This function quantifies the size frequency distribution of forest canopy gaps using Zeta distribution, which is a discrete power-law probability density.
A data.frame containing basic statistics of forest gaps. Output of (
Supplementary parameters for (
A log-log plot of gap-size Frequency Distributions and a vector containing the λ and minimum value of the likelihood. The parameter λ is the scaling exponent for the power-law Zeta distribution fitted to the data using maximum likelihood. See details section.
For the Zeta distribution with parameter λ, the probability that gap size takes the integer value k is:
f(k) = k^-λ/ζ(λ)
where the denominator is the Riemann zeta function, and is undefined for λ = 1. The function calculates maximum likelihood estimates (MLE) of λ by minimizing a negative log-likelihood function (Asner et 2013).
Carlos Alberto Silva. This function was implemented based on the R script provided by Asner et al. (2013)
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<e2><80><93>912.
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#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)
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