Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey

Keitt, Timothy H.; Amaral, Luı́s A. Nunes; Buldyrev, Sergey V.; Stanley, H. Eugene

doi:10.1098/rstb.2001.1013

Cited by 39 publications

(45 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simplest model to explain the dependence of r (v) on ͳVO 2 ʹ would be to assume that an organism is made up of n equally sized cells of mass m c , each consuming oxygen at independent rates. The central limit theorem predicts r (v) decays as n Ϫ1/2 or equivalently under this general assumption, as M Ϫ1/2 (37,40). If ͳVO 2 ʹ is assumed to be proportional to n, we would also expect that r (v) ϰ ͗VO 2 ͘ Ϫ1/2 .…”

Section: Discussionmentioning

confidence: 99%

Scaling metabolic rate fluctuations

Labra¹,

Marquet²,

Bozinovic³

2007

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

View full text Add to dashboard Cite

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...

show abstract

Section: Discussionmentioning

confidence: 99%

Scaling metabolic rate fluctuations

Labra¹,

Marquet²,

Bozinovic³

2007

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

View full text Add to dashboard Cite

show abstract

“…In other words, under an expectation of lognormal population abundances, population growth rates should exhibit a Gaussian probability distribution. Interestingly, as shown by Keitt and Stanley (1998), the growth rates in an avian ensemble over a large geographical scale in North America are not distributed following a Gaussian distribution, but rather follow a power-law with a characteristic tent shape (Fig.·9A), which is well described by an exponential or log-Laplace distribution (Keitt and Stanley, 1998;Keitt et al, 2002). Furthermore, the same tent-shaped power-law form is also observed when examining the conditional probability density distributions of growth rates r s given an initial abundance class p(r s |N), defined by grouping observations into bins or categories of initial total abundance (Fig.·9B).…”

Section: Power-laws In Population Growth Ratesmentioning

confidence: 99%

“…Notice that all the data collapse upon the universal curve p scal ϵe (-|r scal|) . (After Keitt et al, 2002.) Scaling and power-laws in ecology many species are increasing in abundance as are decreasing over the 31-year period studied, be it over the whole ensemble, or when grouping by initial abundance bins.…”

Section: Power-laws In Population Growth Ratesmentioning

confidence: 99%

Scaling and power-laws in ecological systems

Marquet

Quiñones

Abades

et al. 2005

Journal of Experimental Biology

342

308

View full text Add to dashboard Cite

Scaling relationships (where body size features as the independent variable) and power-law distributions are commonly reported in ecological systems. In this review we analyze scaling relationships related to energy acquisition and transformation and power-laws related to fluctuations in numbers. Our aim is to show how individual level attributes can help to explain and predict patterns at the level of populations that can propagate at upper levels of organization. We review similar relationships also appearing in the analysis of aquatic ecosystems (i.e. the biomass spectra) in the context of ecological invariant relationships (i.e. independent of size) such as the 'energetic equivalence rule' and the 'linear biomass hypothesis'. We also discuss some power-law distributions emerging in the analysis of numbers and fluctuations in ecological attributes as they point to regularities that are yet to be integrated with traditional scaling relationships and which we foresee as an exciting area of future research.

show abstract

“…An additional relevant model for generating power-law distributions is the class of random multiplicative processes, often used to model growth of entities, such as business firms, cities, and biological populations [18][19][20][21][22][23][24][25]. The common starting point to explain the mechanisms of power-law formation in those growth phenomena is the Gibrat's law of proportional growth, stating that an entity grows proportionally to its current size but with a growth rate independent of it [26].…”

Section: Introductionmentioning

confidence: 99%

Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes

Sousa

Takayasu

Sornette

et al. 2017

Entropy

View full text Add to dashboard Cite

Abstract:We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations.

show abstract

Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey

Cited by 39 publications

References 32 publications

Scaling metabolic rate fluctuations

Scaling metabolic rate fluctuations

Scaling and power-laws in ecological systems

Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes

Contact Info

Product

Resources

About