In the red zone

Blarer, Albert; Doebeli, Michael

doi:10.1038/380589b0

Cited by 23 publications

(28 citation statements)

References 5 publications

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“…(Alternate statistical analysis, including testing for the e¡ects of environmental colour and species identity on the relative power of low-and high-frequency portions of the spectra (e.g. Blarer & Doebeli 1996;White et al 1996a), led to the same conclusions as the ANCOVA presented here. )…”

Section: (B) Experimental Designmentioning

confidence: 76%

“…Other studies have emphasized the importance of the intrinsic properties of populations (Cohen 1995;Blarer & Doebeli 1996;Kaitala & Ranta 1996;White et al 1996a), interspeci¢c interactions (Ripa et al 1998) or population subdivision (White et al 1996b) for reddened population dynamics. Population dynamics should be redder in reddened environments than in white environments if environmental colour does in£uence population colour (Roughgarden 1975;Kaitala et al 1997a).…”

Section: (I) Population Colourmentioning

confidence: 99%

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Environmental colour affects aspects of single–species population dynamics

Petchey

2000

Proc. R. Soc. Lond. B

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Single-species populations of ciliates (Colpidium and Paramecium) experienced constant temperature or white or reddened temperature £uctuations in aquatic microcosms in order to test three hypotheses about how environmental colour in£uences population dynamics. (i) Models predict that the colour of population dynamics is tinged by the colour of the environmental variability. However, environmental colour had no e¡ect on the colour of population dynamics. All population dynamics in this experiment were reddened, regardless of environmental colour. (ii) Models predict that populations will track reddened environmental variability more closely than white environmental variability and that populations with a higher intrinsic growth rate (r) will track environmental variability more closely than populations with a low r. The experimental populations behaved as predicted. (iii) Models predict that population variability is determined by interaction between r and the environmental variability. The experimental populations behaved as predicted. These results show that (i) reddened population dynamics may need no special explanation, such as reddened environments, spatial subdivision or interspeci¢c interactions, and (ii) and (iii) that population dynamics are sensitive to environmental colour, in agreement with population models. Correct speci¢cation of the colour of the environmental variability in models is required for accurate predictions. Further work is needed to study the e¡ects of environmental colour on communities and ecosystems.

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Section: (B) Experimental Designmentioning

confidence: 76%

Section: (I) Population Colourmentioning

confidence: 99%

Environmental colour affects aspects of single–species population dynamics

Petchey

2000

Proc. R. Soc. Lond. B

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“…The 'colour' of population fluctuations has been a pervasive subject in the recent ecological literature, with titles such as 'From out of the blue' (Sugihara 1995), 'In the red zone' (Blarer & Doebeli 1996), and 'Red, blue, green: dyeing population dynamics' (Kaitala et al 1997a). Although the subject has been approached with modern tools and ideas, including chaotic dynamics and stochasticity, it has deep roots in the early debate of whether population and community patterns are intrinsic, generated by ecological interactions and density dependence, or extrinsic, merely reflecting chance and environmental fluctuations (Gleason 1926;Clements 1936;Nicholson 1958;Smith 1961).…”

Section: Introductionmentioning

confidence: 99%

Cluster size distributions: signatures of self–organization in spatial ecologies

Pascual

Roy

Guichard

et al. 2002

Phil. Trans. R. Soc. Lond. B

106

112

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Three different lattice-based models for antagonistic ecological interactions, both nonlinear and stochastic, exhibit similar power-law scalings in the geometry of clusters. Specifically, cluster size distributions and perimeter-area curves follow power-law scalings. In the coexistence regime, these patterns are robust: their exponents, and therefore the associated Korcak exponent characterizing patchiness, depend only weakly on the parameters of the systems. These distributions, in particular the values of their exponents, are close to those reported in the literature for systems associated with self-organized criticality (SOC) such as forest-fire models; however, the typical assumptions of SOC need not apply. Our results demonstrate that power-law scalings in cluster size distributions are not restricted to systems for antagonistic interactions in which a clear separation of time-scales holds. The patterns are characteristic of processes of growth and inhibition in space, such as those in predator-prey and disturbance-recovery dynamics. Inversions of these patterns, that is, scalings with a positive slope as described for plankton distributions, would therefore require spatial forcing by environmental variability.

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“…of spectra of Eq. 4 can change if the competition parameter b is varied, whereas the growth rate is fixed at a low value (12,13). As b increases, the periods of low population size get larger (cf.…”

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confidence: 99%

Population dynamics, demographic stochasticity, and the evolution of cooperation

Doebeli

Blarer

Ackermann

1997

Proc. Natl. Acad. Sci. U.S.A.

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A basic evolutionary problem posed by the Iterated Prisoner's Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner's Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks. The Prisoner's Dilemma game contains the basic paradox for the evolution of reciprocal altruism (1, 2). In this game, each of two players can either cooperate or defect. This leads to four possible payoffs S Ͻ P Ͻ R Ͻ T: if one player cooperates and the other defects, the cooperator gets S and the defector gets T, if both players cooperate they both get R, and if both defect they get P. No matter what the other does, it is always best to defect (R Ͻ T and S Ͻ P), but if both would cooperate they would both receive a higher payoff than if both defect (P Ͻ R). If payoffs are interpreted as Darwinian fitness, this game exemplifies the advantage of selfish mutants and the evolution of maladaptive noncooperative behavior. The paradox has a solution in the Iterated Prisoner's Dilemma (1), in which opponents meet again with a certain probability. In this new game, the Tit-for-Tat (TFT) strategy-cooperate in the first round, then do whatever the opponent did in the previous round-does very well against a wide variety of other strategies (3). TFT captures the essence of reciprocal altruism (4), and once established, TFT can catalyze the evolution of even more cooperative strategies (5, 6). Thus, TFT represents a cornerstone in the evolution of cooperation, and it is important to determine the conditions under which TFT can evolve in a population of pure defectors.We consider the evolutionary game between the strategies TFT and AD-always defect, regardless of the opponent's decisions-in the Iterated Prisoner's Dilemma. Let w be the probability that opponents meet again. Then the payoffs between TFT and AD are as shown in Table 1, in which the entries are the payoffs received by the strategy in the left column when playing against the strategy in the top row. For example, when TFT plays against AD, it gets S in the first round and P in all successive rounds, hence a total of S ϩ wP ϩ w 2 P ϩ . . . . AD gets T in the first round and P thereafter. Thus the payoff for TFT is S ϩ wP͞(1 Ϫ w), whereas that of AD is T ϩ wP͞(1 Ϫ w). The other payoffs are calculated similarly. In a population consisting of a mixture of TFT and AD, the payoffs of the two strategies depend on their frequencies. If p is the frequency of TFT...

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In the red zone

Cited by 23 publications

References 5 publications

Environmental colour affects aspects of single–species population dynamics

Environmental colour affects aspects of single–species population dynamics

Cluster size distributions: signatures of self–organization in spatial ecologies

Population dynamics, demographic stochasticity, and the evolution of cooperation

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