Performs a test proposed by Hart and Martínez (2011) for the equivalence of the relative frequencies of purines (\(A+G\)) and pyrimidines (\(C+T\)) in DNA sequences. It does this by checking whether or not the mononucleotide frequencies of a DNA sequence satisfy the relationship A+G=C+T.
agct.test(x, alg=c("exact", "simulate", "lower", "Lower", "upper"), n)A list with class "htest.ext" containing the following components:
the value of the test statistic.
the p-value of the test.
a character string indicating what type of test was performed.
a character string giving the name of the data.
the probability vector used to derive the test statistic.
a brief description of the test statistic.
the null hypothesis (\(H_0\)) of the test.
the alternative hypothesis (\(H_1\)) of the test.
either a vector containing the relative frequencies of each of the 4 nucleotides A, C, G, T, a character vector representing a DNA sequence in which each element contains a single nucleotide, or a DNA sequence stored using the SeqFastadna class from the seqinr package.
the algorithm for computing the p-value. If set to “simulate”, the p-value is obtained via Monte Carlo simulation. If set to “lower”, an analytic lower bound on the p-value is computed. If set to “upper”, an analytic upper bound on the p-value is computed. “lower” and “upper” are based on formulae in Hart and Martínez (2011). a Tighter (though unpublished) lower bound on the p-value may be obtained by specifying “Lower”. If alg is specified as “exact” (the default value), the p-value for the test is computed exactly.
The number of replications to use for Monte Carlo simulation. If computationally feasible, a value >= 10000000 is recommended.
Andrew Hart and Servet Martínez
The first argument may be a character vector representing a DNA sequence, a DNA sequence represented using the SeqFastadna class from the seqinr package, or a vector containing the relative frequencies of the A, C, G and T nucleic acids.
Let A, C, G and T denote the relative frequencies of the nucleotide bases appearing in a DNA sequence. This function carries out a statistical hypothesis test that the relative frequencies satisfy the relation \(A+G=C+T\), or that purines \(\{A, G\}\) occur equally as often as pyrimidines \(\{C,T\}\) in a DNA sequence. The relationship can be rewritten as \(A-T=C-G\), from which it is easy to see that the property being tested is a generalisation of Chargaff's second parity rule for mononucleotides, which states that \(A=T\) and \(C=G\). The test is set up as follows:
\(H_0\): \(A+G \neq C+T\)
\(H_1\): \(A+G = C+T\)
The vector \((A,C,G,T)\) is assumed to come from a Dirichlet(1,1,1,1) distribution on the 3-simplex under the null hypothesis.
The test statistic \(\eta_V\) is the Euclidean distance from the relative frequency vector \((A,C,G,T)\) to the closest point in the square set \(\theta_V=\{(x,y,1/2-x,1/2-y) : 0 <= x,y <= 1/2\}\), which divides the 3-simplex into two equal parts. \(\eta_V\) lies in the range \([0,\sqrt{3/8}]\).
Hart, A.G. and Martínez, S. (2011) Statistical testing of Chargaff's second parity rule in bacterial genome sequences. Stoch. Models 27(2), 1--46.
chargaff0.test, chargaff1.test,
chargaff2.test, ag.test,
chargaff.gibbs.test
#Demonstration on real viral sequence
data(pieris)
agct.test(pieris)
#Simulate synthetic DNA sequence that does not exhibit Purine-Pyrimidine parity
trans.mat <- matrix(c(.4, .1, .4, .1, .2, .1, .6, .1, .4, .1, .3, .2, .1, .2, .4, .3),
ncol=4, byrow=TRUE)
seq <- simulateMarkovChain(500000, trans.mat, states=c("a", "c", "g", "t"))
agct.test(seq)
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