# Morphlogical Character and Range Data for late Ordovician and Early Silurian Graptoloidea

### Description

This dataset contains a morphological character matrix (containing both a set of 45 discrete characters, and 4 continuous characters coded as minimum and maximum range values), along with biostratigraphic range data for 183 graptoloid species-level taxa from Bapst et al. (2012, PNAS). Also includes a pre-calculated distance matrix based on the character matrix, using the algorithm applied by Bapst et al (2012). Interval dates for biostratigraphic zones is taken from Sadler et al. 2011.

### Format

This dataset is composed of three objects:

- graptCharMatrix
A matrix composed of mixed character data and a group code for 183 graptoloid taxa, with rows named with species names and columns named with character names.

- graptRanges
A list containing two matrices: the first matrix describes the first and last interval times for 20 graptolite biozones and the second matrix contains the first and last appearances of 183 graptolite species in those same biozones. (In other words, graptRanges has the 'timeList' format called by some paleotree functions).

- graptDistMat
A 183x183 matrix of pair-wise distances (dissimilarities) for the 183 graptolite species, using the algorithm for discrete characters and min-max range values described in Bapst et al.

### Details

The character matrix contains characters of two differing types with a (very) small but non-neglible amount of missing character data for some taxa. This required the use of an unconventional ad hoc distance metric for the published analysis, resulting in a (very slightly) non-Euclidean distance matrix. This breaks some assumptions of some statistical analyses or requires special corrections, such as with PCO.

Note that taxonomic data were collected only for species present within an interval
defined by the base of the Uncinatus biozone (~448.57 Ma) to the end of the cyphus
biozone (~439.37 Ma). Many taxa have first and last appearance dates listed in `graptRanges`

which are outside of this interval (see examples).

### Source

Source for stratigraphic ranges and character data:

Bapst, D. W., P. C. Bullock, M. J. Melchin, H. D. Sheets, and C. E. Mitchell.
2012. Graptoloid diversity and disparity became decoupled during the Ordovician
mass extinction. *Proceedings of the National Academy of Sciences*
109(9):3428-3433.

Source for interval dates for graptolite zones:

Sadler, P. M., R. A. Cooper,
and M. Melchin. 2009. High-resolution, early Paleozoic (Ordovician-Silurian)
time scales. *Geological Society of America Bulletin* 121(5-6):887-906.

### See Also

For more example graptolite datasets, see `retiolitinae`

This data was added mainly to provide an example dataset
for `nearestNeighborDist`

### 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 | ```
#load data
data(graptDisparity)
#separate out two components of character matrix
#45 discrete characters
discChar <- graptCharMatrix[,1:45]
#min ranges for 4 continuous characters
cMinChar <- graptCharMatrix[,c(46,48,50,52)]
#max ranges for 4 continuous characters
cMaxChar <- graptCharMatrix[,c(47,49,51,53)]
#group (clade/paraclade) coding
groupID <- graptCharMatrix[,54]
#number of species
nspec <- nrow(graptCharMatrix)
#some plotting information from Bapst et al.'s plotting scripts
grpLabel <- c("Normalo.","Monogr.","Climaco.",
"Dicrano.","Lasiogr.","Diplogr.","Retiol.")
grpColor <- c("red","purple",colors()[257],colors()[614],
colors()[124],"blue",colors()[556])
##########
#plot diversity curve of taxa
taxicDivDisc(graptRanges)
#but the actual study interval for the data is much smaller
abline(v=448.57,lwd=3) #start of study interval
abline(v=439.37,lwd=3) #end of study interval
#plot diversity curve just for study interval
taxicDivDisc(graptRanges, timelims=c(448.57,439.37))
############
#distance matrix is given as graptDistMat
#to calculate yourself, see code below in DoNotRun section
#now, is the diagonal zero? (it should be)
all(diag(graptDistMat)==0)
#now, is the matrix symmetric? (it should be)
isSymmetric(graptDistMat)
#can apply cluster analysis
clustRes <- hclust(as.dist(graptDistMat))
plot(clustRes,labels=FALSE)
#use ape to plot with colors at the tips
dev.new(width=15) # for a prettier plot
plot.phylo(as.phylo(clustRes),show.tip.label=FALSE,
no.margin=TRUE,direction="upwards")
tiplabels(pch=16,col=grpColor[groupID+1])
legend("bottomright",legend=grpLabel,col=grpColor,pch=16)
dev.set(2)
#can apply PCO (use lingoes correction to account for negative values
#resulting from non-euclidean matrix
pco_res <- pcoa(graptDistMat,correction="lingoes")
#relative corrected eigenvalues
rel_corr_eig <- pco_res$values$Rel_corr_eig
layout(1:2)
plot(rel_corr_eig)
#cumulative
plot(cumsum(rel_corr_eig))
#first few axes account for very little variance!!
#well let's look at those PCO axes anyway
layout(1)
pco_axes <- pco_res$vectors
plot(pco_axes[,1],pco_axes[,2],pch=16,col=grpColor[groupID+1],
xlab=paste("PCO Axis 1, Rel. Corr. Eigenvalue =",round(rel_corr_eig[1],3)),
ylab=paste("PCO Axis 2, Rel. Corr. Eigenvalue =",round(rel_corr_eig[2],3)))
legend("bottomright",legend=grpLabel,col=grpColor,pch=16,ncol=2,cex=0.8)
##########m##############
## Not run:
#calculate a distance matrix (very slow!)
#Bapst et al. calculated as # char diffs / total # of chars
#but both calculated for only non-missing characters for both taxa
#non-identical discrete states = difference for discrete traits
#non-overlapping ranges for continuous characters = difference for cont traits
distMat<-matrix(,nspec,nspec)
rownames(distMat)<-colnames(distMat)<-rownames(graptCharMatrix)
for(i in 1:nspec){ for(j in 1:nspec){ #calculate for each pair of species
#discrete characters
di <- discChar[i,] #discrete character vector for species i
dj <- discChar[j,] #discrete character vector for species j
#now calculate pair-wise differences for non-missing characters
discDiff <- (di!=dj)[!is.na(di)&!is.na(dj)] #logical vector
#
#continuous characters: need another for() loop
contDiff <- numeric()
for(ct in 1:4){
#if they do not overlap, a min must be greater than a max value
contDiff[ct] <- cMinChar[i,ct]>cMaxChar[j,ct] | cMinChar[j,ct]>cMaxChar[i,ct]
}
#remove NAs
contDiff <- contDiff[!is.na(contDiff)]
#combine
totalDiff <- c(discDiff,contDiff)
#divide total difference
distMat[i,j] <- sum(totalDiff)/length(totalDiff)
}}
#but is it identical to the distance matrix already provided?
identical(distMat,graptDistMat)
#ehh, numerical rounding issues...
#A somewhat speeder alternative to calculate a distance matrix
distMat<-matrix(,nspec,nspec)
rownames(distMat)<-colnames(distMat)<-rownames(graptCharMatrix)
for(i in 1:(nspec-1)){ for(j in (i+1):nspec){ #calculate for each pair of species
#now calculate pair-wise differences for non-missing characters
discDiff <- (discChar[i,]!=discChar[j,])[
!is.na(discChar[i,])&!is.na(discChar[j,])] #logical vector
#continuous characters: if they do not overlap, a min must be greater than a max value
contDiff<-sapply(1:4,function(ct)
cMinChar[i,ct]>cMaxChar[j,ct] | cMinChar[j,ct]>cMaxChar[i,ct])
#remove NAs, combine, divide total difference
distMat[i,j] <- distMat[j,i] <- sum(c(discDiff,contDiff[!is.na(contDiff)]))/length(
c(discDiff,contDiff[!is.na(contDiff)]))
}}
diag(distMat)<-0
#but is it identical to the distance matrix already provided?
identical(distMat,graptDistMat)
#ehh, MORE numerical rounding issues...
## End(Not run)
``` |