Statistical properties of pairwise distances between leaves on a random Yule tree

Probability Distribution of Tree Age for the Simple Birth-Death Process, with Applications to Distributions of Number of Ancestral Lineages and Divergence Times for Pairs of Taxa in a Yule Tree

In this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth-death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the number of taxa existing at any time in the past in a tree of a known number of extant species, and given birth and death rates, and second, that of determining the TMRCA of two randomly selected taxa in an unobserved tree that is produced by a simple birth-only, or Yule, process. In the latter case, it is assumed that only the rate of bifurcation (speciation) and the size, or number of tips, are known. This is shown to lead to a closed-form analytical expression for the probability distribution of this parameter, which is arrived at based on the known mathematical form of the age distribution of Yule trees of a given size and branching rate, which is derived here de novo, and a similar distribution which additionally is conditioned on tree age. The new distribution is the exact Yule prior for divergence times of pairs of taxa under the stated conditions and is potentially useful in statistical (Bayesian) inference studies of phylogenies.

DNA barcoding and phylogenetics of freshwater fish fauna of Ranganadi River, Arunachal Pradesh

Arunachal Pradesh, the largest state of North-East India covers almost 60.93% of the Eastern Himalayan hotspot. Fish diversity and species identification is utmost important for fisheries management. But, in some cases morphological characteristics based identification is difficult for a non-specialist to perform. In view of the above, the present study emphasized on the assessment of DNA barcoding, phylogenetics and genetic diversity of fish species in the Ranganadi River, Arunachal Pradesh, India. India. Arunachal Pradesh, the largest state of North-East India covers almost 60.93% of the Eastern Himalayan hotspot. Altogether 114 specimens, representing 22 species, belonging to 3 orders and 5 families were successfully barcoded and found to be 98-100% identical from both GenBank and BOLD databases. Out of these 22 fish species, it was found that one species assessed was Endangered, three species as Near Threatened and one species as Vulnerable. A Neighbour Joining (NJ) tree was constructed using Rstudio for the purpose of a phylogenetic analysis of the identified species. The barcoding gap analysis using K2P, P-distance and Jukes-Cantor was done to detect the presence of cryptic species and barcoding success. The nucleotide base composition and genetic distance analysis were also performed, using MEGA 6.0. DNA Sequence Polymorphism v6.12.03 analysis revealed the nucleotide diversity (p) and haplotype diversity (Hd). The Hd for the whole dataset was found to be 0.975, which showed high genetic diversity in the Ranganadi River. Both morphological key identifying characters and molecular data corroborated the phylogenetic analysis. This COI barcode library, generated in the present study, not only helped in species identification and molecular study, but also in cryptic species identification.

Evolutionary dynamics of selfish DNA explains the abundance distribution of genomic subsequences

Since the sequencing of large genomes, many statistical features of their sequences have been found. One intriguing feature is that certain subsequences are much more abundant than others. In fact, abundances of subsequences of a given length are distributed with a scale-free power-law tail, resembling properties of human texts, such as Zipf's law. Despite recent efforts, the understanding of this phenomenon is still lacking. Here we find that selfish DNA elements, such as those belonging to the Alu family of repeats, dominate the power-law tail. Interestingly, for the Alu elements the power-law exponent increases with the length of the considered subsequences. Motivated by these observations, we develop a model of selfish DNA expansion. The predictions of this model qualitatively and quantitatively agree with the empirical observations. This allows us to estimate parameters for the process of selfish DNA spreading in a genome during its evolution. The obtained results shed light on how evolution of selfish DNA elements shapes non-trivial statistical properties of genomes.

Comparing the Statistical Fate of Paralogous and Orthologous Sequences

For several decades, sequence alignment has been a widely used tool in bioinformatics. For instance, finding homologous sequences with a known function in large databases is used to get insight into the function of nonannotated genomic regions. Very efficient tools like BLAST have been developed to identify and rank possible homologous sequences. To estimate the significance of the homology, the ranking of alignment scores takes a background model for random sequences into account. Using this model we can estimate the probability to find two exactly matching subsequences by chance in two unrelated sequences. For two homologous sequences, the corresponding probability is much higher, which allows us to identify them. Here we focus on the distribution of lengths of exact sequence matches between protein-coding regions of pairs of evolutionarily distant genomes. We show that this distribution exhibits a power-law tail with an exponent [Formula: see text] Developing a simple model of sequence evolution by substitutions and segmental duplications, we show analytically and computationally that paralogous and orthologous gene pairs contribute differently to this distribution. Our model explains the differences observed in the comparison of coding and noncoding parts of genomes, thus providing a better understanding of statistical properties of genomic sequences and their evolution.