Markov Maximum Likelihood ancestral states inference
We inferred ancestral states using the rayDISC function in the R package
corHMM (Beaulieu, O’Meara, & Donoghue, 2013), with
node.states=”marginal”, state.recon=”subsequently” and
root.p=”maddfitz”. This algorithm allows multistate tip input, and
infers marginal likelihoods (probabilities) for each state at each node
including tips, the latter being in effect an implied state of common
ancestor of the multistate tip (Felsenstein 2004, p. 255). Options for
interpreting this post-analysis tip state marginal are to i) use these
values or ii) to recode as equal probabilities to partially account for
terminal dispersals within the tip lineage, or iii) explicitly count all
implied terminal dispersals. In our eight-region scheme 86% of species
are endemic to a single region, hence the moderate proportion (14%) of
multistate species is a tolerable level for this type of ancestral state
method to accommodate.
In order to select an optimal ML model structure, we applied an
approximation intended to achieve a practical fair evaluation of what
can be a prohibitively large number of possible rate models (Huelsenbecket al. , 2003; Felsenstein, 2004). Using the single consensus
tree, an average of ER, SYM and ARD model rates (in order to buffer
against potentially miss-specified extreme values) were rank ordered
into a serially increasing number of rate category models from the
simplest single rate (ER), evaluated by BIC (Table S5). We selected a
four-rate model structure representing a balance of complexity and
support, which was then used for all subsequent analyses (Table S6).
Rather than produce a single best ancestral state result, we focussed on
broad biogeographical inferences summarizing both model ancestral state
and phylogenetic uncertainty. To do this we applied stochastic node
state mapping using 200 re-samplings of node state marginal likelihoods,
to each of 100 BEAST tree samples. Randomly sampling node states
according to marginal likelihoods selects an explicit node state –
multiple resampling then fairly represents the marginal likelihood
(Huelsenbeck et al. , 2003; Revell, 2012; O’Hara et al. ,
2019). Doing this for a set of tree samples then includes phylogenetic
uncertainty in the whole inference.
Transition events are summarized according to parent to daughter node
(including tip) states; cases where the state remains the same are
referred to as endemic cladogenesis. These results can be divided up by
divergence age into time-bins, assigned by daughter node age. For
counting state lineages, branches spanning a time point can be assigned
to closest parent or daughter node state. These procedures for
summarizing an explicitly resolved set of ancestral states are
straightforward (Revell, 2012) and can be applied to any ancestral state
method including DEC models (Bribiesca-Contreras et al. , 2019).
This entire procedure can be repeated on multiple trees and the entire
set of transition events and state lineages per time-bin combined into a
final matrix integrating the tree and model variation
(Bribiesca-Contreras et al. , 2019). Such summary results of
events per time-bin are best interpreted as a summary of the relative
frequency or probability density of such events rather than an explicit
count. Results can further be integrated by post-hoc combining several
individual states and changes into larger summary categories, such as
continental versus islands. By summarizing the results across the whole
marginal likelihood the method accounts for multiple solutions and hence
in effect to some degree accounts for multistate solutions, particularly
for combined region summaries.
Analyses were executed, and summarized into 2 million year time-bin
profile plots, in R using a custom script ASSMR2. For phylogenetic
visualizations onto the single MCC consensus tree, we averaged marginal
likelihoods across all 100 sample trees plus consensus tree, for all
nodes in common with the consensus tree (identical taxon bipartitions)
and the linked parent node. Nodes (hence branches) with maximum state
probability <67% were then marked as indecisive. Except for
inclusion of the parent node, these are often used procedures (Matzke,
2013; O’Hara et al. , 2019).