Cross-feeding dynamics described by a series expansion of the replicator equation.

Abstract:

:Understanding how ecosystems evolve and how they respond to external perturbations is critical if we are to predict the effects of human intervention. A particular class of ecosystems whose dynamics are poorly understood are those in which the species are related via cross-feeding. In these ecosystems the metabolic output of one species is being used as a nutrient or energy source by another species. In this paper we derive a mathematical description of cross-feeding dynamics based on the replicator equation. We show that under certain assumptions about the system (e.g., high flow of nutrients and time scale separation), the governing equations reduce to a second-order series expansion of the replicator equation. By analysing the case of two and three species we derive conditions for co-existence and show under which parameter conditions one can expect an increase in mean fitness. Finally, we discuss how the model can be parameterised from experimental data.

journal_name

Bull Math Biol

authors

Lundh T,Gerlee P

doi

10.1007/s11538-013-9828-3

subject

Has Abstract

pub_date

2013-05-01 00:00:00

pages

709-24

issue

5

eissn

0092-8240

issn

1522-9602

journal_volume

75

pub_type

杂志文章
  • Competing effects of toxin-producing phytoplankton on overall plankton populations in the bay of Bengal.

    abstract::The coexistence of a large number of phytoplankton species on a seemingly limited variety of resources is a classical problem in ecology, known as 'the paradox of the plankton'. Strong fluctuations in species abundance due to the external factors or competitive interactions leading to oscillations, chaos and short-ter...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-006-9109-5

    authors: Roy S,Alam S,Chattopadhyay J

    更新日期:2006-11-01 00:00:00

  • Sex, Mosquitoes and Epidemics: An Evaluation of Zika Disease Dynamics.

    abstract::Since the first major outbreak reported on the island Yap in 2007, the Zika virus spread has alerted the scientific community worldwide. Zika is an arbovirus transmitted by Aedes mosquitoes; particularly in Central and South America, the main vector is the same mosquito that transmits dengue and chikungunya, Aedes aeg...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0219-4

    authors: Baca-Carrasco D,Velasco-Hernández JX

    更新日期:2016-11-01 00:00:00

  • Modeling transcriptional control in gene networks--methods, recent results, and future directions.

    abstract::Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章,评审

    doi:10.1006/bulm.1999.0155

    authors: Smolen P,Baxter DA,Byrne JH

    更新日期:2000-03-01 00:00:00

  • A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems.

    abstract::This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we ca...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-009-9496-5

    authors: Datta S,Delius GW,Law R

    更新日期:2010-08-01 00:00:00

  • Identifiability and Reconstructibility of Species Phylogenies Under a Modified Coalescent.

    abstract::Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees, and consequently, a site pattern probability distribution. It has been shown that the unrooted topology of the species tree parameter of the multispecies coalescen...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0456-9

    authors: Long C,Kubatko L

    更新日期:2019-02-01 00:00:00

  • Multiscale Persistent Functions for Biomolecular Structure Characterization.

    abstract::In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entrop...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0362-6

    authors: Xia K,Li Z,Mu L

    更新日期:2018-01-01 00:00:00

  • A within-host virus model with periodic multidrug therapy.

    abstract::This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if R0<1, ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9820-y

    authors: Wang Z,Zhao XQ

    更新日期:2013-03-01 00:00:00

  • Estimating the selective advantage of mutant p53 tumour cells to repeated rounds of hypoxia.

    abstract::The tumour suppressor gene, p53, plays an important role in tumour development. Under low levels of oxygen (hypoxia), cells expressing wild-type p53 undergo programmed cell death (apoptosis), whereas cells expressing mutations in the p53 gene may survive and express angiogenic growth factors that stimulate tumour vasc...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.2000.0210

    authors: Gammack D,Byrne HM,Lewis CE

    更新日期:2001-01-01 00:00:00

  • Polymorphic Evolutionary Games and Non-Mendelian Genetics.

    abstract::Classical evolutionary game theory (EGT) focuses on competition among phenotypes while assuming asexual transmission of these phenotypes to the next generation. However, phenotypic selection and sexual recombination are not necessarily mutually reinforcing in populations with sexual reproduction. In particular, it has...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00705-2

    authors: Fishman MA

    更新日期:2020-02-06 00:00:00

  • The effect of chemical information on the spatial distribution of fruit flies: II Parameterization, calibration, and sensitivity.

    abstract::In a companion paper (Lof et al., in Bull. Math. Biol., 2008), we describe a spatio-temporal model for insect behavior. This model includes chemical information for finding resources and conspecifics. As a model species, we used Drosophila melanogaster, because its behavior is documented comparatively well. We divide ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-008-9329-y

    authors: de Gee M,Lof ME,Hemerik L

    更新日期:2008-10-01 00:00:00

  • Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China.

    abstract::Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-00537-1

    authors: Huang J,Ruan S,Shu Y,Wu X

    更新日期:2019-04-01 00:00:00

  • On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg-Marquardt Algorithm with Broyden's Rank-one Updates for the Jacobian Operator.

    abstract::Rigorously calibrating dynamic models with time-series data can pose roadblocks. Oftentimes, the problem is ill-posed and one has to rely on appropriate regularization techniques to ensure stable parameter estimation from which forward projections with quantified uncertainty could be generated. If the inversion proced...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00650-9

    authors: Smirnova A,Sirb B,Chowell G

    更新日期:2019-10-01 00:00:00

  • Optimizing the Timing and Composition of Therapeutic Phage Cocktails: A Control-Theoretic Approach.

    abstract::Viruses that infect bacteria, i.e., bacteriophage or 'phage,' are increasingly considered as treatment options for the control and clearance of bacterial infections, particularly as compassionate use therapy for multi-drug-resistant infections. In practice, clinical use of phage often involves the application of multi...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00751-w

    authors: Li G,Leung CY,Wardi Y,Debarbieux L,Weitz JS

    更新日期:2020-06-12 00:00:00

  • The role of space in the exploitation of resources.

    abstract::In order to understand the role of space in ecological communities where each species produces a certain type of resource and has varying abilities to exploit the resources produced by its own species and by the other species, we carry out a comparative study of an interacting particle system and its mean-field approx...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9649-1

    authors: Kang Y,Lanchier N

    更新日期:2012-01-01 00:00:00

  • Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

    abstract::The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this s...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章,评审

    doi:10.1007/s11538-016-0214-9

    authors: Eftimie R,Gillard JJ,Cantrell DA

    更新日期:2016-10-01 00:00:00

  • Computational experiments support a competitive function in the CA3 region of the hippocampus.

    abstract::The comprehension of activities and functions of complex brain structures requires, among other things, information on simultaneous activities in several regions. Results reported in the literature using multi(micro/macro)electrode recordings or imaging techniques provide incomplete information due either to the small...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.1997.0032

    authors: Ventriglia F

    更新日期:1998-03-01 00:00:00

  • Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span.

    abstract::Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the un...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-008-9382-6

    authors: Demetrius L,Legendre S,Harremöes P

    更新日期:2009-05-01 00:00:00

  • An algebraic approach to signaling cascades with N layers.

    abstract::Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modi...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9658-0

    authors: Feliu E,Knudsen M,Andersen LN,Wiuf C

    更新日期:2012-01-01 00:00:00

  • Experimental and computational investigation of the role of stress fiber contractility in the resistance of osteoblasts to compression.

    abstract::The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniqu...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9812-y

    authors: Weafer PP,Ronan W,Jarvis SP,McGarry JP

    更新日期:2013-08-01 00:00:00

  • Impact of Harvesting on a Bioeconomic Predator-Prey Fishery Model Subject to Environmental Toxicant.

    abstract::The present paper studies a predator-prey fishery model which incorporates the independent harvesting strategies and nonlinear impact of an anthropogenic toxicant. Both fish populations are harvested with different harvesting efforts, and the cases for the presence and non-presence of harvesting effort are discussed. ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00627-8

    authors: Ang TK,Safuan HM,Sidhu HS,Jovanoski Z,Towers IN

    更新日期:2019-07-01 00:00:00

  • Analysis of individual cell trajectories in lattice-gas cellular automaton models for migrating cell populations.

    abstract::Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also i...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-015-0079-3

    authors: Mente C,Voss-Böhme A,Deutsch A

    更新日期:2015-04-01 00:00:00

  • A mathematical model for fibro-proliferative wound healing disorders.

    abstract::The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor media...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02459482

    authors: Olsen L,Sherratt JA,Maini PK

    更新日期:1996-07-01 00:00:00

  • Computational fluid dynamics of fish gill rakers during crossflow filtration.

    abstract::We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow tra...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-011-9709-6

    authors: Cheer A,Cheung S,Hung TC,Piedrahita RH,Sanderson SL

    更新日期:2012-04-01 00:00:00

  • Mathematical model for early development of the sea urchin embryo.

    abstract::In Xenopus and Drosophila, the nucleocytoplasmic ratio controls many aspects of cell-cycle remodeling during the transitory period that leads from fast and synchronous cell divisions of early development to the slow, carefully regulated growth and divisions of somatic cells. After the fifth cleavage in sea urchin embr...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.1999.0129

    authors: Ciliberto A,Tyson JJ

    更新日期:2000-01-01 00:00:00

  • Exact probability distributions of selected species in stochastic chemical reaction networks.

    abstract::Chemical reactions are discrete, stochastic events. As such, the species' molecular numbers can be described by an associated master equation. However, handling such an equation may become difficult due to the large size of reaction networks. A commonly used approach to forecast the behaviour of reaction networks is t...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-014-9985-z

    authors: López-Caamal F,Marquez-Lago TT

    更新日期:2014-09-01 00:00:00

  • A bovine babesiosis model with dispersion.

    abstract::Bovine Babesiosis (BB) is a tick borne parasitic disease with worldwide over 1.3 billion bovines at potential risk of being infected. The disease, also called tick fever, causes significant mortality from infection by the protozoa upon exposure to infected ticks. An important factor in the spread of the disease is the...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9912-8

    authors: Friedman A,Yakubu AA

    更新日期:2014-01-01 00:00:00

  • Pulse Generation in the Quorum Machinery of Pseudomonas aeruginosa.

    abstract::Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involv...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0288-z

    authors: Alfiniyah C,Bees MA,Wood AJ

    更新日期:2017-06-01 00:00:00

  • Directional Hydrodynamic Sensing by Free-Swimming Organisms.

    abstract::Many aquatic organisms detect the presence of moving objects in their environment, such as predators, by sensing the hydrodynamic disturbances the movements produce. The resultant water flow is readily detectable by stationary organisms, but free-swimming organisms are carried with the surrounding water and may not de...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0368-0

    authors: Takagi D,Hartline DK

    更新日期:2018-01-01 00:00:00

  • The adaptiveness of defence strategies against cuckoo parasitism.

    abstract::Host bird species of the Eurasian Cuckoo, Cuculus canorus, often display egg-discrimination behaviour but chick-rejection behaviour has never been reported. In this paper, we analyse a host-cuckoo association in which both population dynamics and evolutionary dynamics are explored in a discrete-time model. We introduc...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.2002.0311

    authors: Planqué R,Britton NF,Franks NR,Peletier MA

    更新日期:2002-11-01 00:00:00

  • Analysis of Multilevel Replicator Dynamics for General Two-Strategy Social Dilemma.

    abstract::Here, we consider a game-theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on multilevel social dilemmas: games in which individuals are best off cheating, while groups of individuals do best whe...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00742-x

    authors: Cooney DB

    更新日期:2020-05-30 00:00:00