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From Wikipedia, the free encyclopedia

Rate = 1 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 concomitantly variable codons, is a technique in computational phylogenetics that allows the hypothesized rate of molecular evolution at individual codons in a set of nucleotide sequences to vary in an 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 set of DNA or RNA 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 such as the gamma distribution. Covarions is a concrete form of the more general concept of heterotachy.

Developing a computational algorithm 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 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 methods to the covarion model.

The matrix at right represents a covarion-based modification to the three-parameter Kimura substitution model, 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 and transversion 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.

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  • Attribution Theory - Basic covariation | Individuals and Society | MCAT | Khan Academy
  • Kelley Covariation Model - Attribution Theory
  • Kelley's Co-Variation Theory

Transcription

- [Voiceover] So how do we go about trying to explain the behavior of other people around us? Well, we do it in a few different ways. One of the things that we do is try and break down our understanding and explanations of their behavior into factors about them and factors related to their environment and surroundings. And there's two terms for each one of these that I want you to know. So, if it's about them, I want you to know internal. Another word for that would be dispositional. And also external, and another word for that would be situational. And what we're really talking about here is a theory called Attribution Theory. And this is how we find explanations for the behaviors of others. And I want you to actually pay attention to this blue line that I've drawn in the middle. Because in reality, the behavior of other people is on a spectrum. There may very well be a combination of internal and external factors. So what bits of information can we use to determine whether we think someone's behavior is attributed to internal or distributional causes, or it's related more to external factors and their situation? And one of the theories we can use is the covariation model. So, let us take our forever flaky friend, and let us look at a calendar. What we're trying to do with our friend is we're trying to go and watch a movie. And what we find is our friend forever cancels on us. We can't ever get them to go to the movie. "I have to wash my laundry. "I have to dry my hair. "I have to fix my car." And over the course of a month, we notice that they have consistently displayed the same behavior over time. And when there's a high level of this consistent behavior over time, we are more likely to think that this is related to our friend being a forever flaky friend. It's more likely related to them as a person, as opposed to the world working against them to stop them coming and watching this movie with us. So, when consistency is high, we're more likely to attribute it towards, the behavior, towards internal factors. Now, let us consider another one of our friends. So, Jim... Is one our most relaxed, friendly, warm friends. We really don't have a friend that's more relaxed or more warm than Jim. Now, one of the things we find is one day, Jim goes to get pizza. And what happens is Jim becomes furious. Jim becomes absolutely furious. They get his order wrong. They drop the pizza on the floor. He gets so mad. It's really, really, really out of character and distinctive. And really, we're like, "Wow, this is such "an unusual situation." This is really out of character for Jim. And in this case what we think is that this is much more related to the situation or the environment that we find ourselves in. That this is much more related to the situation of being in a pizza parlor. We don't think that Jim is naturally this aggressive and hostile person, but his behavior we're going to attribute to this situational, or these external factors. And finally, in the covariation model, we have a third factor. Have you ever heard of the term group lateness? You probably haven't, because I kind of just made that term up. But what that means is that if you arrive late to a meeting, but you're with 20 other people, and they're all late, there's a high degree of consensus. And what that means is that a lot of people are demonstrating the same behavior. When a lot of people are demonstrating the same behavior, we start to think, "You know what? "If everybody's late, it's probably something to do "with their environment, something probably to do "with their situation. "There's no parking, the weather was bad, "the elevator got stuck." And in that case, a high level of consensus means that we're more likely to attribute the behavior to a situational cause, as opposed to an internal factor. So these are the three important cues of Kelley's Covariation Model.

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. FullText
This page was last edited on 2 June 2022, at 08:46
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