Relations between Shannon entropy and genome order index in segmenting DNA sequences

Information compression exploits patterns of genome composition to discriminate populations and highlight regions of evolutionary interest

Background

Genomic information allows population relatedness to be inferred and selected genes to be identified. Single nucleotide polymorphism microarray (SNP-chip) data, a proxy for genome composition, contains patterns in allele order and proportion. These patterns can be quantified by compression efficiency (CE). In principle, the composition of an entire genome can be represented by a CE number quantifying allele representation and order.

Results

We applied a compression algorithm (DEFLATE) to genome-wide high-density SNP data from 4,155 human, 1,800 cattle, 1,222 sheep, 81 dogs and 49 mice samples. All human ethnic groups can be clustered by CE and the clusters recover phylogeography based on traditional fixation index (F_ST) analyses. CE analysis of other mammals results in segregation by breed or species, and is sensitive to admixture and past effective population size. This clustering is a consequence of individual patterns such as runs of homozygosity. Intriguingly, a related approach can also be used to identify genomic loci that show population-specific CE segregation. A high resolution CE ‘sliding window’ scan across the human genome, organised at the population level, revealed genes known to be under evolutionary pressure. These include SLC24A5 (European and Gujarati Indian skin pigmentation), HERC2 (European eye color), LCT (European and Maasai milk digestion) and EDAR (Asian hair thickness). We also identified a set of previously unidentified loci with high population-specific CE scores including the chromatin remodeler SCMH1 in Africans and EDA2R in Asians. Closer inspection reveals that these prioritised genomic regions do not correspond to simple runs of homozygosity but rather compositionally complex regions that are shared by many individuals of a given population. Unlike F_ST, CE analyses do not require ab initio population comparisons and are amenable to the hemizygous X chromosome.

Conclusions

We conclude with a discussion of the implications of CE for a complex systems science view of genome evolution. CE allows one to clearly visualise the evolution of individual genomes and populations through a formal, mathematically-rigorous information space. Overall, CE makes a set of biological predictions, some of which are unique and await functional validation.

Is agriculture driving the diversification of the Bemisia tabaci species complex (Hemiptera: Sternorrhyncha: Aleyrodidae)?: Dating, diversification and biogeographic evidence revealed

BACKGROUND

Humans and insect herbivores are competing for the same food crops and have been for thousands of years. Despite considerable advances in crop pest management, losses due to insects remain considerable. The global homogenisation of agriculture has supported the range expansion of numerous insect pests and has been driven in part by human-assisted dispersal supported through rapid global trade and low-cost air passenger transport. One of these pests, is the whitefly, Bemisia tabaci, a cryptic species complex that contains some of the world's most damaging pests of agriculture. The complex shows considerable genetic diversity and strong phylogeographic relationships. One consequence of the considerable impact that members of the B. tabaci complex have on agriculture, is the view that human activity, particularly in relation to agricultural practices, such as use of insecticides, has driven the diversification found within the species complex. This has been particularly so in the case of two members of the complex, Middle East-Asia Minor 1 (MEAM1) and Mediterranean (MED), which have become globally distributed invasive species. An alternative hypothesis is that diversification is due to paleogeographic and paleoclimatological changes.

RESULTS

The idea that human activity is driving speciation within the B. tabaci complex has never been tested, but the increased interest in fossil whiteflies and the growth in molecular data have enabled us to apply a relaxed molecular clock and so estimate divergence dates for the major lineages within the B. tabaci species complex. The divergence estimates do not support the view that human activity has been a major driver of diversification.

CONCLUSIONS

Our analysis suggests that the major lineages within the complex arose approximately 60-30 mya and the highly invasive MED and MEAM1 split from the rest of the species complex around 12 mya well before the evolution of Homo sapiens and agriculture. Furthermore, the divergence dates coincide with a period of global diversification that occurred broadly across the plant and animal kingdoms and was most likely associated with major climatic and tectonic events.

A rebuttal to the comments on the genome order index and the Z-curve

Background

Elhaik, Graur and Josic recently commented on the genome order index (S) and the Z-curve (Elhaik et al. Biol Direct 2010, 5: 10). S is a quantity defined as S = a² + c² + g² + t², where a, c, g and t denote corresponding base frequencies. The Z-curve is a three dimensional curve that represents a DNA sequence in the manner that each can be uniquely reconstructed given the other. Elhaik et al. made 4 major claims. 1) In the previous mapping system with the regular tetrahedron, calculation of the radius of the inscribed sphere is "a mathematical error". 2) S follows an exponential distribution and is narrowly distributed with a range of (0.25 - 0.33). 3) Based on the Chargaff's second parity rule (PR2), "S is equivalent to H [Shannon entropy]" and they are derivable from each other. 4) Z-curve "suffers from over dimensionality", because based on the analysis of 235 bacterial genomes, x and y components contributed only less than 1% of the variance and therefore "would be of little use".

Results

1) Elhaik et al. mistakenly neglected the parameter 4/3 when calculating the radius of the inscribed sphere. 2) The exponential distribution of S is a restatement of our previous conclusion, and the range of (0.25 - 0.33) only paraphrases the previously suggested S range (0.25 -1/3). 3) Elhaik et al. incorrectly disregard deviations from PR2 by treating the deviations as 0 altogether, reduce S and H, both having 4 variables, a, c, g and t, into functions of one single variable, a only, and apply this treatment to all DNA sequences as the basis of their "demonstration", which is therefore invalid. 4) Elhaik et al. confuse numeral smallness with biological insignificance, and disregard the distributions of purine/pyrimidine and amino/keto bases (x and y components), the variations of which, although can be less than that of GC content, contain rich information that is important and useful, such as in locating replication origins of bacterial and archaeal genomes, and in studies of gene recognition in various species.

Conclusion

Elhaik et al. confuse S (a single number) with Z-curve (a series of 3D coordinates), which are distinct. To use S as a case study of Z-curve, by itself, is invalid. S and H are neither equivalent nor derivable from each other. The criticisms of Elhaik, Graur and Josic are wrong.

Reviewers

This article was reviewed by Erik van Nimwegen.

'Genome order index' should not be used for defining compositional constraints in nucleotide sequences--a case study of the Z-curve

Background

The Z-curve is a three dimensional representation of DNA sequences proposed over a decade ago and has been extensively applied to sequence segmentation, horizontal gene transfer detection, and sequence analysis. Based on the Z-curve, a "genome order index," was proposed, which is defined as S = a²+ c²+t²+g², where a, c, t, and g are the nucleotide frequencies of A, C, T, and G, respectively. This index was found to be smaller than 1/3 for almost all tested genomes, which was taken as support for the existence of a constraint on genome composition. A geometric explanation for this constraint has been suggested. Each genome was represented by a point P whose distance from the four faces of a regular tetrahedron was given by the frequencies a, c, t, and g. They claimed that an inscribed sphere of radius r = 1/ contains almost all points corresponding to various genomes, implying that S <r². The distribution of the points P obtained by S was studied using the Z-curve.

Results

In this work, we studied the basic properties of the Z-curve using the "genome order index" as a case study. We show that (1) the calculation of the radius of the inscribed sphere of a regular tetrahedron is incorrect, (2) the S index is narrowly distributed, (3) based on the second parity rule, the S index can be derived directly from the Shannon entropy and is, therefore, redundant, and (4) the Z-curve suffers from over dimensionality, and the dimension stands for GC content alone suffices to represent any given genome.

Conclusion

The "genome order index" S does not represent a constraint on nucleotide composition. Moreover, S can be easily computed from the Gini-Simpson index and be directly derived from entropy and is redundant. Overall, the Z-curve and S are over-complicated measures to GC content and Shannon H index, respectively.

Reviewers

This article was reviewed by Claus Wilke, Joel Bader, Marek Kimmel and Uladzislau Hryshkevich (nominated by Itai Yanai).