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  1. Article: A new universal system of tree shape indices.

    Noble, Robert / Verity, Kimberley

    bioRxiv : the preprint server for biology

    2023  

    Abstract: The comparison and categorization of tree diagrams is fundamental to large parts of biology, linguistics, computer science, and other fields, yet the indices currently applied to describing tree shape have important flaws that complicate their ... ...

    Abstract The comparison and categorization of tree diagrams is fundamental to large parts of biology, linguistics, computer science, and other fields, yet the indices currently applied to describing tree shape have important flaws that complicate their interpretation and limit their scope. Here we introduce a new system of indices with no such shortcomings. Our indices account for node sizes and branch lengths and are robust to small changes in either attribute. Unlike currently popular phylogenetic diversity, phylogenetic entropy, and tree balance indices, our definitions assign interpretable values to all rooted trees and enable meaningful comparison of any pair of trees. Our self-consistent definitions further unite measures of diversity, richness, balance, symmetry, effective height, effective outdegree, and effective branch count in a coherent system, and we derive numerous simple relationships between these indices. The main practical advantages of our indices are in 1) quantifying diversity in non-ultrametric trees; 2) assessing the balance of trees that have non-uniform branch lengths or node sizes; 3) comparing the balance of trees with different leaf counts or outdegrees; 4) obtaining a coherent, generic, multidimensional quantification of tree shape that is robust to sampling error and inferential error. We illustrate these features by comparing the shapes of trees representing the evolution of HIV and of Uralic languages, and trees generated by computational models of tumour evolution. Given the ubiquity of tree structures, we identify a wide range of applications across diverse domains.
    Language English
    Publishing date 2023-11-27
    Publishing country United States
    Document type Preprint
    DOI 10.1101/2023.07.17.549219
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article: A seven-step guide to spatial, agent-based modelling of tumour evolution.

    Colyer, Blair / Bak, Maciej / Basanta, David / Noble, Robert

    Evolutionary applications

    2024  Volume 17, Issue 5, Page(s) e13687

    Abstract: Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, ... ...

    Abstract Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non-technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend.
    Language English
    Publishing date 2024-05-02
    Publishing country England
    Document type Journal Article ; Review
    ZDB-ID 2405496-3
    ISSN 1752-4563 ; 1752-4571
    ISSN (online) 1752-4563
    ISSN 1752-4571
    DOI 10.1111/eva.13687
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article: Selective sweep probabilities in spatially expanding populations.

    Stein, Alexander / Kizhuttil, Ramanarayanan / Bak, Maciej / Noble, Robert John

    bioRxiv : the preprint server for biology

    2024  

    Abstract: Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference ... ...

    Abstract Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep through the population to fixation. However, most theoretical investigations of range expansions have been confined to regimes in which selective sweeps are effectively impossible, while studies of selective sweeps have either assumed constant population size or have ignored spatial structure. Here we use mathematical modelling and analysis to investigate selective sweep probabilities in the alternative yet biologically relevant scenario in which mutants can outcompete and displace a slowly spreading wildtype. Assuming constant radial expansion speed, we derive probability distributions for the arrival time and location of the first surviving mutant and hence find surprisingly simple approximate and exact expressions for selective sweep probabilities in one, two and three dimensions, which are independent of mutation rate. Namely, the selective sweep probability is approximately (1 -
    Language English
    Publishing date 2024-05-02
    Publishing country United States
    Document type Preprint
    DOI 10.1101/2023.11.27.568915
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article: Preventing Evolutionary Rescue in Cancer.

    Patil, Srishti / Viossat, Yannick / Noble, Robert

    bioRxiv : the preprint server for biology

    2023  

    Abstract: Extinction therapy aims to eradicate tumours by optimally scheduling multiple treatment strikes to exploit the vulnerability of small cell populations to stochastic extinction. This concept was recently shown to be theoretically sound but has not been ... ...

    Abstract Extinction therapy aims to eradicate tumours by optimally scheduling multiple treatment strikes to exploit the vulnerability of small cell populations to stochastic extinction. This concept was recently shown to be theoretically sound but has not been subjected to thorough mathematical analysis. Here we obtain quantitative estimates of tumour extinction probabilities using a deterministic analytical model and a stochastic simulation model of two-strike extinction therapy, based on evolutionary rescue theory. We find that the optimal time for the second strike is when the tumour is close to its minimum size before relapse. Given that this exact time point may be difficult to determine in practice, we show that striking slightly after the relapse has begun is typically better than switching too early. We further reveal and explain how demographic and environmental parameters influence the treatment outcome. Surprisingly, a low dose in the first strike paired with a high dose in the second is shown to be optimal. As one of the first investigations of extinction therapy, our work establishes a foundation for further theoretical and experimental studies of this promising evolutionarily-informed cancer treatment strategy.
    Language English
    Publishing date 2023-11-22
    Publishing country United States
    Document type Preprint
    DOI 10.1101/2023.11.22.568336
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: A theoretical analysis of tumour containment.

    Viossat, Yannick / Noble, Robert

    Nature ecology & evolution

    2021  Volume 5, Issue 6, Page(s) 826–835

    Abstract: Recent studies have shown that a strategy aiming for containment, not elimination, can control tumour burden more effectively in vitro, in mouse models and in the clinic. These outcomes are consistent with the hypothesis that emergence of resistance to ... ...

    Abstract Recent studies have shown that a strategy aiming for containment, not elimination, can control tumour burden more effectively in vitro, in mouse models and in the clinic. These outcomes are consistent with the hypothesis that emergence of resistance to cancer therapy may be prevented or delayed by exploiting competitive ecological interactions between drug-sensitive and drug-resistant tumour cell subpopulations. However, although various mathematical and computational models have been proposed to explain the superiority of particular containment strategies, this evolutionary approach to cancer therapy lacks a rigorous theoretical foundation. Here we combine extensive mathematical analysis and numerical simulations to establish general conditions under which a containment strategy is expected to control tumour burden more effectively than applying the maximum tolerated dose. We show that containment may substantially outperform more aggressive treatment strategies even if resistance incurs no cellular fitness cost. We further provide formulas for predicting the clinical benefits attributable to containment strategies in a wide range of scenarios and compare the outcomes of theoretically optimal treatments with those of more practical protocols. Our results strengthen the rationale for clinical trials of evolutionarily informed cancer therapy, while also clarifying conditions under which containment might fail to outperform standard of care.
    MeSH term(s) Animals ; Biological Evolution ; Mice ; Neoplasms/drug therapy
    Language English
    Publishing date 2021-04-12
    Publishing country England
    Document type Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
    ISSN 2397-334X
    ISSN (online) 2397-334X
    DOI 10.1038/s41559-021-01428-w
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  6. Book ; Online: Warlock

    Bak, Maciej / Colyer, Blair / Manojlović, Veselin / Noble, Robert

    an automated computational workflow for simulating spatially structured tumour evolution

    2023  

    Abstract: A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial structure or ... ...

    Abstract A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial structure or are mathematically intractable. Here we present warlock, an open-source automated computational workflow for fast, efficient simulation of intratumour population genetics in any of a diverse set of spatial structures. Warlock encapsulates a deme-based oncology model (demon), designed to bridge the divide between agent-based simulations and analytical population genetics models, such as the spatial Moran process. Model output can be readily compared to multi-region and single-cell sequencing data for model selection or biological parameter inference. An interface for High Performance Computing permits hundreds of simulations to be run in parallel. We discuss prior applications of this workflow to investigating human cancer evolution.

    Comment: 5 pages, 2 figures
    Keywords Quantitative Biology - Quantitative Methods ; Quantitative Biology - Tissues and Organs
    Subject code 006
    Publishing date 2023-01-18
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

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  7. Book ; Online: A seven-step guide to spatial, agent-based modelling of tumour evolution

    Colyer, Blair / Bak, Maciej / Basanta, David / Noble, Robert

    2023  

    Abstract: Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to developing such a model ...

    Abstract Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to developing such a model from first principles, aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of this approach. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterisation, visualisation, and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasise the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system.

    Comment: 19 pages, 4 figures
    Keywords Quantitative Biology - Quantitative Methods ; Quantitative Biology - Populations and Evolution ; Quantitative Biology - Tissues and Organs
    Subject code 612
    Publishing date 2023-11-06
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Article ; Online: Robust, Universal Tree Balance Indices.

    Lemant, Jeanne / Le Sueur, Cécile / Manojlović, Veselin / Noble, Robert

    Systematic biology

    2022  Volume 71, Issue 5, Page(s) 1210–1224

    Abstract: Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet, existing indices are not defined for all rooted trees, are unreliable for ... ...

    Abstract Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet, existing indices are not defined for all rooted trees, are unreliable for comparing trees with different numbers of leaves, and are sensitive to the presence or absence of rare types. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless' index but can account for population sizes, are defined for trees with any degree distribution, and enable meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalized reciprocal of Sackin's index. Hence, we both unify and generalize the two most popular existing tree balance indices. Our indices are intrinsically normalized and can be computed in linear time. We conclude that these more widely applicable indices have the potential to supersede those in current use. [Cancer; clone tree; Colless index; Sackin index; species tree; tree balance.].
    MeSH term(s) Algorithms ; Biological Evolution ; Phylogeny ; Population Density
    Language English
    Publishing date 2022-04-11
    Publishing country England
    Document type Journal Article ; Research Support, N.I.H., Extramural
    ZDB-ID 1482572-7
    ISSN 1076-836X ; 1063-5157
    ISSN (online) 1076-836X
    ISSN 1063-5157
    DOI 10.1093/sysbio/syac027
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  9. Article ; Online: A framework for how environment contributes to cancer risk.

    Hochberg, Michael E / Noble, Robert J

    Ecology letters

    2017  Volume 20, Issue 2, Page(s) 117–134

    Abstract: Evolutionary theory explains why metazoan species are largely protected against the negative fitness effects of cancers. Nevertheless, cancer is often observed at high incidence across a range of species. Although there are many challenges to quantifying ...

    Abstract Evolutionary theory explains why metazoan species are largely protected against the negative fitness effects of cancers. Nevertheless, cancer is often observed at high incidence across a range of species. Although there are many challenges to quantifying cancer epidemiology and assessing its causes, we claim that most modern-day cancer in animals - and humans in particular - are due to environments deviating from central tendencies of distributions that have prevailed during cancer resistance evolution. Such novel environmental conditions may be natural and/or of anthropogenic origin, and may interface with cancer risk in numerous ways, broadly classifiable as those: increasing organism body size and/or life span, disrupting processes within the organism, and affecting germline. We argue that anthropogenic influences, in particular, explain much of the present-day cancer risk across life, including in humans. Based on a literature survey of animal species and a parameterised mathematical model for humans, we suggest that combined risks of all cancers in a population beyond c. 5% can be explained to some extent by the influence of novel environments. Our framework provides a basis for understanding how natural environmental variation and human activity impact cancer risk, with potential implications for species ecology.
    MeSH term(s) Animals ; Environment ; Human Activities ; Humans ; Neoplasms/epidemiology ; Neoplasms/etiology ; Risk Factors
    Language English
    Publishing date 2017-02
    Publishing country England
    Document type Journal Article
    ZDB-ID 1441608-6
    ISSN 1461-0248 ; 1461-023X
    ISSN (online) 1461-0248
    ISSN 1461-023X
    DOI 10.1111/ele.12726
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  10. Article: When, why and how tumour clonal diversity predicts survival.

    Noble, Robert / Burley, John T / Le Sueur, Cécile / Hochberg, Michael E

    Evolutionary applications

    2020  Volume 13, Issue 7, Page(s) 1558–1568

    Abstract: The utility of intratumour heterogeneity as a prognostic biomarker is the subject of ongoing clinical investigation. However, the relationship between this marker and its clinical impact is mediated by an evolutionary process that is not well understood. ...

    Abstract The utility of intratumour heterogeneity as a prognostic biomarker is the subject of ongoing clinical investigation. However, the relationship between this marker and its clinical impact is mediated by an evolutionary process that is not well understood. Here, we employ a spatial computational model of tumour evolution to assess when, why and how intratumour heterogeneity can be used to forecast tumour growth rate and progression-free survival. We identify three conditions that can lead to a positive correlation between clonal diversity and subsequent growth rate: diversity is measured early in tumour development; selective sweeps are rare; and/or tumours vary in the rate at which they acquire driver mutations. Opposite conditions typically lead to negative correlation. In cohorts of tumours with diverse evolutionary parameters, we find that clonal diversity is a reliable predictor of both growth rate and progression-free survival. We thus offer explanations-grounded in evolutionary theory-for empirical findings in various cancers, including survival analyses reported in the recent TRACERx Renal study of clear-cell renal cell carcinoma. Our work informs the search for new prognostic biomarkers and contributes to the development of predictive oncology.
    Language English
    Publishing date 2020-07-18
    Publishing country England
    Document type Journal Article
    ZDB-ID 2405496-3
    ISSN 1752-4563 ; 1752-4571
    ISSN (online) 1752-4563
    ISSN 1752-4571
    DOI 10.1111/eva.13057
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