Classification of DNA sequences is an important issue in the bioinformatics study, yet most existing methods for phylogenetic analysis including Multiple Sequence Alignment (MSA) are time-consuming and computationally expensive. The alignment-free methods are popular nowadays, whereas the manual intervention in those methods usually decreases the accuracy. Also, the interactions among nucleotides are neglected in most methods. Here we propose a new Accumulated Natural Vector (ANV) method which represents each DNA sequence by a point in ℝ¹⁸. By calculating the Accumulated Indicator Functions of nucleotides, we can further find an Accumulated Natural Vector for each sequence. This new Accumulated Natural Vector not only can capture the distribution of each nucleotide, but also provide the covariance among nucleotides. Thus global comparison of DNA sequences or genomes can be done easily in ℝ¹⁸. The tests of ANV of datasets of different sizes and types have proved the accuracy and time-efficiency of the new proposed ANV method.

The severe respiratory disease COVID-19 was initially reported in Wuhan, China, in December 2019, and spread into many provinces from Wuhan. The corresponding pathogen was soon identified as a novel coronavirus named SARS-CoV-2 (formerly, 2019-nCoV). As of 2 May, 2020, over 3 million COVID-19 cases had been confirmed, and 235,290 deaths had been reported globally, and the numbers are still increasing. It is important to understand the phylogenetic relationship between SARS-CoV-2 and known coronaviruses, and to identify its hosts for preventing the next round of emergency outbreak. In this study, we employ an effective alignment-free approach, the Natural Vector method, to analyze the phylogeny and classify the coronaviruses based on genomic and protein data. Our results show that SARS-CoV-2 is closely related to, but distinct from the SARS-CoV branch. By analyzing the genetic distances from the SARS-CoV-2 strain to the coronaviruses residing in animal hosts, we establish that the most possible transmission path originates from bats to pangolins to humans.

Omicron, the latest SARS-CoV-2 Variant of Concern (VOC), first appeared in Africa in November 2021. At present, the question of whether a new VOC will out-compete the currently predominant variant is important for governments seeking to determine if current surveillance strategies and responses are appropriate and reasonable. Based on both virus genomes and daily-confirmed cases, we compare the additive differences in growth rates and reproductive numbers ($R_0$) between VOCs and their predominant variants through a Bayesian framework and phylo-dynamics analysis. Faced with different variants, we evaluate the effects of current policies and vaccinations against VOCs and predominant variants. The model also predicts the date on which a VOC may become dominant based on simulation and real data in the early stage. The results suggest that the overall additive difference in growth rates of B.1.617.2 and predominant variants was 0.44 (95% confidence interval, 95% CI: −0.38, 1.25) in February 2021, and that the VOC had a relatively high $R_0$. The additive difference in the growth rate of BA.1 in the United Kingdom was 6.82 times the difference between Delta and Alpha, and the model successfully predicted the dominating process of Alpha, Delta and Omicron. Current vaccination strategies remain similarly effective against Delta compared to the previous variants. Our model proposes a reliable Bayesian framework to predict the spread trends of VOCs based on early-stage data, and evaluates the effects of public health policies, which may help us better prepare for the upcoming Omicron variant, which is now spreading at an unprecedented speed.

Advances in sequencing technology have made large amounts of biological data available. Evolutionary analysis of data such as DNA sequences is highly important in biological studies. As alignment methods are ineffective for analyzing large-scale data due to their inherently high costs, alignment-free methods have recently attracted attention in the field of bioinformatics. In this paper, we introduce a new positional correlation natural vector (PCNV) method that involves converting a DNA sequence into an 18-dimensional numerical feature vector. Using frequency and position correlation to represent the nucleotide distribution, it is possible to obtain a PCNV for a DNA sequence. This new numerical vector design uses six suitable features to characterize the correlation among nucleotide positions in sequences. PCNV is also very easy to compute and can be used for rapid genome comparison. To test our novel method, we performed phylogenetic analysis with several viral and bacterial genome datasets with PCNV. For comparison, an alignment-based method, Bayesian inference, and two alignment-free methods, feature frequency profile and natural vector, were performed using the same datasets. We found that the PCNV technique is fast and accurate when used for phylogenetic analysis and classification of viruses and bacteria.