Scaling in Ecology

Pablo A. Marquet

External FacultyThe Santa Fe Institute

Why is scaling important?• Provides a way to deal with the diversity of scales and

organisms found in ecological systems

• Makes apparent the fundamental similarity that underlies diversity in nature and how this has been molded by evolution

• Provides a benchmark against which species, populations and ecosystems can be compared

Scaling EquationMany ecological attributes scale with size as

𝑦 ∝ 𝑀$

From: White et al. (2012)

Scaling of life-history events

From: Sibly (2012)

Scaling in individuals and ecosystems

From:Tucker et al (2014) From: Anderson-Teixeira and Vitousek (2012)

From: Enquist and Bentley (2012)

The central role of energyThe size (M) of an individual affects the amount of energy it requires to maintain itself (basal metabolism)

From:Schmidt-Nielsen (1984)

𝐵 ∝ 𝑀 ⁄' (

Kleiber´s Law

The West, Brown & Enquistmodel…

A general model for the origin of allometric scaling laws in biology.

• The properties of resource delivery networks determine the properties of whole-organism metabolic rate.

• Biological systems have evolved under natural selection to optimize performance (delivery networksminimize energy loss)

From:West et al (1997)

Some implicationsWhat is the maximum number of individuals that can be found in a given area?

R= Energy or resources per unit area

B= Individual resource requirements 𝐵 ∝ 𝑀'/(

𝑁+,- ∝.

/0/1

or

𝑁+,- ∝ 𝑀2'/(

After: Damuth (1981)

Mammalian Herbivores

Populations of different organisms tend to use the same amount of energy

𝑃𝐸𝑈 ∝ 𝑁×𝐵

𝑃𝐸𝑈 ∝ 𝑀2 ⁄' (×𝑀 ⁄' (

𝑃𝐸𝑈 ∝ 𝑀7

(1)

(3)

(2)

From: Enquist et al. (1998)

PEU= Population energy use

Text

Humans the hyper-dense species

Weinberger and Marquet (unpublished)

ReferencesAnderson-Teixeira, K.J., and Vitousek, P.M. (2012. Ecosystems. In: Sibly, R M, James H Brown, and Astrid Kodric-

Brown. (eds) Metabolic Ecology. Wiley-Blackwell.Pp. 99-111.

Damuth, J. (1981). Population density and body size in mammals. Nature, 290(5808), 699.

Enquist, B. J., Brown, J. H., & West, G. B. (1998). Allometric scaling of plant energetics and population density. Nature, 395(6698), 163-165.

Enquist, B.J., and Bentley L.P. (2012) Land plants: new theoretical directions andempirical prospects. In: Sibly, R M, James H Brown, and Astrid Kodric-Brown. (eds) Metabolic Ecology. Wiley-Blackwell.Pp. 164-187.

Marquet, P. A. et al. (2005) Scaling and Power-Laws in Ecological Systems. Journal of Experimental Biology 208: 1749–69.

Schmidt-Nielsen, K. (1984) Scaling. Why Is Animal Size so Important? Cambridge University Press.

Sibly, R M, James H Brown, and Astrid Kodric-Brown. (eds) (2012) Metabolic Ecology. Wiley-Blackwell.

Sibly, R M (2012) Life history. In: Sibly, R M, James H Brown, and Astrid Kodric-Brown. (eds) Metabolic Ecology. Wiley-Blackwell.Pp. 57-66.

Tucker, Marlee A., Terry J. Ord, and Tracey L. Rogers. “Evolutionary Predictors of Mammalian Home Range Size: Body Mass, Diet and the Environment: Home Range-Body Mass Patterns: Are All Mammals Equal?” Global Ecology and Biogeography 23, no. 10 (October 2014): 1105–14.

West, G. B., Brown, J. H. Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122-126.

White, E.P., Xiao X., Isaac, N.J.B and Sibly, R.M. Methodological tools. In: Sibly, R M, James H Brown, and Astrid Kodric-Brown. (eds) Metabolic Ecology. Wiley-Blackwell.Pp. 9-20.