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Extracting useful information about reversible evolutionary processes from irreversible evolutionary accumulation models

This paper demonstrates that while irreversible evolutionary accumulation models may yield inaccurate uncertainty estimates and feature interaction details, they can still reliably infer the relative ordering of events and the core dynamic structure of evolutionary pathways even when the underlying biological processes are reversible.

Original authors: Iain G. Johnston

Published 2026-03-13

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Iain G. Johnston

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are a detective trying to figure out the order in which a thief broke into a house. You find a list of items that are missing: a TV, a laptop, a gold watch, and a diamond ring.

The Old Way (Irreversible Models):
Most detectives (and most computer models used in biology) assume a simple rule: Once something is stolen, it's gone forever. You can't steal the TV, then the laptop, then return the TV. The thief only adds items to their pile; they never take anything back out. This makes the math easy and fast.

The Real World (Reversible Dynamics):
But in reality, things are messier. Maybe the thief stole the TV, realized it was too heavy, and left it in the hallway before stealing the laptop. Or maybe they swapped the gold watch for the diamond ring. In biology, this is like a bacteria gaining a drug resistance, losing it, and gaining it again.

The Big Question:
The paper asks: If we use the "simple" detective rule (that nothing is ever returned), can we still figure out the correct order of events, even if the thief actually did return some items?

The Main Findings (The "Aha!" Moments)

The author, Iain Johnston, ran thousands of computer simulations to test this. Here is what he found, translated into everyday terms:

1. The "Big Picture" is Robust (The Highway vs. The Detour)
Even if the thief occasionally put an item back (reversibility), the main order of the theft usually stays clear.

Analogy: Imagine a highway with an exit ramp. Sometimes cars take the exit and come back on (reversibility). If you look at a traffic camera from a distance, you can still clearly see that most cars go from Exit A to Exit B. The "core route" is still visible.
Result: The models can still tell you that "Feature A usually happens before Feature B," even if the model thinks the process is one-way only.

2. The "Details" Get Blurry (The Foggy Map)
While the main route is clear, the uncertainty and the exact interactions get messy.

Analogy: If you try to guess exactly how many times the thief went back and forth, or why they swapped the watch for the ring, the "simple" model will get it wrong. It might invent fake reasons for the swap (like "The thief hates gold") just to explain the data, because it doesn't know the thief actually just dropped the item.
Result: You can trust the order of events, but you shouldn't trust the model's guess about how likely an event is to happen or why one feature influences another.

3. The "Family Tree" Problem (Pseudoreplication)
Sometimes, the data comes from related groups (like a family of bacteria). If you treat every member of the family as a totally new, independent thief, you might get the wrong idea about how common a theft is.

Analogy: If one family of thieves steals 10 TVs and another family steals 1 laptop, and you count every TV as a separate event, you'll think "TVs are the most popular theft." But if you realize they are all from the same family, you see it's just one family with a TV obsession.
Result: The paper found that while ignoring family trees messes up the confidence in the numbers, it rarely changes the main conclusion about the order of events.

Real-World Application: Superbugs

The author tested this on Antimicrobial Resistance (AMR) in bacteria (like Klebsiella pneumoniae). These bacteria often gain and lose drug resistance genes rapidly (like a thief swapping items).

The Good News: Even though these bacteria are "reversible" (they lose resistance easily), the simple, fast models can still tell us the likely order in which they become resistant to different drugs. This is crucial for doctors to know which drugs to use first.
The Caveat: We shouldn't use these simple models to predict exactly how often a bug will lose a resistance or to calculate the precise "risk" of a specific mutation.

The Bottom Line

Think of the "Irreversible Model" as a rough sketch of a crime scene.

Is it perfect? No. It misses the details of items being returned or swapped.
Is it useful? Yes, absolutely. It correctly identifies the main sequence of events (the "who, what, and when" of the theft).

If you need a quick, reliable answer about the order of evolution, the simple, fast models work great, even if the real process is messy and reversible. But if you need to know the exact probabilities or the hidden reasons behind the changes, you need the more complex, slower models that account for the "returning" of features.

1. Problem Statement

Evolutionary Accumulation Models (EvAMs) are machine learning methods used to infer the pathways by which binary features (e.g., mutations, drug resistances, gene transfers) are acquired over time. These models are widely applied in cancer evolution, antimicrobial resistance (AMR), and comparative biology.

The Core Assumption: Many existing EvAMs assume irreversibility (once a feature is acquired, it cannot be lost). This assumption simplifies computation and improves statistical stability but is biologically unrealistic for many systems where features can be lost (reversible dynamics).
The Challenge: Fully reversible models (e.g., HyperMk) are computationally expensive and statistically less stable, especially with large numbers of features.
The Research Question: Can irreversible models, despite their restrictive assumptions, still extract useful and reliable information about the underlying dynamics of systems that are actually reversible? Specifically, what information is robust to the assumption of irreversibility, and what is lost?

2. Methodology

The study employs a simulation-based approach to compare the performance of irreversible models against known "ground truth" reversible dynamics.

Data Generation:
- Generative Models: The authors simulated evolutionary processes on phylogenetic trees (using a birth-death model).
- Dynamics: They tested various scenarios:
  - Hard Pathways: Explicit interactions enforce a strict order of acquisition (e.g., Feature 1 must precede Feature 2).
  - Soft Pathways: Order is probabilistic based on different acquisition rates ( $\alpha$ ) rather than strict dependencies.
  - Reversibility: Features could be lost with a characteristic rate ( $\beta$ ), creating reversible transitions.
  - Pathway Structures: Single dominant pathways vs. competing pathways (e.g., 1→2→3 vs. 4→3→2).
- Data Types: Both cross-sectional (independent samples) and phylogenetically linked data were generated.
Inference Models:
- HyperMk: A reversible model capable of handling both gain and loss of features (used as the "gold standard" for comparison and for fitting reversible data).
- HyperHMM: An irreversible model. It was tested in two modes:
  1. Treating all observations as independent (cross-sectional).
  2. Reconstructing ancestral states deterministically (assuming rare, irreversible changes) before fitting a phylogenetically informed model.
- HyperTraPS: Used to estimate interactions between features (promotion/repression) under the assumption of irreversibility.
Evaluation Metrics:
- Ordering Matrix ( $M$ ): A matrix where $M_{ij}$ represents the probability that feature $i$ is acquired while feature $j$ is absent. This summarizes the relative ordering of acquisitions.
- Transition Network Overlap: Comparing the proportion of ground-truth transitions captured by the inferred models.
- Principal Component Analysis (PCA): Used to visualize the similarity between inferred dynamics and ground truth in a low-dimensional space.

3. Key Contributions

Quantification of Irreversibility Errors: The paper systematically quantifies the errors introduced when applying irreversible models to reversible data.
Robustness of Core Structure: It demonstrates that the relative ordering of acquisitions and the core dynamic structure of pathways are largely robust to the assumption of irreversibility.
Vulnerability of Interactions and Uncertainty: It identifies that estimates of feature interactions (how one feature influences another) and uncertainty quantification are highly sensitive to the irreversibility assumption and prone to error.
Phylogenetic Context: The study clarifies that while neglecting phylogenetic information leads to pseudoreplication (artificially inflating sample size and shrinking uncertainty estimates), it rarely alters the point estimates of the pathway structure itself, unless there is extreme lineage imbalance.

4. Key Results

Pathway Structure Preservation: In simulations involving "hard" pathways with loss events, irreversible models (HyperHMM) successfully recovered the correct sequence of acquisitions (e.g., 1→2→3→4) even when the true process allowed for the loss of Feature 1. The inferred transition networks captured 75% or more of the ground-truth edges.
Soft Pathways and Noise: For "soft" pathways (where order is rate-dependent), reversibility acted similarly to increased observational noise. While the inferred pathways were less precise (more spread in probability), the general trend remained consistent with the ground truth.
Competing Pathways: In cases with two competing pathways, reversible dynamics reduced the precision of estimating the weight of each pathway but did not destroy the detection of the "bimodal" structure.
Failure of Interaction Inference: When using irreversible models (like HyperTraPS) on data generated with reversibility, the inferred interactions between features were unreliable. The model often invented spurious interactions to explain loss events as alternative acquisition pathways.
Real-World Application (AMR): Applied to Klebsiella pneumoniae antimicrobial resistance data (where resistance genes can be gained and lost via plasmids), the irreversible and reversible models produced highly similar transition networks and ordering statistics. The main difference was increased uncertainty in the initial steps of the reversible model.

5. Significance and Implications

Practical Utility: The study provides "cautious optimism" for researchers using computationally tractable irreversible models. Even in systems where features are reversible (like plasmid-mediated drug resistance), these models can reliably infer which features are likely present when another is acquired.
Guidance for Model Selection:
- Use Irreversible Models When: The primary goal is to determine the relative order of events or the core topology of evolutionary pathways, and computational resources are limited.
- Use Reversible Models When: The goal is to quantify uncertainty precisely, infer specific interactions between features (promotion/repression), or when the loss of features is the primary biological question.
Ancestral State Reconstruction: The findings suggest that errors in ancestral state reconstruction caused by assuming irreversibility have a limited impact on the overall inference of pathway structure, provided the sample size is sufficient to represent the dynamics.
Future Directions: The authors note that while simulation results are robust, a theoretical complement is needed to fully characterize the error bounds of neglecting reversibility across all possible generative mechanisms.

In summary, the paper argues that while the assumption of irreversibility is a simplification, it does not render EvAMs useless for reversible systems. The "core signal" of evolutionary order is preserved, allowing researchers to extract meaningful biological insights from complex, reversible data using simpler, faster models.