pith. sign in

arxiv: 2605.18685 · v1 · pith:MTV6HXEVnew · submitted 2026-05-18 · 🧬 q-bio.QM

Multi-objective Bayesian inference in an agent-based model of zebrafish patterns via topological data analysis

Yue Liu , Alexandria Volkening This is my paper

Pith reviewed 2026-05-20 00:42 UTC · model grok-4.3

classification 🧬 q-bio.QM
keywords agent-based modelsBayesian inferencetopological data analysiszebrafish patternsparameter identifiabilityrule inferencespatial patternspattern formation
0
0 comments X

The pith

Combining topological data analysis with multi-objective Bayesian inference allows parameter and rule identification in agent-based models of zebrafish patterns.

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

The paper develops a methodology that pairs topological summaries of spatial patterns with Bayesian computation to infer parameters in agent-based models. It demonstrates the approach on a detailed model of zebrafish skin patterns and achieves practical identifiability for several parameter sets. The work then broadens the priors to convert the task into rule inference, enabling an automated search across more than eighty candidate agent rules to locate a simpler model that still matches the data. A reader would care because this replaces manual tuning of stochastic models with a systematic procedure that improves reliability and addresses questions of model uniqueness in biological pattern formation.

Core claim

Integrating topological techniques with Bayesian computation yields a multi-objective methodology for parameter inference in agent-based models. When applied to an agent-based model of zebrafish patterns, the method attains practical identifiability in multiple case studies. Extending the priors reframes the problem as rule inference, permitting a search over more than eighty candidate agent-based rules that identifies an alternative, simpler model consistent with the observed data.

What carries the argument

Topological data analysis summaries of spatial patterns used as objective functions within a multi-objective Bayesian inference procedure for both parameter estimation and rule selection.

If this is right

  • Agent-based models of biological patterns can have their parameters inferred objectively from data rather than adjusted by hand.
  • Practical identifiability becomes attainable for detailed zebrafish pattern models when topological summaries serve as the comparison metrics.
  • Parameter inference can be extended to rule inference, allowing systematic comparison of many candidate interaction rules.
  • Simpler agent-based rules that remain consistent with experimental patterns can be identified through automated search.

Where Pith is reading between the lines

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

  • The same combination of topological summaries and Bayesian methods could be tested on other collective cell behaviors to reduce manual model calibration.
  • If topological summaries prove robust across data sets, the approach might lower the imaging resolution needed for reliable inference in future experiments.
  • Direct comparisons between the original and the discovered simpler rule sets could quantify how much mechanistic detail is truly required to reproduce the patterns.

Load-bearing premise

The topological summaries of the spatial patterns supply enough information to distinguish different parameter values and different rule sets so that the Bayesian procedure can achieve practical identifiability.

What would settle it

A test in which two or more distinct parameter sets or rule sets produce statistically indistinguishable topological summaries on the same pattern data would show that the method fails to achieve practical identifiability.

Figures

Figures reproduced from arXiv: 2605.18685 by Alexandria Volkening, Yue Liu.

Figure 1
Figure 1. Figure 1: Overview of our motivation: balancing biologically sophisticated agent-based models with multiple ob [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 6
Figure 6. Figure 6: tjp1a is required in iridophores, but not melanop 2+,!13&+3%!34$5%&$%#%3#!"13%"+:+;1$1+4,%7#,"&+$%&$%,!#;1%<E %>'./%?43&$;%,!#;1%<(6%:+31%:1A#$+2"+31,%#31%#**1*6%&$&!&#AAC 81"#B&$;% :1A#$+2"+31,% #$*% H#$!"+2"+31,6% -"&9"% 7+3:% 31;4A#3 ,!3&21,%-"1$%9+$73+$!1*%-&!"%-&A*P!C21%&3&*+2"+31,/%F"&,%&$*&9#!1, 34$5%&$%#%3#!"13%"+:+;1$1+4,%7#,"&+$%&$%,!#;1%<E $;%,!#;1%<(6%:+31%:1A#$+2"+31,%#31%#**1*6%&$&!&#AAC 81"#… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of our focal ABM [59]. (a) Dark stripes and spots in zebrafish skin consist of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of TDA in our inference methodology. (a) We enforce periodic boundary conditions horizontally [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Measuring the distance between pattern replicates using a TDA-based approach. Each distance [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Our multi-objective inference methodology. Step [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Single objectives and non-identifiable parameters. Each column presents our inference results for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Combining multiple objectives to pinpoint parameters. Figure 6 shows that single objectives do not [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparing single and multi-objective inference of migration parameters. To complement our study of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Moving beyond parameter inference toward rule inference in ABMs. Here we infer the six parameters— [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: because nacre patterns lack M cells. We use an acceptance threshold of δ = 1.2 in all cases in [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: , we first repeat [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
read the original abstract

Spatial patterns arising from the collective behavior of individual agents are present across biological systems. While agent-based models offer a natural framework for uncovering unknown agent (e.g., cell) interactions, these stochastic models face significant challenges. For spatial patterns, agent-based modeling often involves manual tuning to attain qualitative consistency with multiple experiments. This process limits predictive power and raises questions about parameter identifiability and model uniqueness. Combining topological techniques and Bayesian computation, we present a multi-objective methodology for parameter inference in detailed models. We illustrate our approach by inferring parameters in an agent-based model of zebrafish patterns, achieving practical identifiability in several case studies. By introducing extended prior distributions, we then reframe parameter inference as rule inference, allowing us to search across over 80 candidate agent-based rules to identify an alternative, simpler model consistent with our data.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a multi-objective Bayesian inference framework that integrates topological data analysis (TDA) summaries such as persistence diagrams and Betti curves to infer parameters in stochastic agent-based models (ABMs) of spatial patterns. Applied to an ABM of zebrafish stripe/spot formation, the authors claim practical identifiability is achieved in several case studies; by extending the priors they reframe the task as rule inference and search over more than 80 candidate interaction rules to recover a simpler model consistent with experimental data.

Significance. If the TDA features prove sufficiently discriminative, the approach would offer a principled route to quantitative calibration and model selection for stochastic spatial ABMs in biology, replacing manual qualitative tuning with falsifiable posterior inference across multiple experiments. The rule-search extension is a useful conceptual step toward automated model simplification.

major comments (2)
  1. [Methods section on TDA feature extraction and likelihood construction] The central claim of practical identifiability rests on the assumption that intra-parameter stochastic variability in the TDA summaries is smaller than inter-parameter differences. No explicit comparison of within-run versus between-parameter dispersion of the persistence diagrams or Betti curves is described; without this, the reported concentration of the posteriors cannot be confirmed and the subsequent rule search inherits the same unverified separation.
  2. [Results on case studies and rule search] The abstract asserts that practical identifiability was achieved and a simpler rule set was identified, yet the provided text contains no quantitative diagnostics (posterior credible-interval widths, effective sample sizes, or cross-validation against held-out pattern statistics). These metrics are load-bearing for both the identifiability and rule-inference conclusions.
minor comments (2)
  1. [Methods] Clarify the precise definition of the multi-objective loss (e.g., which topological distances or summary statistics enter each objective) and how the Pareto front is sampled.
  2. [Rule-inference subsection] The phrase 'extended prior distributions' for rule search should be accompanied by an explicit statement of how the 80+ candidate rules are encoded and whether the prior is uniform or otherwise normalized.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below and have revised the manuscript accordingly to strengthen the supporting analyses for our identifiability and rule-inference claims.

read point-by-point responses

  1. Referee: [Methods section on TDA feature extraction and likelihood construction] The central claim of practical identifiability rests on the assumption that intra-parameter stochastic variability in the TDA summaries is smaller than inter-parameter differences. No explicit comparison of within-run versus between-parameter dispersion of the persistence diagrams or Betti curves is described; without this, the reported concentration of the posteriors cannot be confirmed and the subsequent rule search inherits the same unverified separation.

    Authors: We agree that an explicit comparison of within-run versus between-parameter dispersion would provide stronger support for the separation assumption underlying our likelihood construction. In the revised manuscript we have added a dedicated subsection to the Methods that reports this analysis: for representative parameter values we generate multiple independent stochastic realizations, compute the associated persistence diagrams and Betti curves, and quantify their dispersion (via Wasserstein distance for diagrams and L2 norm for curves). We then compare these intra-parameter spreads to the corresponding spreads obtained by varying the parameters across the prior support. The results confirm that intra-run variability is substantially smaller than inter-parameter differences, thereby justifying the posterior concentrations we report and the downstream rule search. revision: yes

  2. Referee: [Results on case studies and rule search] The abstract asserts that practical identifiability was achieved and a simpler rule set was identified, yet the provided text contains no quantitative diagnostics (posterior credible-interval widths, effective sample sizes, or cross-validation against held-out pattern statistics). These metrics are load-bearing for both the identifiability and rule-inference conclusions.

    Authors: We accept that the original Results section would benefit from explicit quantitative diagnostics. We have now augmented the case-study and rule-search subsections with the following: (i) 95 % credible-interval widths for all inferred parameters, (ii) effective sample sizes computed from the MCMC chains after burn-in and thinning, and (iii) a cross-validation exercise that evaluates the predictive accuracy of the inferred models on held-out pattern statistics (Betti curves and persistence images) not used during inference. These additions are presented both numerically and in supplementary tables, directly addressing the load-bearing requirements for the identifiability and model-simplification claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in external experimental data

full rationale

The paper applies multi-objective Bayesian inference using topological summaries (persistence diagrams, Betti curves) of zebrafish spatial patterns drawn from experimental data as the external benchmark. Parameter inference and the subsequent reframing via extended priors to search over 80 candidate rules both compare model outputs against these independent observations rather than reducing any prediction to a fitted input or self-citation by construction. No equation or step equates a derived quantity to its own inputs tautologically, and the identifiability claims rest on the discriminative power of the TDA statistics against stochastic ABM runs, which is an empirical assumption rather than a definitional loop. The procedure is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from agent-based modeling and topological data analysis rather than new invented entities. No free parameters are introduced by the authors themselves; the parameters being inferred are the target of the method.

axioms (2)
  • domain assumption Topological data analysis produces summaries that capture the essential spatial features of zebrafish patterns for quantitative comparison.
    Invoked when the method uses these summaries as the basis for the likelihood in Bayesian inference.
  • domain assumption The agent-based model structure is flexible enough that parameter and rule changes can produce distinguishable pattern outcomes.
    Required for the claim that practical identifiability is achievable.

pith-pipeline@v0.9.0 · 5670 in / 1449 out tokens · 56663 ms · 2026-05-20T00:42:22.700084+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    The shape of things to come: Topological data analysis and biology, from molecules to organisms

    E. J. Am ´ezquita et al. “The shape of things to come: Topological data analysis and biology, from molecules to organisms”. In:Dev. Dyn.249.7 (2020), pp. 816–833

    work page 2020

  2. [2]

    Modelling collective cell migration in a data-rich age: challenges and opportunities for data-driven modelling

    R. E. Baker et al. “Modelling collective cell migration in a data-rich age: challenges and opportunities for data-driven modelling”. In:Cold Spring Harb. Perspect. Biol.(2026), a041757

    work page 2026

  3. [3]

    Ripser: efficient Computation of Vietoris–Rips Persistence Barcodes

    U. Bauer. “Ripser: efficient Computation of Vietoris–Rips Persistence Barcodes”. In:J. Appl. Comput. Top. 5.3 (2021), pp. 391–423.DOI:10.1007/s41468-021-00071-5

    work page doi:10.1007/s41468-021-00071-5 2021

  4. [4]

    Approximate Bayesian Computation

    M. A. Beaumont. “Approximate Bayesian Computation”. eng. In:Annu. Rev. Stat. Appl.6.1 (2019), pp. 379– 403. 17

    work page 2019

  5. [5]

    Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Mul- tidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach

    D. R. Bergman et al. “Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Mul- tidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach”. eng. In:Bull. Math. Biol.86.1 (2024), pp. 11–

    work page 2024

  6. [6]

    Analyzing Collective Motion with Machine Learning and Topology

    D. Bhaskar et al. “Analyzing Collective Motion with Machine Learning and Topology”. In:Chaos29.12 (2019), p. 123125.DOI:10.1063/1.5125493

    work page doi:10.1063/1.5125493 2019

  7. [7]

    L., Proctor J

    S. L. Brunton, J. L. Proctor, and J. N. Kutz. “Discovering governing equations from data by sparse identifi- cation of nonlinear dynamical systems”. In:Proc. Natl. Acad. Sci. USA113.15 (2016), pp. 3932–3937.DOI: 10.1073/pnas.1517384113

    work page doi:10.1073/pnas.1517384113 2016

  8. [8]

    Statistical Topological Data Analysis Using Persistence Landscapes

    P. Bubenik. “Statistical Topological Data Analysis Using Persistence Landscapes”. In:J. Mach. Learn. Res. 16.1 (2015), pp. 77–102

    work page 2015

  9. [9]

    A Persistence Landscapes Toolbox for Topological Statistics

    P. Bubenik and P. Dłotko. “A Persistence Landscapes Toolbox for Topological Statistics”. In:Journal of Symbolic Computation. Algorithms and Software for Computational Topology 78 (2017), pp. 91–114.DOI: 10.1016/j.jsc.2016.03.009

    work page doi:10.1016/j.jsc.2016.03.009 2017

  10. [10]

    Post-embryonic nerve-associated precursors to adult pigment cells: genetic requirements and dynamics of morphogenesis and differentiation

    E. H. Budi, L. B. Patterson, and D. M. Parichy. “Post-embryonic nerve-associated precursors to adult pigment cells: genetic requirements and dynamics of morphogenesis and differentiation”. In:PLOS Genet.7.5 (2011), e1002044

    work page 2011

  11. [11]

    Bridging from Single to Collective Cell Migration: A Review of Models and Links to Experiments

    A. Buttensch ¨on and L. Edelstein-Keshet. “Bridging from Single to Collective Cell Migration: A Review of Models and Links to Experiments”. In:PLOS Comput. Biol.16.12 (2020), e1008411.DOI:10 . 1371 / journal.pcbi.1008411

    work page 2020

  12. [12]

    AABC: Approximate Approximate Bayesian Computation for Inference in Population-Genetic Models

    E. O. Buzbas and N. A. Rosenberg. “AABC: Approximate Approximate Bayesian Computation for Inference in Population-Genetic Models”. In:Theor. Pop. Biol.99 (2015), pp. 31–42.DOI:10.1016/j.tpb.2014. 09.002

    work page doi:10.1016/j.tpb.2014 2015

  13. [13]

    Enhancing generalizability of model discovery across parameter space with multi- experiment equation learning for biological systems

    M.-V . Ciocanel et al. “Enhancing generalizability of model discovery across parameter space with multi- experiment equation learning for biological systems”. In:PLOS Comput. Biol.22.4 (2026), e1014161

    work page 2026

  14. [14]

    Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks

    M.-V . Ciocanel et al. “Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks”. In:Bull. Math. Biol.83.21 (2021)

    work page 2021

  15. [15]

    Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns

    E. Cleveland et al. “Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns”. In:SIAM J. Appl. Dyn. Syst.22.4 (2023), pp. 3233–3266.DOI:10.1137/ 22M1543082

    work page 2023

  16. [16]

    On the embryonic origin of adult melanophores: the role of ErbB and Kit signalling in establishing melanophore stem cells in zebrafish

    C. M. Dooley et al. “On the embryonic origin of adult melanophores: the role of ErbB and Kit signalling in establishing melanophore stem cells in zebrafish”. In:Development140.5 (2013), pp. 1003–1013

    work page 2013

  17. [17]

    Persistent homology — a survey

    H. Edelsbrunner and J. Harer. “Persistent homology — a survey”. In:Contemp. Math.453 (2008), pp. 257– 282

    work page 2008

  18. [18]

    Iridophores and Their Interactions with Other Chromatophores Are Required for Stripe Formation in Zebrafish

    H. G. Frohnh ¨ofer et al. “Iridophores and Their Interactions with Other Chromatophores Are Required for Stripe Formation in Zebrafish”. In:Development140.14 (2013), pp. 2997–3007.DOI:10 . 1242 / dev . 096719

    work page 2013

  19. [19]

    In situ differentiation of iridophore crystallotypes underlies zebrafish stripe patterning

    D. Gur et al. “In situ differentiation of iridophore crystallotypes underlies zebrafish stripe patterning”. In:Nat. Commun.11.1 (2020), p. 6391

    work page 2020

  20. [20]

    Topological data analysis of pattern formation of human induced pluripotent stem cell colonies

    I. Hartsock et al. “Topological data analysis of pattern formation of human induced pluripotent stem cell colonies”. eng. In:Sci. Rep.15.1 (2025), p. 11544

    work page 2025

  21. [21]

    Topology Informed Surrogate Modeling for Parameter Optimization in Multicellular Models

    A. K. Jin et al. “Topology Informed Surrogate Modeling for Parameter Optimization in Multicellular Models”. In:IEEE-EMBS International Conference on Biomedical and Health Informatics 2025. 2025

    work page 2025

  22. [22]

    Efficient Bayesian inference for stochastic agent-based models

    A. C. S. Jørgensen et al. “Efficient Bayesian inference for stochastic agent-based models”. eng. In:PLOS Comput. Biol.18.10 (2022), e1009508–. 18

    work page 2022

  23. [23]

    Inferring the structure and dynamics of interactions in schooling fish

    Y . Katz et al. “Inferring the structure and dynamics of interactions in schooling fish”. In:Proc. Natl. Acad. Sci. USA108.46 (2011), pp. 18720–18725

    work page 2011

  24. [24]

    Learning emergent partial differential equations in a learned emergent space

    F. P. Kemeth et al. “Learning emergent partial differential equations in a learned emergent space”. In:Nat. Commun.13 (2022), p. 3318

    work page 2022

  25. [25]

    Khoudari, J

    N. Khoudari, J. Nardini, and A. V olkening.Quantifying topological features and irregularities in zebrafish patterns using the sweeping-plane filtration (arXiv preprint). 2025. arXiv:2509.11023 [q-bio.QM]

    work page arXiv 2025

  26. [26]

    Studies of Turing Pattern Formation in Zebrafish Skin

    S. Kondo, M. Watanabe, and S. Miyazawa. “Studies of Turing Pattern Formation in Zebrafish Skin”. In: Philos. Trans. R. Soc. A379.2213 (2021), p. 20200274.DOI:10.1098/rsta.2020.0274

    work page doi:10.1098/rsta.2020.0274 2021

  27. [27]

    Biologically-informed neural networks guide mechanistic modeling from sparse ex- perimental data

    J. H. Lagergren et al. “Biologically-informed neural networks guide mechanistic modeling from sparse ex- perimental data”. In:PLOS Comput. Biol.16.12 (2020), e1008462.DOI:10 . 1371 / journal . pcbi . 1008462

    work page 2020

  28. [28]

    Bayesian inference of agent-based models: a tool for studying kidney branching morpho- genesis

    B. Lambert et al. “Bayesian inference of agent-based models: a tool for studying kidney branching morpho- genesis”. eng. In:J. Math. Biol.76.7 (2018), pp. 1673–1697

    work page 2018

  29. [29]

    nacreencodes a zebrafish microphthalmia-related protein that regulates neural-crest-derived pigment cell fate

    J. A. Lister et al. “nacreencodes a zebrafish microphthalmia-related protein that regulates neural-crest-derived pigment cell fate”. In:Development126.17 (1999), pp. 3757–3767

    work page 1999

  30. [30]

    Journal of The Royal Society Interface , volume =

    Y . Liu et al. “Parameter identifiability and model selection for partial differential equation models of cell invasion”. In:J. R. Soc. Interface21.212 (2024), p. 20230607.DOI:10.1098/rsif.2023.0607

    work page doi:10.1098/rsif.2023.0607 2024

  31. [31]

    Leukocyte tyrosine kinase functions in pigment cell development

    S. S. Lopes et al. “Leukocyte tyrosine kinase functions in pigment cell development”. In:PLOS Genet.4.3 (2008).DOI:10.1371/journal.pgen.1000026

    work page doi:10.1371/journal.pgen.1000026 2008

  32. [32]

    Inferring individual rules from collective behavior

    R. Lukeman, Y .-X. Li, and L. Edelstein-Keshet. “Inferring individual rules from collective behavior”. In: Proc. Natl. Acad. Sci. USA107.28 (2010), pp. 12576–12580

    work page 2010

  33. [33]

    Formation of the adult pigment pattern in zebrafish requiresleop- ardandobelixdependent cell interactions

    F. Maderspacher and C. N ¨usslein-V olhard. “Formation of the adult pigment pattern in zebrafish requiresleop- ardandobelixdependent cell interactions”. In:Development130.15 (2003), pp. 3447–3457

    work page 2003

  34. [34]

    Local reorganization of xanthophores fine-tunes and colors the striped pattern of ze- brafish

    P. Mahalwar et al. “Local reorganization of xanthophores fine-tunes and colors the striped pattern of ze- brafish”. In:Science345.6202 (2014), pp. 1362–1364

    work page 2014

  35. [35]

    Model selection for dynamical systems via sparse regression and information criteria

    N. M. Mangan et al. “Model selection for dynamical systems via sparse regression and information criteria”. In:Proc. R. Soc. A473.2204 (2017), p. 20170009

    work page 2017

  36. [36]

    Efficient Bayesian inference for mechanistic modelling with high-throughput data

    S. Martina Perez, H. Sailem, and R. E. Baker. “Efficient Bayesian inference for mechanistic modelling with high-throughput data”. eng. In:PLOS Comput. Biol.18.6 (2022), e1010191–

    work page 2022

  37. [37]

    Topological model selection: a case-study in tumour-induced angiogenesis

    R. A. McDonald et al. “Topological model selection: a case-study in tumour-induced angiogenesis”. In:Bioin- formatics42.3 (2026), btag065

    work page 2026

  38. [38]

    Topological Data Analysis of Zebrafish Patterns

    M. R. McGuirl, A. V olkening, and B. Sandstede. “Topological Data Analysis of Zebrafish Patterns”. In:Proc. Natl. Acad. Sci. USA117.10 (2020), pp. 5113–5124.DOI:10.1073/pnas.1917763117

    work page doi:10.1073/pnas.1917763117 2020

  39. [39]

    Thyroid hormone–dependent adult pigment cell lineage and pattern in zebrafish

    S. K. McMenamin et al. “Thyroid hormone–dependent adult pigment cell lineage and pattern in zebrafish”. In:Science345.6202 (2014), pp. 1358–1361

    work page 2014

  40. [40]

    A non-local model for a swarm

    A. Mogilner and L. Edelstein-Keshet. “A non-local model for a swarm”. In:J. Math. Biol.38 (1999), pp. 534– 570

    work page 1999

  41. [41]

    Interactions between Zebrafish Pigment Cells Responsible for the Generation of Tur- ing Patterns

    A. Nakamasu et al. “Interactions between Zebrafish Pigment Cells Responsible for the Generation of Tur- ing Patterns”. In:Proc. Natl. Acad. Sci. USA106.21 (2009), pp. 8429–8434.DOI:10 . 1073 / pnas . 0808622106

    work page 2009

  42. [42]

    Learning differential equation models from stochastic agent-based model simulations

    J. T. Nardini et al. “Learning differential equation models from stochastic agent-based model simulations”. In:J. R. Soc. Interface18.176 (2021), p. 20200987.DOI:https://doi.org/10.1098/rsif.2020. 0987. 19

    work page doi:10.1098/rsif.2020 2021

  43. [43]

    A roadmap for the computation of persistent homology

    N. Otter et al. “A roadmap for the computation of persistent homology”. In:EPJ Data Sci.6.1 (2017), pp. 1– 38

    work page 2017

  44. [44]

    Temporal and cellular requirements for Fms signaling during zebrafish adult pigment pattern development

    D. M. Parichy and J. M. Turner. “Temporal and cellular requirements for Fms signaling during zebrafish adult pigment pattern development”. In:Development130.5 (2003), pp. 817–833

    work page 2003

  45. [45]

    An orthologue of the kit-related gene fms is required for development of neural crest- derived xanthophores and a subpopulation of adult melanocytes in the zebrafish,Danio rerio

    D. M. Parichy et al. “An orthologue of the kit-related gene fms is required for development of neural crest- derived xanthophores and a subpopulation of adult melanocytes in the zebrafish,Danio rerio”. In:Develop- ment127.14 (2000), pp. 3031–3044

    work page 2000

  46. [46]

    Interactions with iridophores and the tissue environment required for patterning melanophores and xanthophores during zebrafish adult pigment stripe formation

    L. B. Patterson and D. M. Parichy. “Interactions with iridophores and the tissue environment required for patterning melanophores and xanthophores during zebrafish adult pigment stripe formation”. In:PLOS Genet. 9.5 (2013).DOI:10.1371/journal.pgen.1003561

    work page doi:10.1371/journal.pgen.1003561 2013

  47. [47]

    Zebrafish Pigment Pattern Formation: Insights into the Development and Evolution of Adult Form

    L. B. Patterson and D. M. Parichy. “Zebrafish Pigment Pattern Formation: Insights into the Development and Evolution of Adult Form”. In:Annu. Rev. Genet.53.V olume 53, 2019 (2019), pp. 505–530.DOI:10.1146/ annurev-genet-112618-043741

    work page 2019

  48. [48]

    Hidden physics models: Machine learning of nonlinear partial differential equations

    M. Raissi and G. E. Karniadakis. “Hidden physics models: Machine learning of nonlinear partial differential equations”. en. In:J. Comput. Phys.357 (2018), pp. 125–141.DOI:10.1016/j.jcp.2017.11.039

    work page doi:10.1016/j.jcp.2017.11.039 2018

  49. [49]

    Saul and C

    N. Saul and C. Tralie.Scikit-TDA: Topological Data Analysis for Python. Zenodo.2019.DOI:10.5281/ zenodo.2533369

    work page 2019

  50. [50]

    L. A. Segel and L. Edelstein-Keshet.A primer on mathematical models in biology. eng. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013

    work page 2013

  51. [51]

    Data-informed model reduction for inference and prediction from non-identifiable models

    M. J. Simpson. “Data-informed model reduction for inference and prediction from non-identifiable models”. eng. In:J. Theor. Biol.611 (2025), pp. 112155–

    work page 2025

  52. [52]

    Zebrafish stripes as a model for vertebrate colour pattern formation

    A. P. Singh and C. N ¨usslein-V olhard. “Zebrafish stripes as a model for vertebrate colour pattern formation”. In:Curr. Biol.25.2 (2015), R81–R92

    work page 2015

  53. [53]

    Proliferation, dispersal and patterned aggregation of iri- dophores in the skin prefigure striped colouration of zebrafish

    A. P. Singh, U. Schach, and C. N ¨usslein-V olhard. “Proliferation, dispersal and patterned aggregation of iri- dophores in the skin prefigure striped colouration of zebrafish”. In:Nat. Cell Biol.16.6 (2014), pp. 604–611

    work page 2014

  54. [54]

    Topological data analysis of task-based fMRI data from experiments on schizophrenia

    B. J. Stolz et al. “Topological data analysis of task-based fMRI data from experiments on schizophrenia”. eng. In:J. Phys. Complex.2.3 (2021), p. 035006

    work page 2021

  55. [55]

    Approximate Bayesian Computation

    M. Sunn ˚aker et al. “Approximate Bayesian Computation”. In:PLOS Comput. Biol.9.1 (2013), e1002803. DOI:10.1371/journal.pcbi.1002803

    work page doi:10.1371/journal.pcbi.1002803 2013

  56. [56]

    Topological Approximate Bayesian Computation for Param- eter Inference of an Angiogenesis Model

    T. Thorne, P. D. W. Kirk, and H. A. Harrington. “Topological Approximate Bayesian Computation for Param- eter Inference of an Angiogenesis Model”. In:Bioinformatics38.9 (2022). Ed. by J. Wren, pp. 2529–2535. DOI:10.1093/bioinformatics/btac118

    work page doi:10.1093/bioinformatics/btac118 2022

  57. [57]

    Topological Data Analysis of Biological Aggregation Mod- els

    C. M. Topaz, L. Ziegelmeier, and T. Halverson. “Topological Data Analysis of Biological Aggregation Mod- els”. In:PLOS One10.5 (2015), e0126383.DOI:10.1371/journal.pone.0126383

    work page doi:10.1371/journal.pone.0126383 2015

  58. [58]

    Modelling stripe formation in zebrafish: an agent-based approach

    A. V olkening and B. Sandstede. “Modelling stripe formation in zebrafish: an agent-based approach”. In:J. R. Soc. Interface12.112 (2015), p. 20150812

    work page 2015

  59. [59]

    Iridophores as a Source of Robustness in Zebrafish Stripes and Variability inDanioPatterns

    A. V olkening and B. Sandstede. “Iridophores as a Source of Robustness in Zebrafish Stripes and Variability inDanioPatterns”. In:Nat. Commun.9.1 (2018), p. 3231.DOI:10.1038/s41467-018-05629-z

    work page doi:10.1038/s41467-018-05629-z 2018

  60. [60]

    Homotypic cell competition regulates proliferation and tiling of zebrafish pigment cells during colour pattern formation

    B. Walderich et al. “Homotypic cell competition regulates proliferation and tiling of zebrafish pigment cells during colour pattern formation”. In:Nat. Commun.7 (2016).DOI:10.1038/ncomms11462

    work page doi:10.1038/ncomms11462 2016

  61. [61]

    A. R. Wenzel et al.Topologically-Based Parameter Inference for Agent-Based Model Selection from Spa- tiotemporal Cellular Data (arXiv preprint). 2025.DOI:10.1101/2025.06.13.659586

    work page doi:10.1101/2025.06.13.659586 2025

  62. [62]

    Pattern regulation in the stripe of zebrafish suggests an un- derlying dynamic and autonomous mechanism

    M. Yamaguchi, E. Yoshimoto, and S. Kondo. “Pattern regulation in the stripe of zebrafish suggests an un- derlying dynamic and autonomous mechanism”. In:Proc. Natl. Acad. Sci. USA104.12 (2007), pp. 4790– 4793. 20 6 Supporting Information 6.1 Summary of Models Considered in our Rule Inference Case Study In our last case study in the main manuscript, we intr...

    work page 2007