Bifurcations analysis of oscillating hypercycles

Guillamón, Antoni; Fontich, Ernest; Sardanyés, Josep

doi:10.1016/j.jtbi.2015.09.018

Cited by 14 publications

(33 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bifurcation analysis of oscillating hypercycles (n ! 4) has been reported recently [48]. A series of studies on small hypercycles n ¼ 2, 3, 4 revealed interesting dynamical phenomena such as delayed transitions and ghosts [49,50].…”

Section: ð4:1cþmentioning

confidence: 91%

Some mechanistic requirements for major transitions

Schuster

2016

Phil. Trans. R. Soc. B

View full text Add to dashboard Cite

One contribution of 13 to a theme issue 'The major synthetic evolutionary transitions'. Major transitions in nature and human society are accompanied by a substantial change towards higher complexity in the core of the evolving system. New features are established, novel hierarchies emerge, new regulatory mechanisms are required and so on. An obvious way to achieve higher complexity is integration of autonomous elements into new organized systems whereby the previously independent units give up their autonomy at least in part. In this contribution, we reconsider the more than 40 years old hypercycle model and analyse it by the tools of stochastic chemical kinetics. An open system is implemented in the form of a flow reactor. The formation of new dynamically organized units through integration of competitors is identified with transcritical bifurcations. In the stochastic model, the fully organized state is quasi-stationary whereas the unorganized state corresponds to a population with natural selection. The stability of the organized state depends strongly on the number of individual subspecies, n, that have to be integrated: two and three classes of individuals, n ¼ 2 and n ¼ 3, readily form quasi-stationary states. The four-membered deterministic dynamical system, n ¼ 4, is stable but in the stochastic approach self-enhancing fluctuations drive it into extinction. In systems with five and more classes of individuals, n ! 5, the state of cooperation is unstable and the solutions of the deterministic ODEs exhibit large amplitude oscillations. In the stochastic system self-enhancing fluctuations lead to extinction as observed with n ¼ 4. Interestingly, cooperative systems in nature are commonly two-membered as shown by numerous examples of binary symbiosis. A few cases of symbiosis of three partners, called three-way symbiosis, have been found and were analysed within the past decade. Four-way symbiosis is rather rare but was reported to occur in fungus-growing ants. The model reported here can be used to illustrate the interplay between competition and cooperation whereby we obtain a hint on the role that resources play in major transitions. Abundance of resources seems to be an indispensable prerequisite of radical innovation that apparently needs substantial investments. Economists often claim that scarcity is driving innovation. Our model sheds some light on this apparent contradiction. In a nutshell, the answer is: scarcity drives optimization and increase in efficiency but abundance is required for radical novelty and the development of new features.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

show abstract

Section: ð4:1cþmentioning

confidence: 91%

Some mechanistic requirements for major transitions

Schuster

2016

Phil. Trans. R. Soc. B

View full text Add to dashboard Cite

show abstract

“…where β = 1/2. This scaling law has been identified in physical systems (Strogatz & Westervelt 1989;Trickey & Virgin 1998), in metapopulation mathematical models for autocatalytic species (Sardanyés & Fontich 2010), in lowdimension (Sardanyés & Solé 2006;Sardanyés & Solé 2007) and high-dimensional replicator models exhibiting cooperation (Silvestre & Fontanari 2008;Guillamon et al 2015), as well as in single-species discrete models with Allee effects (Duarte et al 2012). If ghosts appear in green-desert transitions, the take home message is simple but leads to a grim picture: a given ecosystem might be on its way towards collapse despite the apparent stability.…”

Section: Introductionmentioning

confidence: 88%

Exploiting delayed transitions to sustain semiarid ecosystems after catastrophic shifts

Vidiella

Sardanyés

Solé

2017

Preprint

Self Cite

View full text Add to dashboard Cite

Semiarid ecosystems (including arid, semiarid and dry-subhumid ecosystems) span more than 40% of extant habitats and a similar percentage of human population. As a consequence of global warming, these habitats face future potential shifts towards the desert state characterized by an accelerated loss of diversity and stability leading to collapse. Such possibility has been raised by several mathematical and computational models, along with several early warning signal methods applied to spatial vegetation patterns. Here we show that just after a catastrophic shift has taken place an expected feature is the presence of a ghost, i.e., a delayed extinction associated to the underlying dynamical flows. As a consequence, a system might exhibit for very long times an apparent stationarity hiding in fact an inevitable collapse. Here we explore this problem showing that the ecological ghost is a generic feature of standard models of green-desert transitions including facilitation. If present, the ghost could hide warning signals, since statistical patterns are not be expected to display growing fluctuations over time. We propose and computationally test a novel intervention method based on the restoration of small fractions of desert areas with vegetation as a way to maintain the fragile ecosystem beyond the catastrophic shift caused by a saddle-node bifurcation, taking advantage of the delaying capacity of the ghost just after the bifurcation.

show abstract

“…More recently, Guillamon et al, [2015] investigated the periodic orbits in symmetric hypercycles with n = 5. In particular, they studied how these orbits behave in terms of Q using both numerical and analytical methods.…”

Section: Introductionmentioning

confidence: 99%

“…Under this scenario, the flows display transient periodic behavior since the trivial attractor is asymptotically globally stable. (B) Bifurcation curves of periodic orbits (red) and of fixed points (blue) taking coordinate x 4 (see [Guillamon et al, 2015] for details) with respect to parameter Q for the symmetric hypercycle, i.e., δ = 0, with A = 0.5 and k = 1. The parametric region in green allows for the coexistence of the hypercycle members in an oscillatory regime.…”

Section: Introductionmentioning

confidence: 99%

“…The bifurcation value of periodic orbits, Q P O , and of the fixed points, Q SS , are indicated with dashed vertical lines. Notice that both bifurcation values do not coincide, fact which has been denoted as a bifurcation gap [Guillamon et al, 2015]. The smaller panels display time series for all hypercycle members in the extinction and coexistence scenarios.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles

Puig

Farré

Guillamón

et al. 2018

Int. J. Bifurcation Chaos

Self Cite

View full text Add to dashboard Cite

Hypercycles are catalytic systems with cyclic architecture. These systems have been suggested to play a key role in the maintenance and increase of information in prebiotic replicators. It is known that for a large enough number of hypercycle species (n > 4) the coexistence of all hypercycle members is governed by a stable periodic orbit. Previous research has characterized saddle-node (s-n) bifurcations involving abrupt transitions from stable hypercycles to extinction of all hypercycle members, or, alternatively, involving the outcompetition of the hypercycle by so-called mutant sequences or parasites. Recently, the presence of a bifurcation gap between a s-n bifurcation of periodic orbits and a s-n of fixed points has been described for symmetric five-member hypercycles. This gap was found between the value of the replication quality factor Q from which the periodic orbit vanishes (QP O ) and the value where two unstable (nonzero) equilibrium points collided (QSS). Here, we explore the persistence of this gap considering asymmetries in replication rates in five-member hypercycles as well as considering symmetric, larger hypercycles. Our results indicate that both the asymmetry in Malthusian replication constants and the increase in hypercycle members enlarge the size of this * Version previous to that published in the International Journal of Bifurcation and Chaos (2018), https://doi.1 gap. The implications of this phenomenon are discussed in the context of delayed transitions associated to the so-called saddle remnants.

show abstract

Bifurcations analysis of oscillating hypercycles

Cited by 14 publications

References 24 publications

Some mechanistic requirements for major transitions

Some mechanistic requirements for major transitions

Exploiting delayed transitions to sustain semiarid ecosystems after catastrophic shifts

Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles

Contact Info

Product

Resources

About