Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part II: Perturbation analyses

Kiyoshi Ezawa; Dan Graur; Giddy Landan

doi:10.1101/023606

Home/Archive/bioRxiv

bioRxiv · 10.1101/023606

Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part II: Perturbation analyses

Kiyoshi Ezawa·Dan Graur·Giddy Landan

View original source ↗Export metadata ↓

Abstract

BackgroundInsertions and deletions (indels) account for more nucleotide differences between two related DNA sequences than substitutions do, and thus it is imperative to develop a stochastic evolutionary model that enables us to reliably calculate the probability of the sequence evolution through indel processes. In a separate paper (Ezawa, Graur and Landan 2015a), we established a theoretical basis of our ab initio perturbative formulation of a genuine evolutionary model, more specifically, a continuous-time Markov model of the evolution of an entire sequence via insertions and deletions. And we showed that, under some conditions, the ab initio probability of an alignment can be factorized into the product of an overall factor and contributions from regions (or local alignments) separated by gapless columns.\n\nResultsThis paper describes how our ab initio perturbative formulation can be concretely used to approximately calculate the probabilities of all types of local pairwise alignments (PWAs) and some typical types of local multiple sequence alignments (MSAs). For each local alignment type, we calculated the fewest-indel contribution and the next-fewest-indel contribution to its probability, and we compared them under various conditions. We also derived a system of integral equations that can be numerically solved to give \"exact solutions\" for some common types of local PWAs. And we compared the obtained \"exact solutions\" with the fewest-indel contributions. The results indicated that even the fewest-indel terms alone can quite accurately approximate the probabilities of local alignments, as long as the segments and the branches in the tree are of modest lengths. Moreover, in the light of our formulation, we examined parameter regions where other indel models can safely approximate the correct evolutionary probabilities. The analyses also suggested some modifications necessary for these models to improve the accuracy of their probability estimations.\n\nConclusionsAt least under modest conditions, our ab initio perturbative formulation can quite accurately calculate alignment probabilities under biologically realistic indel models. It also provides a sound reference point that other indel models can be compared to. [This paper and three other papers (Ezawa, Graur and Landan 2015a,b,c) describe a series of our efforts to develop, apply, and extend the ab initio perturbative formulation of a general continuous-time Markov model of indels.]

Explore related subjects

Evolutionary Biology Preprint

Keep this discovery

BibTeX RIS

Kiyoshi Ezawa, Dan Graur, Giddy Landan. 2015-07-31. Perturbative formulation of general continuous-time Markov model of sequence evolution via insertions/deletions, Part II: Perturbation analyses. https://doi.org/10.1101/023606

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2016

Using the Price equation to analyze multi-level selection on the reproductive policing mechanism of bacterial plasmids

The replication control system of non-conjugative bacterial plasmids constitutes a simple and elegant example of a reproductive policing mechanism that moderates competition in the intra-cellular replication pool and establishes a mutually beneficial partnership among plasmids within a bacterial host and between plasmids and their hosts. The emergence of these partnerships is a product of the conflict between the evolutionary interests of hosts, who seek to maximize their growth rates within the population, and plasmids, who seek to maximize their growth rates within hosts. We employ a multi-scale computational model describing the growth, division and death of hosts, as well as the independent replication of plasmids within hosts, in order to investigate the implications of this conflict for the evolution of the plasmid replication parameters. We apply the multi-level form of the Price equation in order to quantify and elucidate the various selective pressures that drive the evolution of plasmid replication control. Our analysis shows how the evolution of the constituent components of the plasmid replication control system are shaped by selection acting at the level of hosts and the level of plasmids. In addition, we calculate finer-grained selective pressures that are attributed to atomic plasmid-related events (such as intra-cellular replication and plasmid loss due to host death) and demonstrate their special role at the early stages of the evolution of policing. Our approach constitutes a novel application of the Price equation for discerning and discussing the synergies between the levels of selection given the availability of a mechanistic model for the generation of the systems dynamics. We show how the Price equation, particularly in its multi-level form, can provide significant insight by quantifying the relative importance of the various selective forces that shape the evolution of policing in bacterial plasmids.

Evolutionary Biology↗

bioRxiv2016

Sexual selection drives floral scent diversification in carnivorous pitcher plants (NA Sarraceniaceae)

Plant volatiles play vital roles in signaling with their insect associates. Empirical studies show that both pollinators and herbivores exert strong selective pressures on plant phenotypes. While studies often evoke the assumption that volatiles from floral and vegetative tissues are distinct due to strong pollinator-mediated selection operating on the flowers or selection from herbivores acting on the leaves, explicit tests of these assumptions are often lacking. In this study, we examined the evolution of floral and vegetative volatiles in the North American (NA) pitcher plants (Sarraceniaceae). In these taxa, insects are attracted for both pollination and prey capture, providing an ideal opportunity to understand the evolution of scent compounds across different plant organs. We collected a comprehensive dataset of floral and vegetative volatiles from across the NA Sarraceniaceae. We used multivariate analysis methods to examine whether volatile profiles are distinct between plant tissues, and investigated rates of scent evolution in these unique taxa. Our major findings revealed that (i) flowers and pitchers produced highly distinct scent profiles, consistent with the hypothesis that volatiles alleviate trade-offs due to incidental pollinator consumption; (ii) across species, floral scent separated into distinct regions of scent space, while pitchers showed little evidence of clustering - this may be due to convergence on a generalist strategy for insect capture; and (iii) rates of scent evolution depended on tissue type, suggesting that pollinators and herbivores differentially influence the evolution of chemical traits. We emphasize the need for additional functional studies to further distinguish between volatile functions.

Evolutionary Biology↗

bioRxiv2016

Contrasting patterns of genome-level diversity across distinct co-occurring bacterial populations

To understand the forces driving differentiation and diversification in wild bacterial populations, we must be able to delineate and track ecologically relevant units through space and time. Mapping metagenomic sequences to reference genomes derived from the same environment can reveal genetic heterogeneity within populations, and in some cases, be used to identify boundaries between genetically similar, but ecologically distinct, populations. Here we examine population-level heterogeneity within abundant and ubiquitous freshwater bacterial groups such as the acI Actinobacteria and LD12 Alphaproteobacteria (the freshwater sister clade to the marine SAR11) using 33 single cell genomes and a 5-year metagenomic time series. The single cell genomes grouped into 15 monophyletic clusters (termed \"tribes\") that share at least 97.9% 16S rRNA identity. Distinct populations were identified within most tribes based on the patterns of metagenomic read recruitments to single-cell genomes representing these tribes. Genetically distinct populations within tribes of the acI actinobacterial lineage living in the same lake had different seasonal abundance patterns, suggesting these populations were also ecologically distinct. In contrast, sympatric LD12 populations were less genetically differentiated. This suggests that within one lake, some freshwater lineages harbor genetically discrete (but still closely related) and ecologically distinct populations, while other lineages are composed of less differentiated populations with overlapping niches. Our results point at an interplay of evolutionary and ecological forces acting on these communities that can be observed in real time.

Evolutionary Biology↗