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Bulletin of Mathematical Biology

Caterina Vitale, Eva Kisdi
Under the threat of predation, a species of prey can evolve to its own extinction. Matsuda and Abrams (Theor Popul Biol 45:76-91, 1994a) found the earliest example of evolutionary suicide by demonstrating that the foraging effort of prey can evolve until its population dynamics cross a fold bifurcation, whereupon the prey crashes to extinction. We extend this model in three directions. First, we use critical function analysis to show that extinction cannot happen via increasing foraging effort. Second, we extend the model to non-equilibrium systems and demonstrate evolutionary suicide at a fold bifurcation of limit cycles...
August 17, 2018: Bulletin of Mathematical Biology
David F Anderson, Daniele Cappelletti, Masanori Koyama, Thomas G Kurtz
We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relatively to the transition rates, then the model is non-explosive. In particular, complex-balanced reaction networks are non-explosive.
August 16, 2018: Bulletin of Mathematical Biology
Alexandru Hening, Dang H Nguyen
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J Math Biol 76:697-754, 2018b) where we have characterized the persistence and extinction of such a food chain under the assumption that there is no intraspecific competition among predators. In the current paper, we focus on the case when all the species experience intracompetition. The food chain we analyze consists of one prey and [Formula: see text] predators...
August 14, 2018: Bulletin of Mathematical Biology
J M Wentz, A R Mendenhall, D M Bortz
Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein-16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypothesized mechanism that could lead to this patterned response and develop a mathematical model of this system to test our hypothesis. We propose that the patterned expression of heat shock protein is caused by a diffusion-driven instability within the pseudocoelom, or fluid-filled cavity, that borders the intestinal cells in C...
August 10, 2018: Bulletin of Mathematical Biology
M H Kabir, M Mimura, J C Tsai
The Neolithic transition began the spread of early agriculture throughout Europe through interactions between farmers and hunter-gatherers about 10,000 years ago. Archeological evidence produced by radiocarbon dating indicates that the expanding velocity of farming is roughly constant all over Europe. Theoretical understanding of such evidence has been performed from mathematical modeling viewpoint. However, the expanding velocity determined by existing modeling approaches is faster than the observed velocity...
August 10, 2018: Bulletin of Mathematical Biology
Xiaoquan Yu, Xiang-Yi Li
In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods widely used in studying such physical systems, for instance, Wentzel-Kramers-Brillouin (WKB) and Fokker-Planck methods, can be applied to solve similar biological problems. In this article, we comparatively analyse applications of WKB and Fokker-Planck methods to some typical stochastic population dynamical models, including the logistic growth, endemic SIR, predator-prey, and competitive Lotka-Volterra models...
August 10, 2018: Bulletin of Mathematical Biology
Cinthia M Tanaka, Joung-Hun Lee, Yoh Iwasa
In recent decades, cultural diversity loss has been a growing issue, which can be analyzed mathematically through the use of the formalism of the theory of cultural evolution. We here study the evolutionary dynamics of dialects in order to find the key processes for mitigating the loss of language diversity. We define dialects as different speech systems of the same language which are mutually intelligible. Specifically, we focus on the survival of a local dialect when competing against a national standard language, with the latter giving an advantage in occupational and economic contexts...
August 10, 2018: Bulletin of Mathematical Biology
Anudeep Surendran, Michael J Plank, Matthew J Simpson
Birth-death-movement processes, modulated by interactions between individuals, are fundamental to many cell biology processes. A key feature of the movement of cells within in vivo environments is the interactions between motile cells and stationary obstacles. Here we propose a multi-species model of individual-level motility, proliferation and death. This model is a spatial birth-death-movement stochastic process, a class of individual-based model (IBM) that is amenable to mathematical analysis. We present the IBM in a general multi-species framework and then focus on the case of a population of motile, proliferative agents in an environment populated by stationary, non-proliferative obstacles...
August 10, 2018: Bulletin of Mathematical Biology
Alex Kasman
It is well known that sequences of bases in DNA are translated into sequences of amino acids in cells via the genetic code. More recently, it has been discovered that the sequence of DNA bases also influences the geometry and deformability of the DNA. These two correspondences represent a naturally arising example of duplexed codes, providing two different ways of interpreting the same DNA sequence. This paper will set up the notation and basic results necessary to mathematically investigate the relationship between these two natural DNA codes...
August 10, 2018: Bulletin of Mathematical Biology
Hector Baños
We show that many topological features of level-1 species networks are identifiable from the distribution of the gene tree quartets under the network multi-species coalescent model. In particular, every cycle of size at least 4 and every hybrid node in a cycle of size at least 5 are identifiable. This is a step toward justifying the inference of such networks which was recently implemented by Solís-Lemus and Ané. We show additionally how to compute quartet concordance factors for a network in terms of simpler networks, and explore some circumstances in which cycles of size 3 and hybrid nodes in 4-cycles can be detected...
August 9, 2018: Bulletin of Mathematical Biology
Julie Simons, Lisa Fauci
The acrosome reaction is a complex, calcium-dependent reaction that results in an exocytotic event required for successful fertilization of the egg. It has long been thought that the acrosome reaction occurs upon sperm binding to the zona pellucida, a viscoelastic layer surrounding the oocyte. Recent studies have suggested that the reaction may even occur before the sperm encounters the zona, perhaps mediated by progesterone or some other agonist. It has been particularly difficult to understand differences between progesterone-induced and zona-induced reactions experimentally and whether one substance is the more biologically relevant trigger...
August 9, 2018: Bulletin of Mathematical Biology
Hélène Leman
More and more evidence shows that mating preference is a mechanism that may lead to a reproductive isolation event. In this paper, a haploid population living on two patches linked by migration is considered. Individuals are ecologically and demographically neutral on the space and differ only on a trait, a or A, affecting both mating success and migration rate. The special feature of this paper is to assume that the strengths of the mating preference and the migration depend on the trait carried. Indeed, patterns of mating preferences are generally asymmetrical between the subspecies of a population...
August 9, 2018: Bulletin of Mathematical Biology
Corin Stratton, Allison Kolpas, Josh R Auld
The optimal timing for initiating reproduction (i.e., the age at first reproduction) is a critical life history trait describing aspects of an individual's resource-allocation strategy. Recent theoretical and empirical work has demonstrated that this trait is also tied to mating system expression when individuals have the opportunity to reproduce via both self-fertilization and cross-fertilization. A strategy of "delayed selfing" has emerged as a "best of both worlds" arrangement where, in the absence of a mate, an individual will delay reproduction (selfing) to "wait" for a mate...
August 9, 2018: Bulletin of Mathematical Biology
E Vendel, V Rottschäfer, E C M de Lange
The development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration-time profile of a drug (pharmacokinetics) within the brain. So far, there are no studies on predicting the drug concentration within the brain that focus not only on the transport of drugs to the brain through the blood-brain barrier (BBB), but also on drug transport and binding within the brain. Here, we develop a new model for a 2D square brain tissue unit, consisting of brain extracellular fluid (ECF) that is surrounded by the brain capillaries...
August 8, 2018: Bulletin of Mathematical Biology
Elisa Tonello, Matthew D Johnston
Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species...
August 7, 2018: Bulletin of Mathematical Biology
Longxing Qi, Meng Xue, Jing-An Cui, Qizhi Wang, Tianping Wang
National Bureau of Statistics of China reports that the incidence of schistosomiasis has been increasing in recent years. To study dynamic behaviors of schistosomiasis transmission, based on practical experience of staff in Anhui Institute of Schistosomiasis, a mathematical schistosomiasis model with reinfection of recovered people is established in this paper. Metzler matrix theory and center manifold theorem are used to analyze stability of equilibria. Parameter estimation has been performed by combining model and monitoring data...
August 7, 2018: Bulletin of Mathematical Biology
Raul Abreu de Assis, Luca Pietro Casacci, Simona Bonelli, Francesca Barbero, Luciana Mafalda Elias de Assis, Ezio Venturino
A model of interspecific host competition in a system with one parasite (butterfly-Maculinea) and multiple potential hosts (ants-Myrmica) is presented. Results indicate that host interspecific competition increases the occurrence of multiple host behaviour in Maculinea natural populations but decreases the ability of the parasite populations to adapt to the most abundant host species. These qualitative predictions were compared with data on host specificity, with good agreement. Analysis of the data also indicates that Maculinea teleius and Maculinea arion respond differently to changes in relative host abundances...
August 6, 2018: Bulletin of Mathematical Biology
Lan Zou, Jing Chen, Xiaomei Feng, Shigui Ruan
There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium...
August 6, 2018: Bulletin of Mathematical Biology
Yuanshi Wang, Hong Wu, Shikun Wang, Wen Shi
This paper considers intraguild predation (IGP) systems where species in the same community kill and eat each other and there is intraspecific competition in each species. The IGP systems are characterized by a lattice gas model, in which reaction between sites on the lattice occurs in a random and independent way. Global dynamics of the model with two species demonstrate mechanisms by which IGP leads to survival/extinction of species. It is shown that an intermediary level of predation promotes survival of species, while over-predation or under-predation could result in species extinction...
August 6, 2018: Bulletin of Mathematical Biology
Jeremy G Sumner, Michael D Woodhams
We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. We show that our construction is a natural generalization of the concept of group-based models...
August 2, 2018: Bulletin of Mathematical Biology
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