Estimating the Minimum Number of Character Transitions Using Maximum Parsimony
Description
minCharChange
is a function which takes a cladogram and a discrete trait and finds the
solutions of inferred character states for ancestral nodes that minimizes the number of
character state transitions (either gains or losses/reversals) for a given topology and a set of
discrete character data. minCharChange
relies on ancPropStateMat
, which is a wrapper
for phangorn
's function ancestral.pars
.
Usage
1 2 3 4 5 6 7 8  minCharChange(trait, tree, randomMax = 10000, maxParsimony = TRUE,
orderedChar = FALSE, type = "MPR", cost = NULL, printMinResult = TRUE,
ambiguity = c(NA, "?"), dropAmbiguity = FALSE, polySymbol = "&",
contrast = NULL)
ancPropStateMat(trait, tree, orderedChar = FALSE, type = "MPR",
cost = NULL, ambiguity = c(NA, "?"), dropAmbiguity = FALSE,
polySymbol = "&", contrast = NULL, returnContrast = FALSE)

Arguments
trait 
A vector of trait values for a discrete character, preferably named with taxon names identical to the tip labels on the input tree. 
tree 
A cladogram of type 'phylo'. Any branch lengths are ignored. 
randomMax 
The maximum number of cladograms examined when searching a large number of solutions
consistent with the reconstructed ancestral states from 
maxParsimony 
If maxParsimony is TRUE (the default) then only solutions with the smallest
number of total transitions examined will be returned. Note that since solutions are stochastically
'guessed' at, and the number of possible solutions may not be exhaustively searched, there may have
been solutions not examined with a lower number of transitions even if 
orderedChar 
If TRUE (not the default), then the character will be reconstructed with a cost (step)
matrix of a linear, ordered character. This is not applicable if 
type 
The parsimony algorithm applied by 
cost 
A matrix of the cost (i.e. number of steps) necessary to change between states of the input
character trait. If NULL (the
default), the character is assumed to be unordered with equal cost to change from any state to another.
Cost matrices only impact the "MPR" algorithm; if a cost matrix is given but 
printMinResult 
If TRUE (the default), a summary of the results is printed to the terminal. The information in this summary may be more detailed if the results of the analysis are simpler (i.e. fewer unique solutions). 
ambiguity 
A vector of values which indicate ambiguous (i.e. missing or unknown) character state codings
in supplied 
dropAmbiguity 
A logical. If 
polySymbol 
A single symbol which separates alternative states for polymorphic codings; the default symbol is

contrast 
A matrix of type integer with cells of 0 and 1, where each row is labelled with a string value
used for indicating character states in 
returnContrast 
If TRUE, the contrast table used by 
Details
The wrapper function ancPropStateMat
simply automates the application of functions
ancestral.pars
and phyDat
from phangorn
, along with several additional checks
and code to present the result as a matrix, rather than a specialized list.
Note that although the default orderedChar
argument assumes that multistate characters are unordered,
the results of character change will always be reported as gains and losses relative to the numbering of the
states in the output transitionSumChanges
, exactly as if they had been ordered. In the case
where the character is actually ordered, this may be
considered a conservative approach, as using a parsimony algorithm for unordered character states allows fewer
gains or losses to be counted on branches where multiple gains and losses are reported. If the character is
presumably unordered and multistate, however, then the gains and losses division
is arbitrary nonsense and should be combined to
to obtain the total number of character changes.
Value
By default, ancPropStateMat
returns a matrix, with rows corresponding to the ID numbers of tips and nodes in
$edge
, and columns corresponding to character states, with the value representing the proportional
weight of that node being that state under the algorithm used (known tip values are always 1).
If argument returnContrast
is TRUE
then ancPropStateMat
will instead return the final
contrast table used by phyDat
for interpreting character state strings.
minCharChange
invisibly returns a list containing the following elements, several of which are printed
by default to the console, as controlled by argument printMinResult
:
message
Describes the performance of
minCharChange
at searching for a minimum solution.sumTransitions
A vector recording the total number of necessary transitions (sum total of gains and losses/reversal) for each solution; effectively the parsimony cost of each solution.
minTransitions
A symmetrical matrix with number of rows and columns equal to the number of character states, with values in each cell indicating the minimum number of transitions from one ancestral state (i.e. the rows) to a descendant state (i.e. the columns), taken across the set of kept solutions (dependent on which are kept as decided by argument
maxParsimony
). Generally guaranteed not to add up to the number of edges contained within the input tree, and thus may not represent any realistic evolutionary scenario but does represent a conservative approach for asking 'what is the smallest possible number of transitions from 0 to 1' or 'smallest possible number of transitions from 1 to 0', independently of each other.solutionArray
A threedimensional array, where for each solution, we have a matrix with edges for rows and two columns indicating the ancestral and child nodes of that edge, with values indicating the states inferred for those nodes in a particular solution.
transitionArray
A labelled threedimensional array where for each solution we have a symmetrical matrix with number of rows and columns equal to the number of character states, with values in each cell indicating the total number of transitions from one ancestral state (i.e. the rows) to a descendant state (i.e. the columns).
transitionSumChanges
Which is a three column matrix with a row for every solution, with the values in the three columns measuring the number of edges (branches) inferred to respectively have gains, no change or losses (i.e. reversals), as calculated relative to the order of character states.
Author(s)
David W. Bapst
References
Hanazawa, M., H. Narushima, and N. Minaka. 1995. Generating most parsimonious reconstructions on a tree: A generalization of the FarrisSwoffordMaddison method. Discrete Applied Mathematics 56(23):245265.
Narushima, H., and M. Hanazawa. 1997. A more efficient algorithm for MPR problems in phylogeny. Discrete Applied Mathematics 80(23):231238.
Schliep, K. P. 2011. phangorn: phylogenetic analysis in R. Bioinformatics 27(4):592593.
Swofford, D. L., and W. P. Maddison. 1987. Reconstructing ancestral character states under Wagner parsimony. Mathematical Biosciences 87(2):199229.
See Also
The functions described here are effectively wrapers of phangorn
's function
ancestral.pars
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147  # let's write a quick & dirty ancestral trait plotting function
quickAncPlotter<function(tree,ancData,cex){
ancCol<(1:ncol(ancData))+1
plot(tree,show.tip.label=FALSE,no.margin=TRUE,direction="upwards")
tiplabels(pch=16,pie=ancData[(1:Ntip(tree)),],cex=cex,piecol=ancCol,
col=0)
nodelabels(pie=ancData[(1:Ntip(tree)),],cex=cex,piecol=ancCol)
}
# example with retiolitid graptolite data
data(retiolitinae)
#unordered, MPR
ancMPR<ancPropStateMat(retioTree, trait=retioChar[,2], type="MPR")
#unordered, ACCTRAN
ancACCTRAN<ancPropStateMat(retioTree, trait=retioChar[,2], type="ACCTRAN")
#let's compare MPR versus ACCTRAN results
layout(1:2)
quickAncPlotter(retioTree,ancMPR,cex=0.5)
text(x=4,y=5,"type='MPR'",cex=1.5)
quickAncPlotter(retioTree,ancACCTRAN,cex=0.5)
text(x=5,y=5,"type='ACCTRAN'",cex=1.5)
minCharChange(retioTree,trait=retioChar[,2],type="MPR")
minCharChange(retioTree,trait=retioChar[,2],type="ACCTRAN")
# with simulated data
set.seed(444)
tree<rtree(50)
#simulate under a likelihood model
char<rTraitDisc(tree,k=3,rate=0.7)
tree$edge.length<NULL
tree<ladderize(tree)
#unordered, MPR
ancMPR<ancPropStateMat(tree, trait=char, type="MPR")
#unordered, ACCTRAN
ancACCTRAN<ancPropStateMat(tree, trait=char, type="ACCTRAN")
#ordered, MPR
ancMPRord<ancPropStateMat(tree, trait=char, orderedChar=TRUE, type="MPR")
#let's compare MPR versus ACCTRAN results
layout(1:2)
quickAncPlotter(tree,ancMPR,cex=0.3)
text(x=8,y=15,"type='MPR'",cex=1.5)
quickAncPlotter(tree,ancACCTRAN,cex=0.3)
text(x=9,y=15,"type='ACCTRAN'",cex=1.5)
#MPR has much more uncertainty in node estimates
#but that doesn't mean ACCTRAN is preferable
#let's compare unordered versus ordered under MPR
layout(1:2)
quickAncPlotter(tree,ancMPR,cex=0.3)
text(x=8,y=15,"unordered char\nMPR",cex=1.5)
quickAncPlotter(tree,ancMPRord,cex=0.3)
text(x=9,y=15,"ordered char\nMPR",cex=1.5)
layout(1)
## Not run:
# what ancPropStateMat automates (with lots of checks):
require(phangorn)
char1<matrix(char,,1)
rownames(char1)<names(char)
#translate into something for phangorn to read
char1<phyDat(char1,type="USER",levels=sort(unique(char1)))
x<ancestral.pars(tree,char1,type="MPR")
y<ancestral.pars(tree,char1,type="ACCTRAN")
## End(Not run)
#estimating minimum number of transitions with MPR
minCharChange(tree,trait=char,type="MPR")
#and now with ACCTRAN
minCharChange(tree,trait=char,type="ACCTRAN")
#POLYMORPHISM IN CHARACTER DATA
# example trait data with a polymorphic taxon
# separated with '&' symbol
# similar to polymorphic data output by ReadMorphNexus from package Claddis
charPoly<as.character(c(1,2,NA,0,0,1,"1&2",2,0,NA,0,2,1,1,"1&2"))
#simulate a tree with 16 taxa
set.seed(444)
tree<rtree(15)
tree$edge.length<NULL
tree<ladderize(tree)
names(charPoly)<tree$tip.label
charPoly
# need a contrast matrix that takes this into account
#can build row by row, by hand
#first, build contrast matrix for basic states
contrast012<rbind(c(1,0,0),c(0,1,0),c(0,0,1))
colnames(contrast012)<rownames(contrast012)<0:2
contrast012
#add polymorphic state and NA ambiguity as new rows
contrastPoly<c(0,1,1)
contrastNA<c(1,1,1)
contrastNew<rbind(contrast012,'1&2'=contrastPoly,contrastNA)
rownames(contrastNew)[5]<NA
#let's look at contrast
contrastNew
# now try this contrast table we've assembled
# default: unordered, MPR
ancPoly<ancPropStateMat(tree, trait=charPoly, contrast=contrastNew)
# but...!
# we can also do it automatically,
# by default, states with '&' are automatically treated
# as polymorphic character codings by ancPropStateMat
ancPolyAuto<ancPropStateMat(tree, trait=charPoly, polySymbol="&")
# but does this match what the table we constructed?
ancPropStateMat(tree, trait=charPoly,
polySymbol="&", returnContrast=TRUE)
# compare to contrastNew above!
# only difference should be the default ambiguous
# character '?' is added to the table
#compare reconstructions
layout(1:2)
quickAncPlotter(tree,ancPoly,cex=0.5)
text(x=3.5,y=1.2,"manuallyconstructed\ncontrast",cex=1.3)
quickAncPlotter(tree,ancPolyAuto,cex=0.5)
text(x=3.5,y=1.2,"autoconstructed\ncontrast",cex=1.3)
layout(1)
#look pretty similar!
#i.e. the default polySymbol="&", but could be a different symbol
#such as "," or "\"... it can only be *one* symbol, though
# all of this machinery should function just fine in minCharChange
# again, by default polySymbol="&" (included anyway here for kicks)
minCharChange(tree, trait=charPoly, polySymbol="&")

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