Description Usage Arguments Details Value References See Also Examples
View source: R/TreeQuartetHypTest.R
Test the hypothesis H_0= T1 or T3 model of \insertCiteMAR19;textualMSCquartets, vs. H_1 = everything else. T1 is for a specific species quartet topology, and T3 for any species quartet topology.
1 2 3 4 5 6 7 8  quartetTreeTest(
obs,
model = "T3",
lambda = 0,
method = "MLest",
smallcounts = "approximate",
bootstraps = 10^4
)

obs 
vector of 3 counts of resolved quartet frequencies 
model 

lambda 
parameter for powerdivergence statistic (e.g., 0 for likelihood ratio statistic, 1 for Chisquared statistic) 
method 

smallcounts 

bootstraps 
number of samples for bootstrapping 
This function implements two of the versions of the test given by \insertCiteMAR19;textualMSCquartets as well as parametric boostrapping, with other procedures for when some expected counts are small. When the topology and/or the internal quartet branch length is not specified by the null hypothesis these are more accurate tests than, say, a Chisquare with one degree of freedom, which is not theoretically justified near the singularities and boundaries of the models.
If method="MLtest"
, this uses the test by that name described in Section 7 of \insertCiteMAR19;textualMSCquartets.
For both the T1 and T3 models the test is slightly anticonservative over a small range of true internal edges of the quartet species tree.
Although the test generally performs well in practice, it lacks a uniform asymptotic guarantee over
the full parameter space for either T1 or T3.
If method="conservative"
, a conservative test described by \insertCiteMAR19;textualMSCquartets is used. For model T3 this
uses the Chisquare distribution with 1 degree of freedom
(the "least favorable" approach), while for model T1
it uses the Minimum Adjusted Bonferroni, based on precomputed values from simulations with n=1e+6.
These conservative tests are asymptotically guaranteed to reject the null
hypothesis at most at a specified level, but at the expense of increased type II errors.
If method="bootstrap"
, then parametric bootstrapping is performed, based on parameter estimates of the quartet topology
and internal edge length. The bootstrap sample size is given by the bootstrap
argument.
When some expected topology counts are small, the methods "MLest"
and "conservative"
are not appropriate.
The argument smallcounts
determines whether bootstrapping or a faster approximate method is used.
These both involve estimates of the quartet topology and internal edge length. The approximate approach
returns a precomputed pvalue, found by replacing the largest observed count
with 1e+6 and performing 1e+8 bootstraps for the model T3. When n is sufficiently large (at least 30) and
some expected counts are small, the quartet tree error probability is small and the bootstrap pvalue is
approximately independent of the choice of T3 or T1 and of the largest observed count.
For model T1, the first entry of obs
is treated as the count of gene quartets concordant with the species tree.
The returned pvalue should be taken with caution when there is a small sample size, e.g. less than 30 gene trees.
The returned value of bl
is a consistent estimator, but not the MLE, of the internal
edge length in coalescent units. Although consistent, the MLE for t is biased.
Our consistent estimator is still biased, but with less bias than the MLE. See \insertCiteMAR19;textualMSCquartets
for more discussion on dealing with the bias of parameter estimates in the
presence of boundaries and/or singularities of parameter spaces.
(pvalue, bl)
where bl
is a consistent estimator of the
internal edge length in coalescent units, possibly Inf
.
MAR19MSCquartets
1 2 3 4  quartetTreeTest(c(17,72,11),"T3")
quartetTreeTest(c(17,72,11),"T1")
quartetTreeTest(c(72,11,17),"T1")
quartetTreeTest(c(11,17,72),"T1")

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