data using maximum likelihood. See details section.

Details

For the Zeta distribution with parameter , the probability that gap size takes the integer value k is: $$f(k) =\frac{k^{-\lambda}}{\\zeta(\lambda)}$$ where the denominator is the Riemann zeta function, and is undefined for = 1. The function calculates maximum likelihood estimates (MLE) of by minimizing a negative log-likelihood function (Asner et 2013).

References

Asner, G.P., Kellner, J.R., Kennedy-Bowdoin, T., Knapp, D.E., Anderson, C. & Martin, R.E. (2013). Forest canopy gap distributions in the Southern Peruvian Amazon. PLoS One, 8, e60875.

White EP, Enquist BJ, Green JL (2008) On estimating the exponent of powerlaw frequency distributions. Ecology 89: 905<U+2013>912.

Examples

# NOT RUN {
#Loading raster library
library(raster)

# ALS-derived CHM over Adolpho Ducke Forest Reserve - Brazilian tropical forest
data(ALS_CHM_DUC)

# set height tresholds (e.g. 10 meters)
threshold<-10
size<-c(1,10^4) # m2

# Detecting forest gaps
gaps_duc<-getForestGaps(chm_layer=ALS_CHM_DUC, threshold=threshold, size=size)

# Computing basic statistis of forest gap
gaps_stats<-GapStats(gap_layer=gaps_duc, chm_layer=ALS_CHM_DUC)

# Gap-size Frequency Distributions
GapSizeFDist(gaps_stats=gaps_stats, col="forestgreen", pch=16, cex=1,
axes=FALSE,ylab="Gap Frequency",xlab=as.expression(bquote("Gap Size" ~ (m^2) )))
axis(1);axis(2)
grid(4,4)

# }