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t35 t53 a a a a a a levels a b for completeness let s start by fitting our null model using fitmultiou we can then confirm that this fitted model matches to a reasonable degree they will only converge exactly as levs goes towards infty what we d obtain using geiger fitcontinuous and phytools fitmk under the same model assumptions i m going to set levs 200 for this analysis but this actually takes a very long time to run much more than twice as long as levs 100 fit null model fit_null fitmultiou phy x y model er levs 200 parallel true ncores 10 root mle trace 1 null_model true iter theta alpha sigsq q 1 log l 0 1 9456 0 0721 1 1329 0 0914 175 6004 100 0 6244 0 0116 0 0897 0 0271 98 3007 200 0 6123 0 0053 0 0892 0 0283 98 2222 271 0 6338 0 0004 0 0860 0 0292 98 1838 done optimizing fit_null object of class fitmultiou based on a discretization with k 200 levels fitted multi theta ou model parameters levels a b theta 0 6338 alpha 4e 04 sigsq 0 086 estimated q matrix a b a 0 02921177 0 02921177 b 0 02921177 0 02921177 log likelihood 98 1838 r thinks optimization may not have converged fit single regime ou model using fitcontinuous ou_fit geiger fitcontinuous phy x model ou ou_fit now again let s compare to geiger fitcontinuous and phytools fitmk geiger fitted comparative model of continuous data fitted ou model parameters alpha 0 000000 sigsq 0 085106 z0 0 625022 model summary log likelihood 68 250476 aic 142 500953 aicc 142 750953 free parameters 3 convergence diagnostics optimization iterations 100 failed iterations 0 number of iterations with same best fit 50 frequency of best fit 0 500 object summary lik likelihood function bnd bounds for likelihood search res optimization iteration summary opt maximum likelihood parameter estimates fit mk model using fitmk mk_fit fitmk phy y model er pi equal mk_fit object of class fitmk fitted or set value of q a b a 0 028064 0 028064 b 0 028064 0 028064 fitted or set value of pi a b 0 5 0 5 due to treating the root prior as a flat log likelihood 29 168076 optimization method used was nlminb r thinks it has found the ml solution you can compare the model parameter estimates but let s also assure ourselves that the likelihood seems to be converging on the same value as follows compute null log l from fitcontinuous fitmk results null_logl loglik ou_fit loglik mk_fit attr null_logl df 4 fix d f null_logl 1 97 41855 attr df 1 4 compare to fitmultiou loglik fit_null 1 98 18378 attr df 1 4 this is pretty close again we would expect these two values to get even closer for higher levs but as currently implemented this already takes a really long time to run ok now let s bring ouwie into the picture we can start by loading the package which i recently updated from cran load ouwie library ouwie now for ouwie we need to put our data in a special data frame format as follows compile our data for ouwie ouwie data data frame genus_species names x reg y x x head ouwie data genus_species reg x t2 t2 a 0 3416784 t3 t3 a 0 6347880 t89 t89 a 0 3128115 t90 t90 a 0 5001694 t35 t35 a 0 7747887 t53 t53 a 0 5183583 why don t we start by simply re fitting our null ou model in ouwie this should give us a result that quite closely matches what we obtained using geiger fitcontinuous i ll still give it our known discrete character data history but i set model ou1 to specify that i want a single theta model only fit ouwie null model fitou smp ouwie sim_tree ouwie data model ou1 simmap tree true root station false warning an algorithm was not specified defaulting to computing the determinant and inversion of the vcv initializing finished begin thorough search finished summarizing results fitou smp fit lnl aic aicc bic model ntax 68 25048 142 501 142 751 150 3165 ou1 100 rates alpha sigma sq 1 524044e 08 8 510672e 02 optima 1 estimate 0 6250224 se 0 3348563 half life another way of reporting alpha alpha 45480781 arrived at a reliable solution hopefully we see that this fitted model pretty closely matches what we got using fitcontinuous earlier next i m going to go ahead fit our discrete character dependent multi theta ou model using phytools fitmultiou this is the model that i ve been blogging about recently but to remind the reader this is a joint discrete continuous trait model not the fixed regime model of ouwie but i m hypothesizing that our continuous trait model parameter estimates should pretty closely match what we d get from ouwie using the true history or for that matter a stochastic character history just because our discrete character changes so infrequently on the tree to start with i m going to try to get reasonable starting values for my fitmultiou parameters as follows identify sensible starting parameter values init setnames c mean x y levels y 1 mean x y levels y 2 log 2 max nodeheights phy var x max nodeheights phy fitmk phy y model er rates c theta a theta b alpha sigsq q 1 init theta a theta b alpha sigsq q 1 0 27841916 1 61842864 0 06931472 0 12828760 0 02806402 then i can go ahead and fit the joint model fit discrete trait dependent model fit_mou fitmultiou phy x y model er levs 200 parallel true ncores 10 root mle trace 1 maxit 2000 init init iter the a the b alpha sigsq q 1 log l 0 0 2784 1 6184 0 0693 0 1283 0 0281 92 1417 100 0 4558 1 8575 0 3260 0 1157 0 0268 72 4242 200 0 4520 1 8537 0 3254 0 1143 0 0267 72 4172 300 0 4531 1 8535 0 3252 0 1145 0 0269 72 4170 400 0 4520 1 8523 0 3246 0 1142 0 0271 72 4163 404 0 4519 1 8523 0 3246 0 1141 0 0271 72 4163 done optimizing fit_mou object of class fitmultiou based on a discretization with k 200 levels fitted multi theta ou model parameters levels a b theta 0 4519 1 8523 alpha 0 3246 sigsq 0 1141 estimated q matrix a b a 0 02713072 0 02713072 b 0 02713072 0 02713072 log likelihood 72 4163 r thinks it has found the ml solution finally we can fit our fixed regime model using the ouwie package here don t forget that though i will be using the true discrete character history this is almost never known in practice indeed if we genuinely knew the discrete character history i would always recommend fitting a fixed regime model not a joint model fit multi regime ou model using ouwie fitoum smp ouwie sim_tree ouwie data model oum simmap tree true root station false warning an algorithm was not specified defaulting to computing the determinant and inversion of the vcv initializing finished begin thorough search finished summarizing results fitoum smp fit lnl aic aicc bic model ntax 44 47594 96 95187 97 37292 107 3726 oum 100 rates b a alpha 0 3007500 0 3007500 sigma sq 0 1198701 0 1198701 optima b a estimate 1 75307314 0 5184579 se 0 09854245 0 1132707 half life another way of reporting alpha b a 2 304729 2 304729 arrived at a reliable solution cool now if we look closely at our results we should see that our parameter estimates do in fact match up fairly well keeping in mind of course that these are not the same models the ouwie model is based on fixed regimes while our fitmultiou function implements a joint discrete trait continuous character evolutionary model i would expect this similarity to hold whenever our discrete character history is pretty unambiguous usually because the character changes quite infrequently on the tree but to diminish as the rate or number of changes of our discrete trait increases that s all folks posted by liam revell at 10 55 am 3 comments email this blogthis share to x share to facebook share to pinterest tuesday july 14 2026 visualizing a multi regime ou process on the tree using phytools in a recent tweet about phytools new discrete character dependent multi optimum ou model i included an illustration of this process that was not derived from the original blog post more on a discrete character dependent multi optimum ou model in phytools https t co lplhskjoo6 pic twitter com jrmalmqpbh liam revell phytools_liam july 13 2026 just in case it might become useful later i decided to post the code for that cool illustration here in contrast to my prior use here i decided to set different values for alpha sigma 2 as well as for theta between the three regimes load packages library phytools in this first chunk i m going to generate the data and objects i need for the plot simulate a tree tree pbtree n 100 scale 10 add singleton unbranching nodes tt map to singleton make era map tree limits seq 0 10 length out 1001 set the transition matrix for the discrete trait q 0 2 q matrix c 2 q q q q 2 q q q q 2 q 3 3 dimnames list letters 1 3 letters 1 3 generate a character history of the discrete trait s tt sim history tt q anc a done simulation s set the parameters of the multi regime ou process theta setnames c 0 5 0 9 2 2 letters 1 3 sigsq setnames c 0 12 0 05 0 08 letters 1 3 alpha setnames c 0 7 0 4 0 8 letters 1 3 generate data for tips and nodes under the multi regime ou process x multiou s tt alpha alpha sig2 sigsq theta theta a0 theta a internal true now for our plot set colors cols setnames hcl colors n 3 letters 1 3 set plot layout layout matrix c 1 2 2 1 heights c 0 4 0 6 plot discrete character history on the tree plot s tt cols ftype off mar c 1 1 4 1 2 1 2 1 xlim c 0 11 mtext a adj 0 line 0 set margins for second subplot par mar c 5 1 4 1 2 1 2 1 plot continuous character history phenogram s tt x ftype off colors make transparent cols 0 5 xlim c 0 11 cex axis 0 8 las 1 mtext b adj 0 line 1 5 add the predicted equilibrium distribution at the tips for i in 1 length theta stat_theta dnorm seq min x max x length out 200 mean theta i sd sqrt sigsq i 2 alpha i stat norm stat_theta max stat_theta polygon x c 0 stat norm 0 10 y c min x seq min x max x length out 200 max x border false col make transparent cols i 0 5 nothing to it posted by liam revell at 12 11 pm 1 comment email this blogthis share to x share to facebook share to pinterest monday july 13 2026 more on a discrete character dependent multi optimum ou model in phytools good morning blog readers recently i ve posted about a new discrete character dependent multi theta i e multi optimum ou model in phytools e g 1 2 3 since this is very new it should only be used with the utmost caution nonetheless i thought i d post up a quick demo of how it works and how to do a model comparison to a simpler model of joint discrete continuous trait evolution but without dependence we also might consider an alternative null model with hidden characters but this will have to be covered in a future post this will only work on recent at the time of writing versions of phytools so we can start by loading the package checking which version we have library phytools loading required package ape loading required package maps packageversion phytools 1 2 6 3 to fit this model i m going to need some data with none readily at hand i m going to use phytools to simulate some we can start with a tree n 200 number of taxa phy pbtree n n scale 10 phy phylogenetic tree with 200 tips and 199 internal nodes tip labels t6 t7 t44 t57 t136 t177 rooted includes branch length s next we want a generating discrete character history for our multi regime ou process note that though we use this regime history for simulation in an empirical case it would ve been unknown so shall naturally be set aside when we move forward to estimation set the transition matrix of our discrete trait q 0 2 q matrix c 2 q q q q 2 q q q q 2 q 3 3 dimnames list letters 1 3 letters 1 3 q a b c a 0 4 0 2 0 2 b 0 2 0 4 0 2 c 0 2 0 2 0 4 k nrow q trait levels k 1 3 sim_tree sim history phy q anc a done simulation s sim_tree phylogenetic tree with 200 tips and 199 internal nodes tip labels t6 t7 t44 t57 t136 t177 the tree includes a mapped 3 state discrete character with states a b c rooted includes branch lengths let s plot our generating tree as follows cols setnames hcl colors n 3 letters 1 k plot sim_tree cols ftype off lwd 1 direction upwards par lend 1 legend bottomleft letters 1 3 lwd 3 col hcl colors n k cex 0 8 bty n next we can set the generating conditions for our continous trait simulation our model allows for multiple theta by discrete character state but assumes constant alpha and sigma 2 across the k levels of our discrete trait so let s simulate that alpha setnames rep 0 3 k letters 1 k alpha a b c 0 3 0 3 0 3 sig2 setnames rep 0 1 k letters 1 k sig2 a b c 0 1 0 1 0 1 theta setnames c 0 5 1 2 letters 1 k theta a b c 0 5 1 0 2 0 now we re nearly ready to simulate our continuous trait to do that i ll use phytools multiou as i have in prior posts x multiou sim_tree alpha sig2 theta a0 0 head x t6 t7 t44 t57 t136 t177 1 9418267 0 5788125 1 2039455 0 7955580 0 6064443 0 9103976 though we ve simulated our discrete character history already for our analysis we ll use just the tip states so let s pull those into a factor vector using phytools getstates y as factor getstates sim_tree tips head y t6 t7 t44 t57 t136 t177 a b c a c c levels a b c awesome now let s first fit our null model using fitmultiou fit_null fitmultiou phy x y model er levs 100 parallel true ncores 10 root mle trace 1 null_model true iter theta alpha sigsq q 1 log l 0 1 0601 0 2025 0 2682 0 0177 409 2704 100 0 4702 0 0182 0 0846 0 2622 287 2005 200 0 5735 0 0150 0 0829 0 2569 287 0941 279 0 5743 0 0141 0 0829 0 2555 287 0493 done optimizing fit_null object of class fitmultiou based on a discretization with k 100 levels fitted multi theta ou model parameters levels a b c theta 0 5743 alpha 0 0141 sigsq 0 0829 estimated q matrix a b c a 0 5109335 0 2554668 0 2554668 b 0 2554668 0 5109335 0 2554668 c 0 2554668 0 2554668 0 5109335 log likelihood 287 0493 r thinks it has found the ml solution let s confirm that our parameter estimates and log likelihood match what we would ve obtained using a geiger fitcontinuous and phytools fitmk this isn t hard ou_fit geiger fitcontinuous phy x model ou ou_fit geiger fitted comparative model of continuous data fitted ou model parameters alpha 0 012919 sigsq 0 081833 z0 0 655514 model summary log likelihood 89 743851 aic 185 487702 aicc 185 610151 free parameters 3 convergence diagnostics optimization iterations 100 failed iterations 0 number of iterations with same best fit 50 frequency of best fit 0 500 object summary lik likelihood function bnd bounds for likelihood search res optimization iteration summary opt maximum likelihood parameter estimates mk_fit fitmk phy y model er pi equal mk_fit object of class fitmk fitted or set value of q a b c a 0 511178 0 255589 0 255589 b 0 255589 0 511178 0 255589 c 0 255589 0 255589 0 511178 fitted or set value of pi a b c 0 333333 0 333333 0 333333 due to treating the root prior as a flat log likelihood 195 760975 optimization method used was nlminb r thinks it has found the ml solution null_logl loglik ou_fit loglik mk_fit null_logl 1 285 5048 attr df 1 3 this should be very close to the values we obtained in fit_null in fact the two values are a bit farther apart than i m comfortable with but would undoubtedly converge if we were to increase levs we should do this with some caution th...