aphylo: Statistical Inference of Annotated Phylogenetic Trees

The aphylo R package implements estimation and data imputation methods for Functional Annotations in Phylogenetic Trees. The core function consists of the log-likelihood computation of observing a given phylogenetic tree with functional annotation on its leaves and the probabilities associated to gain and loss of function, including probabilities of experimental misclassification. The log-likelihood is computed using peeling algorithms, which required developing and implementing efficient algorithms for re-coding and preparing phylogenetic tree data to be used with the package. Finally, aphylo works smoothly with popular tools for analysis of phylogenetic data such as ape R package, “Analyses of Phylogenetics and Evolution.”

The package is under MIT License and is developed by the Computing and Software Cores of the Biostatistics Division’s NIH Project Grant (P01) at the Department of Preventive Medicine at the University of Southern California.

Citation 

citation(package="aphylo")
To cite aphylo in publications use the following paper:

  Vega Yon GG, Thomas DC, Morrison J, Mi H, Thomas PD, et al. (2021)
  Bayesian parameter estimation for automatic annotation of gene
  functions using observational data and phylogenetic trees. PLOS
  Computational Biology 17(2): e1007948.
  https://doi.org/10.1371/journal.pcbi.1007948

And the actual R package:

  Vega Yon G (2022). _Statistical Inference of Annotated Phylogenetic
  Trees_. R package version 0.3-2,
  <https://github.com/USCBiostats/aphylo>.

To see these entries in BibTeX format, use 'print(<citation>,
bibtex=TRUE)', 'toBibtex(.)', or set
'options(citation.bibtex.max=999)'.

Install

This package depends on another on-development R package, the fmcmc. So first, you need to install it:

devtools::install_github("USCbiostats/fmcmc")

Then you can install the aphylo package

devtools::install_github("USCbiostats/aphylo")

Reading data 

Loading required package: ape
# This datasets are included in the package
data("fakeexperiment")
data("faketree")

head(fakeexperiment)
     LeafId f1 f2
[1,]      1  0  0
[2,]      2  0  1
[3,]      3  1  0
[4,]      4  1  1
head(faketree)
     ParentId NodeId
[1,]        6      1
[2,]        6      2
[3,]        7      3
[4,]        7      4
[5,]        5      6
[6,]        5      7
O <- new_aphylo(
  tip.annotation = fakeexperiment[,2:3],
  tree           = as.phylo(faketree)
)

O
Phylogenetic tree with 4 tips and 3 internal nodes.

Tip labels:
  1, 2, 3, 4
Node labels:
  5, 6, 7

Rooted; no branch lengths.

 Tip (leafs) annotations:
  f1 f2
1  0  0
2  0  1
3  1  0
4  1  1

 Internal node annotations:
  f1 f2
5  9  9
6  9  9
7  9  9
Phylogenetic tree with 4 tips and 3 internal nodes.

Tip labels:
  1, 2, 3, 4
Node labels:
  5, 6, 7

Rooted; no branch lengths.
# We can visualize it
plot(O)

Simulating annotated trees 

set.seed(198)
dat <- raphylo(
  50,
  P    = 1, 
  psi  = c(0.05, 0.05),
  mu_d = c(0.8, 0.3),
  mu_s = c(0.1, 0.1),
  Pi   = .4
  )

dat
Phylogenetic tree with 50 tips and 49 internal nodes.

Tip labels:
  1, 2, 3, 4, 5, 6, ...
Node labels:
  51, 52, 53, 54, 55, 56, ...

Rooted; no branch lengths.

 Tip (leafs) annotations:
  fun0000
1       1
2       0
3       0
4       1
5       0
6       0

...(44 obs. omitted)...


 Internal node annotations:
  fun0000
1       1
2       1
3       1
4       1
5       1
6       0

...(43 obs. omitted)...

Likelihood 

# Parameters and data
psi     <- c(0.020,0.010)
mu_d    <- c(0.40,.10)
mu_s    <- c(0.04,.01)
eta     <- c(.7, .9)
pi_root <- .05

# Computing likelihood
str(LogLike(dat, psi = psi, mu_d = mu_d, mu_s = mu_s, eta = eta, Pi = pi_root))
List of 2
 $ Pr:List of 1
  ..$ : num [1:99, 1:2] 0.018 0.686 0.686 0.018 0.686 0.686 0.018 0.018 0.018 0.686 ...
 $ ll: num -40.4

Estimation 

# Using L-BFGS-B (MLE) to get an initial guess
ans0 <- aphylo_mle(dat ~ psi + mu_d + Pi + eta)


# MCMC method
ans2 <- aphylo_mcmc(
  dat ~ mu_d + mu_s + Pi,
  prior   = bprior(c(9, 1, 1, 1, 5), c(1, 9, 9, 9, 5)),
  control = list(nsteps=5e3, burnin=500, thin=10, nchains=2))
Warning: While using multiple chains, a single initial point has been passed
via `initial`: c(0.9, 0.5, 0.1, 0.05, 0.5). The values will be recycled.
Ideally you would want to start each chain from different locations.

Convergence has been reached with 5500 steps. Gelman-Rubin's R: 1.0314. (500 final count of samples).
ans2
ESTIMATION OF ANNOTATED PHYLOGENETIC TREE

 Call: aphylo_mcmc(model = dat ~ mu_d + mu_s + Pi, priors = bprior(c(9, 
    1, 1, 1, 5), c(1, 9, 9, 9, 5)), control = list(nsteps = 5000, 
    burnin = 500, thin = 10, nchains = 2))
 LogLik (unnormalized): -20.0599 
 Method used: mcmc (5500 steps)
 # of Leafs: 50
 # of Functions 1
 # of Trees: 1

         Estimate  Std. Err.
 mu_d0   0.9093    0.0827
 mu_d1   0.1608    0.0767
 mu_s0   0.1015    0.0669
 mu_s1   0.1022    0.0443
 Pi      0.5318    0.1443
plot(
  ans2,
  nsample = 200,
  loo     = TRUE,
  ncores  = 2L
  )

# MCMC Diagnostics with coda
library(coda)
gelman.diag(ans2$hist)
Potential scale reduction factors:

      Point est. Upper C.I.
mu_d0       1.00       1.02
mu_d1       1.02       1.11
mu_s0       1.00       1.01
mu_s1       1.01       1.06
Pi          1.01       1.02

Multivariate psrf

1.03
plot(ans2$hist)

Prediction 

pred <- prediction_score(ans2, loo = TRUE)
pred
Prediction score (H0: Observed = Random)

 N obs.      : 99

 Observed    : 0.71 ***
 Random      : NA 
 P(<t)       : 0.0000
--------------------------------------------------------------------------------
Values scaled to range between 0 and 1, 1 being best.

Significance levels: *** p < .01, ** p < .05, * p < .10
AUC 0.79.
MAE 0.29.
plot(pred)

Misc

During the development process, we decided to allow the user to choose what ‘tree-reader’ function he would use, particularly between using either the rncl R package or ape. For such, we created a short benchmark that compares both functions here.