Treemble: Phylogenetic & Combinatorial Methods

• Treemble is a dual-use term referring to a phylogenetic desktop app that converts annotated tree images to Newick strings and a combinatorial process that trims binary trees.
• In phylogenetics, it employs a human-guided, coordinate-based workflow that achieves high accuracy (R² ≈ 0.99997) and scales to large trees.
• In probability, it implements a best-of-three erasure rule preserving uniform tree structures and yielding a càdlàg process on the Brownian Continuum Random Tree.

Treemble is a name used in recent arXiv literature for two unrelated tree-centered constructs. In phylogenetics, it denotes a desktop application for converting published phylogenetic tree images into machine-readable Newick strings, with an emphasis on human-guided node marking rather than brittle image segmentation (Allard et al., 9 Aug 2025). In probability and combinatorics, it denotes a best-of-three leaf-trimming process on labeled binary plane trees that yields a monotone coupling of uniform trees of successive sizes and, after rescaling, a càdlàg erasure process on the Brownian Continuum Random Tree (CRT) (Caraceni et al., 15 Apr 2026). The shared name is therefore cross-disciplinary rather than conceptual: one usage concerns reconstruction of empirical phylogenies from figures, while the other concerns exact uniformity, nested random trees, and scaling limits.

1. Scope and nomenclature

The two principal meanings of Treemble in the supplied literature can be summarized as follows.

Usage	Domain	Core definition
Treemble	Phylogenetics / scientific software	A desktop application for generating Newick strings from phylogenetic tree images
Treemble	Probability / combinatorics	A leaf-trimming process on labeled binary plane trees using a best-of-three rule

The phylogenetic software addresses a practical gap in biology: many published phylogenies are available only as figures, not as underlying Newick files, even though downstream analyses, comparisons, and supertree construction require machine-readable trees (Allard et al., 9 Aug 2025). The combinatorial Treemble addresses a different problem: how to erase leaves one-by-one from a uniformly random labeled binary tree while preserving the uniform law of the smaller tree, thereby producing a coherent nested family of uniform trees (Caraceni et al., 15 Apr 2026).

A possible source of confusion is terminological proximity to literature on tremor detection. The paper "An explainable hierarchical self attention-based approach for tremor detection in the time domain" studies 3D kinematic marker time-series data, a DeepConvLSTM, and a transformer-based session-level classifier; it is not presented as a Treemble method and belongs to a separate clinical machine-learning context (Odonga et al., 30 May 2026). This suggests that, in current usage, “Treemble” should be read as a homonymous label rather than a unified research program.

2. Treemble as phylogenetic reconstruction software

In phylogenetics, Treemble is a desktop application designed to turn phylogenetic tree images into machine-readable Newick strings. Its motivating premise is that phylogenetic trees are ubiquitous and central to biology, yet thousands of published trees remain unavailable for computational reuse because they were disseminated only as visual diagrams rather than as underlying data files (Allard et al., 9 Aug 2025). Since phylogenetic trees often encode both topology and branch lengths or divergence times, the absence of Newick files obstructs follow-up analyses and forces manual reconstruction.

The paper positions Treemble against earlier semi-automated tools such as TreeSnatcher and TreeRipper. Those systems relied heavily on image processing, typically attempting to detect dark branch pixels against a light background. The reported difficulty is that real published figures are rarely clean: branches are frequently overlain by error bars, boxes, silhouettes, labels, and other graphical elements that interfere with segmentation. TreeRipper’s success rate was reported as low, and its web application is no longer available at the published URL (Allard et al., 9 Aug 2025).

Treemble’s central design choice is to avoid this bottleneck by not relying on image processing at all. Instead, it uses a human-guided, coordinate-based workflow in which the user clicks node locations and the system reconstructs the tree from those coordinates alone. This makes the method semi-automatic rather than fully automatic, but it also makes it applicable to the heavily annotated figures that defeat purely image-based approaches. A plausible implication is that Treemble shifts the main difficulty from foreground extraction to geometric inference, where user input supplies the critical structural cues.

3. Workflow, reconstruction algorithm, and supported tree types

The workflow begins with opening a tree image and marking node locations. Internal nodes and tip nodes can be marked in any order, after which Treemble algorithmically assembles the connectivity and overlays the inferred tree on the original figure for verification (Allard et al., 9 Aug 2025). It also highlights nodes that could not be fully connected, allowing users to identify missing or mis-marked points. The paper reports that clicking a node takes about one second per node, so a tree with 50 tips can be marked in roughly two minutes.

A particularly important feature is that tip nodes can be automatically detected by drawing a rectangle around them, which the paper describes as especially helpful for timetrees. Treemble also supports automatic reading of tip names. Users may import a text file of labels produced by OCR or by the project’s own Tip Name Extractor GPT tool; the labels are displayed next to the tips, where they can be visually checked and edited directly within the interface (Allard et al., 9 Aug 2025). This matters because earlier tools often still required manual typing of tip names.

For rectangular trees, the reconstruction algorithm treats clicked nodes as points with $X$ and $Y$ coordinates, classifies them as tip or internal nodes, and processes internal nodes from youngest to oldest, defined as from largest to smallest $X$ coordinate. For each internal node, it finds the two currently unconnected descendant nodes nearest in the positive and negative $Y$ directions and attaches them as children. In the paper’s notation, the free nodes are partitioned into sets above and below the current node, and the nearest node in each set is chosen by minimizing vertical distance. Once connectivity has been assembled, a Newick string is generated recursively from the adjacency graph. Branch lengths are read directly from the time axis as

$L_{u-v} = X_v - X_u.$

Treemble also supports circular trees. In that case, the software transforms coordinates into polar form around a user-defined center point and a chosen break angle, then applies the same reconstruction logic in angular space, distinguishing clockwise and counter-clockwise descendants (Allard et al., 9 Aug 2025). The paper explicitly states that this circular-tree support, including circular scale calibration and radial branch lengths, was not offered by prior peer software.

The software further supports polytomies and more freeform connectivities by allowing the user to manually connect nodes to the correct parent through a simple two-click interaction. If branch lengths are not desired, a cladogram mode exports the tree without them. Beyond image reconstruction, Treemble can also be used in a blank-canvas drawing mode to sketch a tree by hand and generate a Newick string, and it can export the extracted tree as an SVG (Allard et al., 9 Aug 2025).

4. Evaluation, implementation, and practical limitations

The paper reports a simulation-based performance evaluation using 10 simulated trees with 25 taxa each. Trees were generated with a lineage birth-death process using DendroPy, rendered as images with Biopython, and then reconstructed in Treemble (Allard et al., 9 Aug 2025). In all trials, the resulting Newick strings matched the original topology perfectly. Internal-node heights were recovered with $R^2 = 0.99997$, and branch lengths had $R^2 = 0.99994$. The mean absolute error in branch lengths was 0.1118 relative to a mean branch length of 19.6067, or about 0.57\%. The average extraction time per simulated tree image was about 2 minutes.

The trials used relatively low-resolution images, specifically 1000 pixels wide, and the authors note that higher-resolution figures should perform even better. They also report successfully constructing a Newick string from a much larger phylogeny with 1,382 tips, which suggests scalability to large trees, although the paper does not present a broader benchmark suite for such large instances (Allard et al., 9 Aug 2025).

Implementation details are also emphasized. Treemble is a native desktop application built with the Tauri framework, using a Rust backend and a webview-based interface written in TypeScript/React. It runs on macOS and Windows; Linux support exists at the framework level, but the released installers are specifically for MacOS and Windows. Because Tauri reuses the host system’s browser engine rather than bundling a full Chromium runtime, the installers are reported to be under 8 MB (Allard et al., 9 Aug 2025).

The interface includes keyboard shortcuts, autosave and session recovery, diff tools for comparing two tip-name sets, automatic equalization of tip positions for ultrametric trees, grayscale mode, dark mode support, and the ability to save node-location data as CSV so a session can later be reopened and edited. The paper’s stated limitations are largely implicit rather than polemical: the system remains semi-automatic, accurate reconstruction depends on correct node marking, and tip-label correctness still depends on either user editing or correct label import. This suggests that Treemble is best understood as a high-leverage expert-assistance tool rather than a fully autonomous figure-mining system.

5. Treemble as a best-of-three erasure process on labeled binary plane trees

In the second usage, Treemble is the name of a very simple leaf-trimming process on labeled binary plane trees. The trees are rooted at a leaf, every vertex has degree either 1 or 3, and a labeled tree carries a bijection from its leaves to

$\{0,1,\dots,|t|+1\},$

with the root labeled $0$ (Caraceni et al., 15 Apr 2026). The trimming operation is defined through fringe subtrees above branching nodes and a relabeling convention after cuts.

The discrete procedure is the best-of-three erasure. Starting at the branching node attached to the root leaf, the process repeatedly inspects the three smallest labels in the active fringe. If the fringe contains no branching node, the current node is the cut point. Otherwise, at least two of the three smallest labels lie in the same child subtree, and the procedure moves to that child. Iterating this rule eventually reaches a node whose fringe is just two leaves joined at a cherry; cutting there removes exactly one leaf from the whole tree after relabeling (Caraceni et al., 15 Apr 2026).

The erased leaf is the Best-of-Three leaf (BoT leaf): specifically, the deleted leaf is the larger label among the two leaves in the final cherry, while its sibling has the smaller label. The one-step erase operation maps a labeled binary tree of size $n$ to one of size $Y$0. Its key combinatorial property is exact uniformity: if $Y$1 is uniformly random among labeled binary trees of size $Y$2, then one best-of-three erasure produces a uniformly random labeled binary tree of size $Y$3 (Caraceni et al., 15 Apr 2026).

The proof is combinatorial. The map from size $Y$4 trees to size $Y$5 trees is exactly $Y$6-to-1. Given the smaller tree, one reconstructs a preimage by choosing the erased label, relabeling increasingly, and grafting a leaf in one of the allowed positions. The count is

$Y$7

This is the discrete mechanism that preserves the uniform law under erasure (Caraceni et al., 15 Apr 2026).

Repeated application produces a chain

$Y$8

such that $Y$9 is the best-of-three erasure of $X$0 for every $X$1. In that sense the trees are nested, yielding a monotone coupling of uniform trees of successive sizes. The paper explicitly relates this to the earlier couplings of Luczak–Winkler and Caraceni–Stauffer, stating that the best-of-three construction specializes to their one-step coupling while making the entire chain coherent through built-in labels rather than resampling labels at each step (Caraceni et al., 15 Apr 2026).

6. Scaling limit, Brownian CRT interpretation, and conceptual significance

The same paper develops a scaling limit in terms of Brownian Continuum Random Trees. After rescaling by $X$2, the nested discrete trees converge to a process $X$3 inside a Brownian CRT $X$4, where each $X$5 is a closed subtree with the same law as

$X$6

(Caraceni et al., 15 Apr 2026). More precisely, there exists a space-filling function

$X$7

such that

$X$8

and the discrete process converges in the supremum Gromov–Hausdorff metric over time.

The paper describes this limit as a càdlàg erasure of the Brownian tree. The associated map $X$9 records the time at which each branch point is erased, and the inverse map $Y$0 extends to a càdlàg space-filling function (Caraceni et al., 15 Apr 2026). In this formulation, branch-point erasure time is defined by

$Y$1

the total mass of the subtrees erased up to and including $Y$2. The image of this map is dense in $Y$3.

The authors remark that the limiting growth is reminiscent of SLE-type growth because the Brownian CRT grows through a single point rather than by adding mass everywhere (Caraceni et al., 15 Apr 2026). They also emphasize a compatibility lemma for span trees: the BoT-erasure order on branch points is compatible across finite leaf-spans, and newly appearing branch points lie in nested fringe regions. This compatibility is presented as the discrete backbone of the limiting construction.

Taken together, these properties explain why the probabilistic Treemble is more than a generic pruning rule. In the paper’s framing, it is a coupling mechanism that simultaneously provides exact one-step uniformity, a nested chain of uniform binary plane trees, and a continuum-limit interpretation as a tree-valued càdlàg erasure flow on the Brownian CRT (Caraceni et al., 15 Apr 2026). A plausible implication is that the construction matters not only for random-tree combinatorics but also for how discrete monotone couplings can persist into continuum random geometry.

7. Comparative interpretation across the two usages

The two Treembles share a name and a concern with trees, but otherwise operate at different levels of abstraction. The phylogenetic Treemble is an applied reconstruction environment: it turns published figures into Newick strings through quick human marking plus algorithmic assembly, supports both rectangular and circular trees, and emphasizes practical reuse of phylogenetic information that would otherwise remain locked inside images (Allard et al., 9 Aug 2025). The probabilistic Treemble is a discrete stochastic process: it deletes leaves one-by-one by a best-of-three rule, preserves exact uniformity under size reduction, and converges after rescaling to a Brownian-tree erasure process (Caraceni et al., 15 Apr 2026).

This divergence also clarifies what Treemble is not. It is not a single methodology spanning biology and probability, and it is not synonymous with work on tremor detection in clinical time-series modeling. The tremor-detection paper in the supplied corpus concerns a two-stage hierarchical framework combining a DeepConvLSTM and a vision-transformer-style aggregator for session-level tremor classification from raw 3D kinematic time series, with attention-based and Grad-CAM-based interpretability (Odonga et al., 30 May 2026). Its presence underscores only a lexical overlap between “Treemble” and “tremor,” not a technical relationship.

In current arXiv usage, therefore, Treemble is best treated as a context-dependent term. In phylogenetics it denotes a tool for recovering machine-readable evolutionary trees from images. In probabilistic combinatorics it denotes a best-of-three trimming algorithm with exact finite-$Y$4 and Brownian-CRT limiting structure. The commonality is nominal; the significance in each field is domain-specific.