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Editorial. 社论。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2021-05-01 Epub Date: 2021-05-11 DOI: 10.1080/17513758.2021.1925406
Abba Gumel, Yang Kuang
The 7th International Conference on Mathematical Modelling and Analysis of Populations in Biology (ICMA-VII) was held at Arizona State University, Tempe, Arizona, USA, on 12–14 October 2019. This conference series has been held every two years since its inception in 2007 at the University of Arizona. Previous conferences were held at the University of Arizona in Tucson, University of Alabama inHuntsville, TrinityUniversity in San Antonio, Texas, Texas TechUniversity in Lubbock, Texas, andWesternUniversity, London, Ontario. ICMAVII, which built on the successes of previous ICMA conferences, attracted established and up-and-coming researchers and students from numerous disciplines in the mathematical and biological sciences. Specifically, the conference attracted 192 participants from 10 countries. The conference featured 108 oral and poster presentations, 79 of which were delivered by graduate students, postdoctoral fellows and early-career faculty on a number of broad general themes that included the formulation, validation, analysis and simulation of mathematical models for the spatiotemporal dynamics of biological populations. Specific topics covered included modelling, data analytics and analysis of phenomena in population biology, epidemiology, molecular and synthetic biology; mathematical oncology (cancer systems biology); genetic models; multi-host-vector-pathogen systems; persistence of ecosystems andmathematics of gene editing. The Plenary speakers at ICMA VII were Dr Natalia Komarova (Department of Mathematics, University of California, Irvine), DrQingNie (Department ofMathematics and Center forMathematical and Computational Biology, University of California, Irvine), Dr Sebastian Schreiber (Department of Evolution and Ecology, University of California, Davis) and Dr HaoWang (Department of Mathematics, University of Alberta, Canada). The conference featured a plenary lecture by the winners of the Lord Robert May Prize for the Best Paper Published in the Journal of Biological Dynamics 2017-2018. The prize was given to Drs Brian P. Yurk (Department of Mathematics, Hope College, MI, USA) and Christina A. Cobbold (School of Mathematics and Statistics, University of Glasgow, UK) for their paper titled "Homogenization techniques for population dynamics in strongly heterogeneous landscapes”. We are very grateful to the members of the Local Organizing Committee and the Scientific Advisory Committee for their invaluable contributions to the success of ICMA-VII. We are especially very grateful to Professors JamesM. Cushing (University of Arizona) and Saber N. Elaydi (Trinity University) for their tireless contributions and support throughout the whole process of planning, fund-raising and running the conference, as well as in helping us edit this special issue.
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引用次数: 0
Contrasting stoichiometric dynamics in terrestrial and aquatic grazer-producer systems. 陆地和水生食草-生产者系统的化学计量动力学对比。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2021-05-01 Epub Date: 2020-05-27 DOI: 10.1080/17513758.2020.1771442
Colleen M Davies, Hao Wang

The turnover rate of producer biomass in aquatic ecosystems is generally faster than in terrestrial. That is, aquatic producer biomass grows, is consumed, and is replaced considerably faster than terrestrial. The WKL model describes the flow of phosphorus and carbon through a grazer-producer system, hence varying the model parameters allows for analysis of different ecosystems of this type. Here we explore the impacts of the intrinsic growth rate of the producer and the maximal ingestion rate of the grazer on these dynamics because these parameters determine turnover rate. Simulations show that for low intrinsic growth rate and maximal ingestion rate, the grazer goes extinct; for higher values of these parameters, coexistence occurs in oscillations. Sensitivity analysis reveals the relative importance of all parameters on asymptotic dynamics. Lastly, the impacts of changing these two parameters in the LKE model appears to be quantitatively similar to the impacts in the WKL model.

水生生态系统中生产者生物量的周转率通常比陆地生态系统快。也就是说,水生生产者的生物量增长、消耗和替换的速度比陆地快得多。WKL模型描述了磷和碳在放牧-生产者系统中的流动,因此改变模型参数可以分析这种类型的不同生态系统。在这里,我们探讨了生产者的内在生长率和食草动物的最大摄食率对这些动态的影响,因为这些参数决定了周转率。模拟结果表明,当内在生长率和最大摄食率较低时,食草动物会灭绝;对于这些参数较高的值,共存发生在振荡中。灵敏度分析揭示了各参数对渐近动力学的相对重要性。最后,LKE模型中改变这两个参数的影响在数量上似乎与WKL模型中的影响相似。
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引用次数: 3
A discrete/continuous time resource competition model and its implications. 离散/连续时间资源竞争模型及其意义。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2021-05-01 Epub Date: 2020-12-21 DOI: 10.1080/17513758.2020.1862927
Glenn Ledder, Richard Rebarber, Terrance Pendleton, Amanda N Laubmeier, Jonathan Weisbrod

We use a mixed time model to study the dynamics of a system consisting of two consumers that reproduce only in annual birth pulses, possibly at different times, with interaction limited to competition for a resource that reproduces continuously. Ecological theory predicts competitive exclusion; this expectation is met under most circumstances, the winner being the species with the greater 'power', defined as the time average consumer level at the fixed point. Instability of that fixed point for the stronger competitor slightly weakens its domination, so that a resident species with an unstable fixed point can sometimes be invaded by a slightly weaker species, leading ultimately to coexistence. Differences in birth pulse times can lead to qualitatively different long-term coexistence behaviour, including cycles of different lengths or chaos. We also determine conditions under which the timing of an annual pulse of a toxin can change the balance of power.

我们使用一个混合时间模型来研究一个由两个消费者组成的系统的动力学,这两个消费者只在每年的出生脉冲中繁殖,可能在不同的时间,相互作用仅限于对持续繁殖的资源的竞争。生态理论预测竞争排斥;在大多数情况下,这一期望都是满足的,胜利者是拥有更大“功率”的物种,定义为固定点的平均消费水平。较强竞争者固定点的不稳定性会略微削弱其统治地位,因此固定点不稳定的常驻物种有时会被稍弱的物种入侵,最终导致共存。不同的出生脉冲时间会导致不同的长期共存行为,包括不同长度的周期或混沌。我们还确定在何种条件下,毒素每年的脉冲时间可以改变力量的平衡。
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引用次数: 1
A bifurcation theorem for Darwinian matrix models and an application to the evolution of reproductive life-history strategies. 达尔文矩阵模型的分岔定理及其在生殖生活史策略进化中的应用。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2021-05-01 Epub Date: 2020-12-09 DOI: 10.1080/17513758.2020.1858196
J M Cushing

We prove bifurcation theorems for evolutionary game theoretic (Darwinian dynamic) versions of nonlinear matrix equations for structured population dynamics. These theorems generalize existing theorems concerning the bifurcation and stability of equilibrium solutions when an extinction equilibrium destabilizes by allowing for the general appearance of the bifurcation parameter. We apply the theorems to a Darwinian model designed to investigate the evolutionary selection of reproductive strategies that involve either low or high post-reproductive survival (semelparity or iteroparity). The model incorporates the phenotypic trait dependence of two features: population density effects on fertility and a trade-off between inherent fertility and post-reproductive survival. Our analysis of the model determines conditions under which evolution selects for low or for high reproductive survival. In some cases (notably an Allee component effect on newborn survival), the model predicts multiple attractor scenarios in which low or high reproductive survival is initial condition dependent.

我们证明了结构种群动力学非线性矩阵方程的进化博弈(达尔文动力学)版本的分岔定理。这些定理通过允许分岔参数的一般出现,推广了关于消光平衡失稳时平衡解的分岔和稳定性的现有定理。我们将这些定理应用于一个达尔文模型,该模型旨在研究生殖策略的进化选择,包括低或高的生殖后存活率(半平价或互操作性)。该模型结合了两个特征的表型性状依赖性:人口密度对生育力的影响以及固有生育力和生殖后存活率之间的权衡。我们对模型的分析决定了进化选择低繁殖存活率或高繁殖存活率的条件。在某些情况下(特别是Allee成分对新生儿存活率的影响),该模型预测了多吸引子情景,其中低或高的生殖存活率依赖于初始条件。
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引用次数: 2
The competition model with Holling type II competitive response to interfering time. 干扰时间对Holling II型竞争反应的竞争模型。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1742392
Hamlet Castillo-Alvino, Marcos Marvá

In Nature, species coexistence is much more frequent than what the classical competition model predicts, so that scientists look for mechanisms that explain such a coexistence. We revisit the classical competition model assuming that individuals invest time in competing individuals of the other species. This assumption extends the classical competition model (that becomes a particular case of the model presented) under the form of a Holling type II term, that we call competitive response to interfering time. The resulting model expands the outcomes allowed by the classical model by (i) enlarging the range of parameter values that allow coexistence scenarios and (ii) displaying dynamical scenarios not allowed by the classical model: namely, bi-stable conditional coexistence in favour of i (either species coexist or species i wins) or tri-stable conditional coexistence (either species coexist or any of them goes extinct), being exclusion in both cases due to priority effects.

在《自然》中,物种共存比经典竞争模型预测的要频繁得多,因此科学家们寻找解释这种共存的机制。我们重新审视经典的竞争模型,假设个体在其他物种的竞争个体中投入时间。这一假设以Holling II型术语的形式扩展了经典竞争模型(成为本文模型的一个特例),我们称之为对干扰时间的竞争反应。由此产生的模型扩展了经典模型所允许的结果:(i)扩大了允许共存情景的参数值范围;(ii)显示了经典模型所不允许的动态情景:即有利于i的双稳定条件共存(物种共存或物种i获胜)或三稳定条件共存(物种共存或其中任何一个灭绝),由于优先效应在两种情况下都被排除在外。
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引用次数: 6
Asymptotic analysis of a vector-borne disease model with the age of infection. 媒介传播疾病模型与感染年龄的渐近分析。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1745912
Xia Wang, Yuming Chen, Maia Martcheva, Libin Rong

Vector-borne infectious diseases may involve both horizontal transmission between hosts and transmission from infected vectors to susceptible hosts. In this paper, we incorporate these two transmission modes into a vector-borne disease model that includes general nonlinear incidence rates and the age of infection for both hosts and vectors. We show the existence, uniqueness, nonnegativity, and boundedness of solutions for the model. We study the existence and local stability of steady states, which is shown to be determined by the basic reproduction number. By showing the existence of a global compact attractor and uniform persistence of the system, we establish the threshold dynamics using the Fluctuation Lemma and the approach of Lyapunov functionals. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable and otherwise the disease will be established when there is initial infection force for the hosts. We also study a model with the standard incidence rate and discuss the effect of different incidence rates on the disease dynamics.

病媒传播的传染病既可能涉及宿主之间的水平传播,也可能涉及受感染的病媒向易感宿主的传播。在本文中,我们将这两种传播模式纳入到一个媒介传播疾病模型中,该模型包括宿主和媒介的一般非线性发病率和感染年龄。我们证明了该模型解的存在唯一性、非负性和有界性。研究了稳态的存在性和局部稳定性,证明了稳态的存在性和局部稳定性是由基本再现数决定的。利用涨落引理和Lyapunov泛函的方法,证明了系统的全局紧吸引子的存在性和一致持久性,建立了系统的阈值动力学。当基本繁殖数小于1时,无病稳态全局渐近稳定,否则,当宿主存在初始感染力时,疾病建立。我们还研究了具有标准发病率的模型,并讨论了不同发病率对疾病动力学的影响。
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引用次数: 6
Global stability of the boundary solution of a nonautonomous predator-prey system with Beddington-DeAngelis functional response. 具有Beddington-DeAngelis泛函响应的非自治捕食-食饵系统边界解的全局稳定性。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1772999
Dingyong Bai, Jinshui Li, Wenrui Zeng

In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results.

考虑一类具有Beddington-DeAngelis泛函响应的非自治捕食-食饵系统,研究其边界解的全局稳定性。基于logistic方程的动力学性质,给出了一般时变情况下边界解全局渐近稳定的几个新的充分条件。研究结果表明:(1)在种内竞争较弱或不存在种内竞争的情况下,长期无效的捕食行为或高死亡率将导致捕食物种的灭绝;(ii)长期激烈的种内竞争可能导致捕食者物种灭绝,即使长期累积的捕食收益高于死亡损失。当所有参数都是共周期的周期函数时,得到了边界周期解全局稳定的充分必要条件。此外,通过数值模拟对理论结果进行了验证。
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引用次数: 9
A comparative analysis of host-parasitoid models with density dependence preceding parasitism. 寄主-拟寄主模式在寄生前密度依赖的比较分析。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1783005
Kelsey Marcinko, Mark Kot

We present a systematic comparison and analysis of four discrete-time, host-parasitoid models. For each model, we specify that density-dependent effects occur prior to parasitism in the life cycle of the host. We compare density-dependent growth functions arising from the Beverton-Holt and Ricker maps, as well as parasitism functions assuming either a Poisson or negative binomial distribution for parasitoid attacks. We show that overcompensatory density-dependence leads to period-doubling bifurcations, which may be supercritical or subcritical. Stronger parasitism from the Poisson distribution leads to loss of stability of the coexistence equilibrium through a Neimark-Sacker bifurcation, resulting in population cycles. Our analytic results also revealed dynamics for one of our models that were previously undetected by authors who conducted a numerical investigation. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete-time model in order to promote communication and broader understanding.

我们提出了一个系统的比较和分析四个离散时间,寄主-寄生虫模型。对于每个模型,我们指定密度依赖效应发生在寄主的生命周期寄生之前。我们比较了由Beverton-Holt和Ricker图产生的密度依赖性生长函数,以及寄生性函数,假设寄生性攻击为泊松分布或负二项分布。我们表明,过度补偿密度依赖导致周期加倍分岔,这可能是超临界或亚临界。泊松分布的强寄生性导致共存平衡通过neimmark - sacker分岔失去稳定性,导致种群周期。我们的分析结果还揭示了我们的一个模型的动力学,这是以前没有被进行数值调查的作者发现的。最后,我们强调明确提出离散时间模型结构固有的生物学假设的重要性,以促进交流和更广泛的理解。
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引用次数: 4
Effects of age-targeted sequestration for COVID-19. 针对年龄的隔离对COVID-19的影响。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2020.1795285
Alastair Jamieson-Lane, Eric Cytrynbaum

We model the extent to which age-targeted protective sequestration can be used to reduce ICU admissions caused by novel coronavirus COVID-19. Using demographic data from New Zealand, we demonstrate that lowering the age threshold to 50 years of age reduces ICU admissions drastically and show that for sufficiently strict isolation protocols, sequestering one-third of the countries population for a total of 8 months is sufficient to avoid overwhelming ICU capacity throughout the entire course of the epidemic. Similar results are expected to hold for other countries, though some minor adaption will be required based on local age demographics and hospital facilities.

我们模拟了针对年龄的保护性隔离在多大程度上可以用于减少由新型冠状病毒COVID-19引起的ICU入院。利用新西兰的人口统计数据,我们证明,将年龄门槛降低到50岁,可以大幅减少ICU入院人数,并表明,对于足够严格的隔离方案,将该国三分之一的人口隔离8个月,足以避免在整个疫情过程中ICU容量过大。预计其他国家也会出现类似的结果,不过需要根据当地的年龄人口统计和医院设施进行一些细微的调整。
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引用次数: 2
Global dynamics and optimal harvesting in a stochastic two-predators one-prey system with distributed delays and Lévy noise. 具有分布延迟和lsamvy噪声的随机双捕食者单捕食系统的全局动力学和最优收获。
IF 2.8 4区 数学 Q3 ECOLOGY Pub Date : 2020-12-01 DOI: 10.1080/17513758.2019.1707888
Nafeisha Tuerxun, Xamxinur Abdurahman, Zhidong Teng

In this paper, we first investigate a stochastic two-predators one-prey model with Lévy noise and distributed delays. The global dynamical behaviour is discussed. The criteria on the existence of global positive solutions, stochastic boundedness, extinction and global asymptotic stability in the mean with probability one are established. And then, the harvesting for each species is introduced to the model. The optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY, for short) are further established.

本文首先研究了一类随机双捕食者单捕食模型,该模型具有l杂讯和分布延迟。讨论了系统的全局动力学行为。建立了全局正解的存在性、随机有界性、消光性和概率为1的全局渐近稳定性的判据。然后,每个物种的收获被引入到模型中。进一步建立了最优收获策略和最大可持续产量预期(MESY)。
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引用次数: 5
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Journal of Biological Dynamics
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