Scaling and power-laws in ecological systems

Marquet, Pablo A.; Quiñones, Renato A.; Abades, Sebastián; Labra, Fabio A.; Tognelli, Marcelo F.; Arim, Matı́as; Rivadeneira, Marcelo M.

doi:10.1242/jeb.01588

Cited by 342 publications

(323 citation statements)

References 256 publications

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“…These relationships were a spatial TL (spatial variance in population density was a power-law function of the spatial mean population density); DMA (the spatial mean population density was a power-law function of mean body mass); and VMA (the spatial variance in population density was a power-law function of mean body mass). Third, TL and DMA, both classic relationships known for decades, accurately predicted the form and parameter values of VMA, a power-law relationship predicted only within the last decade (8,9,23), and previously tested empirically only once (9). To our knowledge, we provided here the first empirical confirmation of VMA for any animal community.…”

Section: Discussionsupporting

confidence: 61%

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Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

Lagrue

Poulin

Cohen

2014

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

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How do the lifestyles (free-living unparasitized, free-living parasitized, and parasitic) of animal species affect major ecological power-law relationships? We investigated this question in metazoan communities in lakes of Otago, New Zealand. In 13,752 samples comprising 1,037,058 organisms, we found that species of different lifestyles differed in taxonomic distribution and body mass and were well described by three power laws: a spatial Taylor's law (the spatial variance in population density was a power-law function of the spatial mean population density); density-mass allometry (the spatial mean population density was a power-law function of mean body mass); and variance-mass allometry (the spatial variance in population density was a power-law function of mean body mass). To our knowledge, this constitutes the first empirical confirmation of variance-mass allometry for any animal community. We found that the parameter values of all three relationships differed for species with different lifestyles in the same communities. Taylor's law and density-mass allometry accurately predicted the form and parameter values of variance-mass allometry. We conclude that species of different lifestyles in these metazoan communities obeyed the same major ecological power-law relationships but did so with parameters specific to each lifestyle, probably reflecting differences among lifestyles in population dynamics and spatial distribution.parasite | metazoan | power law | Taylor's law | allometry V ariation in population density has long been a central topic in ecology (e.g., ref. 1). Taylor's law (TL) (2, 3) is a pattern of variation that has been widely verified for population density in basic and applied ecology and for other quantities in other fields. In its ecological interpretations, TL asserts that, in multiple sets of populations, the sample variance in population density within each set is proportional to a power (usually positive) of the sample mean population density within that set. We specify TL in greater detail below.Morand and Guégan (4) showed that TL described well the variations of abundance per host in 828 populations of parasitic nematodes from 66 terrestrial mammalian species. Morand and Krasnov (5) reviewed examples of TL in parasitology and epidemiology and interpreted the exponent of the TL power law in terms of the aggregation of parasites and epidemiological dynamics. These studies used the number of individual parasites per individual host as the measure of population density. Following a suggestion of Taylor (2), these studies interpreted the exponent of the power-law relationship of variance of population density to mean of population density as an index of parasite aggregation among hosts. A purely random distribution of parasites per host leads to a Poisson distribution, which gives a TL exponent equal to 1 as the mean population density varies. A TL exponent greater than 1 reflects greater heterogeneity in numbers of individuals per host than expected from a purely random distribution. More ...

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Section: Discussionsupporting

confidence: 61%

“…Marquet et al (8) and Cohen et al (9) independently showed theoretically that TL and DMA combine to predict the form and parameters of an allometric relationship between the variance of population density and mean body mass (variance-mass allometry, or VMA). (The details of these predictions are in SI Appendix.)…”

Section: Significancementioning

confidence: 99%

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

Lagrue

Poulin

Cohen

2014

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

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“…The relationship between phytoplankton abundance and cell size in aquatic ecosystems follows a power function, N ¼ a V b , where N is the cell density and a is the intercept of the resulting linear regression. The size-scaling exponent, b, is a synthetic descriptor of community size structure [2] and generally takes values between 21.3 and 20.6. The value of the size-scaling exponent is strongly related to ecosystem's productivity.…”

Section: Introductionmentioning

confidence: 99%

Isometric size-scaling of metabolic rate and the size abundance distribution of phytoplankton

et al. 2011

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The relationship between phytoplankton cell size and abundance has long been known to follow regular, predictable patterns in near steady-state ecosystems, but its origin has remained elusive. To explore the linkage between the size-scaling of metabolic rate and the size abundance distribution of natural phytoplankton communities, we determined simultaneously phytoplankton carbon fixation rates and cell abundance across a cell volume range of over six orders of magnitude in tropical and subtropical waters of the Atlantic Ocean. We found an approximately isometric relationship between carbon fixation rate and cell size (mean slope value: 1.16; range: 1.03-1.32), negating the idea that Kleiber's law is applicable to unicellular autotrophic protists. On the basis of the scaling of individual resource use with cell size, we predicted a reciprocal relationship between the size-scalings of phytoplankton metabolic rate and abundance. This prediction was confirmed by the observed slopes of the relationship between phytoplankton abundance and cell size, which have a mean value of 21.15 (range: 21.29 to 20.97), indicating that the size abundance distribution largely results from the size-scaling of metabolic rate. Our results imply that the total energy processed by carbon fixation is constant along the phytoplankton size spectrum in near steady-state marine ecosystems.

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“…A striking feature of complex systems is that they show regularities in the behavior of macroscopic variables, which emerge as the result of nonlinear interactions among multiple components and because of the competition of opposing control forces (4-6). These regularities commonly take the form of simple scaling relationships or power-laws (7,8). A macroscopic variable that shows scaling relationships is metabolic rate (VO 2 ) (the rate at which an animal consumes oxygen), which scales with body mass (M) such that VO 2 ϰ M a with ␣Ͻ1.…”

mentioning

confidence: 99%

Scaling metabolic rate fluctuations

Labra¹,

Marquet²,

Bozinovic³

2007

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

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Complex ecological and economic systems show fluctuations in macroscopic quantities such as exchange rates, size of companies or populations that follow non-Gaussian tent-shaped probability distributions of growth rates with power-law decay, which suggests that fluctuations in complex systems may be governed by universal mechanisms, independent of particular details and idiosyncrasies. We propose here that metabolic rate within individual organisms may be considered as an example of an emergent property of a complex system and test the hypothesis that the probability distribution of fluctuations in the metabolic rate of individuals has a ''universal'' form regardless of body size or taxonomic affiliation. We examined data from 71 individuals belonging to 25 vertebrate species (birds, mammals, and lizards). We report three main results. First, for all these individuals and species, the distribution of metabolic rate fluctuations follows a tent-shaped distribution with power-law decay. Second, the standard deviation of metabolic rate fluctuations decays as a powerlaw function of both average metabolic rate and body mass, with exponents ؊0.352 and ؊1/4 respectively. Finally, we find that the distributions of metabolic rate fluctuations for different organisms can all be rescaled to a single parent distribution, supporting the existence of general principles underlying the structure and functioning of individual organisms.allometry ͉ body mass ͉ Laplace distribution L iving organisms have been described as the most complex system in the universe, emerging from the activity of an adaptive network of interacting components that allows energy, materials, and information to be acquired, stored, distributed, and transformed (1, 2), and whose end result is the maintenance and reproduction of the network itself (3). A striking feature of complex systems is that they show regularities in the behavior of macroscopic variables, which emerge as the result of nonlinear interactions among multiple components and because of the competition of opposing control forces (4-6). These regularities commonly take the form of simple scaling relationships or power-laws (7,8). A macroscopic variable that shows scaling relationships is metabolic rate (VO 2 ) (the rate at which an animal consumes oxygen), which scales with body mass (M) such that VO 2 ϰ M a with ␣Ͻ1.For over a century, biologists have documented and tried to explain both the value of ␣, and the effects ecological factors have on it (1, 9-17). Most of these studies focus on average values of VO 2 and M, and do not consider the temporal variability in individual energy use. However, physiological variables, such as cardiac and breathing dynamics, display complex rhythms, which often show changes both with disease and aging (17)(18)(19)(20). In this context, the study of fluctuations in VO 2 can shed light on the determinants of metabolic scaling and provide a way to test competing models and explanations. Indeed, work on complex systems has shown that study of the scaling prope...

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Scaling and power-laws in ecological systems

Cited by 342 publications

References 256 publications

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

Parasitism alters three power laws of scaling in a metazoan community: Taylor’s law, density-mass allometry, and variance-mass allometry

Isometric size-scaling of metabolic rate and the size abundance distribution of phytoplankton

Scaling metabolic rate fluctuations

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