The index of dispersion of molecular evolution: slow fluctuations

The most simple neutral model of molecular evolution predicts that the number of substitutions within a lineage in T generations ought to be Poisson distributed. Therefore, the variance in the number of substitutions ought to equal the mean number. The ratio of the variance to the mean number of substitutions is called the index of dispersion, R(T). Assuming infinite sites, no recombination model of the gene, and a haploid, Moran population structure, R(T) is derived for a general stationary model of molecular evolution. R(T) is shown to be affected by fluctuations in parameters only when they occur on a very slow time scale. In order for parameter fluctuations to cause R(T) to deviate significantly from one, the time between parameter changes must be roughly as large, or larger, than the time between substitutions.     

On the dispersion index of a Markovian molecular clock

The number of nucleotide substitutions accumulated in a gene or in a lineage is an important random variable in the study of molecular evolution. Of particular interest is the ratio of the variance to the mean of that random variable, often known as the dispersion index. Because nucleotide substitution is most commonly modeled by a continuous-time four-state Markov chain, this paper provides a systematic method of computing the dispersion indices exhibited by a continuous-time four-state Markov chain. Using this method along with computer algebra and Monte Carlo simulation, this paper offers partially proven conjectures that were supported by thorough computer experiments. It is believed that the Tamura model, the equal-input model and the Takahata-Kimura model always exhibit dispersion indices less than 2. It is also believed that a general four-state model can be chosen to exhibit a dispersion index of any desired magnitude, although the chance of a randomly chosen such model exhibiting a dispersion index greater than 2 is as small as about 2%. Relevance of these findings to the neutral theory is discussed.     

Lineage selection and the evolution of multistage carcinogenesis

A wide array of proto-oncogenes and tumour suppressor genes are involved in the prevention of cancer. Each form of cancer requires mutations in a characteristic group of genes, but no single group controls all cancers. This lack of generality shows that the control of cancer is not an ancient, fixed property of cells. By contrast, it supports a dynamic evolutionary model, whereby genetic controls over unregulated cell growth are recruited independently through evolutionary time in different tissues within different taxa. The complexity of this genetic control can be predicted from a population genetic model of lineage selection driven by the detrimental fitness effects of cancer. Cancer occurs because the genetic control of cell growth is vulnerable to somatic mutations (or 'hits'), particularly in large, continuously dividing tissues. Thus, compared to small rodents, humans must have evolved more complex genetic controls over cell growth in at least some of their tissues because of their greater size and longevity; an expectation relevant to the application of mouse data to humans. Similarly, the 'two-hit' model so successfully applied to retinoblastoma, which originates in a small embryonic tissue, is unlikely to be generally applicable to other human cancers; instead, more complex scenarios are expected to dominate, with complexity depending upon a tissue's size and its pattern of proliferation.     

Local recombination and mutation effects on molecular evolution in Drosophila.

I studied the cause of the significant difference in the synonymous-substitution pattern found in the achaete-scute complex genes in two Drosophila lineages, higher codon bias in Drosophila yakuba, and lower bias in D. melanogaster. Besides these genes, the functionally unrelated yellow gene showed the same substitution pattern, suggesting a region-dependent phenomenon in the X-chromosome telomere. Because the numbers of A/T --> G/C substitutions were not significantly different from those of G/C --> A/T in the yellow noncoding regions of these species, a AT/GC mutational bias could not completely account for the synonymous-substitution biases. In contrast, we did find an approximately 14-fold difference in recombination rates in the X-chromosome telomere regions between the two species, suggesting that the reduction of recombination rates in this region resulted in the reduction of the efficacy of selection in D. melanogaster. In addition, the D. orena yellow showed a 5% increase in the G + C content at silent sites in the coding and noncoding regions since the divergence from D. erecta. This pattern was significantly different from those at the orena Adh and Amy loci. These results suggest that local changes in recombination rates and mutational pressures are contributing to the irregular synonymous-substitution patterns in Drosophila.     

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

The role of macromolecular crowding in the evolution of lens crystallins with high molecular refractive index

Crystallins are present in the lens at extremely high concentrations in order to provide transparency and generate a high refractive power of the lens. The crystallin families prevalent in the highest density lens tissues are γ-crystallins in vertebrates and S-crystallins in cephalopods. As shown elsewhere, in parallel evolution, both have evolved molecular refractive index increments 5-10% above those of most proteins. Although this is a small increase, it is statistically very significant and can be achieved only by very unusual amino acid compositions. In contrast, such a molecular adaptation to aid in the refractive function of the lens did not occur in crystallins that are preferentially located in lower density lens tissues, such as vertebrate α-crystallin and taxon-specific crystallins. In the current work, we apply a model of non-interacting hard spheres to examine the thermodynamic contributions of volume exclusion at lenticular protein concentrations. We show that the small concentration decrease afforded by the higher molecular refractive index increment of crystallins can amplify nonlinearly to produce order of magnitude differences in chemical activities, and lead to reduced osmotic pressure and the reduced propensity for protein aggregation. Quantitatively, this amplification sets in only at protein concentrations as high as those found in hard lenses or the nucleus of soft lenses, in good correspondence to the observed crystallin properties in different tissues and different species. This suggests that volume exclusion effects provide the evolutionary driving force for the unusual refractive properties and the unusual amino acid compositions of γ-crystallins and S-crystallins.     

Estimating the rate of evolution of the rate of molecular evolution

A simple model for the evolution of the rate of molecular evolution is presented. With a Bayesian approach, this model can serve as the basis for estimating dates of important evolutionary events even in the absence of the assumption of constant rates among evolutionary lineages. The method can be used in conjunction with any of the widely used models for nucleotide substitution or amino acid replacement. It is illustrated by analyzing a data set of rbcL protein sequences.      

Unalignable sequences and molecular evolution

Alignment ambiguity is a widespread problem in molecular evolutionary studies that has received insufficient attention. Most studies ignore such regions by deleting them before analyses, even though alignment-ambiguous regions can contain useful phylogenetic and evolutionary information. The alignment ambiguity might affect only one taxon, the region being readily alignable and phylogenetically informative across all other taxa. Alternatively, all possible alignments can consistently imply certain relationships. Because they are usually the most rapidly evolving regions, alignment-ambiguous regions might be those that are most able to resolve closely spaced divergences and contribute to estimates of branch lengths, evolutionary rates and divergence times. Three methods to incorporate such regions into phylogenetic and evolutionary analyses have been devised. The multiple analysis method evaluates each plausible alignment separately and seeks areas of congruence among the resultant trees, whereas the elision method combines all plausible alignments into a single analysis. Fragment-level alignment (= fixed states, INAASE) treats the entire unalignable section as a single but highly complex multistate character. Although these methods still need refining, they are preferable to discarding large portions of hard-earned and potentially informative sequence data.     

Translational selection and molecular evolution

An interplay among experimental studies of protein synthesis, evolutionary theory, and comparisons of DNA sequence data has shed light on the roles of natural selection and genetic drift in ‘silent’ DNA evolution.     

Mechanisms of molecular evolution

Both drift and selection are important for nucleotide substitutions in evolution. The nearly neutral theory was developed to clarify the effects of these processes. In this article, the nearly neutral theory is presented with special reference to the nature of weak selection. The mean selection coefficient is negative, and the variance is dependent on the environmental diversity. Some facts relating to the theory are reviewed. As well as nucleotide substitutions, illegitimate recombination events such as duplications, deletions and gene conversions leave indelible marks on molecular evolution. Gene duplication and conversion are sources of the evolution of new gene functions. Positive selection is necessary for the evolution of novel functions. However, many examples of current gene families suggest that both drift and selection are at work on their evolution.