Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models

Kendal, Wayne S.

doi:10.1016/j.ecocom.2004.05.001

Cited by 76 publications

(78 citation statements)

References 65 publications

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“…It has been confirmed for hundreds of species or groups of related species in field observations [3][4][5] and laboratory experiments with stem cells [6] and ecological microcosms [7][8][9]. Numerous models have been proposed to explain TL under various assumptions [10][11][12][13][14][15][16] and probability distributions compatible with TL have been analysed [17][18][19][20][21][22][23][24]. Nevertheless, it remains unclear why the ecological pattern called TL is so widely observed, how its estimated parameters should be interpreted in terms of underlying population dynamics and when it should be expected to fail.…”

Section: Introductionmentioning

confidence: 91%

“…Prior models of TL covered a range of abstraction, from phenomenological to mechanistic [3][4][5]16,23,24,[43][44][45][46]. Among the phenomenological models [13], some assumed a power-law relationship between the variance and mean [18,19,22,42] or imposed a constraint on the parameters of probability distributions that was equivalent to such an assumption [17]. Some phenomenological models [20,21] preceded Taylor's first paper [3] on the topic.…”

Section: Discussionmentioning

confidence: 99%

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Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

2013

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Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin-Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.

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Section: Introductionmentioning

confidence: 91%

Section: Discussionmentioning

confidence: 99%

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

2013

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“…Kilpatrick and Ives (2003) report that many empirical analyses identify values between 1 and 2 for the slope b, due to environmental and demographic stochasticity as well as competitive interactions between species. Kendal (2004b) gives a detailed overview of the history of TL. He shows that TL has mostly been found for population densities in ecology, but that power laws have also been identified in other contexts, such as outbreaks of infectious diseases (Anderson and May 1988;Rhodes and Anderson 1996) and for physical distributions of gene structures within chromosomes (Kendal 2004a).…”

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confidence: 99%

Taylor's power law in human mortality

Bohk¹,

Rau²,

Cohen³

2015

DemRes

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“…The recent development of relevant statistical techniques (e.g., De Valpine andHastings 2002, Clark andBjørnstad 2004) has facilitated the widespread application of this approach in the analysis of ecological time series to elucidate spatial and temporal variations in the strength of density-dependent and density-independent processes on population growth (e.g., Saitoh et al 2003, Fukaya et al 2010. In contrast, Taylor's power law describes a power-law relationship between the mean and variance of the size of a population (Taylor 1961) which has been shown to provide a good characterization of ecological time series (reviewed in Kendal 2004). The temporal meanvariance relationship can be characterized by the coefficients of temporal Taylor's power law, which can be estimated from the coefficients in the regression of log variance versus log mean population size over time (Taylor 1961).…”

Section: Introductionmentioning

confidence: 99%

Variable processes that determine population growth and an invariant mean‐variance relationship of intertidal barnacles

et al. 2013

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Abstract. Although researchers recognize that population dynamics can vary in space and time as a result of differences in biotic and abiotic conditions, spatial and temporal variability in the patterns and processes of population dynamics have not been well documented on a seasonal time frame. We quantified seasonal changes in the coverage of intertidal barnacles, Chthamalus spp., with data collected for as many as 9 years at 88 plots in five regions located along more than 1800 km of the Pacific coastline of Japan from 318 N to 438 N. To examine how seasonal changes and the spatial heterogeneity of environments can interact to influence patterns and processes of population dynamics, we analyzed the data with two models of population variability: a population dynamics model, which provides knowledge about processes that determine population growth rates; and Taylor's power law, which summarizes the relationship between the temporal mean and variance of the size of a population (temporal mean-variance relationship). We found that seasonal differences were prevalent in population growth rates, as well as in the strength and spatial scales of processes that determine population growth rates. In addition, the seasonality of these rates and processes varied between habitats at different spatial scales ranging from the scale of amongrocks within a shore to that of among-regions located in different latitudes, suggesting that the effects of seasonal environmental fluctuations on population growth can depend on the spatial heterogeneity of biotic and abiotic conditions that vary at multiple spatial scales. In contrast, the evidence for spatiotemporal differences in temporal mean-variance relationships was weak. Unlike theoretical expectations, spatiotemporal differences in the variability of population size were best explained by a unique power law, despite remarkable regional and seasonal differences in the processes that determine population growth rates. These results suggest that spatiotemporal environmental variability can affect population dynamics at multiple spatial scales but do not necessarily alter the scaling law of population size variability.

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Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models

Cited by 76 publications

References 65 publications

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Taylor's power law in human mortality

Variable processes that determine population growth and an invariant mean‐variance relationship of intertidal barnacles

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