Thursday, February 9, 2017

More user control of optimization in ratebytree

I just made some updates to the new phytools function ratebytree which compares the rate of continuous character evolution between two or more trees (e.g., 1, 2). The method is essentially the same as the censored approach of O'Meara et al. (2006).

The updates consist of adding the two option arguments: init & trace.

init, the initial conditions of the optimization, needs to be supplied as a list with elements corresponding to the different parameters of the common- and multi-rate models. The names for these elements should be sigc & ac, for the rate & ancestral states for the common-rate model; and sigm & sigm for the initial values of the multi-rate model.

The argument trace is a logical value that tells the function to trace the progress of the optimization.

So, for instance:

library(phytools)
packageVersion("phytools")
## [1] '0.5.73'
t1
## 
## Phylogenetic tree with 26 tips and 25 internal nodes.
## 
## Tip labels:
##  A, B, C, D, E, F, ...
## 
## Rooted; includes branch lengths.
x
##          A          B          C          D          E          F 
## -0.1397195 -0.1996443 -0.5827639 -0.3396014 -1.9785818 -2.2452530 
##          G          H          I          J          K          L 
##  1.5195967  1.6068486  0.5919871  1.6156654  1.2425888 -0.5789243 
##          M          N          O          P          Q          R 
## -1.1352832 -0.5962740  0.8352019  1.1925811  0.1434599 -0.1649340 
##          S          T          U          V          W          X 
## -0.2620791 -0.8017158 -0.8558019 -1.2876484  1.1789504 -0.4589235 
##          Y          Z 
##  0.7054512  0.4988762
t2
## 
## Phylogenetic tree with 40 tips and 39 internal nodes.
## 
## Tip labels:
##  t4, t8, t9, t1, t25, t26, ...
## 
## Rooted; includes branch lengths.
y
##          t4          t8          t9          t1         t25         t26 
## -0.50044880 -0.33976877 -0.22155547 -1.66246432  0.29014161  0.50776830 
##         t27         t28         t11         t19         t20          t5 
##  0.12476121  0.29866183  1.84948814 -0.63734157  0.70780071 -2.29781879 
##         t13         t14         t12         t33         t34         t22 
##  2.54743880  3.51220356  2.56567363  2.06829938  1.85838926  0.82279334 
##         t39         t40          t2          t3         t31         t32 
##  0.22717955  0.20327362  1.87257199  2.97804036  4.62874247  5.10710664 
##         t35         t36          t7         t23         t24          t6 
##  5.36174612  5.16948164 -0.21639416 -1.44359129  0.05346218 -0.93556170 
##         t37         t38         t17         t18         t10         t15 
## -0.02599676 -0.29860201 -0.35398678 -1.42592744 -0.50920027  3.03128846 
##         t16         t21         t29         t30 
##  2.65445859 -0.41292712 -0.69210806 -0.78368040
t3
## 
## Phylogenetic tree with 20 tips and 19 internal nodes.
## 
## Tip labels:
##  1, 2, 3, 4, 5, 6, ...
## 
## Rooted; includes branch lengths.
z
##           1           2           3           4           5           6 
## -0.01050003 -0.48649665 -0.34190675  0.37566749  1.75862664  1.58447168 
##           7           8           9          10          11          12 
##  1.67743120  0.28316167  0.22031546  1.07939448 -0.69795686  1.63538094 
##          13          14          15          16          17          18 
## -0.01273937  0.48345033  1.44212231 -0.09246575  0.05411407  1.53395177 
##          19          20 
##  1.85086405  4.48540981
fit1<-ratebytree(c(t1,t2,t3),list(x,y,z),trace=TRUE,digits=7)
## 
## Optimizing multi-rate model....
## sig[1]       sig[2]      sig[3]      logL
## 0.5988996    1.5493864   1.0621323   -109.4408658    
## 0.5998996    1.5493864   1.0621323   -109.4417174    
## 0.5978996    1.5493864   1.0621323   -109.4400477    
## 0.5988996    1.5503864   1.0621323   -109.4411925    
## 0.5988996    1.5483864   1.0621323   -109.4405471    
## 0.5988996    1.5493864   1.0631323   -109.4413405    
## 0.5988996    1.5493864   1.0611323   -109.440399 
## 0.5988996    1.5493864   1.0621323   -109.4408677    
## 0.5988996    1.5493864   1.0621323   -109.4408677    
## 0.5988996    1.5493864   1.0621323   -109.4408661    
## 0.5988996    1.5493864   1.0621323   -109.4408661    
## 0.5988996    1.5493864   1.0621323   -109.4408666    
## 0.5988996    1.5493864   1.0621323   -109.4408666    
## 0    1.2266815   0.5913863   -748624418.916421   
## 0.001    1.2266815   0.5913863   -7502.1407998   
## 0    1.2266815   0.5913863   -748624418.916421   
## 0    1.2276815   0.5913863   -748624418.912656   
## 0    1.2256815   0.5913863   -748624418.920205   
## 0    1.2266815   0.5923863   -748624418.904514   
## 0    1.2266815   0.5903863   -748624418.928397   
## 0    1.2266815   0.5913863   -748624530.012055   
## 0    1.2266815   0.5913863   -748624530.012055   
## 0    1.2266815   0.5913863   -748624418.916421   
## 0    1.2266815   0.5913863   -748624418.916421   
## 0    1.2266815   0.5913863   -748624418.916422   
## 0    1.2266815   0.5913863   -748624418.916422   
## 0.3996009    1.4419983   0.9054799   -110.4784866    
## 0.4006009    1.4419983   0.9054799   -110.4642129    
## 0.3986009    1.4419983   0.9054799   -110.4929135    
## 0.3996009    1.4429983   0.9054799   -110.4778315    
## 0.3996009    1.4409983   0.9054799   -110.4791522    
## 0.3996009    1.4419983   0.9064799   -110.4772312    
## 0.3996009    1.4419983   0.9044799   -110.479757 
## 0.3996009    1.4419983   0.9054799   -110.4784894    
## 0.3996009    1.4419983   0.9054799   -110.4784894    
## 0.3996009    1.4419983   0.9054799   -110.4784869    
## 0.3996009    1.4419983   0.9054799   -110.4784869    
## 0.3996009    1.4419983   0.9054799   -110.4784875    
## 0.3996009    1.4419983   0.9054799   -110.4784875    
## 0.5701688    1.5339054   1.0395494   -109.4190706    
## 0.5711688    1.5339054   1.0395494   -109.4188632    
## 0.5691688    1.5339054   1.0395494   -109.4193188    
## 0.5701688    1.5349054   1.0395494   -109.4192724    
## 0.5701688    1.5329054   1.0395494   -109.4188771    
## 0.5701688    1.5339054   1.0405494   -109.4193574    
## 0.5701688    1.5339054   1.0385494   -109.4187925    
## 0.5701688    1.5339054   1.0395494   -109.4190726    
## 0.5701688    1.5339054   1.0395494   -109.4190726    
## 0.5701688    1.5339054   1.0395494   -109.4190709    
## 0.5701688    1.5339054   1.0395494   -109.4190709    
## 0.5701688    1.5339054   1.0395494   -109.4190714    
## 0.5701688    1.5339054   1.0395494   -109.4190714    
## 0.571337 1.5234701   1.0245243   -109.4139814    
## 0.572337 1.5234701   1.0245243   -109.4138212    
## 0.570337 1.5234701   1.0245243   -109.414182 
## 0.571337 1.5244701   1.0245243   -109.4140961    
## 0.571337 1.5224701   1.0245243   -109.4138752    
## 0.571337 1.5234701   1.0255243   -109.4141336    
## 0.571337 1.5234701   1.0235243   -109.4138383    
## 0.571337 1.5234701   1.0245243   -109.4139833    
## 0.571337 1.5234701   1.0245243   -109.4139833    
## 0.571337 1.5234701   1.0245243   -109.4139816    
## 0.571337 1.5234701   1.0245243   -109.4139816    
## 0.571337 1.5234701   1.0245243   -109.4139822    
## 0.571337 1.5234701   1.0245243   -109.4139822    
## 0.5761806    1.5104399   1.0080879   -109.4117139    
## 0.5771806    1.5104399   1.0080879   -109.4117458    
## 0.5751806    1.5104399   1.0080879   -109.4117211    
## 0.5761806    1.5114399   1.0080879   -109.4117164    
## 0.5761806    1.5094399   1.0080879   -109.4117201    
## 0.5761806    1.5104399   1.0090879   -109.4117096    
## 0.5761806    1.5104399   1.0070879   -109.4117281    
## 0.5761806    1.5104399   1.0080879   -109.4117158    
## 0.5761806    1.5104399   1.0080879   -109.4117158    
## 0.5761806    1.5104399   1.0080879   -109.4117142    
## 0.5761806    1.5104399   1.0080879   -109.4117142    
## 0.5761806    1.5104399   1.0080879   -109.4117147    
## 0.5761806    1.5104399   1.0080879   -109.4117147    
## 0.5758686    1.5107979   1.0089505   -109.4117076    
## 0.5768686    1.5107979   1.0089505   -109.4117272    
## 0.5748686    1.5107979   1.0089505   -109.4117271    
## 0.5758686    1.5117979   1.0089505   -109.4117132    
## 0.5758686    1.5097979   1.0089505   -109.4117107    
## 0.5758686    1.5107979   1.0099505   -109.4117117    
## 0.5758686    1.5107979   1.0079505   -109.4117132    
## 0.5758686    1.5107979   1.0089505   -109.4117095    
## 0.5758686    1.5107979   1.0089505   -109.4117095    
## 0.5758686    1.5107979   1.0089505   -109.4117078    
## 0.5758686    1.5107979   1.0089505   -109.4117078    
## 0.5758686    1.5107979   1.0089505   -109.4117083    
## 0.5758686    1.5107979   1.0089505   -109.4117083    
## 0.5758622    1.5107246   1.0089937   -109.4117075    
## 0.5768622    1.5107246   1.0089937   -109.4117269    
## 0.5748622    1.5107246   1.0089937   -109.4117272    
## 0.5758622    1.5117246   1.0089937   -109.4117125    
## 0.5758622    1.5097246   1.0089937   -109.4117112    
## 0.5758622    1.5107246   1.0099937   -109.411712 
## 0.5758622    1.5107246   1.0079937   -109.4117127    
## 0.5758622    1.5107246   1.0089937   -109.4117094    
## 0.5758622    1.5107246   1.0089937   -109.4117094    
## 0.5758622    1.5107246   1.0089937   -109.4117077    
## 0.5758622    1.5107246   1.0089937   -109.4117077    
## 0.5758622    1.5107246   1.0089937   -109.4117083    
## 0.5758622    1.5107246   1.0089937   -109.4117083    
## 
## Optimizing common-rate model....
## sig          logL
## 1.0318602    -112.90808  
## 1.0328602    -112.9048916    
## 1.0308602    -112.9113149    
## 1.0318602    -112.908081 
## 1.0318602    -112.908081 
## 1.0318602    -112.9080803    
## 1.0318602    -112.9080803    
## 1.0318602    -112.9080807    
## 1.0318602    -112.9080807    
## 2.0318602    -119.2505125    
## 2.0328602    -119.2601002    
## 2.0308602    -119.2409257    
## 2.0318602    -119.250513 
## 2.0318602    -119.250513 
## 2.0318602    -119.2505127    
## 2.0318602    -119.2505127    
## 2.0318602    -119.2505129    
## 2.0318602    -119.2505129    
## 1.1400755    -112.800431 
## 1.1410755    -112.8013959    
## 1.1390755    -112.7994976    
## 1.1400755    -112.800432 
## 1.1400755    -112.800432 
## 1.1400755    -112.8004314    
## 1.1400755    -112.8004314    
## 1.1400755    -112.8004317    
## 1.1400755    -112.8004317    
## 1.1153898    -112.7868598    
## 1.1163898    -112.7870153    
## 1.1143898    -112.7867385    
## 1.1153898    -112.7868608    
## 1.1153898    -112.7868608    
## 1.1153898    -112.7868601    
## 1.1153898    -112.7868601    
## 1.1153898    -112.7868605    
## 1.1153898    -112.7868605    
## 1.1111754    -112.7865826    
## 1.1121754    -112.7865928    
## 1.1101754    -112.7866074    
## 1.1111754    -112.7865836    
## 1.1111754    -112.7865836    
## 1.1111754    -112.786583 
## 1.1111754    -112.786583 
## 1.1111754    -112.7865834    
## 1.1111754    -112.7865834    
## 1.1113867    -112.7865819    
## 1.1123867    -112.7865993    
## 1.1103867    -112.7865992    
## 1.1113867    -112.7865829    
## 1.1113867    -112.7865829    
## 1.1113867    -112.7865822    
## 1.1113867    -112.7865822    
## 1.1113867    -112.7865826    
## 1.1113867    -112.7865826    
## 1.1113852    -112.7865819    
## 1.1123852    -112.7865993    
## 1.1103852    -112.7865993    
## 1.1113852    -112.7865829    
## 1.1113852    -112.7865829    
## 1.1113852    -112.7865822    
## 1.1113852    -112.7865822    
## 1.1113852    -112.7865826    
## 1.1113852    -112.7865826    
fit1
## ML common-rate model:
##  s^2  a[1]   a[2]    a[3]    k   logL
## value    1.1114  -0.2344 0.9677  1.7855  4   -112.7866   
## 
## ML multi-rate model:
##   s^2[1] s^2[2]  s^2[3]   a[1]   a[2]    a[3]    k   logL
## value    0.5759  1.5107  1.009   -0.2344 0.9677  1.7855  6   -109.4117   
## 
## Likelihood ratio: 6.7497 
## P-value (based on X^2): 0.0342 
## 
## R thinks it has found the ML solution.

Now, how about using different values to commence the optimization:

fit2<-ratebytree(c(t1,t2,t3),list(x,y,z),trace=TRUE,digits=7,
    init=list(sigc=2,sigm=rep(2,3)))
## 
## Optimizing multi-rate model....
## sig[1]       sig[2]      sig[3]      logL
## 2    2   2   -118.9455945    
## 2.001    2   2   -118.9502223    
## 1.999    2   2   -118.9409654    
## 2    2.001   2   -118.9480425    
## 2    1.999   2   -118.9431491    
## 2    2   2.001   -118.948072 
## 2    2   1.999   -118.9431171    
## 2    2   2   -118.9455951    
## 2    2   2   -118.9455951    
## 2    2   2   -118.9455947    
## 2    2   2   -118.9455947    
## 2    2   2   -118.9455949    
## 2    2   2   -118.9455949    
## 1.4226497    1.4226497   1.4226497   -113.9958273    
## 1.4236497    1.4226497   1.4226497   -114.0012657    
## 1.4216497    1.4226497   1.4226497   -113.9903876    
## 1.4226497    1.4236497   1.4226497   -113.9949632    
## 1.4226497    1.4216497   1.4226497   -113.9967024    
## 1.4226497    1.4226497   1.4236497   -113.997872 
## 1.4226497    1.4226497   1.4216497   -113.9937846    
## 1.4226497    1.4226497   1.4226497   -113.995828 
## 1.4226497    1.4226497   1.4226497   -113.995828 
## 1.4226497    1.4226497   1.4226497   -113.9958276    
## 1.4226497    1.4226497   1.4226497   -113.9958276    
## 1.4226497    1.4226497   1.4226497   -113.9958278    
## 1.4226497    1.4226497   1.4226497   -113.9958278    
## 0    1.421147    0.7341634   -748624417.333641   
## 0.001    1.421147    0.7341634   -7500.5580194   
## 0    1.421147    0.7341634   -748624417.333641   
## 0    1.422147    0.7341634   -748624417.33276    
## 0    1.420147    0.7341634   -748624417.334533   
## 0    1.421147    0.7351634   -748624417.328558   
## 0    1.421147    0.7331634   -748624417.338757   
## 0    1.421147    0.7341634   -748624528.429275   
## 0    1.421147    0.7341634   -748624528.429274   
## 0    1.421147    0.7341634   -748624417.333641   
## 0    1.421147    0.7341634   -748624417.333641   
## 0    1.421147    0.7341634   -748624417.333642   
## 0    1.421147    0.7341634   -748624417.333642   
## 0.948767 1.4221492   1.1933158   -110.963321 
## 0.949767 1.4221492   1.1933158   -110.968708 
## 0.947767 1.4221492   1.1933158   -110.9579372    
## 0.948767 1.4231492   1.1933158   -110.9624514    
## 0.948767 1.4211492   1.1933158   -110.9642018    
## 0.948767 1.4221492   1.1943158   -110.9646176    
## 0.948767 1.4221492   1.1923158   -110.9620293    
## 0.948767 1.4221492   1.1933158   -110.9633222    
## 0.948767 1.4221492   1.1933158   -110.9633222    
## 0.948767 1.4221492   1.1933158   -110.9633213    
## 0.948767 1.4221492   1.1933158   -110.9633213    
## 0.948767 1.4221492   1.1933158   -110.9633217    
## 0.948767 1.4221492   1.1933158   -110.9633217    
## 0.4743835    1.4216481   0.9637396   -109.7209006    
## 0.4753835    1.4216481   0.9637396   -109.7150794    
## 0.4733835    1.4216481   0.9637396   -109.7268043    
## 0.4743835    1.4226481   0.9637396   -109.7200254    
## 0.4743835    1.4206481   0.9637396   -109.7217869    
## 0.4743835    1.4216481   0.9647396   -109.7204189    
## 0.4743835    1.4216481   0.9627396   -109.7213941    
## 0.4743835    1.4216481   0.9637396   -109.7209029    
## 0.4743835    1.4216481   0.9637396   -109.7209029    
## 0.4743835    1.4216481   0.9637396   -109.7209009    
## 0.4743835    1.4216481   0.9637396   -109.7209009    
## 0.4743835    1.4216481   0.9637396   -109.7209014    
## 0.4743835    1.4216481   0.9637396   -109.7209014    
## 0.7133097    1.4219005   1.0793671   -109.7489584    
## 0.7143097    1.4219005   1.0793671   -109.7524779    
## 0.7123097    1.4219005   1.0793671   -109.7454546    
## 0.7133097    1.4229005   1.0793671   -109.748086 
## 0.7133097    1.4209005   1.0793671   -109.7498419    
## 0.7133097    1.4219005   1.0803671   -109.7495659    
## 0.7133097    1.4219005   1.0783671   -109.7483583    
## 0.7133097    1.4219005   1.0793671   -109.7489599    
## 0.7133097    1.4219005   1.0793671   -109.7489599    
## 0.7133097    1.4219005   1.0793671   -109.7489587    
## 0.7133097    1.4219005   1.0793671   -109.7489587    
## 0.7133097    1.4219005   1.0793671   -109.7489591    
## 0.7133097    1.4219005   1.0793671   -109.7489591    
## 0    1.6531789   1.0249276   -748624416.811883   
## 0.001    1.6531789   1.0249276   -7500.0362621   
## 0    1.6531789   1.0249276   -748624416.811883   
## 0    1.6541789   1.0249276   -748624416.812929   
## 0    1.6521789   1.0249276   -748624416.810843   
## 0    1.6531789   1.0259276   -748624416.812039   
## 0    1.6531789   1.0239276   -748624416.811736   
## 0    1.6531789   1.0249276   -748624527.907516   
## 0    1.6531789   1.0249276   -748624527.907518   
## 0    1.6531789   1.0249276   -748624416.811883   
## 0    1.6531789   1.0249276   -748624416.811883   
## 0    1.6531789   1.0249276   -748624416.811884   
## 0    1.6531789   1.0249276   -748624416.811884   
## 0.4758741    1.4988849   1.0612462   -109.6770468    
## 0.4768741    1.4988849   1.0612462   -109.6713474    
## 0.4748741    1.4988849   1.0612462   -109.6828278    
## 0.4758741    1.4998849   1.0612462   -109.6769466    
## 0.4758741    1.4978849   1.0612462   -109.6771561    
## 0.4758741    1.4988849   1.0622462   -109.6775145    
## 0.4758741    1.4988849   1.0602462   -109.6765872    
## 0.4758741    1.4988849   1.0612462   -109.6770492    
## 0.4758741    1.4988849   1.0612462   -109.6770492    
## 0.4758741    1.4988849   1.0612462   -109.6770471    
## 0.4758741    1.4988849   1.0612462   -109.6770471    
## 0.4758741    1.4988849   1.0612462   -109.6770476    
## 0.4758741    1.4988849   1.0612462   -109.6770476    
## 0.6174096    1.4529944   1.0720481   -109.4758583    
## 0.6184096    1.4529944   1.0720481   -109.4772898    
## 0.6164096    1.4529944   1.0720481   -109.4744562    
## 0.6174096    1.4539944   1.0720481   -109.4753172    
## 0.6174096    1.4519944   1.0720481   -109.4764096    
## 0.6174096    1.4529944   1.0730481   -109.4764105    
## 0.6174096    1.4529944   1.0710481   -109.4753137    
## 0.6174096    1.4529944   1.0720481   -109.4758601    
## 0.6174096    1.4529944   1.0720481   -109.4758601    
## 0.6174096    1.4529944   1.0720481   -109.4758585    
## 0.6174096    1.4529944   1.0720481   -109.4758585    
## 0.6174096    1.4529944   1.0720481   -109.475859 
## 0.6174096    1.4529944   1.0720481   -109.475859 
## 0.5490137    1.4881159   1.0371591   -109.4327838    
## 0.5500137    1.4881159   1.0371591   -109.4316493    
## 0.5480137    1.4881159   1.0371591   -109.4339656    
## 0.5490137    1.4891159   1.0371591   -109.4325849    
## 0.5490137    1.4871159   1.0371591   -109.432992 
## 0.5490137    1.4881159   1.0381591   -109.4330497    
## 0.5490137    1.4881159   1.0361591   -109.4325267    
## 0.5490137    1.4881159   1.0371591   -109.4327858    
## 0.5490137    1.4881159   1.0371591   -109.4327858    
## 0.5490137    1.4881159   1.0371591   -109.4327841    
## 0.5490137    1.4881159   1.0371591   -109.4327841    
## 0.5490137    1.4881159   1.0371591   -109.4327846    
## 0.5490137    1.4881159   1.0371591   -109.4327846    
## 0.5756508    1.5094148   1.0429111   -109.4171106    
## 0.5766508    1.5094148   1.0429111   -109.4171218    
## 0.5746508    1.5094148   1.0429111   -109.4171387    
## 0.5756508    1.5104148   1.0429111   -109.4171042    
## 0.5756508    1.5084148   1.0429111   -109.4171259    
## 0.5756508    1.5094148   1.0439111   -109.4174265    
## 0.5756508    1.5094148   1.0419111   -109.4168034    
## 0.5756508    1.5094148   1.0429111   -109.4171125    
## 0.5756508    1.5094148   1.0429111   -109.4171125    
## 0.5756508    1.5094148   1.0429111   -109.4171109    
## 0.5756508    1.5094148   1.0429111   -109.4171109    
## 0.5756508    1.5094148   1.0429111   -109.4171114    
## 0.5756508    1.5094148   1.0429111   -109.4171114    
## 0.578788 1.4910265   1.0149255   -109.4137608    
## 0.579788 1.4910265   1.0149255   -109.4138934    
## 0.577788 1.4910265   1.0149255   -109.4136666    
## 0.578788 1.4920265   1.0149255   -109.4135888    
## 0.578788 1.4900265   1.0149255   -109.413942 
## 0.578788 1.4910265   1.0159255   -109.4138229    
## 0.578788 1.4910265   1.0139255   -109.4137083    
## 0.578788 1.4910265   1.0149255   -109.4137627    
## 0.578788 1.4910265   1.0149255   -109.4137627    
## 0.578788 1.4910265   1.0149255   -109.4137611    
## 0.578788 1.4910265   1.0149255   -109.4137611    
## 0.578788 1.4910265   1.0149255   -109.4137616    
## 0.578788 1.4910265   1.0149255   -109.4137616    
## 0.5759546    1.5111591   1.0083125   -109.4117112    
## 0.5769546    1.5111591   1.0083125   -109.4117343    
## 0.5749546    1.5111591   1.0083125   -109.4117273    
## 0.5759546    1.5121591   1.0083125   -109.41172  
## 0.5759546    1.5101591   1.0083125   -109.4117112    
## 0.5759546    1.5111591   1.0093125   -109.4117091    
## 0.5759546    1.5111591   1.0073125   -109.4117232    
## 0.5759546    1.5111591   1.0083125   -109.4117131    
## 0.5759546    1.5111591   1.0083125   -109.4117131    
## 0.5759546    1.5111591   1.0083125   -109.4117115    
## 0.5759546    1.5111591   1.0083125   -109.4117115    
## 0.5759546    1.5111591   1.0083125   -109.411712 
## 0.5759546    1.5111591   1.0083125   -109.411712 
## 0.5758751    1.5106832   1.0090684   -109.4117074    
## 0.5768751    1.5106832   1.0090684   -109.4117274    
## 0.5748751    1.5106832   1.0090684   -109.4117267    
## 0.5758751    1.5116832   1.0090684   -109.4117121    
## 0.5758751    1.5096832   1.0090684   -109.4117116    
## 0.5758751    1.5106832   1.0100684   -109.4117128    
## 0.5758751    1.5106832   1.0080684   -109.4117119    
## 0.5758751    1.5106832   1.0090684   -109.4117094    
## 0.5758751    1.5106832   1.0090684   -109.4117094    
## 0.5758751    1.5106832   1.0090684   -109.4117077    
## 0.5758751    1.5106832   1.0090684   -109.4117077    
## 0.5758751    1.5106832   1.0090684   -109.4117082    
## 0.5758751    1.5106832   1.0090684   -109.4117082    
## 0.5758675    1.5106518   1.0090267   -109.4117074    
## 0.5768675    1.5106518   1.0090267   -109.4117271    
## 0.5748675    1.5106518   1.0090267   -109.411727 
## 0.5758675    1.5116518   1.0090267   -109.4117118    
## 0.5758675    1.5096518   1.0090267   -109.4117118    
## 0.5758675    1.5106518   1.0100267   -109.4117123    
## 0.5758675    1.5106518   1.0080267   -109.4117123    
## 0.5758675    1.5106518   1.0090267   -109.4117094    
## 0.5758675    1.5106518   1.0090267   -109.4117094    
## 0.5758675    1.5106518   1.0090267   -109.4117077    
## 0.5758675    1.5106518   1.0090267   -109.4117077    
## 0.5758675    1.5106518   1.0090267   -109.4117082    
## 0.5758675    1.5106518   1.0090267   -109.4117082    
## 
## Optimizing common-rate model....
## sig          logL
## 2    -118.9455945    
## 2.001    -118.9551477    
## 1.999    -118.9360425    
## 2    -118.9455951    
## 2    -118.9455951    
## 2    -118.9455947    
## 2    -118.9455947    
## 2    -118.9455949    
## 2    -118.9455949    
## 1    -113.0350348    
## 1.001    -113.0302715    
## 0.999    -113.0398507    
## 1    -113.0350359    
## 1    -113.0350359    
## 1    -113.0350352    
## 1    -113.0350352    
## 1    -113.0350356    
## 1    -113.0350356    
## 1.3339499    -113.4612924    
## 1.3349499    -113.4666788    
## 1.3329499    -113.4559222    
## 1.3339499    -113.4612933    
## 1.3339499    -113.4612933    
## 1.3339499    -113.4612928    
## 1.3339499    -113.4612928    
## 1.3339499    -113.4612931    
## 1.3339499    -113.4612931    
## 1.1138276    -112.7866855    
## 1.1148276    -112.7867874    
## 1.1128276    -112.7866181    
## 1.1138276    -112.7866865    
## 1.1138276    -112.7866865    
## 1.1138276    -112.7866858    
## 1.1138276    -112.7866858    
## 1.1138276    -112.7866862    
## 1.1138276    -112.7866862    
## 1.1118507    -112.7865857    
## 1.1128507    -112.7866192    
## 1.1108507    -112.7865868    
## 1.1118507    -112.7865867    
## 1.1118507    -112.7865867    
## 1.1118507    -112.786586 
## 1.1118507    -112.786586 
## 1.1118507    -112.7865864    
## 1.1118507    -112.7865864    
## 1.1113832    -112.7865819    
## 1.1123832    -112.7865992    
## 1.1103832    -112.7865994    
## 1.1113832    -112.7865829    
## 1.1113832    -112.7865829    
## 1.1113832    -112.7865822    
## 1.1113832    -112.7865822    
## 1.1113832    -112.7865826    
## 1.1113832    -112.7865826    
## 1.1113852    -112.7865819    
## 1.1123852    -112.7865993    
## 1.1103852    -112.7865993    
## 1.1113852    -112.7865829    
## 1.1113852    -112.7865829    
## 1.1113852    -112.7865822    
## 1.1113852    -112.7865822    
## 1.1113852    -112.7865826    
## 1.1113852    -112.7865826    
fit2
## ML common-rate model:
##  s^2  a[1]   a[2]    a[3]    k   logL
## value    1.1114  -0.2344 0.9677  1.7855  4   -112.7866   
## 
## ML multi-rate model:
##   s^2[1] s^2[2]  s^2[3]   a[1]   a[2]    a[3]    k   logL
## value    0.5759  1.5107  1.009   -0.2344 0.9677  1.7855  6   -109.4117   
## 
## Likelihood ratio: 6.7497 
## P-value (based on X^2): 0.0342 
## 
## R thinks it has found the ML solution.

Neat.

Here's a visualization of the evolution of our tree different trees as I showed last time:

ylim<-range(c(x,y,z))
par(mfrow=c(1,3))
phenogram(t1,x,ylim=ylim,spread.cost=c(1,0),ftype="i")
phenogram(t2,y,ylim=ylim,spread.cost=c(1,0),ftype="i")
## Optimizing the positions of the tip labels...
phenogram(t3,z,ylim=ylim,spread.cost=c(1,0),ftype="i")

plot of chunk unnamed-chunk-3

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