{, class="wikitable" align="right" , - ! ! colspan=4 , Rate = 1 ! colspan=4 , Rate = 0 , - , , A1 , G1 , C1 , T1 , A0 , G0 , C0 , T0 , - , A1 , – , α , β , γ , δ , 0 , 0 , 0 , - , G1 , α , – , γ , β , 0 , δ , 0 , 0 , - , C1 , β , γ , – , α , 0 , 0 , δ , 0 , - , T1 , γ , β , α , – , 0 , 0 , 0 , δ , - , A0 , κδ , 0 , 0 , 0 , – , 0 , 0 , 0 , - , G0 , 0 , κδ , 0 , 0 , 0 , – , 0 , 0 , - , C0 , 0 , 0 , κδ , 0 , 0 , 0 , – , 0 , - , T0 , 0 , 0 , 0 , κδ , 0 , 0 , 0 , – , - The method of covarions, or ''co''ncomitantly ''vari''able cod''ons'', is a technique in

computational phylogenetics Computational phylogenetics is the application of computational algorithms, methods, and programs to phylogenetic "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary hist ...

that allows the hypothesized rate of molecular evolution at individual codons in a set of nucleotide sequences to vary in an autocorrelation, autocorrelated manner. Under the covarion model, the rates of evolution on different branches of a hypothesized phylogenetic tree vary in an autocorrelated way, and the rates of evolution at different codon sites in an

aligned ''Aligned'' is a 2023 drama film written and directed by Apollo Bakopoulos. The film had its world premiere at the Brooklyn Film Festival in 2023 and, in the UK, at the BFI Flare: London LGBTIQ+ Film Festival in 2024. The story centers around t ...

set of DNA or

RNA Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...

sequences vary in a separate but autocorrelated manner. This provides additional and more realistic constraints on evolutionary rates versus the simpler technique of allowing the rate of evolution on each branch to be selected randomly from a suitable

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...

such as the

gamma distribution In probability theory and statistics, the gamma distribution is a two- parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of the gamma dis ...

. Covarions is a concrete form of the more general concept of

heterotachy Heterotachy refers to variations in lineage-specific evolutionary rates over time. In the field of molecular evolution, the principle of heterotachy states that the substitution rate of sites in a gene can change through time. It has been proposed t ...

. Developing a computational

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

suitable for identifying sites with high evolutionary rates from a static dataset is a challenge due to the constraints of autocorrelation. The original statement of the method used a rough

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...

model of the evolutionary process designed to identify transiently high-variability codon sites. Abandoning the requirement that rates be autocorrelated on a given DNA or RNA molecule allows extension of

substitution matrix In bioinformatics and evolutionary biology, a substitution matrix describes the frequency at which a character in a nucleotide sequence or a protein sequence changes to other character states over evolutionary time. The information is often in ...

methods to the covarion model. The matrix at right represents a covarion-based modification to the three-parameter Kimura

substitution model In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as seque ...

, where the vertical axis represents the original state and the horizontal axis the destination state. The two rates, 0 and 1, define a pair of mutation states; transitions can occur between state 0 and state 1 at any time, but nucleotides can only mutate in state 1. That is, the rate of mutation in state 0 is 0. Here α and β are the standard Kimura parameters for

transition Transition or transitional may refer to: Mathematics, science, and technology Biology * Transition (genetics), a point mutation that changes a purine nucleotide to another purine (A ↔ G) or a pyrimidine nucleotide to another pyrimidine (C ↔ ...

and

transversion Transversion, in molecular biology, refers to a point mutation in DNA in which a single (two ring) purine ( A or G) is changed for a (one ring) pyrimidine ( T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ion ...

mutations, κδ is the rate of transition between a site being invariant (state 0) and variable (state 1), and δ is the rate of transition between a site being variable (state 1) and invariant (state 0). Because nucleotide sequences do not themselves reflect the difference between a 0 or 1 state, an observation of a given nucleotide is treated as ambiguous; that is, if a given site contains a C nucleotide, it is ambiguous between C0 and C1 states.

References

* Felsenstein J. (2004). Inferring Phylogenies Sinauer Associates: Sunderland, MA. * Fitch WM, Markowitz E. (1970) An improved method for determining codon variability in a gene and its applications to the rate of fixation of mutations in evolution. ''Biochem Genet'' 4: 579–593
PubMed
* Penny D, McComish BJ, Charleston MA, Hendy MD. (2001) Mathematical elegance with biochemical realism: The covarion model of molecular evolution. ''J Mol Evol'' 53: 711–723
DOI
* Galtier N. (2001) Maximum-likelihood phylogenetic analysis under a covarion-like model. ''Mol Biol Evol'' 18:866–873
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Computational phylogenetics