Abstract：
:Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.
journal_name
J Math Bioljournal_title
Journal of mathematical biologyauthors
Coron C,Costa M,Leman H,Smadi Cdoi
10.1007/s00285-017-1175-9subject
Has Abstractpub_date
2018-05-01 00:00:00pages
1421-1463issue
6eissn
0303-6812issn
1432-1416pii
10.1007/s00285-017-1175-9journal_volume
76pub_type
杂志文章abstract：:We propose here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. We establish the main properties of the system, and also derive the asymptotic speed of spreading in the direction of the line. For low diffusion, the line has no effect, whereas, past a threshold, ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-012-0604-z
更新日期：2013-03-01 00:00:00
abstract：:Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neg...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-012-0574-1
更新日期：2013-11-01 00:00:00
abstract：:Ixodid ticks are acknowledged as one of the most important hematophagous arthropods because of their ability in transmitting a variety of tick-borne diseases. Mathematical models have been developed, based on emerging knowledge about tick ecology, pathogen epidemiology and their interface, to understand tick populatio...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-018-1311-1
更新日期：2019-04-01 00:00:00
abstract：:This article treats the problem of the sharp front observed when a diffusing substance interacts irreversibly with binding sites within the medium. The model consists of two simultaneous partial differential equations that are nonlinear and cannot be solved in closed form. The parameters are the diffusion coefficient ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-006-0029-7
更新日期：2006-12-01 00:00:00
abstract：:This paper is as much about a certain modelling methodology, as it is about the constructive definition of future population states from a description of individual behaviour and an initial population state. The key idea is to build a nonlinear model in two steps, by explicitly introducing the environmental condition ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s002850170002
更新日期：2001-08-01 00:00:00
abstract：:In this paper we consider the phenomenon of backward bifurcation in epidemic modelling illustrated by an extended model for Bovine Respiratory Syncytial Virus (BRSV) amongst cattle. In its simplest form, backward bifurcation in epidemic models usually implies the existence of two subcritical endemic equilibria for R(0...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-008-0206-y
更新日期：2009-07-01 00:00:00
abstract：:Complex regulation of biochemical pathways in a cell is brought about by the interaction of simpler regulatory structures. Among the basic regulatory designs, feedback inhibition of gene expression is the most common motif in gene regulation and a ubiquitous control structure found in nature. In this work, we have stu...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-010-0375-3
更新日期：2011-08-01 00:00:00
abstract：:Aortic dissection is a major aortic catastrophe with a high morbidity and mortality risk caused by the formation of a tear in the aortic wall. The development of a second blood filled region defined as the "false lumen" causes highly disturbed flow patterns and creates local hemodynamic conditions likely to promote th...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-016-0986-4
更新日期：2016-11-01 00:00:00
abstract：:The S leads to I leads to R epidemic model of K. Dietz with annual oscillation in the contact rate is shown to have multiple stable subharmonic solutions of different integral year periods. ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00305758
更新日期：1983-01-01 00:00:00
abstract：:We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New specie...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-007-0101-y
更新日期：2007-11-01 00:00:00
abstract：:A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value R(crit) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-013-0751-x
更新日期：2015-01-01 00:00:00
abstract：:This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the position of a limited number of close group mates. The proposed model is shown t...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-010-0347-7
更新日期：2011-04-01 00:00:00
abstract：:We proposed a delay differential model, associated with the response time for individuals to the current infection, to examine the media impact on the transmission dynamics of infectious diseases. We investigated the global bifurcation by considering the delay as a bifurcation parameter and examined the onset and term...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-017-1173-y
更新日期：2018-04-01 00:00:00
abstract：:The question about whether a periodic solution can exists for a given epidemiological model is a complicated one and has a long history (Hethcote and Levin, Applied math. ecology, biomathematics, vol 18. Springer, Berlin, pp 193-211, 1989). For influenza models, it is well known that a periodic solution can exists for...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-016-1000-x
更新日期：2016-12-01 00:00:00
abstract：:Tags are conspicuous attributes of organisms that affect the behaviour of other organisms toward the holder, and have previously been used to explore group formation and altruism. Homophilic imitation, a form of tag-based selection, occurs when organisms imitate those with similar tags. Here we further explore the use...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-016-1083-4
更新日期：2017-08-01 00:00:00
abstract：:Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- an...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-013-0718-y
更新日期：2014-10-01 00:00:00
abstract：:A mechanism of serial association in the brain is discussed. The passage from one state to another is assumed to be effected by a control operated by the thalamus on the cortex. Memory failure mechanisms are discussed, such as insufficient imprint, as well as Freudian failure phenomena. ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00276196
更新日期：1987-01-01 00:00:00
abstract：:We consider the adaptive learning rule of Harley (J Theor Biol 89:611-633, 1981) for behavior selection in symmetric conflict games in large populations. This rule uses organisms' past, accumulated rewards as the predictor for future behavior, and can be traced in many life forms from bacteria to humans. We derive a p...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-019-01427-3
更新日期：2019-12-01 00:00:00
abstract：:A general method is given to obtain a stationary distribution in a "stochastic" one-dimensional dynamical system in which an environmental parameter specifying the dynamical system is a stationary Markov process with only two states. By applying this method, the exact stationary gene frequency distribution is obtained...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00275437
更新日期：1981-02-01 00:00:00
abstract：:The time evolution of slowly evolving discrete dynamical systems xi + 1 = T(ri, xi), defined on an interval [0, L], where a parameter ri changes slowly with respect to i is considered. For certain transformations T, once ri reaches a critical value the system faces a non-zero probability of extinction because some xj ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00276093
更新日期：1980-12-01 00:00:00
abstract：:Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-013-0692-4
更新日期：2014-06-01 00:00:00
abstract：:Inconsistencies exist in the standard expansions used to approximate selection coefficients for alleles at a locus underlying a quantitative character. Allelic (marginal) fitnesses obtained from expansions based on average excesses differ from allelic fitnesses obtained from expansions based on genotypic values. Simil...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00171516
更新日期：1990-01-01 00:00:00
abstract：:Platelets cohere to one another to form platelet aggregates as part of the blood's clotting response. The ability of a platelet to participate in this process depends on its prior 'activation' by chemicals released into the blood plasma by other activated platelets. We study the piecewise-linear system of reaction-dif...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF00160419
更新日期：1993-01-01 00:00:00
abstract：:In this paper we consider Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified num...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-019-01347-2
更新日期：2019-06-01 00:00:00
abstract：:This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foers...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-010-0387-z
更新日期：2011-10-01 00:00:00
abstract：:In the present paper we make a bifurcation analysis of an SIRS epidemiological model depending on all parameters. In particular we are interested in codimension-2 bifurcations. ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s002850050040
更新日期：1996-11-01 00:00:00
abstract：:Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vecto...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-010-0326-z
更新日期：2010-12-01 00:00:00
abstract：:The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is ...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-005-0358-y
更新日期：2006-03-01 00:00:00
abstract：:Recent research indicates that viruses are much more prevalent in aquatic environments than previously imagined. We derive a model of competition between two populations of bacteria for a single limiting nutrient in a chemostat where a virus is present. It is assumed that the virus can only infect one of the populatio...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-011-0439-z
更新日期：2012-05-01 00:00:00
abstract：:The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spat...
journal_title：Journal of mathematical biology
pub_type： 杂志文章
doi：10.1007/s00285-012-0532-y
更新日期：2013-05-01 00:00:00
