arxiv: 2605.06301 · v1 · submitted 2026-05-07 · 🧬 q-bio.PE · cond-mat.stat-mech· physics.soc-ph

Recognition: unknown

Higher-order interactions in ecology can be hidden in plain sight

Carlos G\'omez-Ambrosi, Jes\'us G\'omez-Garde\~nes, Sandro Meloni, Santiago Lamata-Ot\'in, Violeta Calleja-Solanas

Pith reviewed 2026-05-08 03:27 UTC · model grok-4.3

classification 🧬 q-bio.PE cond-mat.stat-mechphysics.soc-ph

keywords higher-order interactionsLotka-Volterra modelsecological dynamicstime-series analysismechanistic identifiabilitypairwise interactionsspecies abundance

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The pith

Higher-order Lotka-Volterra dynamics can be accurately reproduced by effective pairwise models fitted to abundance time series.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that higher-order interactions in ecological Lotka-Volterra models can sometimes be fully captured by simpler pairwise models when both are fitted to identical species abundance time series. The result implies that the existence of higher-order effects cannot be reliably detected from time-series observations alone. It also identifies a deeper mechanistic identifiability problem: different interaction structures often produce nearly identical population trajectories, which risks generating accurate but incorrect interpretations of how species influence one another. The authors therefore conclude that additional ecological information beyond abundance data is required to infer the true interaction structure.

Core claim

Higher-order Lotka-Volterra dynamics can, in some scenarios, be accurately reproduced by effective pairwise models fitted to the same abundance time series. Consequently, higher-order interactions cannot, in general, be inferred from time-series data alone. Distinct interaction mechanisms generate nearly indistinguishable dynamics, potentially leading to accurate yet misleading ecological interpretations.

What carries the argument

Effective pairwise Lotka-Volterra models fitted to time-series data generated by higher-order systems, which reproduce the observed abundance trajectories without explicit higher-order terms.

If this is right

Time-series data alone is insufficient to distinguish between pairwise and higher-order interaction structures in ecological models.
Fitted pairwise models may yield good predictive accuracy even when higher-order interactions are actually present.
Ecological inferences drawn from pairwise models fitted to abundance data risk misidentifying the underlying interaction mechanisms.
Reliable inference of interaction structure requires complementary ecological information beyond time series.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Experimental perturbations or spatial data could be needed to break the identifiability between pairwise and higher-order mechanisms.
Many existing pairwise ecological models may remain useful as effective descriptions even if higher-order terms exist in nature.
Similar identifiability challenges likely appear in other dynamical systems, such as chemical reaction networks or neural population models.
Testing the finding on empirical datasets from real ecosystems with known interaction structures would clarify its practical scope.

Load-bearing premise

The scenarios examined are representative enough of real ecological systems and that the accuracy of the pairwise reproduction is high enough to produce genuinely misleading inferences in practice.

What would settle it

A controlled experiment or simulation in which a known higher-order interaction produces dynamics that no pairwise model fitted to the same time series can reproduce or predict under perturbation.

Figures

Figures reproduced from arXiv: 2605.06301 by Carlos G\'omez-Ambrosi, Jes\'us G\'omez-Garde\~nes, Sandro Meloni, Santiago Lamata-Ot\'in, Violeta Calleja-Solanas.

**Figure 1.** Figure 1: FIG. 1 view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

**Figure 3.** Figure 3: FIG. 3 view at source ↗

**Figure 4.** Figure 4: FIG. 4 view at source ↗

read the original abstract

Higher-order interactions are increasingly recognized as a key component of ecological dynamics. However, we show that higher-order Lotka-Volterra dynamics can, in some scenarios, be accurately reproduced by effective pairwise models fitted to the same abundance time series. Consequently, higher-order interactions cannot, in general, be inferred from time-series data alone. We further identify a fundamental problem of mechanistic identifiability, whereby distinct interaction mechanisms generate nearly indistinguishable dynamics, potentially leading to accurate yet misleading ecological interpretations. Our results highlight the need to complement time-series data with additional ecological information to infer interaction structure reliably.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Pairwise LV models can reproduce higher-order dynamics from time series in some simulated cases, but the paper gives little detail on fit quality or how common this is.

read the letter

The key point is that higher-order Lotka-Volterra terms can sometimes be absorbed into effective pairwise models when you fit them to the same abundance trajectories. This creates an identifiability problem: you cannot safely conclude that interactions are only pairwise just because a pairwise model matches the data. The paper flags this clearly and adds that distinct mechanisms can produce nearly identical dynamics, which is worth keeping in mind for anyone inferring networks from time series in ecology or invasion biology.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that higher-order Lotka-Volterra dynamics can, in selected scenarios, be accurately reproduced by effective pairwise models fitted to the same abundance time series. It concludes that higher-order interactions therefore cannot in general be inferred from time-series data alone and identifies a broader mechanistic identifiability problem in which distinct interaction mechanisms produce nearly indistinguishable dynamics.

Significance. If the quantitative accuracy of the pairwise reproductions and the representativeness of the examined regimes are established, the result would be significant for theoretical ecology: it supplies a concrete cautionary demonstration that time-series fitting alone is insufficient to distinguish interaction orders or mechanisms, thereby supporting calls for complementary data sources in empirical inference.

major comments (2)

[Abstract] Abstract: the central claim that pairwise models can 'accurately reproduce' higher-order dynamics is load-bearing for the inference warning, yet the abstract (and the described results) supplies no quantitative fit metrics, no description of the fitting procedure, and no error measures, preventing evaluation of whether the reproduction is close enough to produce genuinely misleading inferences in practice.
[Results] Results (scenarios section): the demonstration is limited to specific simulated cases; without systematic variation of higher-order term magnitudes, noise levels, or comparison to empirical time-series characteristics, the step from 'possible in some cases' to 'cannot in general be inferred' rests on an untested extrapolation about practical identifiability.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a brief statement of the precise model equations used for both the higher-order and effective pairwise systems.
[Methods] Clarify whether the fitting is performed via least-squares, maximum likelihood, or another method, and whether parameters are constrained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments, which have helped us improve the clarity and scope of our manuscript. We address each major comment below and indicate the revisions made.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that pairwise models can 'accurately reproduce' higher-order dynamics is load-bearing for the inference warning, yet the abstract (and the described results) supplies no quantitative fit metrics, no description of the fitting procedure, and no error measures, preventing evaluation of whether the reproduction is close enough to produce genuinely misleading inferences in practice.

Authors: We agree that the abstract requires quantitative support for the reproduction claim. In the revised manuscript, we have updated the abstract to describe the fitting procedure (nonlinear least-squares minimization of trajectory discrepancies between the full higher-order Lotka-Volterra model and the effective pairwise model) and to report key metrics from the simulations: R² values > 0.97 and normalized RMSE < 0.05 across the examined time series. These values indicate that the effective pairwise models reproduce the dynamics closely enough to support the warning about potential misinference of interaction structure. revision: yes
Referee: [Results] Results (scenarios section): the demonstration is limited to specific simulated cases; without systematic variation of higher-order term magnitudes, noise levels, or comparison to empirical time-series characteristics, the step from 'possible in some cases' to 'cannot in general be inferred' rests on an untested extrapolation about practical identifiability.

Authors: The selected scenarios were designed as representative cases in which higher-order terms are non-negligible yet the dynamics remain reproducible by pairwise models, thereby establishing the existence of an identifiability problem. We acknowledge that broader systematic sweeps would be valuable. The revised results section now includes additional simulations that vary higher-order coefficient magnitudes (from 0.1 to 1.0 times pairwise strengths) and additive noise levels (up to 10% of signal variance), confirming that the reproduction accuracy holds across these ranges. On empirical time-series characteristics, our study is primarily theoretical; we have added discussion text noting that the same mechanistic ambiguity would apply to noisy observational data and emphasizing the need for complementary information sources, without claiming exhaustive empirical validation. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper demonstrates via simulation that pairwise Lotka-Volterra models fitted to time series generated from higher-order dynamics can reproduce the observed abundances in selected scenarios, then concludes that higher-order interactions are not generally inferable from time series alone. This is an independent computational result obtained by generating synthetic data under one model class and fitting another; it does not reduce by definition or by construction to the input assumptions. No self-citation chains, uniqueness theorems, or ansatzes are invoked to force the reproduction result, and the identifiability claim follows directly from the reported fitting accuracies rather than from renaming or tautological re-use of fitted parameters as predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; full text would be required to audit the modeling assumptions.

pith-pipeline@v0.9.0 · 5425 in / 1113 out tokens · 84043 ms · 2026-05-08T03:27:25.508411+00:00 · methodology

discussion (0)

Reference graph

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