- Research note
- Open Access
Multivariate analysis of genomic variables, effective population size, and mutation rate
BMC Research Notes volume 12, Article number: 60 (2019)
The relationship between genomic variables (genome size, gene number, intron size, and intron number) and evolutionary forces has two implications. First, they help to unravel the mechanism underlying genome evolution. Second, they provide a solution to the debate over discrepancy between genome size variation and organismal complexity. Previously, a clear correlation between genomic variables and effective population size and mutation rate (Neu) led to an important hypothesis to consider random genetic drift as a major evolutionary force during evolution of genome size and complexity. But recent reports also support natural selection as the leading evolutionary force. As such, the debate remains unresolved.
Here, we used a multivariate method to explore the relationship between genomic variables and Neu in order to understand the evolution of genome. Previously reported patterns between genomic variables and Neu were not observed in our multivariate study. We found only one association between intron number and Neu, but no relationships were observed between genome size, intron size, gene number, and Neu, suggesting that Neu of the organisms solely does not influence genome evolution. We, therefore, concluded that Neu influences intron evolution, while it may not be the only force that provides mechanistic insights into genome evolution and complexity.
All eukaryotic genomes possess similar features such as genome size, gene number, intron size, intron number, and transposable elements. These genomic variables can be attributed to the evolutionary forces acting over long evolutionary time. In the previous analysis, genomic variables were shown to have a strong correlation with the effective population size (Ne) and mutation rate (u) of the organism. Expansion of genome size and complexity were attributed to random genetic drift . This is also known as the mutational hazard hypothesis , and it is influential in terms of genome evolution and complexity .
The interplay between Ne and u may impact genome size variation across kingdoms, and can be regarded as a plausible explanation to understand mechanism of genome evolution [2, 4, 5]. On the other hand, many old theories such as mutational pressure, nucleoskeletal, and nucleotypic have emphasized adaptive arguments to explain genome size variation and evolution. But these arguments received minimal recognition . In addition, the mutational equilibrium model stated that each species acquired their own genome size by deletion or insertion, and thus different species showed variation in their genome size . We think that genomic variables being a multivariate dataset of a genome, multivariate statistical analysis is important to examine the relationship between genomic variables and Neu in order to understand genome evolution.
Data on genomic variables and Neu were obtained from reference [1, 8,9,10,11,12,13, NCBI annotation release101]. Some of the species had missing data on either one of the genomic variables or Neu; therefore, we excluded them from the multivariate analysis because it will cause misinterpretation of the dataset. Species were grouped in rows, while genomic variables and Neu were represented as columns to create a multivariate dataset (Additional file 1: Table S1).
Multivariate statistical analysis
Multivariate analysis called principal component analysis (PCA), cluster analysis (CA), and exploratory factor analysis (EFA) were carried out by executing stats package in R software (R version 3.2.3). The correlation matrix was chosen in the PCA analysis for the dataset (Additional file 1: Table S1). In addition, the dataset was standardized, centered, scaled, and prcomp function was used to perform PCA analysis. A hierarchical cluster analysis was carried out after standardization of the dataset (Additional file 1: Table S1), using euclidean distance method. Then, ward. D2 method in R software was applied to construct dendrogram by utilizing hclust function. The exploratory factor analysis was also performed in R by executing factanal function, which is based on maximum-likelihood methods. In addition, the dataset (Additional file 1: Table S1) was standardized, rotated by varimax, and only two factors were considered during analysis. The test for two factors is sufficient for the hypothesis showed Chi square statistic 1.35 and p-value 0.246 for the raw data, while Chi square statistic 2.32 and p-value 0.128 for the phylogenetically independent contrasts in EFA.
Phylogenetically independent contrasts (PICs) analysis
Phylogeny for the species under study was obtained from TimeTree database  with branch length. Then, phylogenetically independent contrasts  analysis was performed with APE package  by executing pic function in R software (R version 3.2.3). After obtaining phylogenetically independent contrasts data of genomic variables and Neu, the matrix was tabulated and then subjected to the same multivariate statistical analysis as described in the above section.
We used raw data to compare with Lynch and Conery  analyses, while phylogenetically independent contrasts method was used to provide nonindependence of species in this study. We could not find relationship between genomic variables and Neu in PCA (Fig. 1a, b), CA (Fig. 2a, b), and EFA (Fig. 3a, b) by applying raw data but in phylogenetically independent contrasts, we found only association between intron number and Neu. Additionally, we did find relationship among genomic variables only.
The PCA analysis reduces the dimensionality of multivariate dataset and explains the variability pattern among multiple variables by showing most of the variation in all original variables as principal components (PC) ; therefore, we chose this method to summarise genomic variables and Neu to uncover any evolutionary patterns. The PC1 explained 61.24% and 44.06% of the variance, while PC2 explained an additional 19.21% and 23.91% of the variance in biplot for raw data and phylogenetically independent contrasts, respectively. Surprisingly, the angles between vector of genomic variables viz. genome size, average intron no per gene, average intron size, gene number, and Neu were wide and in different directions, suggesting there were no correlations in raw data (Fig. 1a). But in phylogenetically independent contrasts (Fig. 1b), we found angle between intron number and Neu to be narrow although they were in opposite directions, suggesting moderate inverse correlation. All vector lengths showed similar magnitude, suggesting almost equal contribution to the overall variance in the analysis. Similarly, we found correlation between genome size and intron size as indicated by small angle between these variable’s vectors in phylogenetically independent contrasts (Fig. 1b).
The cluster analysis is the most parsimonious way to cluster variables in term of correlation or distance in the multivariate dataset , therefore; we used this method to find if any relationship exists between genomic variables and Neu. However, in the cluster analysis, the genomic variables formed one cluster while Neu formed another cluster, indicating no similar variability pattern between them in raw data (Fig. 2a) but in phylogenetically independent contrasts, intron number and Neu clustered together (Fig. 2b). This clearly indicated that intron number tend to vary together with Neu. Similarly, genome size and intron size also formed cluster in phylogenetically independent contrasts (Fig. 2b).
Finally, we performed EFA analysis to disclose any hidden relationships among genomic variables and Neu. Perhaps Neu affects genome evolution by indirectly modulating genomic variables, and we may see some hidden relationships in the EFA analysis. By contrast, we clearly observed that genomic variables and Neu were not at the same location in the plot, revealing that there were no hidden relationships between them in raw data (Fig. 3a) but in phylogenetically independent contrasts (Fig. 3b), intron number and Neu were located at similar position in the plot, indicating association between them therefore we believe that intron evolution was modulated by Neu. In raw data, Factor 1 had the highest loading for average intron size than genome size, suggesting some correlation between these two variables, with 49% of total variance. In Factor 2, gene number had the highest loading compared to average intron no per gene, indicating relatively small correlation, but Neu had the lowest loading thus playing no part, with 26% of total variance. Similarly, in phylogenetically independent contrasts, Factor 1 had the highest loading for average intron size compared to genome size, suggesting some correlation, with 39% of total variance. In Factor 2, we found the highest loading for gene number but intron number and Neu had the lowest loading, implying some correlation, with 21% of total variance. In the current analysis, we deduced that Neu played almost no part in the evolution of genome size and complexity but may have influenced intron evolution.
One of the fundamental questions regarding genome size evolution is to examine if different genomic variables within genome vary together according to their correlations during evolution , and which evolutionary forces cause them to vary in such a correlative fashion is an unsolved mystery. Our multivariate analysis shows no relationship between genomic variables and Neu using only raw data but in phylogenetically independent contrasts, we observed some correlation between Neu and intron number. This observation is remarkably consistent with some results from the previous research . But this observation is contrary to the previous conclusions which were based on the bivariate method only . We found relationship between Neu and intron number by using phylogenetically independent contrasts method only. This shows that intron evolution may be influenced by Neu. Moreover, Ne in higher organisms is always smaller than that in prokaryotes; therefore, it is believed that introns never colonised the prokaryotic genome. Eukaryotes, however, fixed the introns in their genome and the average number of introns per gene increased with an increase in the complexity of organisms . Interestingly, in agreement with the notion that introns were only fixed in eukaryotes, analysis of introns in cellulose synthase gene suggested that introns are eukaryotic invention . A high u in Arabidopsis caused loss of introns, exemplifying the importance of u in intron and genome size evolution, as predicted by the mutational hazard hypothesis . While analysis of non-recombining region of the genome as a site of inefficient selection showed no signs of introns gain. This contradicted the notion that a genetic drift alone was responsible for gain of introns in the multicellular organisms .
Other genomic variables such as genome size and intron size showed similar variability patterns with each other but not with Neu. In contrast, the analysis of a phylogenetically diverse group of species, genome size, average intron length, and Neu showed strong negative correlations, suggesting that random genetic drift plays a significant role in genome size evolution . Equally our multivariate analysis contradicted this theory, as we can see Neu does not have relationship with either genome size or average intron size. Probably, a drift alone may not be responsible for the evolution of genome size. For instance, salamanders have large genome, and they exhibit a persistent long-term reduction in the population size. But there is no evidence of drift in their long evolutionary history. In this regard, the lower mutational hazard may have contributed to large genome size in these tetrapods as opposed to the mutational hazard hypothesis of genome size evolution . In case of seed beetles, the reproductive fitness as a measure of selection was highly correlated with genome size which implies that natural selection has contributed to their genome size .
The variability pattern of gene number of an organism was not similar to Neu. However, a sufficient correlation between average gene number and Neu has already been established . In many other eukaryotes, genome size has been found to show a positive correlation with gene number . To date, genome sequencing in various taxa has revealed that gene number does not correlate with complexity of the organism in case of eukaryotes. For instance, humans are the most complex in terms of development, but they do not possess large number of genes than Caenorhabditis elegans .
A correlation exists between few phenotypic traits such as cell size, metabolic rate, developmental rate, and genome size . Lynch and Conery  attempted to explain genome complexity by considering key population genetic parameter Neu, but received criticism because they could not consider phylogenetic relationships and their association with genomic variables in case of large phylogenies, and all genomic variables did not show a correlation with Neu . The lack of association between genomic variables and Neu may be due to inaccuracy in time estimates of species divergence . Although time estimates are controversial , but we think that phylogenetically independent contrasts data is more reliable than raw data since phylogenetic information is important to obtain meaningful conclusions. Here, we revisited Lynch and Conery dataset with a more holistic approach by multivariate analysis in order to determine any undisclosed patterns among genomic variables and Neu. Our results were not the same as the previous results obtained using the bivariate method only . We confirmed that Neu may influence intron evolution in a correlative fashion but with no other genomic variables, implying that the enigma of genome size variation and organismal complexity needs further investigation.
We acknowledge that our study is based on analysis of previous data using multivariate methods to gain new insights into genome evolution. Here, we could only analyse eukaryotic genome because there are no introns present in the prokaryotic genome. This exclusion of prokaryotic data in this study provides only views regarding eukaryotic genome evolution.
The multivariate statistical analysis methods are exploratory methods, which analyse several variables together for the interpretation of the datasets. Thus, this method lacks quantitative measurements.
principal component analysis
exploratory factor analysis
- Ne :
effective population size
- u :
- Neu :
effective population size and mutation rate
Lynch M, Conery JS. The origins of genome complexity. Science. 2003;302:1401–4.
Lynch M. The origins of genome architecture. Sunderland: Sinauer Associates Inc.; 2007.
Maeso I, Roy SW, Irimia M. Widespread recurrent evolution of genomic Features. Genome Biol Evol. 2012;4:486–506.
Lynch M, Bobay LM, Catania F, Gout JF, Rho M. The repatterning of eukaryotic genomes by random genetic drift. Annu Rev Genomics Hum Genet. 2011;12:347–66.
Smith DS. The mutational hazard hypothesis of organelle genome evolution: 10 years on. Mol Ecol. 2016;25:3769–75.
Gregory TR. Coincidence, coevolution, or causation? DNA content, cell size, and the C-value enigma. Biol Rev. 2001;76:65–101.
Petrov DA. Mutational equilibrium model of genome size evolution. Theor Popul Biol. 2002;61:531–44.
Feng C, Pettersson M, Lamichhaney S, Robin CT, Rafati N, Casini M, Folkvard A, Andersson L. Moderate nucleotide diversity in the Atlantic herring is associated with a low mutation rate. Elife. 2017;6:e23907.
Merchant SS, Prochnik SE, Vallon O, Harris EM, Karpowicz SJ, Witman GB, Terry A, Salamov A, Firtz-Laylin LK, Marechal-Drouard L, et al. The Chlamydomonas genome reveals the evolution of key animal and plant functions. Science. 2007;318:245–51.
Wood V, Gwilliam R, Rajandream MA, Lyne M, Lyne R, Stewart A, Sgourus J, Peat N, Hayles J, Baker S, et al. The genome sequence of Schizosaccharomyces pombe. Nature. 2002;415:871–80.
Ye Z, Xu S, Spitze K, Asselman J, Jiang X, Ackerman MS, Lopez J, Harker B, Raborn RT, Thomas WK, et al. A new reference genome assembly for the microcrustacean Daphnia pulex. G3. 2017;7:1405–16.
Elsik CG, Tellam RL, Worley KC, Gibbs RA, Abatepaulo ARR, Abbey CA, Adelson DL, Aerts J, Ahola V, et al. The genome sequence of taurine cattle: a window to ruminant biology and evolution. Science. 2009;324:522–8.
Mikkelsen TS, Hillier LW, Eicher EE, Zody MC, Jaffe DB, Yang SP, Altheide TK, et al. Initial sequence of the chimpanzee genome and comparison with the human genome. Nature. 2005;437:69–87.
Kumar S, Stretcher G, Suleski M, Hedges SB. TimeTree: a resource for timelines, timetrees, and divergence times. Mol Biol Evol. 2017;34:1812–9.
Felsenstein J. Phylogenies and the comparative method. Am Nat. 1985;125:1–15.
Paradis E, Claude J, Strimmer K. APE: analyses of phylogenetics and evolution in R language. Bioinformatics. 2004;20:289–90.
Everitt B, Hothorn T. An introduction to applied multivariate analysis with R. 2011. New York: Springer; 2011.
Petrov DA. Evolution of genome size: new approaches to an old problem. Trends Genet. 2001;17:23–8.
Whitney KD, Garland TJ. Did genetic drift drive increases in genome complexity? PLoS Genet. 2010;6(8):e1001080.
Lynch M. Intron evolution as a population-genetic process. Proc Natl Acad Sci USA. 2002;99:6118–23.
Bhattachan P, Dong B. Origin and evolutionary implications of introns from analysis of cellulose synthase gene. J Syst Evol. 2017;55:142–8.
Yang FY, Zhu T, Niu DK. Association of intron loss with high mutation rate in Arabidopsis: implications for genome size evolution. Genome Biol Evol. 2013;5:723–33.
Roy SW. Is genome complexity a consequence of inefficient selection? Evidence from intron creation in non-recombining regions. Mol Biol Evol. 2016;33:3088–94.
Mohlhenrich ER, Mueller RL. Genetic drift and mutational hazard in the evolution of salamander genomic gigantism. Evolution. 2016;70:2865–78.
Arnqvist G, Sayadi A, Immonen E, Hotzy C, Rankin D, Tuda M, Hjelmen CE, Johnston JS. Genome size correlates with reproductive fitness in seedbeetles. Proc R Soc B. 2015;282:20151421.
Elliott TA, Gregory TR. What’s in a genome? The C-value enigma and the evolution of eukaryotic genome content. Phil Trans R Soc B. 2015;370:20140331.
Copley RR. The animal in the genome: comparative genomics and evolution. Phil Trans R Soc B. 2008;363:1453–61.
Graur D, Martin W. Reading the entrails of chickens: molecular timescales of evolution and the illusion of precision. Trends Genet. 2004;20:80–6.
Hedges SB, Kumar S. Precision of molecular time estimates. Trends Genet. 2004;4:242–7.
PB performed research and analysis. BD supervised the study. PB wrote the draft. BD substantively revised the final version of the manuscript. Both authors read and approved the final manuscript.
We would like to thank the anonymous reviewer for improving our manuscript.
The authors declare that they have no competing interests.
Availability of data and materials
Consent for publication
Ethics approval and consent to participate
This work was supported by the National Key Research and Development Program of China (2018YFD0900705), the Fundamental Research Funds for the Central Universities (201822016), and the Taishan Scholar Program of Shandong Province, China (201502035). The funding bodies have no roles in the design of the study, in collection, analysis, and interpretation of data, and in writing of the manuscript.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Bhattachan, P., Dong, B. Multivariate analysis of genomic variables, effective population size, and mutation rate. BMC Res Notes 12, 60 (2019). https://doi.org/10.1186/s13104-019-4097-3
- Genomic variables
- Multivariate analysis
- Genome evolution
- Genetic drift