Description Rank Abundance Distributions (RAD) MaxRank Normalization Source

RADanalysis package has tools for normalizing rank abundance distributions (RAD) to a desired number of ranks using MaxRank Normalization method. RADs are commonly used in biology/ecology and mathematically equivalent to complementary cumulative distributions (CCDFs) which are used in physics, linguistics and sociology and more generally in data science.

Rank Abundance Distributions (RADs) are a way to capture the distribution of biological species in communities, where we use the term "species" for all types of distinct biological entities, e.g. microbial species in a microbiome, viral strains in a quasi-species, the diverse variants B cells in a person, etc. A RAD can be thought of as a plot with the two axes rank (x-axis) and abundance (y-axis). For the most abundant species we draw a point at the (x,y) coordinates (1,a1) , with a1 the abundance of this most abundant species. For the second most abundant species we draw a point at (2,a2).

MaxRank normalization is the method to normalize RADs. MaxRank normalization maps all rank abundance vectors to the same rank range from 1 to a common maximum rank R. First we chose the maximum rank or "MaxRank" or "R". Second generated for each sample s a pool of N_s of all individuals in s. From this pool we drew individuals at random with uniform probability and without replacement as long as the number of sampled ranks of the original RAD did not exceed R. In this way we generated a new, reduced abundance vector of R ranks, with a reduced number of individuals. Division of these reduced abundances by sum of reduced abundances transforms the reduced abundance vector to a probability distribution for the R ranks with rank probabilities summing up to 1. If R < total number of ranks in the original sample , the random drawing of individuals from the pool in general introduces a sampling error in the abundances. To control this error, one should repeat the procedure several times (typically 10-100 times) and averaged over all sampled abundance distributions.

Saeedghalati et al. 2016 "Quantitative comparison of abundance structures of genetic communities", submitted

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