PL-curves_Gini-coefficient_method.txt

Generating and plotting Pareto-Lorenz curves and calculating Gini coefficients for relative abundance data

DATA LAYOUT:
Column A: a list of unique "species"(bins/OTUs/TRFs) in numerical or alpha-numerical format (regardless of format, think of them as "names of species")
Columns B-end: each column is a separate sample, contaning the relative abundance of each bin/species within that sample. Each sample column should sum to 1
Row 1: headings (name of species approximation method (bin, TRF, OTU etc) in column A, sample IDs in remaining columns) -- Name each sample after its row 1 value!

Bins	Sample1	Sample2	Sample3	Sample4
Bin1	0   	0.25	0.1 	0.2
Bin2	0.4 	0.20	0.7 	0.1
Bin3	0.5 	0.25	0.05	0.1	
Bin4	0.1 	0.30	0.05	0.6
Bin5	0   	0   	0   	0
Bin6	0   	0   	0.1 	0



PROCESS:
Check that the values in each sample column sums to 1 (otherwise something is wrong, data missing, or it might be counts rather than relative abundance data)
Remove any bins for which _ALL_ samples have a relative abundance = 0 (any row for which columns B-end have zero values only)  Example: Bin5 above (remove!) <-- this step is not needed for newer data sets, where there are no all-zero bins in the final data set. 
Do not remove any bins that have at least one cell where rel abund > 0! Example: Bin6 above (keep!)

For EACH sample:
	sort bins after decreasing relative abundance (bin with largest rel abund first)		
	
	associate the new order of bins with the cumulative number of bins (1, 2, 3, ... N)
	
	calculate the cumulative relative abundance	for each step (for cum bin = 1, 2, 3, ..., N)    <--- Cum rel abund: these are the y-values!
	
	remove all empty bins, i.e. once cum rel abund have reach 1, all subsequent bins with cum rel abund=1 are removed (leaving the first cum bin with a value of 1)
	
	note down the number of bins remaining (n)  (NB! n <= N)
	
	calculate the cumulative proportion of bins (1/n, 2/n, 3/n .... n/n)   <--- Cum prop bins: these are the x-values!
	
	Calculate Gini coefficient for each sample (G= 1-|Σ[k=1->n](y[k-1]+y[k])(x[k]-x[k-1])|) where x=cum prop bins, y= cum rel abund
	Calculate corrected Gini coefficient for each sample (G[corr] = G(n/(n-1))

Then:	
Collate the x and y values for all samples.

Plot all samples on one graph: Scatter plot but with connecting lines and  no visible markers, x=cum proportion of bins, y= cum rel abund, both axes are going from 0 to 1, lable lines using sample names from Row 1, also plot a dotted 1:1 line (running diagonally from origin to top right hand corner).

Make a table with all Gcorr values listed against sample names.