Extinction phase transitions in a model of ecological and evolutionary dynamics

Barghathi, Hatem; Tackkett, Skye; Vojta, Thomas

doi:10.1140/epjb/e2017-80220-7

Cited by 12 publications

(4 citation statements)

References 31 publications

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“…This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. The RG predictions were later confirmed by Monte Carlo simulations [30,31]. In addition, Vazquez et al [32] identified a temporal analog of the Griffiths phase in spatially disordered systems that features an unusual power-law relation between lifetime and system size on the active side of the phase transition.…”

Section: Introductionmentioning

confidence: 89%

Contact process with simultaneous spatial and temporal disorder

Ye¹,

Vojta²

2022

Preprint

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We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched in the language of epidemic spreading, this means that some spatial regions are, at all times, more favorable than others for infections, and some time periods are more favorable than others independent of spatial location. We employ a generalized Harris criterion to discuss the stability of the directed percolation universality class against such disorder. We then perform large-scale Monte Carlo simulations to analyze the critical behavior in detail. We also discuss how the Griffiths singularities that accompany the nonequilibrium phase transition are affected by the simultaneous presence of both disorders.

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Section: Introductionmentioning

confidence: 89%

Contact process with simultaneous spatial and temporal disorder

Ye¹,

Vojta²

2022

Preprint

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“…which has the advertised structure of a power law with c D = 2D/σ 2 , and a lower cutoff set by c D ȳ. Power laws arising from models with seascape noise are quite common, so this is well precedented [8,35,77,[85][86][87][88]. However, the continuous variation of the exponent with the ratio c D is unusual and likely a feature of the mean-field limit, though some similarly continuous nonuniversal exponents have also appeared in directed percolation under temporal disorder [89,90].…”

Section: A Stochastic Explorationmentioning

confidence: 99%

Seascape origin of Richards growth

2022

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First proposed as an empirical rule over half a century ago, the Richards growth equation has been frequently invoked in population modeling and pandemic forecasting. Central to this model is the advent of a fractional exponent γ , typically fitted to the data. While various motivations for this nonanalytical form have been proposed, it is still considered foremost an empirical fitting procedure. Here, we find that Richards-like growth laws emerge naturally from generic analytical growth rules in a distributed population, upon inclusion of (i) migration (spatial diffusion) among different locales, and (ii) stochasticity in the growth rate, also known as "seascape noise." The latter leads to a wide (power law) distribution in local population number that, while smoothened through the former, can still result in a fractional growth law for the overall population. This justification of the Richards growth law thus provides a testable connection to the distribution of constituents of the population.

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“…On the other hand, when ξ E much larger than the linear size of the system temporal stochasticity is a relevant operator and the transition belongs to a different equivalence class [42]. In that case a series of bad years may kill the whole system and the chance of recolonization is small since the state of all neighboring sites is correlated.…”

Section: Spatial Effectsmentioning

confidence: 99%

Comprehensive phase diagram for logistic populations in fluctuating environment

2019

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Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density.A whole family of simple and popular deterministic models (like logistic growth) support a transcritical bifurcation point between an extinction phase and an active phase. Here we provide a comprehensive analysis of the phases of that system, taking into account both the endogenous demographic noise (random birth and death events) and the effect of environmental stochasticity that causes variations in birth and death rates. Three phases are identified: in the inactive phase the mean time to extinction T is independent of the carrying capacity N , and scales logarithmically with the initial population size. In the power-law phase T ∼ N q and the exponential phase T ∼ exp(αN ). All three phases and the transitions between them are studied in detail. The breakdown of the continuum approximation is identified inside the power-law phase, and the accompanied changes in decline modes are analyzed. The applicability of the emerging picture to the analysis of ecological timeseries and to the management of conservation efforts is briefly discussed.

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Extinction phase transitions in a model of ecological and evolutionary dynamics

Cited by 12 publications

References 31 publications

Contact process with simultaneous spatial and temporal disorder

Contact process with simultaneous spatial and temporal disorder

Seascape origin of Richards growth

Comprehensive phase diagram for logistic populations in fluctuating environment

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