- Introduction
- 1. Background
- 2. Retrieving sequences
- 3. Sequence alignment
- 4. Distance-based analyses
- 5. Recombination
- 6. Maximum likelihood based analyses
- 7. Visualising trees
- 8. Time-stamped phylogenies
- 9. Bayesian reconstruction of time trees
- 10. Effective population size estimation
- 11. Structured populations
- 12. References
- Published with GitBook
'Clockifying' maximum likelihood trees
Load the libraries
library(ape)
library(stringr)
library(phangorn)
library(magrittr)
source("chronos.R")
Preprocessing the data
We need is a tree, plus how long the sequences were used to construct the tree. I will use a tree generated using ExaML, but in principle, you could use any tree, including one generated using optim.pml in phangorn.
stub <- "village_examl"
seq.len <- 6987
tr.fn <- paste(stub,".tre",sep="")
td.fn <- paste(stub,".td",sep="")
tr <- read.tree(tr.fn)
The sample times are in the sequence names at the end.
tipnames <- tr$tip.label
tipdates <- tipnames %>% strsplit(.,"_",fixed=TRUE) %>% lapply(.,tail,1) %>% unlist %>% as.double
Now save the sequence names and tip dates to a file.
write.table(rbind(c(length(tipnames),""),cbind(tipnames,tipdates)),td.fn,col.names=FALSE,row.names=FALSE,quote=FALSE)
Root to tip regression
Using the tree and the tip dates (in the same order as the tip labels in the tree), we can root the tree using rtt.
tr.rtt <- rtt(tr,tipdates)
tr.rtt$edge.length[tr.rtt$edge.length<0.00000001] <- 0.00000001
tr.rtt.tipnames <- tr.rtt$tip.label
tr.rtt.tipdates <- tr.rtt.tipnames %>% strsplit(.,"_",fixed=TRUE) %>% lapply(.,tail,1) %>% unlist %>% as.double
Now the tree is rooted, we can calculate the evolutionary rate, as the slope of the regression of root-to-tip distances against sampling times.
rootdistance <- distRoot(tr.rtt)
pathlm <- lm(rootdistance~tr.rtt.tipdates)
rate <- coef(pathlm)[2]
rate
## tr.rtt.tipdates
## 0.002587992
The time to the most recent common ancestor can then be obtained using the intercept term and the slope, as it is the point at which the regression line crosses zero.
tmrca <- unname(-coef(pathlm)[1]/coef(pathlm)[2])
tmrca
## [1] 0.732083
Chronos
For us to be able to run chronos, we have to set up a quite complex calibration structure.
max.time <- max(tipdates)
ncat <- 1
strict.clock.ctrl <- chronos.control(nb.rate.cat=as.integer(ncat))
calibrating.values <- makeChronosCalib(tr)
calibrating.values$age.min <- max.time - tmrca
calibrating.values$age.max <- max.time - tmrca
# pins the tips to sampling years
calibrating.values <- rbind(calibrating.values,
data.frame(node=seq(1,length(td)),
age.min=max.time - td,
age.max=max.time - td,
soft.bounds=FALSE))
We now set options for the model.
ncat <- 1
sub.rate.model <- "discrete"
strict.clock.ctrl <- chronos.control(nb.rate.cat=as.integer(ncat))
We can now fit a dated tree.
chronos.tree <- RLchronos(tr,
lambda=1,
model=sub.rate.model,
calibration=calibrating.values,
control=strict.clock.ctrl,
quiet=TRUE)
## Initial dates set.
plot(chronos.tree,show.tip.label=FALSE)
add.scale.bar()
We can write the tree to a file as a Newick string with write.tree.
write.tree(dated.tree,file="village_chronos.tre")
Least squares dating
lsd is an external application, which can be run using a system call. It requires:
- The filename of the tree
- The filename of the sampling times
- A variance parameter (default 10)
- The sequence length
lsd.cmd <- sprintf("lsd -i %s -d %s -c -n 1 -r -b %s -s %s -v",tr.fn,td.fn,paste(10),seq.len)
lsd.cmd
## [1] "lsd -i village_examl.tre -d village_examl.td -c -n 1 -r -b 10 -s 6987 -v"
lsd <- system(lsd.cmd,intern=TRUE)
There is lots of information in the result.
lsd
## [1] "Reading the tree 1..."
## [2] "Pre-estimating the root without constraints ..."
## [3] "Optimizing the root position on the branch 1 ... 0.0100313653"
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## [902] "Optimizing the root position on the branch 900 ... 0.0110691821"
## [903] "Optimizing the root position on the branch 901 ... 0.0117023513"
## [904] "Optimizing the root position on the branch 902 ... 0.0118227929"
## [905] "Optimizing the root position on the branch 903 ... 0.0118501675"
## [906] "Optimizing the root position on the branch 904 ... 0.0118816208"
## [907] "Optimizing the root position on the branch 905 ... 0.0119144362"
## [908] "Optimizing the root position on the branch 906 ... 0.0119202176"
## [909] "Optimizing the root position on the branch 907 ... 0.0118794543"
## [910] "Optimizing the root position on the branch 908 ... 0.0118517398"
## [911] "Optimizing the root position on the branch 909 ... 0.0118384320"
## [912] "Optimizing the root position on the branch 910 ... 0.0116760550"
## [913] "Optimizing the root position on the branch 911 ... 0.0126074479"
## [914] "Optimizing the root position on the branch 912 ... 0.0094526925"
## [915] "Optimizing the root position on the branch 913 ... 0.0095641528"
## [916] "Optimizing the root position on the branch 914 ... 0.0096823426"
## [917] "Optimizing the root position on the branch 915 ... 0.0110242974"
## [918] "Optimizing the root position on the branch 916 ... 0.0111411925"
## [919] "Optimizing the root position on the branch 917 ... 0.0115332703"
## [920] "Optimizing the root position on the branch 918 ... 0.0115797532"
## [921] "Optimizing the root position on the branch 919 ... 0.0115794709"
## [922] "Optimizing the root position on the branch 920 ... 0.0117080009"
## [923] "Optimizing the root position on the branch 921 ... 0.0096449675"
## [924] "Optimizing the root position on the branch 922 ... 0.0140697856"
## [925] "Optimizing the root position on the branch 923 ... 0.0095582370"
## [926] "Optimizing the root position on the branch 924 ... 0.0096059207"
## [927] "Optimizing the root position on the branch 925 ... 0.0138095378"
## [928] "Optimizing the root position on the branch 926 ... 0.0140717466"
## [929] "Optimizing the root position on the branch 927 ... 0.0096004608"
## [930] "Optimizing the root position on the branch 928 ... 0.0108714009"
## [931] "Optimizing the root position on the branch 929 ... 0.0094301945"
## [932] "Optimizing the root position on the branch 930 ... 0.0112976064"
## [933] "Optimizing the root position on the branch 931 ... 0.0114139429"
## [934] "Optimizing the root position on the branch 932 ... 0.0114688626"
## [935] "Optimizing the root position on the branch 933 ... 0.0116282110"
## [936] "Optimizing the root position on the branch 934 ... 0.0117195291"
## [937] "Optimizing the root position on the branch 935 ... 0.0114557729"
## [938] "Optimizing the root position on the branch 936 ... 0.0112873714"
## [939] "Optimizing the root position on the branch 937 ... 0.0118394841"
## [940] "Optimizing the root position on the branch 938 ... 0.0094158324"
## [941] "Optimizing the root position on the branch 939 ... 0.0092979954"
## [942] "Optimizing the root position on the branch 940 ... 0.0092878075"
## [943] "Optimizing the root position on the branch 941 ... 0.0092736556"
## [944] "Optimizing the root position on the branch 942 ... 0.0092909890"
## [945] "Optimizing the root position on the branch 943 ... 0.0094423865"
## [946] "Optimizing the root position on the branch 944 ... 0.0096351005"
## [947] "Optimizing the root position on the branch 945 ... 0.0094184718"
## [948] "Optimizing the root position on the branch 946 ... 0.0092564143"
## [949] "Optimizing the root position on the branch 947 ... 0.0111941601"
## [950] "Optimizing the root position on the branch 948 ... 0.0117399824"
## [951] "Optimizing the root position on the branch 949 ... 0.0119077971"
## [952] "Optimizing the root position on the branch 950 ... 0.0124122369"
## [953] "Optimizing the root position on the branch 951 ... 0.0124630827"
## [954] "Optimizing the root position on the branch 952 ... 0.0130438308"
## [955] "Optimizing the root position on the branch 953 ... 0.0119218124"
## [956] "Optimizing the root position on the branch 954 ... 0.0119793103"
## [957] "Optimizing the root position on the branch 955 ... 0.0120508879"
## [958] "Optimizing the root position on the branch 956 ... 0.0119671449"
## [959] "Optimizing the root position on the branch 957 ... 0.0121375746"
## [960] "Optimizing the root position on the branch 958 ... 0.0117164879"
## [961] "Optimizing the root position on the branch 959 ... 0.0127279316"
## [962] "Optimizing the root position on the branch 960 ... 0.0112376619"
## [963] "Optimizing the root position on the branch 961 ... 0.0092160081"
## [964] "Optimizing the root position on the branch 962 ... 0.0110774689"
## [965] "Optimizing the root position on the branch 963 ... 0.0119082229"
## [966] "Optimizing the root position on the branch 964 ... 0.0091480617"
## [967] "Optimizing the root position on the branch 965 ... 0.0092352783"
## [968] "Optimizing the root position on the branch 966 ... 0.0114802755"
## [969] "Optimizing the root position on the branch 967 ... 0.0127714380"
## [970] "Optimizing the root position on the branch 968 ... 0.0131109261"
## [971] "Optimizing the root position on the branch 969 ... 0.0133235850"
## [972] "Optimizing the root position on the branch 970 ... 0.0133360096"
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## [974] "Optimizing the root position on the branch 972 ... 0.0092247899"
## [975] "Optimizing the root position on the branch 973 ... 0.0095518543"
## [976] "Optimizing the root position on the branch 974 ... 0.0103665163"
## [977] "Optimizing the root position on the branch 975 ... 0.0106064870"
## [978] "Optimizing the root position on the branch 976 ... 0.0107310071"
## [979] "Optimizing the root position on the branch 977 ... 0.0105668711"
## [980] "Optimizing the root position on the branch 978 ... 0.0095527307"
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## [986] "Optimizing the root position on the branch 984 ... 0.0129571021"
## [987] "Optimizing the root position on the branch 985 ... 0.0125145273"
## [988] "Optimizing the root position on the branch 986 ... 0.0118765946"
## [989] "Optimizing the root position on the branch 987 ... 0.0119208932"
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## [991] "Optimizing the root position on the branch 989 ... 0.0143237843"
## [992] "Optimizing the root position on the branch 990 ... 0.0142614703"
## [993] "Optimizing the root position on the branch 991 ... 0.0129577183"
## [994] "Optimizing the root position on the branch 992 ... 0.0129533386"
## [995] "Optimizing the root position on the branch 993 ... 0.0106899129"
## [996] "Optimizing the root position on the branch 994 ... 0.0114776537"
## [997] "Optimizing the root position on the branch 995 ... 0.0126884609"
## [998] "Optimizing the root position on the branch 996 ... 0.0130431647"
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## [1000] "Optimizing the root position on the branch 998 ... 0.0141050977"
## [1001] "Optimizing the root position on the branch 999 ... 0.0141105470"
## [1002] "Optimizing the root position on the branch 1000 ... 0.0138195140"
## [1003] "Optimizing the root position on the branch 1001 ... 0.0138237633"
## [1004] "Optimizing the root position on the branch 1002 ... 0.0109121895"
## [1005] "Optimizing the root position on the branch 1003 ... 0.0119753380"
## [1006] "Optimizing the root position on the branch 1004 ... 0.0122297921"
## [1007] "Optimizing the root position on the branch 1005 ... 0.0121944296"
## [1008] "Optimizing the root position on the branch 1006 ... 0.0118713033"
## [1009] "Optimizing the root position on the branch 1007 ... 0.0118862462"
## [1010] "Optimizing the root position on the branch 1008 ... 0.0142830811"
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## [1012] "Optimizing the root position on the branch 1010 ... 0.0126656385"
## [1013] "Optimizing the root position on the branch 1011 ... 0.0121812377"
## [1014] "Optimizing the root position on the branch 1012 ... 0.0121721970"
## [1015] "Optimizing the root position on the branch 1013 ... 0.0121128137"
## [1016] "Optimizing the root position on the branch 1014 ... 0.0121642008"
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## [1022] "Optimizing the root position on the branch 1020 ... 0.0131885697"
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## [1024] "Optimizing the root position on the branch 1022 ... 0.0128656530"
## [1025] "Optimizing the root position on the branch 1023 ... 0.0127335500"
## [1026] "Optimizing the root position on the branch 1024 ... 0.0096125950"
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## [1037] "Optimizing the root position on the branch 1035 ... 0.0114101053"
## [1038] "Optimizing the root position on the branch 1036 ... 0.0116944330"
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## [1100] "Optimizing the root position on the branch 1098 ... 0.0117744462"
## [1101] "Optimizing the root position on the branch 1099 ... 0.0135551251"
## [1102] "Optimizing the root position on the branch 1100 ... 0.0135516487"
## [1103] "Optimizing the root position on the branch 1101 ... 0.0130639700"
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## [1111] "Optimizing the root position on the branch 1109 ... 0.0132233038"
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## [1203] "Optimizing the root position on the branch 1201 ... 0.0118114322"
## [1204] "Optimizing the root position on the branch 1202 ... 0.0101751784"
## [1205] "Optimizing the root position on the branch 1203 ... 0.0123243214"
## [1206] "Optimizing the root position on the branch 1204 ... 0.0122043139"
## [1207] "Optimizing the root position on the branch 1205 ... 0.0152432225"
## [1208] "Optimizing the root position on the branch 1206 ... 0.0153533706"
## [1209] "Optimizing the root position on the branch 1207 ... 0.0098133257"
## [1210] "Optimizing the root position on the branch 1208 ... 0.0098122942"
## [1211] "Optimizing the root position on the branch 1209 ... 0.0092033997"
## [1212] "Optimizing the root position on the branch 1210 ... 0.0191530782"
## [1213] "Optimizing the root position on the branch 1211 ... 0.0203807728"
## [1214] "Optimizing the root position on the branch 1212 ... 0.0212776576"
## [1215] "Optimizing the root position on the branch 1213 ... 0.0212852160"
## [1216] "Optimizing the root position on the branch 1214 ... 0.0193738205"
## [1217] "Optimizing the root position on the branch 1215 ... 0.0195093090"
## [1218] "Optimizing the root position on the branch 1216 ... 0.0195519744"
## [1219] "Optimizing the root position on the branch 1217 ... 0.0195533619"
## [1220] "Optimizing the root position on the branch 1218 ... 0.0183906109"
## [1221] "Optimizing the root position on the branch 1219 ... 0.0183416563"
## [1222] "Optimizing the root position on the branch 1220 ... 0.0183258010"
## [1223] "Optimizing the root position on the branch 1221 ... 0.0182239240"
## [1224] "Optimizing the root position on the branch 1222 ... 0.0148376504"
## [1225] "Optimizing the root position on the branch 1223 ... 0.0147378439"
## [1226] "Optimizing the root position on the branch 1224 ... 0.0178088185"
## [1227] "Optimizing the root position on the branch 1225 ... 0.0178132797"
## [1228] "Optimizing the root position on the branch 1226 ... 0.0158091007"
## [1229] "Optimizing the root position on the branch 1227 ... 0.0157861741"
## [1230] "Optimizing the root position on the branch 1228 ... 0.0158602253"
## [1231] "Optimizing the root position on the branch 1229 ... 0.0158069632"
## [1232] "Optimizing the root position on the branch 1230 ... 0.0096528222"
## [1233] "Optimizing the root position on the branch 1231 ... 0.0136676103"
## [1234] "Optimizing the root position on the branch 1232 ... 0.0139891491"
## [1235] "Optimizing the root position on the branch 1233 ... 0.0137649674"
## [1236] "Optimizing the root position on the branch 1234 ... 0.0138134535"
## [1237] "Optimizing the root position on the branch 1235 ... 0.0124369064"
## [1238] "Optimizing the root position on the branch 1236 ... 0.0124410667"
## [1239] "Optimizing the root position on the branch 1237 ... 0.0124081322"
## [1240] "Optimizing the root position on the branch 1238 ... 0.0127434974"
## [1241] "Optimizing the root position on the branch 1239 ... 0.0129134567"
## [1242] "Optimizing the root position on the branch 1240 ... 0.0130778830"
## [1243] "Optimizing the root position on the branch 1241 ... 0.0131340776"
## [1244] "Optimizing the root position on the branch 1242 ... 0.0131503603"
## [1245] "Optimizing the root position on the branch 1243 ... 0.0131655885"
## [1246] "Optimizing the root position on the branch 1244 ... 0.0131680724"
## [1247] "Optimizing the root position on the branch 1245 ... 0.0129942419"
## [1248] "Optimizing the root position on the branch 1246 ... 0.0130115444"
## [1249] "Optimizing the root position on the branch 1247 ... 0.0130092326"
## [1250] "Optimizing the root position on the branch 1248 ... 0.0130838378"
## [1251] "Optimizing the root position on the branch 1249 ... 0.0130944811"
## [1252] "Optimizing the root position on the branch 1250 ... 0.0136422091"
## [1253] "Optimizing the root position on the branch 1251 ... 0.0136512042"
## [1254] "Optimizing the root position on the branch 1252 ... 0.0143242979"
## [1255] "Optimizing the root position on the branch 1253 ... 0.0146592947"
## [1256] "Optimizing the root position on the branch 1254 ... 0.0147873898"
## [1257] "Optimizing the root position on the branch 1255 ... 0.0147702326"
## [1258] "Optimizing the root position on the branch 1256 ... 0.0110210147"
## [1259] "Optimizing the root position on the branch 1257 ... 0.0135812986"
## [1260] "Optimizing the root position on the branch 1258 ... 0.0136417399"
## [1261] "Optimizing the root position on the branch 1259 ... 0.0136926911"
## [1262] "Optimizing the root position on the branch 1260 ... 0.0137234664"
## [1263] "Optimizing the root position on the branch 1261 ... 0.0137226357"
## [1264] "Optimizing the root position on the branch 1262 ... 0.0133391531"
## [1265] "Optimizing the root position on the branch 1263 ... 0.0135135549"
## [1266] "Optimizing the root position on the branch 1264 ... 0.0137930593"
## [1267] "Optimizing the root position on the branch 1265 ... 0.0137747306"
## [1268] "Optimizing the root position on the branch 1266 ... 0.0135422384"
## [1269] "Optimizing the root position on the branch 1267 ... 0.0097287075"
## [1270] "Optimizing the root position on the branch 1268 ... 0.0097283724"
## [1271] "Optimizing the root position on the branch 1269 ... 0.0151106024"
## [1272] "Optimizing the root position on the branch 1270 ... 0.0162339577"
## [1273] "Optimizing the root position on the branch 1271 ... 0.0162685632"
## [1274] "Optimizing the root position on the branch 1272 ... 0.0175377461"
## [1275] "Optimizing the root position on the branch 1273 ... 0.0175423690"
## [1276] "Optimizing the root position on the branch 1274 ... 0.0174135415"
## [1277] "Optimizing the root position on the branch 1275 ... 0.0174071597"
## [1278] "Optimizing the root position on the branch 1276 ... 0.0171186999"
## [1279] "Optimizing the root position on the branch 1277 ... 0.0096069325"
## [1280] "Optimizing the root position on the branch 1278 ... 0.0139029902"
## [1281] "Optimizing the root position on the branch 1279 ... 0.0138927217"
## [1282] "Optimizing the root position on the branch 1280 ... 0.0137810379"
## [1283] "Optimizing the root position on the branch 1281 ... 0.0138206130"
## [1284] "Optimizing the root position on the branch 1282 ... 0.0129174144"
## [1285] "Optimizing the root position on the branch 1283 ... 0.0129477826"
## [1286] "Optimizing the root position on the branch 1284 ... 0.0126989835"
## [1287] "Optimizing the root position on the branch 1285 ... 0.0129740576"
## [1288] "Optimizing the root position on the branch 1286 ... 0.0142835866"
## [1289] "Optimizing the root position on the branch 1287 ... 0.0143727587"
## [1290] "Optimizing the root position on the branch 1288 ... 0.0096895499"
## [1291] "Optimizing the root position on the branch 1289 ... 0.0102177971"
## [1292] "Optimizing the root position on the branch 1290 ... 0.0110716729"
## [1293] "Optimizing the root position on the branch 1291 ... 0.0116951774"
## [1294] "Optimizing the root position on the branch 1292 ... 0.0117801646"
## [1295] "Optimizing the root position on the branch 1293 ... 0.0115379064"
## [1296] "Optimizing the root position on the branch 1294 ... 0.0119979446"
## [1297] "Optimizing the root position on the branch 1295 ... 0.0119945961"
## [1298] "Optimizing the root position on the branch 1296 ... 0.0119273275"
## [1299] "Optimizing the root position on the branch 1297 ... 0.0119187309"
## [1300] "Optimizing the root position on the branch 1298 ... 0.0118823847"
## [1301] "Optimizing the root position on the branch 1299 ... 0.0119703913"
## [1302] "Optimizing the root position on the branch 1300 ... 0.0119725051"
## [1303] "Optimizing the root position on the branch 1301 ... 0.0119000816"
## [1304] "Optimizing the root position on the branch 1302 ... 0.0119428179"
## [1305] "Optimizing the root position on the branch 1303 ... 0.0119688582"
## [1306] "Optimizing the root position on the branch 1304 ... 0.0120917283"
## [1307] "Optimizing the root position on the branch 1305 ... 0.0120924628"
## [1308] "Optimizing the root position on the branch 1306 ... 0.0121249052"
## [1309] "Optimizing the root position on the branch 1307 ... 0.0121243598"
## [1310] "Optimizing the root position on the branch 1308 ... 0.0120757943"
## [1311] "Optimizing the root position on the branch 1309 ... 0.0125926761"
## [1312] "Optimizing the root position on the branch 1310 ... 0.0126533771"
## [1313] "Optimizing the root position on the branch 1311 ... 0.0127085321"
## [1314] "Optimizing the root position on the branch 1312 ... 0.0127198461"
## [1315] "Optimizing the root position on the branch 1313 ... 0.0127159140"
## [1316] "Optimizing the root position on the branch 1314 ... 0.0104375815"
## [1317] "Optimizing the root position on the branch 1315 ... 0.0121602397"
## [1318] "Optimizing the root position on the branch 1316 ... 0.0121674396"
## [1319] "Optimizing the root position on the branch 1317 ... 0.0119583808"
## [1320] "Optimizing the root position on the branch 1318 ... 0.0119882339"
## [1321] "Optimizing the root position on the branch 1319 ... 0.0119756756"
## [1322] "Optimizing the root position on the branch 1320 ... 0.0117489199"
## [1323] "Optimizing the root position on the branch 1321 ... 0.0118739714"
## [1324] "Optimizing the root position on the branch 1322 ... 0.0128982412"
## [1325] "Optimizing the root position on the branch 1323 ... 0.0133186358"
## [1326] "Optimizing the root position on the branch 1324 ... 0.0140110758"
## [1327] "Optimizing the root position on the branch 1325 ... 0.0140357323"
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## [1331] "Optimizing the root position on the branch 1329 ... 0.0111966513"
## [1332] "Optimizing the root position on the branch 1330 ... 0.0131435142"
## [1333] "Optimizing the root position on the branch 1331 ... 0.0135528593"
## [1334] "Optimizing the root position on the branch 1332 ... 0.0136556014"
## [1335] "Optimizing the root position on the branch 1333 ... 0.0136588710"
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## [1340] "Optimizing the root position on the branch 1338 ... 0.0136595425"
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## [1354] "Optimizing the root position on the branch 1352 ... 0.0115115561"
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## [1371] "Optimizing the root position on the branch 1369 ... 0.0125806062"
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## [1382] "Optimizing the root position on the branch 1380 ... 0.0099113857"
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## [1391] "Optimizing the root position on the branch 1389 ... 0.0113679000"
## [1392] "Optimizing the root position on the branch 1390 ... 0.0113779939"
## [1393] "Optimizing the root position on the branch 1391 ... 0.0105906538"
## [1394] "Optimizing the root position on the branch 1392 ... 0.0096877590"
## [1395] "Optimizing the root position on the branch 1393 ... 0.0095467971"
## [1396] "Optimizing the root position on the branch 1394 ... 0.0172008398"
## [1397] "Optimizing the root position on the branch 1395 ... 0.0173887976"
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## [1400] "Optimizing the root position on the branch 1398 ... 0.0174082624"
## [1401] "Optimizing the root position on the branch 1399 ... 0.0178434301"
## [1402] "Optimizing the root position on the branch 1400 ... 0.0178420343"
## [1403] "Optimizing the root position on the branch 1401 ... 0.0173622625"
## [1404] "Optimizing the root position on the branch 1402 ... 0.0094210631"
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## [1410] "Optimizing the root position on the branch 1408 ... 0.0095450029"
## [1411] "Optimizing the root position on the branch 1409 ... 0.0216123929"
## [1412] "Optimizing the root position on the branch 1410 ... 0.0217835458"
## [1413] "Optimizing the root position on the branch 1411 ... 0.0144586841"
## [1414] "Optimizing the root position on the branch 1412 ... 0.0146732360"
## [1415] "Optimizing the root position on the branch 1413 ... 0.0100222663"
## [1416] "Optimizing the root position on the branch 1414 ... 0.0107170775"
## [1417] "Optimizing the root position on the branch 1415 ... 0.0107039368"
## [1418] "Optimizing the root position on the branch 1416 ... 0.0154043789"
## [1419] "Optimizing the root position on the branch 1417 ... 0.0154364453"
## [1420] "Optimizing the root position on the branch 1418 ... 0.0146126443"
## [1421] "Optimizing the root position on the branch 1419 ... 0.0145506270"
## [1422] "Optimizing the root position on the branch 1420 ... 0.0097060876"
## [1423] "Optimizing the root position on the branch 1421 ... 0.0092622103"
## [1424] "Optimizing the root position on the branch 1422 ... 0.0118765634"
## [1425] "Optimizing the root position on the branch 1423 ... 0.0124770762"
## [1426] "Optimizing the root position on the branch 1424 ... 0.0124253776"
## [1427] "Optimizing the root position on the branch 1425 ... 0.0123711705"
## [1428] "Optimizing the root position on the branch 1426 ... 0.0120675655"
## [1429] "Optimizing the root position on the branch 1427 ... 0.0116168354"
## [1430] "Optimizing the root position on the branch 1428 ... 0.0116780559"
## [1431] "Optimizing the root position on the branch 1429 ... 0.0102756871"
## [1432] "Optimizing the root position on the branch 1430 ... 0.0111262298"
## [1433] "Optimizing the root position on the branch 1431 ... 0.0113001332"
## [1434] "Optimizing the root position on the branch 1432 ... 0.0113469297"
## [1435] "Optimizing the root position on the branch 1433 ... 0.0119112625"
## [1436] "Optimizing the root position on the branch 1434 ... 0.0119300622"
## [1437] "Optimizing the root position on the branch 1435 ... 0.0118102259"
## [1438] "Optimizing the root position on the branch 1436 ... 0.0124841161"
## [1439] "Optimizing the root position on the branch 1437 ... 0.0124995946"
## [1440] "Optimizing the root position on the branch 1438 ... 0.0119713792"
## [1441] "Optimizing the root position on the branch 1439 ... 0.0121350750"
## [1442] "Optimizing the root position on the branch 1440 ... 0.0121682524"
## [1443] "Optimizing the root position on the branch 1441 ... 0.0121673129"
## [1444] "Optimizing the root position on the branch 1442 ... 0.0121650505"
## [1445] "Optimizing the root position on the branch 1443 ... 0.0121587983"
## [1446] "Optimizing the root position on the branch 1444 ... 0.0133038304"
## [1447] "Optimizing the root position on the branch 1445 ... 0.0139760805"
## [1448] "Optimizing the root position on the branch 1446 ... 0.0142890185"
## [1449] "Optimizing the root position on the branch 1447 ... 0.0142816764"
## [1450] "Optimizing the root position on the branch 1448 ... 0.0099749850"
## [1451] "Optimizing the root position on the branch 1449 ... 0.0154577118"
## [1452] "Optimizing the root position on the branch 1450 ... 0.0149754566"
## [1453] "Optimizing the root position on the branch 1451 ... 0.0123906659"
## [1454] "Optimizing the root position on the branch 1452 ... 0.0122001342"
## [1455] "Optimizing the root position on the branch 1453 ... 0.0132345664"
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## [1460] "Optimizing the root position on the branch 1458 ... 0.0142650088"
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## [1470] "Optimizing the root position on the branch 1468 ... 0.0123936496"
## [1471] "Optimizing the root position on the branch 1469 ... 0.0123884091"
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## [1480] "Optimizing the root position on the branch 1478 ... 0.0133201222"
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## [1500] "Optimizing the root position on the branch 1498 ... 0.0131325774"
## [1501] "Optimizing the root position on the branch 1499 ... 0.0131104837"
## [1502] "Optimizing the root position on the branch 1500 ... 0.0184745659"
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## [1504] "Optimizing the root position on the branch 1502 ... 0.0097705569"
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## [1511] "Optimizing the root position on the branch 1509 ... 0.0140311541"
## [1512] "Optimizing the root position on the branch 1510 ... 0.0140360733"
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## [1514] "Optimizing the root position on the branch 1512 ... 0.0138874791"
## [1515] "Optimizing the root position on the branch 1513 ... 0.0139276957"
## [1516] "Optimizing the root position on the branch 1514 ... 0.0142559364"
## [1517] "Optimizing the root position on the branch 1515 ... 0.0142554720"
## [1518] "Optimizing the root position on the branch 1516 ... 0.0160634221"
## [1519] "Optimizing the root position on the branch 1517 ... 0.0168651661"
## [1520] "Optimizing the root position on the branch 1518 ... 0.0172724006"
## [1521] "Optimizing the root position on the branch 1519 ... 0.0174086941"
## [1522] "Optimizing the root position on the branch 1520 ... 0.0173906294"
## [1523] "Optimizing the root position on the branch 1521 ... 0.0120821846"
## [1524] "Optimizing the root position on the branch 1522 ... 0.0120160810"
## [1525] "Optimizing the root position on the branch 1523 ... 0.0101310338"
## [1526] "Optimizing the root position on the branch 1524 ... 0.0101805296"
## [1527] "Optimizing the root position on the branch 1525 ... 0.0153393928"
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## [1534] "Optimizing the root position on the branch 1532 ... 0.0091713091"
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## [1570] "Optimizing the root position on the branch 1568 ... 0.0115764498"
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## [1800] "Optimizing the root position on the branch 1798 ... 0.0140581926"
## [1801] "Optimizing the root position on the branch 1799 ... 0.0103061608"
## [1802] "Optimizing the root position on the branch 1800 ... 0.0101060656"
## [1803] "Optimizing the root position on the branch 1801 ... 0.0136804505"
## [1804] "Optimizing the root position on the branch 1802 ... 0.0135903028"
## [1805] "Optimizing the root position on the branch 1803 ... 0.0106093112"
## [1806] "Optimizing the root position on the branch 1804 ... 0.0107837253"
## [1807] "Optimizing the root position on the branch 1805 ... 0.0108191653"
## [1808] "Optimizing the root position on the branch 1806 ... 0.0106901956"
## [1809] "Optimizing the root position on the branch 1807 ... 0.0105309310"
## [1810] "Optimizing the root position on the branch 1808 ... 0.0107612781"
## [1811] "Optimizing the root position on the branch 1809 ... 0.0109865472"
## [1812] "Optimizing the root position on the branch 1810 ... 0.0112932701"
## [1813] "Optimizing the root position on the branch 1811 ... 0.0115353471"
## [1814] "Optimizing the root position on the branch 1812 ... 0.0115866622"
## [1815] "Optimizing the root position on the branch 1813 ... 0.0116053401"
## [1816] "Optimizing the root position on the branch 1814 ... 0.0116085177"
## [1817] "Optimizing the root position on the branch 1815 ... 0.0116941185"
## [1818] "Optimizing the root position on the branch 1816 ... 0.0117032825"
## [1819] "Optimizing the root position on the branch 1817 ... 0.0124528386"
## [1820] "Optimizing the root position on the branch 1818 ... 0.0125471353"
## [1821] "Optimizing the root position on the branch 1819 ... 0.0115452718"
## [1822] "Optimizing the root position on the branch 1820 ... 0.0116740241"
## [1823] "Optimizing the root position on the branch 1821 ... 0.0119563829"
## [1824] "Optimizing the root position on the branch 1822 ... 0.0125201818"
## [1825] "Optimizing the root position on the branch 1823 ... 0.0125214138"
## [1826] "Optimizing the root position on the branch 1824 ... 0.0119684398"
## [1827] "Optimizing the root position on the branch 1825 ... 0.0118908783"
## [1828] "Optimizing the root position on the branch 1826 ... 0.0120151489"
## [1829] "Optimizing the root position on the branch 1827 ... 0.0120285061"
## [1830] "Optimizing the root position on the branch 1828 ... 0.0105278552"
## [1831] "Optimizing the root position on the branch 1829 ... 0.0129587811"
## [1832] "Optimizing the root position on the branch 1830 ... 0.0129452775"
## [1833] "Optimizing the root position on the branch 1831 ... 0.0122746558"
## [1834] "Optimizing the root position on the branch 1832 ... 0.0117985904"
## [1835] "Optimizing the root position on the branch 1833 ... 0.0132077082"
## [1836] "Optimizing the root position on the branch 1834 ... 0.0134719082"
## [1837] "Optimizing the root position on the branch 1835 ... 0.0134950858"
## [1838] "Optimizing the root position on the branch 1836 ... 0.0140573108"
## [1839] "Optimizing the root position on the branch 1837 ... 0.0140589611"
## [1840] "Optimizing the root position on the branch 1838 ... 0.0168456335"
## [1841] "Optimizing the root position on the branch 1839 ... 0.0166872110"
## [1842] "Optimizing the root position on the branch 1840 ... 0.0094634079"
## [1843] "Optimizing the root position on the branch 1841 ... 0.0171638698"
## [1844] "Optimizing the root position on the branch 1842 ... 0.0171262883"
## [1845] "Optimizing the root position on the branch 1843 ... 0.0157822156"
## [1846] "Optimizing the root position on the branch 1844 ... 0.0100677537"
## [1847] "Optimizing the root position on the branch 1845 ... 0.0104267120"
## [1848] "Optimizing the root position on the branch 1846 ... 0.0104208046"
## [1849] "Optimizing the root position on the branch 1847 ... 0.0139324394"
## [1850] "Optimizing the root position on the branch 1848 ... 0.0138876081"
## [1851] "Optimizing the root position on the branch 1849 ... 0.0115421552"
## [1852] "Optimizing the root position on the branch 1850 ... 0.0140690619"
## [1853] "Optimizing the root position on the branch 1851 ... 0.0140728628"
## [1854] "Optimizing the root position on the branch 1852 ... 0.0130864383"
## [1855] "Optimizing the root position on the branch 1853 ... 0.0130721248"
## [1856] "Optimizing the root position on the branch 1854 ... 0.0130076069"
## [1857] "Optimizing the root position on the branch 1855 ... 0.0127542904"
## [1858] "Optimizing the root position on the branch 1856 ... 0.0101853242"
## [1859] "Optimizing the root position on the branch 1857 ... 0.0120288675"
## [1860] "Optimizing the root position on the branch 1858 ... 0.0120631174"
## [1861] "Optimizing the root position on the branch 1859 ... 0.0121089512"
## [1862] "Optimizing the root position on the branch 1860 ... 0.0121632553"
## [1863] "Optimizing the root position on the branch 1861 ... 0.0109302395"
## [1864] "Optimizing the root position on the branch 1862 ... 0.0114745181"
## [1865] "Optimizing the root position on the branch 1863 ... 0.0114768729"
## [1866] "Optimizing the root position on the branch 1864 ... 0.0112787236"
## [1867] "Optimizing the root position on the branch 1865 ... 0.0110838546"
## [1868] "Optimizing the root position on the branch 1866 ... 0.0110884815"
## [1869] "Optimizing the root position on the branch 1867 ... 0.0110962914"
## [1870] "Optimizing the root position on the branch 1868 ... 0.0110966356"
## [1871] "Optimizing the root position on the branch 1869 ... 0.0110958602"
## [1872] "Optimizing the root position on the branch 1870 ... 0.0125313940"
## [1873] "Optimizing the root position on the branch 1871 ... 0.0125004372"
## [1874] "Optimizing the root position on the branch 1872 ... 0.0142229358"
## [1875] "Optimizing the root position on the branch 1873 ... 0.0141641268"
## [1876] "Optimizing the root position on the branch 1874 ... 0.0154987712"
## [1877] "Optimizing the root position on the branch 1875 ... 0.0156269461"
## [1878] "Optimizing the root position on the branch 1876 ... 0.0139328206"
## [1879] "Optimizing the root position on the branch 1877 ... 0.0149954242"
## [1880] "Optimizing the root position on the branch 1878 ... 0.0158361716"
## [1881] "Optimizing the root position on the branch 1879 ... 0.0158183300"
## [1882] "Optimizing the root position on the branch 1880 ... 0.0128794680"
## [1883] "Optimizing the root position on the branch 1881 ... 0.0128864365"
## [1884] "Optimizing the root position on the branch 1882 ... 0.0128397462"
## [1885] "Optimizing the root position on the branch 1883 ... 0.0128565055"
## [1886] "Optimizing the root position on the branch 1884 ... 0.0109358949"
## [1887] "Optimizing the root position on the branch 1885 ... 0.0119389114"
## [1888] "Optimizing the root position on the branch 1886 ... 0.0118939249"
## [1889] "Optimizing the root position on the branch 1887 ... 0.0141459392"
## [1890] "Optimizing the root position on the branch 1888 ... 0.0154828416"
## [1891] "Optimizing the root position on the branch 1889 ... 0.0154744330"
## [1892] "Optimizing the root position on the branch 1890 ... 0.0154476857"
## [1893] "Optimizing the root position on the branch 1891 ... 0.0156066355"
## [1894] "Optimizing the root position on the branch 1892 ... 0.0155944385"
## [1895] "Optimizing the root position on the branch 1893 ... 0.0160251629"
## [1896] "Optimizing the root position on the branch 1894 ... 0.0160260959"
## [1897] "Optimizing the root position on the branch 1895 ... 0.0108353957"
## [1898] "Optimizing the root position on the branch 1896 ... 0.0122936882"
## [1899] "Optimizing the root position on the branch 1897 ... 0.0123116107"
## [1900] "Optimizing the root position on the branch 1898 ... 0.0121303048"
## [1901] "Optimizing the root position on the branch 1899 ... 0.0123251390"
## [1902] "Optimizing the root position on the branch 1900 ... 0.0123227125"
## [1903] "Optimizing the root position on the branch 1901 ... 0.0121471673"
## [1904] "Optimizing the root position on the branch 1902 ... 0.0121130884"
## [1905] "Optimizing the root position on the branch 1903 ... 0.0121207065"
## [1906] "Optimizing the root position on the branch 1904 ... 0.0121659744"
## [1907] "Optimizing the root position on the branch 1905 ... 0.0121620775"
## [1908] "Optimizing the root position on the branch 1906 ... 0.0103861710"
## [1909] "Optimizing the root position on the branch 1907 ... 0.0115292121"
## [1910] "Optimizing the root position on the branch 1908 ... 0.0121001995"
## [1911] "Optimizing the root position on the branch 1909 ... 0.0128221472"
## [1912] "Optimizing the root position on the branch 1910 ... 0.0128190014"
## [1913] "Optimizing the root position on the branch 1911 ... 0.0131968065"
## [1914] "Optimizing the root position on the branch 1912 ... 0.0131364452"
## [1915] "Optimizing the root position on the branch 1913 ... 0.0114774844"
## [1916] "Optimizing the root position on the branch 1914 ... 0.0115053275"
## [1917] "Optimizing the root position on the branch 1915 ... 0.0114251340"
## [1918] "Optimizing the root position on the branch 1916 ... 0.0114159170"
## [1919] "Optimizing the root position on the branch 1917 ... 0.0111086158"
## [1920] "Optimizing the root position on the branch 1918 ... 0.0110862968"
## [1921] "Optimizing the root position on the branch 1919 ... 0.0112686686"
## [1922] "Optimizing the root position on the branch 1920 ... 0.0111990693"
## [1923] "Optimizing the root position on the branch 1921 ... 0.0112926700"
## [1924] "Optimizing the root position on the branch 1922 ... 0.0112559382"
## [1925] "Optimizing the root position on the branch 1923 ... 0.0106364469"
## [1926] "Optimizing the root position on the branch 1924 ... 0.0206062620"
## [1927] "Optimizing the root position on the branch 1925 ... 0.0205367424"
## [1928] "Optimizing the root position on the branch 1926 ... 0.0110600909"
## [1929] "Optimizing the root position on the branch 1927 ... 0.0110539802"
## [1930] "Optimizing the root position on the branch 1928 ... 0.0143289086"
## [1931] "Optimizing the root position on the branch 1929 ... 0.0146846033"
## [1932] "Optimizing the root position on the branch 1930 ... 0.0147782941"
## [1933] "Optimizing the root position on the branch 1931 ... 0.0147905277"
## [1934] "Optimizing the root position on the branch 1932 ... 0.0153595583"
## [1935] "Optimizing the root position on the branch 1933 ... 0.0153552044"
## [1936] "Optimizing the root position on the branch 1934 ... 0.0139998171"
## [1937] "Optimizing the root position on the branch 1935 ... 0.0139771290"
## [1938] "Optimizing the root position on the branch 1936 ... 0.0138723029"
## [1939] "Optimizing the root position on the branch 1937 ... 0.0091662313"
## [1940] "Optimizing the root position on the branch 1938 ... 0.0118463041"
## [1941] "Optimizing the root position on the branch 1939 ... 0.0118505316"
## [1942] "Optimizing the root position on the branch 1940 ... 0.0131747372"
## [1943] "Optimizing the root position on the branch 1941 ... 0.0134460199"
## [1944] "Optimizing the root position on the branch 1942 ... 0.0134567288"
## [1945] "Optimizing the root position on the branch 1943 ... 0.0134603628"
## [1946] "Optimizing the root position on the branch 1944 ... 0.0134597342"
## [1947] "Optimizing the root position on the branch 1945 ... 0.0133406522"
## [1948] "Optimizing the root position on the branch 1946 ... 0.0118196659"
## [1949] "Optimizing the root position on the branch 1947 ... 0.0160964338"
## [1950] "Optimizing the root position on the branch 1948 ... 0.0161824150"
## [1951] "Optimizing the root position on the branch 1949 ... 0.0101233429"
## [1952] "Optimizing the root position on the branch 1950 ... 0.0102799972"
## [1953] "Optimizing the root position on the branch 1951 ... 0.0108135739"
## [1954] "Optimizing the root position on the branch 1952 ... 0.0108848151"
## [1955] "Optimizing the root position on the branch 1953 ... 0.0121296600"
## [1956] "Optimizing the root position on the branch 1954 ... 0.0124074431"
## [1957] "Optimizing the root position on the branch 1955 ... 0.0130925876"
## [1958] "Optimizing the root position on the branch 1956 ... 0.0131060346"
## [1959] "Optimizing the root position on the branch 1957 ... 0.0126627981"
## [1960] "Optimizing the root position on the branch 1958 ... 0.0126577653"
## [1961] "Optimizing the root position on the branch 1959 ... 0.0178627321"
## [1962] "Optimizing the root position on the branch 1960 ... 0.0187977431"
## [1963] "Optimizing the root position on the branch 1961 ... 0.0187986677"
## [1964] "Optimizing the root position on the branch 1962 ... 0.0154289322"
## [1965] "Optimizing the root position on the branch 1963 ... 0.0154413534"
## [1966] "Optimizing the root position on the branch 1964 ... 0.0097891039"
## [1967] "Optimizing the root position on the branch 1965 ... 0.0199917068"
## [1968] "The pre-estimated root is on the branch 759, the branches are re-enumerated"
## [1969] "Improving the root position with constraints around the pre-estimated root ..."
## [1970] "Optimizing the root position on the original branch 521 ... 0.0093212696"
## [1971] "Optimizing the root position on the branch 1210 ... 0.0098405988"
## [1972] "Optimizing the root position on the branch 761 ... 0.0098405988"
## [1973] "Optimizing the root position on the branch 522 ... 0.0093032799"
## [1974] "Optimizing the root position on the branch 719 ... 0.0093000863"
## [1975] "Optimizing the root position on the branch 757 ... 0.0093060315"
## [1976] "Optimizing the root position on the branch 720 ... 0.0093059911"
## [1977] "Optimizing the root position on the branch 523 ... 0.0092910713"
## [1978] "Optimizing the root position on the branch 569 ... 0.0093173899"
## [1979] "Optimizing the root position on the branch 524 ... 0.0093173899"
## [1980] "Optimizing the root position on the branch 520 ... 0.0093212000"
## [1981] "Optimizing the root position on the branch 819 ... 0.0093212313"
## [1982] "Optimizing the root position on the branch 31 ... 0.0093186229"
## [1983] "Optimizing the root position on the branch 32 ... 0.0093302392"
## [1984] "Optimizing the root position on the branch 30 ... 0.0093302392"
## [1985] "The tree is rooted on the branch 523"
## [1986] "Starting QPD on the new rooted tree ..."
## [1987] "rate\t0.00249613\ttMRCA\t-0.379016\tobjective_function\t0.389403"
## [1988] "Elapsed time: 6.85474 seconds"
The following R code extracts the evolutionary rate.
procresult <- function(fn){
result <- readLines(fn)
line <- result[grep("Tree 1 rate ",result)]
line.split <- strsplit(line, " ")[[1]]
list(rate=as.double(line.split[4]),tmrca=as.double(line.split[6]))
}
procresult(paste(stub,"_result.txt",sep=""))
## $rate
## [1] 0.002496
##
## $tmrca
## [1] -0.379016
We can compare this with our result from rtt.
rate
## tr.rtt.tipdates
## 0.002587992
tmrca
## [1] 0.732083
The time tree is saved with "_result_newick_date.txt" added at the end, as a Newick string.
lsd.tree <- read.tree(paste(stub,"_result_newick_date.txt",sep=""))
How close is the tree to the true tree? We can compare the patristic distances between tips using cophenetic.
true.tree <- read.tree("village_true.tre")
treedist(chronos.tree,true.tree)
## symmetric.difference branch.score.difference
## 96.0000 211.7161
## path.difference quadratic.path.difference
## 877.5665 5623.4920
treedist(lsd.tree,true.tree)
## symmetric.difference branch.score.difference
## 96.00000 28.65891
## path.difference quadratic.path.difference
## 877.56652 1255.70485
Compare pairwise distances.
true.tree.d <- cophenetic.phylo(true.tree)
true.tree.ltri <- true.tree.d[lower.tri(true.tree.d)]
lsd.tree.d <- cophenetic.phylo(lsd.tree)
chronos.tree.d <- cophenetic.phylo(chronos.tree)
ids <- row.names(true.tree.d)
idx <- match(ids,row.names(lsd.tree.d))
lsd.tree.d2 <- lsd.tree.d[idx,idx]
lsd.tree.d2.ltri <- lsd.tree.d2[lower.tri(lsd.tree.d2)]
idx <- match(ids,row.names(chronos.tree.d))
chronos.tree.d2 <- chronos.tree.d[idx,idx]
chronos.tree.d2.ltri <- chronos.tree.d2[lower.tri(chronos.tree.d2)]
The LSD tree gives a very good correlation between the tip-to-tip distances.
summary(lm(lsd.tree.d2.ltri~true.tree.ltri))
##
## Call:
## lm(formula = lsd.tree.d2.ltri ~ true.tree.ltri)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3266 -0.6171 -0.1560 1.2715 5.3937
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6949265 0.0148551 46.78 <2e-16 ***
## true.tree.ltri 1.0085462 0.0001893 5326.69 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.184 on 483634 degrees of freedom
## Multiple R-squared: 0.9832, Adjusted R-squared: 0.9832
## F-statistic: 2.837e+07 on 1 and 483634 DF, p-value: < 2.2e-16
plot(lsd.tree.d2.ltri~true.tree.ltri,xlab="True distance (years)",ylab="Inferred distance (years)",main="LSD")
The chronos tree captures the overall rate, but the association is lower.
summary(lm(chronos.tree.d2.ltri~true.tree.ltri))
##
## Call:
## lm(formula = chronos.tree.d2.ltri ~ true.tree.ltri)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.792 -1.510 0.886 3.125 35.868
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.849e+01 7.369e-02 658.0 <2e-16 ***
## true.tree.ltri 3.858e-01 9.393e-04 410.7 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.874 on 483634 degrees of freedom
## Multiple R-squared: 0.2586, Adjusted R-squared: 0.2586
## F-statistic: 1.687e+05 on 1 and 483634 DF, p-value: < 2.2e-16
plot(chronos.tree.d2.ltri~true.tree.ltri,xlab="True distance (years)",ylab="Inferred distance (years)",main="chronos")
