Abstract：
:We study the invasion of a top predator into a food chain in a chemostat. For each trophic level, a bioenergetic model is used in which maintenance and energy reserves are taken into account. Bifurcation analysis is performed on the set of nonlinear ordinary differential equations which describe the dynamic behaviour of the food chain. In this paper, we analyse how the ability of a top predator to invade the food chain depends on the values of two control parameters: the dilution rate and the concentration of the substrate in the input. We investigate invasion by studying the long-term behaviour after introduction of a small amount of top predator. To that end we look at the stability of the boundary attractors; equilibria, limit cycles as well as chaotic attractors using bifurcation analysis. It will be shown that the invasibility criterion is the positiveness of the Lyapunov exponent associated with the change of the biomass of the top predator. It appears that the region in the control parameter space where a predator can invade increases with its growth rate. The resulting system becomes more resistant to further invasion when the top predator grows faster. This implies that short food chains with moderate growth rate of the top predator are liable to be invaded by fast growing invaders which consume the top predator. There may be, however, biological constraints on the top predator's growth rate. Predators are generally larger than prey while larger organisms commonly grow slower. As a result, the growth rate generally decreases with the trophic level. This may enable short food chains to be resistant to invaders. We will relate these results to ecological community assembly and the debate on the length of food chains in nature.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Kooi BW,Boer MP,Kooijman SAdoi
10.1016/s0025-5564(98)10083-4subject
Has Abstractpub_date
1999-03-15 00:00:00pages
217-36issue
1-2eissn
0025-5564issn
1879-3134pii
S0025-5564(98)10083-4journal_volume
157pub_type
杂志文章abstract：:Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleati...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2011.06.003
更新日期：2011-08-01 00:00:00
abstract：:Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.12.011
更新日期：2014-02-01 00:00:00
abstract：:This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data b...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00215-8
更新日期：2003-04-01 00:00:00
abstract：:The results of recent experimental and epidemiological studies provide evidence on the connection between carcinogenesis, cancer progression, and aging. Existing models, however, are traditionally focused only on one of these aspects of health deterioration. In this paper, we derive a new model of cancer, which descri...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2008.12.007
更新日期：2009-04-01 00:00:00
abstract：:A significant consideration in modeling systems with stages is to obtain models for the individual stages that have probability density functions (pdfs) of residence times that are close to those of the real system. Consequently, the theory of residence time distributions is important for modeling. Here I show first t...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00110-4
更新日期：2002-11-01 00:00:00
abstract：:Half-sib, first cousin, half nth cousin, and nth cousin mating systems are robust in that small deviations from the mating structure will not significantly alter the levels of genetic identity or effect qualitative distinctions between the models. Substitution of nearest kin in matings may either increase or decrease ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(91)90026-f
更新日期：1991-04-01 00:00:00
abstract：:A mathematical model is formulated for diffusive countercurrent exchange of oxygen between paired arterioles and venules. A closed form solution of the problem is obtained by linearizing the nonlinear oxyhemoglobin dissociation curve at the inlet PO2 in the vessel. The closed form solution is compared with the corresp...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(88)90022-3
更新日期：1988-09-01 00:00:00
abstract：:The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model a...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(92)90038-x
更新日期：1992-07-01 00:00:00
abstract：:A simulation method is presented for the demographic and genetic variation of age structured haploid populations. First, we use matrix analytic methods to derive an equilibrium distribution for the age class sizes conditioned on the total population size. Knowledge of this distribution eliminates the need of a burn-in...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.08.003
更新日期：2015-10-01 00:00:00
abstract：:A biofilm material model and a procedure for numerical integration are developed in this article. They enable calculation of a composite Young's modulus that varies in the biofilm and evolves with deformation. The biofilm-material model makes it possible to introduce a modeling example, produced by the Unified Multi-C...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.02.007
更新日期：2014-05-01 00:00:00
abstract：:This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorp...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/j.mbs.2011.08.006
更新日期：2011-12-01 00:00:00
abstract：:We explore the feasibility of deriving generalised expressions for the probability mass function (PMF) of the final epidemic size of a Susceptible - Infected - Recovered (SIR) model on a finite network of an arbitrary number of nodes. Expressions for the probability that the infection progresses along a given pathway ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.02.003
更新日期：2019-05-01 00:00:00
abstract：:We study spatial stochastic epidemic models called households models. The households models have more than two states at each vertex of a graph in contrast to the contact process. We show that, in the households models on trees, two thresholds of infection rates characterize epidemics. The global critical infection ra...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2008.02.004
更新日期：2008-05-01 00:00:00
abstract：:This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to pred...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2017.08.009
更新日期：2017-11-01 00:00:00
abstract：:When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find threshol...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(01)00093-1
更新日期：2002-05-01 00:00:00
abstract：:Isotope labeling systems (ILSs) are sets of balance equations that quantitatively describe the distribution of isotopic tracers in metabolic networks. The solution of ILSs, i.e., the calculation of isotopic labeling distributions (mostly in steady state) is the fundamental computational step of (13)C metabolic flux an...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.02.012
更新日期：2013-07-01 00:00:00
abstract：:Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kappaB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays intro...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2006.08.010
更新日期：2007-02-01 00:00:00
abstract：:Let S be a set of n objects. A binary tree of S is a binary tree whose leaves are labeled without repetition from S. The operation of pruning a tree T is that of removing some leaves from T and suppressing all inner vertices of degree 2 which are formed by this deletion. Given two trees T and U, an agreement tree is a...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)90012-4
更新日期：1994-10-01 00:00:00
abstract：:Recent work has shown that higher-order terms in population dynamics models can increase the stability, promote the diversity, and better explain the dynamics of ecological systems. While it is known that these perceived benefits come from an increasing number of alternative solutions given by the nature of multivaria...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.108222
更新日期：2019-09-01 00:00:00
abstract：:We consider a single-species model which is composed of several patches connected by linear migration rates and having logistic growth with a threshold. We show the existence of an aggregating mechanism that allows the survival of a species which is in danger of extinction due to its low population density. Numerical ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(00)00005-5
更新日期：2000-05-01 00:00:00
abstract：:The acetone-butanol (AB) fermentation process in the anaerobic endospore-forming Gram-positive bacterium Clostridium acetobutylicum is useful as a producer of biofuels, particularly butanol. Recent work has concentrated on trying to improve the efficiency of the fermentation method, either through changes in the envir...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2012.11.004
更新日期：2013-02-01 00:00:00
abstract：:This paper presents a novel epidemiological transmission model of a population affected by two different susceptible-infected-susceptible infectious diseases. For each disease, individuals fall into one of the two susceptibility conditions in which one of the diseases has the highest occurrence level. This model is un...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.01.005
更新日期：2019-03-01 00:00:00
abstract：:Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act wi...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(92)90006-i
更新日期：1992-02-01 00:00:00
abstract：:In a random walk (RW) in Z an individual starts at 0 and moves at discrete unitary steps to the right or left with respective probabilities p and 1-p. Assuming p > 1/2 and finite a, a > 1, the probability that state a will be reached before -a is Q(a, p) where Q(a, p) > p. Here we introduce the cooperative random walk...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.06.011
更新日期：2016-09-01 00:00:00
abstract：:In this paper, a mathematical modeling framework is presented which describes the growth, encapsulation, and transcapsular spread of solid tumors. The model is based on the physical forces and cellular interactions involved in tumorigenesis and is used to test and compare the active (foreign body hypothesis) and passi...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00118-9
更新日期：2002-11-01 00:00:00
abstract：:A stochastic epidemic model is formulated for the study of the protective effects of vaccination in a population that is stratified by vaccine-related factors. The epidemic model is transformed into a counting process, and then martingale-based methods are used to provide estimators of vaccine efficacy and their varia...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(93)90028-9
更新日期：1993-09-01 00:00:00
abstract：:When ionizing radiation strikes a cell it induces DNA double strand breaks (DSBs). Subsequently, some of the DSBs misrejoin and thus cause alterations in the size distribution of the DNA fragments. We derive a system of non-linear integro-differential equations describing the misrejoining interactions of five classes ...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/s0025-5564(98)00006-6
更新日期：1998-05-01 00:00:00
abstract：:Most endocrine cells secrete hormones as a result of Ca2+-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage...
journal_title：Mathematical biosciences
pub_type： 杂志文章,评审
doi：10.1016/j.mbs.2016.11.010
更新日期：2017-01-01 00:00:00
abstract：:In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. Depression has been associated with malfunctions in the hypothalamus-pituitary-adrenal (HPA) axis. We suggest a novel mechanistic non-linear model ca...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2014.07.013
更新日期：2014-11-01 00:00:00
abstract：:Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2007.04.009
更新日期：2007-11-01 00:00:00
