Comprehensive phase diagram for logistic populations in fluctuating environment

Yahalom, Yitzhak; Steinmetz, B.; Shnerb, Nadav M.

doi:10.1103/physreve.99.062417

Cited by 20 publications

(20 citation statements)

References 45 publications

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“…The mean time to extinction is inversely proportional to the rate of extinction,

T : N^{μ / g - 1}

. For all the models described in SIS in discrete time maps , the time to extinction behaves like a power law in

N

(see Yahalom et al 2019). In particular, it has been shown for the Moran process (Hidalgo et al 2017, Danino et al 2018) that

T : N^{μ / g - 1} = N^{1 / δ}

in agreement with Eq.…”

Section: A Quantitative Analysis Of Coexistencementioning

confidence: 99%

“…Invasibility of a given species is then quantified using the mean logarithmic growth rate when rare

E [r]

. Given a time series of (low) frequencies

(}{, x_{t}, x_{t + normalΔ t}, x_{t + 2 normalΔ t} . . .)

E [r]

is defined as (Chesson 2003)

E [r] \equiv \frac{1}{Δ t} E [\ln (\frac{x_{t + Δ t}}{x_{t}})] .

when the number of individuals in the community,

N

, is large, the sign of

E [r]

provides important information about invasibility and persistence properties (Chesson 1982, Schreiber et al 2011, Schreiber 2012, Yahalom et al 2019). If

E [r] < 0

, then the probability of invasion is negligible and the time to extinction depends logarithmically on the initial density of the focal species.…”

Section: Introductionmentioning

confidence: 99%

“…First, we focus on large, well‐mixed communities where the impacts of demographic stochasticity are weak and spatial structure can be neglected. Second, the amplitude of selection depends on the environmental conditions and, for simplicity, we allow the selection coefficients to adopt either of two values (dichotomous, or telegraphic, stochasticity), the generalization to any type of stochasticity being straightforward (Yahalom et al 2019). We believe that these restrictions are irrelevant to the general qualitative and quantitative insights that emerge from the models considered below.…”

Section: Introductionmentioning

confidence: 99%

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Stochasticity‐induced stabilization in ecology and evolution: a new synthesis

Dean

Shnerb

2020

Ecology

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The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log abundances of species, with mean logarithmic growth rates when rare, Er, used as metrics for persistence. However, invasion probabilities and the times to extinction are not single‐valued functions of Er and, in some cases, decrease as Er increases. Here, we present a synthesis of stochasticity‐induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth normalμ and its variance g. When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single‐valued, monotonic functions of μ/g. The storage effect in the lottery model, together with other well‐known examples drawn from population genetics, microbiology, and ecology (including discrete and continuous dynamics, with overlapping and non‐overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life‐history strategies and SIS, and study the dynamics of extinction when SIS fails.

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“…The mean time to extinction is inversely proportional to the rate of extinction,

T : N^{μ / g - 1}

. For all the models described in SIS in discrete time maps , the time to extinction behaves like a power law in

N

(see Yahalom et al 2019). In particular, it has been shown for the Moran process (Hidalgo et al 2017, Danino et al 2018) that

T : N^{μ / g - 1} = N^{1 / δ}

in agreement with Eq.…”

Section: A Quantitative Analysis Of Coexistencementioning

confidence: 99%

“…Invasibility of a given species is then quantified using the mean logarithmic growth rate when rare

E [r]

. Given a time series of (low) frequencies

(}{, x_{t}, x_{t + normalΔ t}, x_{t + 2 normalΔ t} . . .)

E [r]

is defined as (Chesson 2003)

E [r] \equiv \frac{1}{Δ t} E [\ln (\frac{x_{t + Δ t}}{x_{t}})] .

when the number of individuals in the community,

N

, is large, the sign of

E [r]

provides important information about invasibility and persistence properties (Chesson 1982, Schreiber et al 2011, Schreiber 2012, Yahalom et al 2019). If

E [r] < 0

, then the probability of invasion is negligible and the time to extinction depends logarithmically on the initial density of the focal species.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochasticity‐induced stabilization in ecology and evolution: a new synthesis

Dean

Shnerb

2020

Ecology

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“…We have studied the simplest scenario of fitness fluctuations, in which s i (t) takes only two values (dichotomous stochasticity), either +σ 0 or −σ 0 (to keep 0 ≥ P 1 ≤ 1, |σ 0 | < 1). Previous works have shown that this assumption has minimal implications for the resulting system behavior [40,41]. The mean persistence time of the environment is τ generations (where a generation is defined as J duels); to model that, after each elementary time step the environment changes with probability 1/Jτ , and the fitnesses of all traits are re-drawn at random in an uncorrelated manner.…”

Section: Symmetric Modelsmentioning

confidence: 99%

Intra-Specific variability in fluctuating environments - mechanisms of impact on species diversity

Steinmetz

Kalyuzhny

Shnerb

2019

Preprint

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Recent studies have found considerable trait variations within species. The effect of such intraspecific trait variability (ITV) on the stability, coexistence and diversity of ecological communities received considerable attention and in many models it was shown to impede coexistence and decrease species diversity. Here we present a numerical study of the effect of genetically inherited ITV on species persistence and diversity in a temporally fluctuating environment. Two mechanisms are identified. First, ITV buffers populations against varying environmental conditions (portfolio effect) and reduces abundance variations. Second, the interplay between ITV and environmental variations tends to increase the mean fitness of diverse populations. The first mechanism promotes persistence and tends to increase species richness, while the second reduces the chance of a rare species population (which is usually homogenous) to invade and decreases species richness. We show that for large communities the portfolio effect is dominant, leading to ITV promoting species persistence and richness.

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“…We fully agree with this interpretation of the utility of IGR. In general, when N is large and there are no strong Allee effects, the sign of IGR indeed provides important information about persistence (Chesson, 1982;Schreiber et al, 2011;Schreiber, 2012;Yahalom et al, 2019). If IGR<0, the probability of invasion is negligible and the time to extinction of a species depends only on its initial density, not on N. If IGR>0, ɛ þ is non-negligible and Our main reservation with IGR, supported by examples in Pande et al (2020), is that its magnitude does not necessarily show a strong correlation with persistence.…”

Section: Introductionmentioning

confidence: 99%