Allometric and Metabolic Theories in Ecology

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Allometric and metabolictheories in ecology

Nicolas Loeuille,

maître de conférences [email protected]



Rubner (1883): b = 2/3 for metabolism vs. body mass

Ginzburg & Damuth (2008)



Kleiber (1932): b = 3/4

from Hemmingsen (1960)



Beautiful data, beautiful mysteries



Brown: 3/4 as the only option



Glazier (2005): Variability of the exponent



Kleiber (1932): b = 3/4

from Hemmingsen (1960)



Rubner (1883): b = 2/3 for metabolism vs. body mass

Ginzburg & Damuth (2008)



Examples of multipleconstrained dimensions:

3-2 dimension reduction inhumans

A. Metabolic rate scales as the 2/3 power of mass within species because generation

time is constrained.

B. When data are statistically constrained by height, the scaling coefficient becomes1/2.

Figure from Ginzburg and Damuth (2008).



4-3-2 dimension reduction in

plants

A.Across all plants and algae, allometry is4-dimensional with growth rate scaling asthe 3/4 power of mass.

B. Within plants alone, the growth rate

relationship is 2/3, reflecting a geometricconstraint on body plan.

C. In annual plants, generation time is fixed,further reducing the dimensionality to 2 andthus the slope to 1/2, even though theanalysis is still interspecific.

Data from Niklas (2007)



4-3-2 dimension reduction

in mammalsA. Metabolic rate scales as the 3/4 power of mass across species.

B. When data are statistically constrainedfor generation time, the scaling coefficientdecreases.

C.When constrained further by bodylength, the slope decreases to 1/2.

Data are for 149 species over 100 g. Figurefrom Ginzburg and Damuth (2008).



2-1 dimension reduction in

DrosophilaA. Across species, mass-metabolismexponent is 1/2. (Dataset of Promislowand Haselkorn 2002.)

B. Within a single species, nocorrelation between body size andmetabolism. (Van Voorhies, et al.2004).

Slope of 1/2 also found for shrews(Glazier 2005).

B

b = 0.49

A

b = 0



Branching networks (West et al. 1997;

Bananvar et al. 1999, 2002)Emphasizes 3/4 slope to the exclusion of all others.

Currently does not explain slopes of 2/3, 1/2, or 0.Does not explain slopes above 3/4.

Boundary hypotheses (Kooijman 2000; Glazier 2005)Slope results from the weighted sum of surface and volume processes

(2/3 and 1).Supports the diversity of slopes greater than 3/4.Does not explain slopes below 2/3.

Space-lifetime hypothesis (Ginzburg and Damuth 2008)Lifetime metabolism is isometric with body size (slope = 1).

In mammals, dimensional equivalency yields the special case of 3/4allometry.Other taxa deviate from 3/4, but lifetime metabolic isometry remains.Lower slopes are explained by geometric and temporal constraints.Theory supports the full range of slopes observed in nature.

Theoretical Landscape



Temperature correction (Brown et al. 2004)



Rate of biomass production, Brown et al 2004



Developmental rates of eggs, zoop & fishes



Fish mortality rates, Brown et al. 2004



Population growth rates



Links between densities and body size

Most datasets show that D=kM^-3/4 Individual metabolism scales as M^3/4 Therefore, total energy consumption is independent of

body size= energetic equivalence rule (Damuth 1981) Hidden hypothesis: same energy exploited,independent on body size

True within trophic levels, but not accross? Mixed validations

Dependence on scales



Implications for population density



Turnover rate



Dimensionless numbers and invariants



Table of invariants



La remise en cause (Nee 2005)

Allometric and Metabolic Theories in Ecology

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