Genome Sizes and the Benford Distribution
Abstract
Data on the number of Open Reading Frames (ORFs) coded by genomes from the 3 domains of Life show some notable general features including essential differences between the Prokaryotes and Eukaryotes, with the number of ORFs growing linearly with total genome size for the former, but only logarithmically for the latter. Assuming that the (protein) coding and noncoding fractions of the genome must have different dynamics and that the noncoding fraction must be controlled by a variety of (unspecified) probability distribution functions, we are able to predict that the number of ORFs for Eukaryotes follows a Benford distribution and has a specific logarithmic form. Using the data for 1000+ genomes available to us in early 2010, we find excellent fits to the data over several orders of magnitude, in the linear regime for the Prokaryote data, and the full nonlinear form for the Eukaryote data. In their region of overlap the salient features are statistically congruent, which allows us to: interpret the difference between Prokaryotes and Eukaryotes as the manifestation of the increased demand in the biological functions required for the larger Eukaryotes, estimate some minimal genome sizes, and predict a maximal Prokaryote genome size on the order of 812 megabasepairs. These results naturally allow a mathematical interpretation in terms of maximal entropy and, therefore, most efficient information transmission.
 Publication:

PLoS ONE
 Pub Date:
 May 2012
 DOI:
 10.1371/journal.pone.0036624
 arXiv:
 arXiv:1205.6512
 Bibcode:
 2012PLoSO...736624F
 Keywords:

 Quantitative Biology  Genomics;
 Physics  Biological Physics;
 Physics  Data Analysis;
 Statistics and Probability;
 Quantitative Biology  Quantitative Methods
 EPrint:
 23 pages, 1 figure (eps)