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bifrost

Branch-level Inference Framework for Recognizing Optimal Shifts in Traits

bifrost performs branch-level inference of multi-regime, multivariate trait evolution on a phylogeny using penalized-likelihood multivariate GLS fits. The current version searches for evolutionary model shifts under a multi-rate Brownian Motion (BMM) model with proportional regime VCV scaling, operating directly in trait space (e.g., no PCA), and is designed for high-dimensional datasets (p > n) and large trees (> 1000 tips). The method will work with fossil tip-dated trees, and will accept most forms of multivariate comparative data (e.g., GPA aligned morphometric coordinates, linear dimensions, and others). The next major release will enable usage of the multivariate scalar Ornstein–Uhlenbeck process.

Overview

  • Primary goal. Infer where, when, and how patterns of phenotypic evolution change across a tree using many traits simultaneously.
  • Model. Multi-rate Brownian Motion with regime-specific VCVs estimated via penalized-likelihood (mvMORPH::mvgls), supporting p ≳ n.
  • Search. Greedy, step-wise acceptance of shifts guided by information criteria (GIC or BIC), with optional per-shift IC weights.
  • Scale. Parallel candidate scoring using the future ecosystem; practical on thousands of taxa × traits.

Key features

  • Joint multivariate modeling without information loss or distortion due to PCA.
  • Under BMM, proportional VCV scaling across regimes for tractability at high p.
  • Provides a multivariate phylogenetic GLS (mvPGLS)-like framework in which hidden branch-specific rate regimes are inferred and incorporated when estimating predictor effects.
  • Candidate shift nodes are determined by a minimum clade size specified by the user.
  • Greedy step-wise heuristic search using GIC/BIC ΔIC thresholds; optional IC-weight support for inferred shifts.
  • Output includes estimated VCV per regime, shift weights, and SIMMAP-style mappings for downstream visualization and analysis.
  • Parallelization via future / future.apply.

📄 Vignette 1: Getting Started with bifrost

Installation (development version) 

# install.packages("remotes")
remotes::install_github("jakeberv/bifrost")

Windows users:
Install Rtools for your R version and ensure it is added to your system PATH.

macOS users:
You may need to install XQuartz to build or run packages that depend on certain graphical or system libraries.

Quick start 

library(bifrost)
library(ape)
library(phytools)
library(mvMORPH)

set.seed(1)

# Simulate a tree
tr <- pbtree(n = 50, scale = 1)

# Paint a single global baseline state "0" (single regime)
base <- phytools::paintBranches(
  tr,
  edge      = unique(tr$edge[, 2]),
  state     = "0",
  anc.state = "0"
)

# Simulate multivariate traits under a single-regime BM1 model (no shifts)
sigma <- diag(0.1, 2)  # 2×2 variance–covariance matrix for two traits
theta <- c(0, 0)       # ancestral means for the two traits

sim <- mvSIM(
  tree  = base,
  nsim  = 1,
  model = "BM1",
  param = list(
    ntraits = 2,
    sigma   = sigma,
    theta   = theta
  )
)

# mvSIM returns either a matrix or a list of matrices depending on mvMORPH version
X <- if (is.list(sim)) sim[[1]] else sim
rownames(X) <- base$tip.label

# Run bifrost's greedy search for shifts
res <- searchOptimalConfiguration(
  baseline_tree              = base,
  trait_data                 = X,
  formula                    = "trait_data ~ 1",
  min_descendant_tips        = 10,
  num_cores                  = 1,
  shift_acceptance_threshold = 20,  # conservative GIC threshold
  IC                         = "GIC",
  plot                       = FALSE,
  store_model_fit_history    = FALSE,
  verbose                    = FALSE # set TRUE for progress messages 
)

# For this single-regime BM1 simulation, we typically expect no inferred shifts:
res$shift_nodes_no_uncertainty     # typically integer(0)
res$optimal_ic - res$baseline_ic   # typically close to 0

str(res$VCVs)  # regime-specific VCVs (here just the baseline regime "0")

Data requirements

  • Tree and data alignment. rownames(trait_data) must match tree$tip.label (same order and names).
  • Branch lengths. Interpreted in units of time; ultrametric not required.
  • SIMMAP style. Internally, regimes are stored using SIMMAP conventions (e.g., phytools class simmap)
  • Multi-dimensional traits. Works directly in trait space; tune penalties/methods using mvgls (mvMORPH) options for your data.
  • Thresholds. Use conservative shift_acceptance_threshold and ic_uncertainty_threshold to limit false positives; explore sensitivity.

Core workflow 

flowchart TD

subgraph S[Setup]
  A([Start]) --> B[Init and validate]
  B --> C[Paint baseline state 0]
  C --> D[Generate one-shift candidates]
end

subgraph CS[Baseline and scoring]
  D --> E[Fit baseline mvgls]
  E --> F[Baseline IC GIC or BIC]
  F --> G[Score candidates in parallel]
  G --> H[Compute delta IC and sort]
end

subgraph GS[Greedy search]
  H --> I[Init best tree and IC]
  I --> J{More candidates?}

  J -- Yes --> K[Add shift]
  K --> L[Fit shifted model]
  L --> M[Delta IC best minus new]
  M --> N{Delta IC >= threshold?}

  N -- Yes --> O[Accept update best]
  N -- No --> P[Reject keep best]

  O --> Q[Record status]
  P --> Q

  Q --> J
end

subgraph PP[Post processing]
  J -- No --> U[Finalize best model]
  U --> V{Compute IC weights?}

  V -- No --> V0[Skip weights]
  V -- Yes --> W{Any shifts?}
  W -- No --> V0

  W -- Yes --> X{Weights parallel?}
  X -- Yes --> X1[Drop-one refits parallel]
  X -- No --> X2[Drop-one refits serial]

  X1 --> Y[Compute weights aicw and ER]
  X2 --> Y
end

subgraph OUT[Output]
  V0 --> Z[Assemble result]
  Y --> Z
  Z --> ZA[Extract regime VCVs]
  ZA --> ZB([Return])
end

Primary functions

  • searchOptimalConfiguration(): The main function for end-to-end greedy search: candidate generation → parallel fitting → iterative acceptance → optional pruning/IC weights.
  • plot_ic_acceptance_matrix(): Visualize shift acceptance and information-criterion (IC) differences across search iterations.

Helper functions (not exported)

  • Candidate generation: generatePaintedTrees()
  • Model fitting helpers: fitMvglsAndExtractGIC(), fitMvglsAndExtractBIC(), and formula variants.
  • IC utilities: calculateAllDeltaGIC()
  • Tree painting utilities: paintSubTree_mod(), addShiftToModel(), removeShiftFromTree(), paintSubTree_removeShift(), whichShifts()
  • Regime VCVs: extractRegimeVCVs()

Outputs

searchOptimalConfiguration() returns a comprehensive list containing:

  • user_input — All arguments passed to searchOptimalConfiguration(), including the tree, trait data, IC choice, thresholds, and other parameters for reproducibility.
  • tree_no_uncertainty_transformed — Optimal SIMMAP tree with accepted shifts, using transformed branch lengths (if a branch-length transformation was applied).
  • tree_no_uncertainty_untransformed — Same optimal SIMMAP tree but with original, untransformed branch lengths.
  • model_no_uncertainty — Final fitted mvgls model object (BM or multi-rate BMM), including estimated parameters, log-likelihood, and variance–covariance matrices.
  • shift_nodes_no_uncertainty — Node numbers corresponding to accepted evolutionary shifts.
  • optimal_ic — Information criterion (IC) value for the optimal model.
  • baseline_ic — IC value for the null (single-rate) baseline model.
  • IC_used — The information criterion applied ("GIC" or "BIC").
  • num_candidates — Total number of candidate models evaluated during the search.
  • model_fit_history — Per-iteration log of model fits, IC values, and acceptance decisions; useful for visualizing or debugging search behavior.
  • VCVs — Regime-specific penalized-likelihood variance–covariance matrices.
  • ic_weights — Data frame of per-shift IC weights and evidence ratios (if uncertaintyweights_par = TRUE), providing support values for individual shifts.

Performance and scalability

Enable parallel processing using the future package:

library(future)
plan(multisession)   # or multicore on Linux/macOS
  • Reduce plotting (plot = FALSE) for large trees.
  • Increase memory for heavy runs, especially with high p.
  • Consider larger min_descendant_tips and stricter IC thresholds on very large problems.
  • Repeat searches with different seeds and thresholds to check for robustness.

Reproducibility

  • Record sessionInfo() and the mvMORPH version.
  • For projects, consider using renv to lock package versions.

Additional note

Though bifrost was initially developed as a framework for inferring macroevolutionary regime shifts in multivariate trait data, it can also be applied to perform multivariate phylogenetic generalized least squares (pGLS) analyses with factors or continuous predictors (e.g., cbind(trait1, trait2, ...) ~ predictor, or "trait_data[, 1:5] ~ trait_data[, 6]" when working directly with a matrix). In this context, bifrost identifies branch-specific rate variation under a multi-rate Brownian Motion model and fits the pGLS conditional on the resulting residual (phylogenetic) covariance structure, so estimated effect sizes and uncertainties account for “hidden” rate variation not explained by the predictors. This is conceptually similar to hidden-state approaches (e.g., Boyko et al. 2023), except that here the regimes influence variance and evolutionary rate rather than introducing regime-specific means. This use case is an active area of ongoing methodological development.

Citation

If you use bifrost, please cite the references returned by:

citation("bifrost")

Contributing

Bug reports, feature requests, and pull requests are welcome. Please open an issue at https://github.com/jakeberv/bifrost/issues.

License

This project is released under the GPL >= 2 License. See the LICENSE file for details.

Acknowledgements and dependencies

bifrost builds on substantial work from mvMORPH, phytools, ape, future, and future.apply. The greedy search algorithm is adapted from Mitov et al 2019 and Smith et al 2023. See the DESCRIPTION file for complete dependency and version information.

The name of our R package is inspired by the Bifröst, the rainbow bridge of Norse mythology that connects Earth (Midgard) and Asgard within the cosmic structure of Yggdrasil, the Tree of Life, echoing how our framework links observable data to hidden evolutionary shifts across the history of life.

Development of the bifrost R package was supported by the Oxford Research Software Engineering Group, with support from Schmidt Sciences, LLC. and the Michigan Institute for Data Science and AI in Society.

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