Bulletin of Mathematical Biology最新文献

{"title":"A Modeling Approach to Stomatal Conductance under Different Vapor Pressure Conditions.","authors":"Nicole Martínez-Jeraldo, Alejandro Rojas-Palma, Marcos Carrasco-Benavides, Victor Osores","doi":"10.1007/s11538-026-01676-6","DOIUrl":"10.1007/s11538-026-01676-6","url":null,"abstract":"<p><p>Stomatal conductance, determined by the stomatal aperture of leaves, governs gas exchange between plants and the atmosphere. This mechanism is closely related to photosynthesis and the ability of plants to adapt to environmental changes, including those caused by global warming. This study proposes a two-dimensional nonlinear model based on ordinary differential equations to estimate stomatal conductance over time. The model integrates key environmental drivers, air temperature and relative humidity, through the vapor pressure deficit, and couples stomatal conductance with leaf water content. A modified Gompertz-type equation provides a nonlinear structure capable, in principle, of representing delayed and potentially asymmetric stomatal adjustment toward a dynamic steady-state target. We perform both local and global sensitivity analyses to assess parameter influence, revealing vapor pressure deficit as the most influential factor affecting equilibrium stomatal conductance. The findings indicate that the model reproduces the main trend of stomatal conductance in the preliminary hold-out evaluation, while further validation with independent datasets remains necessary.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148238891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Refining Niche Metric Calculations: A Modified Weighting Approach to Colwell and Futuyma's Method.","authors":"Kürşad Özkan, Serkan Özdemir, Bart Muys, Salih Doğan","doi":"10.1007/s11538-026-01672-w","DOIUrl":"10.1007/s11538-026-01672-w","url":null,"abstract":"<p><p>The niche concept is central to ecology, evolution, and conservation biology. To assess resource dynamics in biological communities, the most widely used niche metrics are niche breadth and niche overlap. Colwell and Futuyma (1971) were the first to propose niche metrics that incorporated resource distinctness. In their framework, niche breadth and overlap are calculated using either a relative weighting factor <math> <mfenced><msub><mi>d</mi> <mi>j</mi></msub> </mfenced> </math> or an absolute weighting factor <math> <mfenced><msub><mi>δ</mi> <mi>j</mi></msub> </mfenced> </math> . Hanski (1978) later introduced an alternative weighting factor <math> <mfenced><mmultiscripts><mi>δ</mi> <mrow><mi>j</mi></mrow> <mrow><mrow></mrow> <mo>∗</mo></mrow> </mmultiscripts> </mfenced> </math> , which accounts for both the quality and quantity of resource states in niche calculations. However, metrics based on <math><msub><mi>d</mi> <mi>j</mi></msub> </math> , <math><msub><mi>δ</mi> <mi>j</mi></msub> </math> and <math><mmultiscripts><mi>δ</mi> <mrow><mi>j</mi></mrow> <mrow><mrow></mrow> <mo>∗</mo></mrow> </mmultiscripts> </math> have inherent mathematical and conceptual limitations. To overcome these issues, the present study introduces modified forms of these factors ( <math><mrow><mi>e</mi> <msub><mi>d</mi> <mi>j</mi></msub> </mrow> </math> , <math><mrow><mi>e</mi> <msub><mi>δ</mi> <mi>j</mi></msub> </mrow> </math> and <math><mrow><mi>e</mi> <mmultiscripts><mi>δ</mi> <mrow><mi>j</mi></mrow> <mrow><mrow></mrow> <mo>∗</mo></mrow> </mmultiscripts> </mrow> </math> ) and evaluates their performance using eight hypothetical and one empirical (ecological) resource matrix. The findings indicate that niche metrics incorporating the <math><mrow><mi>e</mi> <msub><mi>d</mi> <mi>j</mi></msub> </mrow> </math> factor represent the most coherent and biologically meaningful option.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13263204/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148238872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cells, Bureaucracy and Corruption.","authors":"Frederick R Adler","doi":"10.1007/s11538-026-01664-w","DOIUrl":"10.1007/s11538-026-01664-w","url":null,"abstract":"<p><p>We like to imagine that our students are cheerfully unaware of the ocean of educational bureaucracy that surrounds their peaceful island of learning. Despite the hassles of registering and paying for classes, students are supposed to run head-on into the dreaded bureaucracy only when they join the so-called real world. What is all that bureaucracy doing anyway? Is it a superstructure created by self-serving and parasitic bureaucrats? Strangely, perhaps the most elaborate bureaucracy we know of lies within each of us, whether student, professor or paper-pushing Vice President. This bureaucracy is the cell. The vast majority of genes and proteins within cells are effectively bureaucrats, regulating each other rather than building things. Regulation requires communication through a complex network of intracellular signaling, which in turn extends beyond the cells as the chatter among cells that regulates tissues. Why is the most remarkable self-organized system in the known universe so bureaucratic? This paper, based on a presentation at the 2025 Annual Meeting of the Society for Mathematical Biology in Edmonton, presents models of how bureaucracy grows, how it can provide robustness, its points of vulnerability, and how these complex systems can be corrupted.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148238867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automated Classification of Homeostasis Structure in Input-Output Networks.","authors":"Xinni Lin, Fernando Antoneli, Yangyang Wang","doi":"10.1007/s11538-026-01679-3","DOIUrl":"10.1007/s11538-026-01679-3","url":null,"abstract":"<p><p>Homeostasis is widely observed in biological systems and refers to their ability to maintain an output quantity approximately constant despite variations in external disturbances. Mathematically, homeostasis can be formulated through an input-output function mapping an external parameter to an output variable. Infinitesimal homeostasis occurs at isolated points where the derivative of this input-output function vanishes, allowing tools from singularity theory and combinatorial matrix theory to characterize and classify homeostatic mechanisms in terms of network topology. Although the theoretical framework allows homeostasis subnetworks to be identified directly from combinatorial structures of the input-output network without numerical simulation, the required combinatorial enumeration becomes increasingly intractable as network size grows. Moreover, the reliance on advanced graph-theoretic concepts limits its broader accessibility and practical use across disciplines, particularly in biological applications. To overcome these limitations, we develop a Python-based algorithm that automates the identification of homeostasis subnetworks and their associated homeostasis conditions directly from network topology. Given an input-output network specified solely by its connectivity structure and the designation of input and output nodes, the algorithm automatically identifies the relevant graph-theoretical structures and enumerates all homeostatic mechanisms. We demonstrate the applicability of the algorithm across a range of biological examples, including small and large networks, networks with a single input parameter (with single or multiple input nodes), multiple input parameters, and cases where input and output coincide. This wide applicability stems from our extension of the theoretical framework from single-input-single-output networks to networks with multiple input nodes through an augmented single-input-node representation. The resulting computational framework provides a scalable and systematic approach to classifying homeostatic mechanisms in complex biological networks, facilitating the application of advanced mathematical theory to a broad range of biological systems.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13260260/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148216421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Delayed Pattern Formation in Two-Dimensional Domains.","authors":"Nirmali Das, István Balázs, Bornali Das, Gergely Röst","doi":"10.1007/s11538-026-01669-5","DOIUrl":"10.1007/s11538-026-01669-5","url":null,"abstract":"<p><p>This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the Schnakenberg model called the LI (ligand internalisation) model. In a one-dimensional domain, a linear relationship has been observed between the gene expression time delay and the time it takes for patterns to form. We extend the model to the two-dimensional domain and confirm that a similar relationship holds there as well. However, our exploration reveals a non-monotonic correlation between domain size and the time required for pattern emergence. In our attempt to unravel these complex dynamics, we expand our analysis by considering a diverse range of initial conditions, including random perturbations of the spatially homogenous steady state as well as initial functions from its unstable manifold, to observe how pattern formation unfolds. To understand the role of these key parameters, we compute a two-parameter chart of patterns, with respect to time delay and domain size.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13260168/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148216396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of Nutrient Input and Zooplankton Immunity to Phytoplankton-Derived Toxins on Shallow Take Algal Blooms and Dynamics.","authors":"Li Juan, Song Yongzhong, Zhu Huaiping","doi":"10.1007/s11538-026-01662-y","DOIUrl":"10.1007/s11538-026-01662-y","url":null,"abstract":"<p><p>Algal blooms in shallow lakes have attracting increasing attention owing to their high frequency and severe ecological harm. Previous studies, which primarily focused on single influencing factors such as nutrient input or toxins released by phytoplankton, have demonstrated that excessive nutrient input can increase the incidence of algal blooms, while high toxin levels exert an inhibitory effect. This study proposes a general analytical framework for exploring zooplankton grazing responses to phytoplankton-derived toxins and nutrient uptake, with a focus on zooplankton immunity to such toxins. A novel nutrient-phytoplankton-zooplankton model is adopted to investigate the combined impacts of nutrient input and phytoplankton-derived toxins on algal blooms, considering zooplankton immunity. We conduct analyses on the existence, stability, and bifurcations of the model to explore its complex dynamic behaviors, including Hopf bifurcation and Bogdanov-Takens bifurcation of codimension 2 and a degenerate case with a nilpotent cusp of codimension at least 3. Specific forms of nutrient uptake and zooplankton grazing functions are employed to validate the relevant theoretical results and perform numerical simulations. Beyond existing findings, this study reveals that oscillation periods tend to lengthen under lower toxin levels or higher nutrient input when oscillations occur.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148210249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Drivers of Variation in the Optimal Spatial Structure of Collective Information Gatherers.","authors":"Ross S Walker, Gabriel Ramos-Fernandez, Denis Boyer, Sandra E Smith-Aguilar, Xander O'Neill, Matthew J Silk","doi":"10.1007/s11538-026-01666-8","DOIUrl":"10.1007/s11538-026-01666-8","url":null,"abstract":"<p><p>Collective systems that self-organise to maximise the group's ability to collect and distribute information can be successful in environments with high spatial and temporal variation. Such organisations are abundant in nature, as sharing information is a key benefit of many biological collective systems, and have been influential in the design of many artificial collectives such as swarm robotics. Understanding how these systems may be spatially distributed to optimise their collective potential is therefore of importance in both ecology and in collective systems design. Here, we develop a mathematical model which uses an optimisation framework to determine the higher-order spatial structure of a collective that optimises group-level knowledge transfer. The domain of the objective function is a set of weighted hypergraphs, which can fully represent the spatial structure from a topological perspective. By varying the parameters within the objective function and the constraints, we determine how the optimal spatial structure may vary when individuals differ in their information gathering ability and how this variation differs in the context of resource constraints. Our key findings are that the amount of resources in the environment can lead to specific subgroup sizes being optimal for the group as a whole when individuals are homogeneous in their information gathering abilities. Further, when there is variation in information gathering abilities, our model implies that the sharing of space between smaller subgroups of the population, rather than the whole population, is optimal for collective knowledge sharing. Our results have applications across diverse contexts from behavioural ecology to bio-inspired collective systems design.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13253601/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148216473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Virulence Evolution in Host Populations with Heterogeneous Immune Responses: The Weakening of the Uncommon Weak.","authors":"Carles Barril, Marina Vegué","doi":"10.1007/s11538-026-01673-9","DOIUrl":"10.1007/s11538-026-01673-9","url":null,"abstract":"<p><p>How and to what extent different factors in pathogen-host dynamics shape virulence has been largely debated due to evolutionary forces acting in opposite directions. Here we present a model of pathogen-host dynamics with the aim of studying how competition between pathogens and the immune response of the host affect virulence. The model describes, and links, the pathogen dynamics inside individual hosts and the dynamics of the susceptible and infected individuals in the host population. We first show that when the hosts have an adequate immune response (so that they completely recover from the infection on a short time scale), pathogens tend to increase their virulence. On the contrary, if the hosts are vulnerable (meaning that they will eventually die from the infection), low virulences will be selected. We then move to a richer scenario in which the host population is mixed and contains a fraction p of vulnerable individuals. We see that the selected virulence exhibits biologically relevant behaviors as p takes intermediate values.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13249619/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148204155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Travelling Waves in Gene Expression: A Mathematical Model of Cell-State Dynamics in Melanoma.","authors":"Charlotte Taylor Barca, Rotem Leshem, Vishaka Gopalan, Sarah Woolner, Kerrie L Marie, Gareth Wyn Jones, Oliver E Jensen","doi":"10.1007/s11538-026-01637-z","DOIUrl":"10.1007/s11538-026-01637-z","url":null,"abstract":"<p><p>Melanoma is a cancer of the melanocyte, known to have an ability to readily switch between different transcriptional cell states that convey different phenotypic properties (e.g. hyper-differentiated, neural crest-like). This ability is believed to underpin intratumour heterogeneity and plastic adaptation, which contributes to resistance to therapy and immune evasion of the tumour. Therefore, understanding the mechanisms underlying acquisition of transcriptional cell states and cell-state switching is crucial for the development of therapies. We model a minimal gene regulatory network comprising three key transcription factors, whose varying gene expression encodes different melanoma cell states, and use deterministic spatiotemporal differential-equation models to study gene-expression dynamics. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise-linear. We classify stable states of the local model in a biologically relevant manner and, using a naïve model of intercellular communication, we explore how a population of cells can take on a shared characteristic through travelling waves of gene expression. We derive a condition determining which characteristic will become dominant, under sufficiently strong cell-cell signalling, which creates a partition of parameter space.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13246587/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148197336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation.","authors":"David F Anderson, Aidan S Howells, Diego Rojas La Luz","doi":"10.1007/s11538-026-01659-7","DOIUrl":"10.1007/s11538-026-01659-7","url":null,"abstract":"<p><p>Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes-biochemical and otherwise-in homogeneous environments. However, cellular reactions are often compartmentalized, either at the cell level or within cells, and hence non-homogeneous. We investigate a model of compartmentalization in which the rate of fragmentation of a compartment depends on the abundance of some designated species inside that compartment. The particular model of study is part of a general framework for compartmentalized chemistry with dynamic compartments that was proposed in Duso and Zechner (2020). This paper builds on Anderson and Howells (2023) where the special case where the compartment dynamics do not depend on their contents was studied mathematically. In particular, we demonstrate that the explosivity characterization from Anderson and Howells (2023) fails in this setting and provide new sufficient conditions for non-explosivity and positive recurrence, under the assumption that the underlying CRN admits a linear Lyapunov function. These results extend the theoretical foundation for modeling content-mediated compartment dynamics, with implications for systems such as cell division and intracellular transport.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"88 7","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13243320/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148197376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}