New thoughts on an old riddle: what determines genetic diversity within and between species?

We just published a preprint on arXiv "New thoughts on an old riddle: what determines genetic diversity within and between species?"

http://arxiv.org/abs/1510.05918 

The abstract and the introduction section of the paper are posted below.

Abstract

The question of what determines genetic diversity both between and within species has long remained unsolved by the modern evolutionary theory (MET). However, it has not deterred researchers from producing interpretations of genetic diversity by using MET. We here examine the two key experimental observations of genetic diversity made in the 1960s, one between species and the other within a population of a species, that directly contributed to the development of MET. The interpretations of these observations as well as the assumptions by MET are widely known to be inadequate. We review the recent progress of an alternative framework, the maximum genetic diversity (MGD) hypothesis, that uses axioms and natural selection to explain the vast majority of genetic diversity as being at optimum equilibrium that is largely determined by organismal complexity. The MGD hypothesis fully absorbs the proven virtues of MET and considers its assumptions relevant only to a much more limited scope. This new synthesis has accounted for the much overlooked phenomenon of progression towards higher complexity, and more importantly, been instrumental in directing productive research into both evolutionary and biomedical problems.   

Introduction

The modern evolutionary theory (MET) consists of Darwin’s theory of natural selection and Kimura’s Neutral theory (also Ohta’s Nearly Neutral theory). The theory treats evolution the same as population genetics. The Darwinian theory is much better known than the Neutral theory. However, for molecular evolution and population genetics, the Neutral theory (and the Nearly Neutral theory) has been more useful. Regardless, however, the MET is still incomplete, as acknowledged by Ohta and Gillespie: "..we have yet to find a mechanistic theory of molecular evolution that can readily account for all of the phenomenology. ..we would like to call attention to a looming crisis as theoretical investigations lag behind the phenomenology." [1].

Key puzzles of evolution remain unsolved by the MET. The central problem of the field is and has always been the old riddle of what determines genetic diversity [2-5]. Is it mostly determined by natural selection or neutral drift? Here we critically examine the historical origins and assumptions of the MET. We show that both the neutral and the selection frameworks were largely mistaken right from the beginning. Key observations that directly inspired the neutral theory were nearly half of a century ahead of their time. Selection schemes on the other hand was largely influenced by the one gene one trait genetics of the early 1900s and always treated single locus as the target of selection, which is in fact rarely the case for most of the commonly observed variations as recent studies have shown [6-11]. Finally, we review a candidate for superseding the MET, the maximum genetic diversity (MGD) hypothesis first published in 2008 [12,13], that fully absorbs the proven virtues of the MET and has more explanatory power as well as greater value in directing productive research in a much wider field of biomedical science [6-11,14]. The old riddle of genetic diversity within and between species is solved as mere deductions of the assumptions of the MGD. Only in this case, the assumptions are, for the first time in biology, self-evident intuitions that are no less true or false than any known axioms of hard sciences or mathematics.

References:
1. Ohta T, Gillespie JH (1996) Development of Neutral and Nearly Neutral Theories. Theor Popul Biol 49: 128-142.
2. Leffler EM, Bullaughey K, Matute DR, Meyer WK, Segurel L, et al. (2012) Revisiting an old riddle: what determines genetic diversity levels within species? PLoS Biol 10: e1001388.
3. Aquadro CF (1992) Why is the genome variable? Insights from Drosophila. Trends Genet 8: 355-362.
4. Lewontin RC (1991) Twenty-five years ago in Genetics: electrophoresis in the development of evolutionary genetics: milestone or millstone? Genetics 128: 657-662.
5. Lewontin RC (1974) The genetic basis of evolutionary change. New York and London: Columbia University Press.
6. Yuan D, Zhu Z, Tan X, Liang J, Zeng C, et al. (2014) Scoring the collective effects of SNPs: association of minor alleles with complex traits in model organisms. Sci China Life Sci 57: 876-888.
7. Zhu Z, Man X, Xia M, Huang Y, Yuan D, et al. (2015) Collective effects of SNPs on transgenerational inheritance in Caenorhabditis elegans and budding yeast. Genomics 106: 23-29.
8. Zhu Z, Yuan D, Luo D, Lu X, Huang S (2015) Enrichment of Minor Alleles of Common SNPs and Improved Risk Prediction for Parkinson's Disease. PLoS ONE 10: e0133421.
9. Yuan D, Zhu Z, Tan X, Liang J, Zeng C, et al. (2012) Minor alleles of common SNPs quantitatively affect traits/diseases and are under both positive and negative selection. arXiv:12092911.
10. Zhu Z, Lu Q, Zeng F, Wang J, Huang S (2015) Compatibility between mitochondrial and nuclear genomes correlates wtih quantitative trait of lifespan in Caenorhabditis elegans. Sci Rep: in press.
11. Zhu Z, Lu Q, Wang J, Huang S (2015) Collective effects of common SNPs in foraging decisions in Caenorhabditis elegans and an integrative method of identification of candidate genes. Sci Rep: in press.
12. Huang S (2009) Inverse relationship between genetic diversity and epigenetic complexity. Preprint available at Nature Precedings <http://dx.doi.org/10.1038/npre.2009.1751.2>
13. Huang S (2008) Histone methylation and the initiation of cancer, Cancer Epigenetics; Tollefsbol T, editor. New York: CRC Press.

14. Huang S (2012) Primate phylogeny: molecular evidence for a pongid clade excluding humans and a prosimian clade containing tarsiers. Sci China Life Sci 55: 709-725.

The Genetic Equidistance Phenomenon at the Whole Proteomic Level

We have just submitted a manuscript. The abstract is here.

The Genetic Equidistance Phenomenon at the Whole Proteomic Level

Denghui Luo and Shi Huang

Abstract

The field of molecular evolution got started with the alignment of a few protein sequences in the early 1960s. Among the first results found at the time, the genetic equidistance result, has turned out to be also the most astonishing and unexpected by any evolutionary theory of the time. It hence directly inspired the ad hoc universal molecular clock hypothesis that in turn inspired the neutral theory. Unfortunately and unknown to most, however, what is only a maximum distance phenomenon was mistakenly transformed into a mutation rate phenomenon and became known as such. Previous studies have suggested the universality of this phenomenon based on results from a small set of selected proteins. We have now confirmed this by whole proteome wide studies of 7 different sets of proteomes involving a total of 15 species. All 7 sets showed that within each set of 3 species the least complex one is approximately equidistant in average proteome wide identity to the two more complex ones. Thus, the genetic equidistance result is a universal phenomenon of maximum distance. There is a reality of constant but stepwise increase in complexity during evolution, the rate of which is what the original universal molecular clock is really about. These results provide additional lines of evidence for the recently proposed maximum genetic diversity (MGD) hypothesis.

Figure 3. The constant rate of complexity increase. The fraction of identical residues between human and a lower complex species is equivalent to the fraction of non-changeable sites in the lower complexity species. The fraction of identical residues in cytochrome C (identity divided by length) between human and each of the species listed in the figure is plotted against the separation time between human and each of the listed species. Data for plots were obtained using homo cytochrome C to BLASTP Genbank.

Figure 4. The prime number staircase. The graph counts the cumulative number of primes up to 100.

The molecular clock interpretation of the maximum genetic equidistance result is really about the constant rate of complexity increases. People since Aristotle have long appreciated the direction of evolution towards higher complexity. Darwin’s theory has long denied this but only by ignoring inconvenient facts including the genetic equidistance phenomenon. The evidence for complexity increase is commonplace and easy to notice by common sense. The first molecular evidence for it is the maximum genetic equidistance phenomenon. What is most striking is the nearly constant rate as measured in years of the complexity increase, which could be quantitatively studied by the fraction of non-changeable positions in a protein or the fraction of identical residues between human and a lower complexity species (Fig. 3).

As nature is written in the language of mathematics, it would be most unusual if the most fundamental natural phenomenon, i.e., the constant rate of evolution towards higher complexity as measured in years, has no counterpart in mathematics. The most relevant mathematics that we could find is the pattern of prime numbers (du Sautoy 2003). The cumulative increase in prime numbers along the progression in natural numbers is well known to follow a nearly constant rate (Fig. 4). Here the progression in natural numbers is like a time clock, rigid and predictable. The appearance of prime numbers is discontinuous or staircase and unpredictable but follows nonetheless a well defined function Li(N) as shown by the Riemann hypothesis, widely known as the most important unproved problem in mathematics (du Sautoy 2003). Each new appearance of a more complex species is like a new prime number, unpredictable, discontinuous, and yet constant. Individual species are well known to appear in the fossil record abruptly as evidence for the punctuated equilibrium model of macroevolution has shown (Gould, Eldredge 1993). However, the discontinuous appearance of higher and higher complexity species still follows a very smooth and regular pattern as shown by the equidistance phenomenon. We speculate that the mystery behind the constant rate of complexity increase in nature might well turn out to be the same as that behind the constant appearance of prime numbers. Indeed, the common speculative and unproven answer to both mysteries has long been random forces.

The branch of biology with the most mathematics is also widely known as the most soft! Why?

The field of population genetics and molecular evolution was largely founded by mathematicians/statisticians such as Fisher, Haldene, and Wright. Even pure mathematician like Hardy has contributed a key equation to the field. But contrary to naive expectations, this field of study is more like soft social science than to hard core physics. In the words of Jerry Coyne (an extremely enthusiastic propagator of the Darwinian evolution theory and a professor of evolutionary studies at the University of Chicago): "In science's pecking order, evolutionary biology lurks somewhere near the bottom, far closer to phrenology than to physics".

Why? The reason is simple. Math depends on assumptions or paradigms. The assumptions for hard core sciences are axioms or self evident intuitions. Euclid and Newtons axioms come to mind. They are all a priori true or self evidently true. In contrast, there is not a single assumption in the evolution field that is self evidently true or can qualify as axiom. Nearly all assumptions in that field are in fact self evidently false. Just a few examples, the infinite sites model, the neutral/junk DNA assumption, random mating, and the independent mutations assumptions.

Key figures in the field has also acknowledged this, as Ohta and Gillespie said in 1996: "all current theoretical models suffer either from assumptions that are not quite realistic or from an inability to account readily for all phenomena." (Theoretical Population Biology,1996, 49: 128-142) 

To show a flavor of the amount of math in the field, below are two pages of my notebook from an undergrad evolutionary genetics course taken 32 years ago at my Alma mater Fudan University.