Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges

Haskell, John P.; Ritchie, Mark E.; Olff, Han

doi:10.1038/nature00840

Cited by 302 publications

(281 citation statements)

References 26 publications

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“…Recalculation of the predicted home range scaling exponents by using a BMR scaling exponent of 0.67 yields predictions of 0.75, 1.25, and 1.42, which differ from the observed exponent by only 0.002. This strengthens the case for a 2/3 exponent by linking BMR with home range size, a variable that integrates behavior, physiology, and population density (28).…”

Section: Discussionmentioning

confidence: 95%

Mammalian basal metabolic rate is proportional to body mass^2/3

White

Seymour

2003

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

643

574

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The relationship between mammalian basal metabolic rate (BMR, ml of O 2 per h) and body mass (M, g) has been the subject of regular investigation for over a century. Typically, the relationship is expressed as an allometric equation of the form BMR ‫؍‬ aM b . The scaling exponent (b) is a point of contention throughout this body of literature, within which arguments for and against geometric (b ‫؍‬ 2/3) and quarter-power (b ‫؍‬ 3/4) scaling are made and rebutted. Recently, interest in the topic has been revived by published explanations for quarter-power scaling based on fractal nutrient supply networks and four-dimensional biology. Here, a new analysis of the allometry of mammalian BMR that accounts for variation associated with body temperature, digestive state, and phylogeny finds no support for a metabolic scaling exponent of 3/4. Data encompassing five orders of magnitude variation in M and featuring 619 species from 19 mammalian orders show that BMR ؔ M 2/3 . P ioneering work published by Max Rubner (1) in the 1880s reported that mammalian basal metabolic rate (BMR) was proportional to M 2/3 . In accordance with simple geometric and physical principles, it was therefore thought that an animal's rate of metabolic heat production was matched to the rate at which heat was dissipated through its body surface. However, Max Kleiber's influential monograph (2), published in 1932, concluded that basal metabolic rate scaled not in proportion with surface area, but with an exponent significantly greater than that of Rubner's surface law. Kleiber's work was later supported by Brody's (3) famous mouse-to-elephant curve, and an exponent of 3/4 (henceforth referred to as Kleiber's exponent) remains in widespread use. Quarter-power scaling is often regarded as ubiquitous in biology: metabolic rate has been reported as proportional to M 3/4 in organisms ranging from simple unicells to plants and endothermic vertebrates (4, 5). Kleiber's exponent has become so widely accepted that metabolic scaling relationships that deviate from an exponent of 3/4 are often considered somehow flawed or are summarily dismissed. However, examination of the species compositions of early studies (2, 3) shows that they poorly reflect Mammalia. Most data points are derived from domestic species, which have been under artificial energetic constraints for many generations (6). Additionally, the order Artiodactyla is consistently over-represented; both Kleiber's (2) and Brody's (3) data sets include Ϸ20% artiodactyls, but only Ϸ5% of Recent mammals are artiodactyls (7). Being near the upper mass limit of the regressions, these animals exert a disproportionate influence on the scaling exponent. Their inclusion is problematic, because microbial fermentation of cellulose may delay or prohibit entrance into a postabsorptive state (8). This elevates metabolic rate above basal levels and, when coupled with a large body mass, artificially inflates the calculated scaling exponent. Examination of Brody's (3) data reveals the same problems (6). Because meas...

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Section: Discussionmentioning

confidence: 95%

Mammalian basal metabolic rate is proportional to body mass^2/3

White

Seymour

2003

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

643

574

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“…It was based on a theoretical argument about niche dimensionality and species packing and attempts to explain the important but surprisingly undersubscribed question of why there are so many more species of small vertebrates than big ones (at the large end of the length-size spectrum). It is a difficult and rather abstract piece of work, but it presaged later interest in the importance of fractal scaling and home range size (H) for this question in ecology (29).…”

Section: The Species-frequency Versus Species-length Exponentmentioning

confidence: 99%

Observations on related ecological exponents

Southwood¹,

May²,

Sugihara³

2006

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

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We observe a relationship among three independently derived power laws in ecology: (i) total number of species versus area, (ii) species frequency versus species length, and (iii) maximal body size versus area. Aside from showing how these historically disparate phenomena are connected, we show how recent empirical results relating the maximal body size of top terrestrial vertebrates to the square root of land area conform to a prior theoretical expectation given by two of the above power laws. Of particular interest is the observation that the exponent relating species length to species frequency suggests a dimension for niche space for terrestrial vertebrate assemblages of D Ϸ 3͞2. This value, along with power law for maximal body size, versus area, gives rise to the canonical species area exponent z Ϸ 1͞4.scaling ͉ power law ͉ dimensionality ͉ species-area ͉ canonical hypothesis M ore often than not in the natural sciences, one variable (e.g., force) is related to another variable (e.g., acceleration) only when it is raised to some power (e.g., 2 in this case). Indeed, the recent proliferation and interest in power laws, allometric scaling relationships, and so-called ''scale-free network'' phenomena suggest the possibility of some common principles operating in distant theaters of science (1-10).However enticing this idea may be, the ubiquity of power laws (particularly empirical ones) must certainly be due in large part to the human tendency to seek parsimonious and ready fits to data, with power laws being perhaps the simplest and most forgiving approximation. Additionally, power laws arise naturally when there is explicit reference to the dimension or covering measure of a quantity, such as when one is seeking to normalize, or make comparable, measurements of length and volume. Thus, it is not surprising to find scaling relationships in diverse fields such as astrophysics, particle physics, turbulence theory, computer science, physiology, ecology, geography, etymology, and terrorist networks, to name a few.On a more concrete level, the diversity of these power laws within a given field suggests that there may be interchangeability among some of them that can be usefully exploited.Our aim here is to show how three common power laws in ecology are related and to show further how this relationship can lead to an independent verification of a recent and very interesting empirical result that relates the body size of the largest resident terrestrial vertebrates (from the Late Pleistocene to present) to modern Holocene land areas (11). On a more ambitious note, we show that the observed exponent relating species length to species frequency suggests a dimension for niche space for terrestrial vertebrate assemblages between D ϭ 3͞2 and D ϭ 2. The Species-Area ExponentOne of the earliest and most ubiquitous scaling relationships in ecology came from the observation that larger areas contain more species in a surprisingly orderly way. This so-called speciesarea relationship emerged in the early 20th century as a sa...

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“…Perhaps the bestknown pattern is the hierarchy of dispersal: both movement rates (McCann et al 2005) and the body size-home range scaling relationship (Haskell et al 2002) tend to increase with trophic level. However, faster movement rates at small scales may not carry over into more frequent interpatch dispersal at larger scales.…”

Section: Introductionmentioning

confidence: 99%

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Pedersen

Marleau

Granados

et al. 2016

The American Naturalist

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Community interactions (e.g., predation, competition) can be characterized by two factors: their strengths and how they are structured between and within species. Both factors play a role in determining community dynamics. In addition to trophic interactions, dispersal acts as an interaction between separate populations. As with other interactions, the structure of dispersal can affect the stability of a system. However, the primary structure that has been studied in consumer-resource models has been hierarchical dispersal, where between-patch dispersal rates increase with trophic level. Here we use analytical, numerical, and simulation approaches on a two-patch, three-species metacommunity model to investigate the relationship between structure and community stability and resilience. We show that metacommunity stability is greater in systems with both weak and strong dispersal rates. Our system is stabilized by the formation of patterns when predators disperse frequently and herbivores disperse rarely, and via asynchrony when both predators and herbivores disperse infrequently. Our results show how interaction strengths within both trophic and spatial networks shape metacommunity stability.

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Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges

Cited by 302 publications

References 26 publications

Mammalian basal metabolic rate is proportional to body mass^2/3

Mammalian basal metabolic rate is proportional to body mass^2/3

Observations on related ecological exponents

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

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Fractal geometry predicts varying body size scaling relationships for mammal and bird home ranges

Cited by 302 publications

References 26 publications

Mammalian basal metabolic rate is proportional to body mass2/3

Mammalian basal metabolic rate is proportional to body mass2/3

Observations on related ecological exponents

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Contact Info

Product

Resources

About

Mammalian basal metabolic rate is proportional to body mass^2/3

Mammalian basal metabolic rate is proportional to body mass^2/3