Year class coexistence or competitive exclusion for strict biennials?

Davydova, N.V.; Diekmann, Odo; Gils, Stephan A. van

doi:10.1007/s00285-002-0167-5

Cited by 54 publications

(49 citation statements)

References 22 publications

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“…In the second case, most juveniles die in years when adult density is high; there will be few adults in the next year but many juveniles, which enjoy high resource abundance and mature into many adults by the year after. These cycles are essentially the same as the single cohort dynamics found by Bulmer (1977) and analyzed in detail by Davydova et al (2003;see Discussion). In this paper, we concentrate on stationary spatial pattern formation and thus do not pursue temporal cyclic behavior further.…”

Section: Dynamics Of An Isolated Populationmentioning

confidence: 70%

Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

2007

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A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects.

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Section: Dynamics Of An Isolated Populationmentioning

confidence: 70%

Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

2007

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“…Bulmer [2] showed that severe inter-class competition stabilizes perfect periodicity and predation reinforces the tendency (e.g. see also [6,9,24]). Appendix 1 shows that (H6) can be realized when inter-class competition is severe.…”

Section: Is Asymptotically Stable In the Subsystem X = 0 If And Only mentioning

confidence: 99%

Permanence induced by life-cycle resonances: the periodical cicada problem

Kon

2012

Journal of Biological Dynamics

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Periodical cicadas are known for their unusually long life cycle for insects and their prime periodicity of either 13 or 17 years. One of the explanations for the prime periodicity is that the prime periods are selected to prevent cicadas from resonating with predators with submultiple periods. This paper considers this hypothesis by investigating a population model for periodical predator and prey. The study shows that if the periods of the two periodical species are not coprime, then the predator cannot resist the invasion of the prey. On the other hand, if the periods are coprime, then the predator can resist the invasion of the prey. It is also shown that if the periods are not coprime, then the life-cycle resonance can induce a permanent system, in which no cohorts are missing in both populations. On the other hand, if the periods are coprime, then the system cannot be permanent.

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“…Mathematically, the dynamics of semelparous populations can be described by a discrete-time nonlinear Leslie matrix model (Cushing 2006;Davydova 2004;Davydova et al 2005;Diekmann and van Gils year;Drissche and Zeeman 1998;Kon 2005;Kon and Iwasa 2007;Mjolhus et al 2005). The phenomenon of periodical insects can be explained by the invariance of coordinate axes and hyperplanes of the full life cycle map (Davydova et al 2003) and the existence of heteroclinic cycles connecting different year cycles (Cushing 2009;Diekmann and van Gils 2009). Diekmann and van Gils (2009) demonstrated that the n-dimensional discrete-time Leslie matrix model can be reduced to a cyclic replicator system on the (n − 1) dimensional simplex and classified the repertoire of the dynamical behavior for n = 2 and 3.…”

Section: Introductionmentioning

confidence: 99%

Periodic orbits near heteroclinic cycles in a cyclic replicator system

Wang

Ruan

2011

J. Math. Biol.

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A species is semelparous if every individual reproduces only once in its life and dies immediately after the reproduction. While the reproduction opportunity is unique per year and the individual's period from birth to reproduction is just n years, the individuals that reproduce in the ith year (modulo n) are called the ith year class, i = 1, 2, . . . , n. The dynamics of the n year-class system can be described by a differential equation system of Lotka-Volterra type. For the case n = 4, there is a heteroclinic cycle on the boundary as shown in previous works. In this paper, we focus on the case n = 4 and show the existence, growth and disappearance of periodic orbits near the heteroclinic cycle, which is a part of the conjecture by Diekmann and van Gils (SIAM J Appl Dyn Syst 8:1160-1189, 2009). By analyzing the Poincaré map near the heteroclinic cycle and introducing a metric to measure the size of the periodic orbit, we show that (i) when the average competitive degree among subpopulations (year classes) in the system is weak, there exists an asymptotically stable periodic orbit near the heteroclinic cycle which is repelling; (ii) the periodic orbit grows in size when some competitive degree increases, and converges to the heteroclinic cycle when the average competitive degree tends to be strong; (iii) when the average competitive degree is strong, there is no periodic orbit near the heteroclinic cycle which becomes asymptotically stable. Our results provide explanations why periodic solutions expand and disappear and why all but one subpopulation go extinct.

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Year class coexistence or competitive exclusion for strict biennials?

Cited by 54 publications

References 22 publications

Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

Permanence induced by life-cycle resonances: the periodical cicada problem

Periodic orbits near heteroclinic cycles in a cyclic replicator system

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