Allenet al.(2005) further show how this framework can be extended to
understand the roles of different sizes and temperatures of plants in the flux
and storage of carbon, and hence in the carbon cycle at scales from local
ecosystems to the globe. Belgranoet al.(2002) developed another extension,
showing that plant density across the spectrum of plant sizes from algae to trees
and across a range of ecosystem types from oceans, freshwaters, wetlands,
grasslands and forests shows the predictedM3/4scaling. These examples
show how MTE can be applied to make more explicit and quantitative links
between the processing of energy and elements at the individual level to the
flux, storage and turnover of these elements at the level of ecosystems.
Our second example concerns the role of metabolism in trophic relationships,
including the structure and dynamics of food webs. Above, we have shown how
MTE can be applied to understand theM3/4scaling and theM^0 energy equi-
valence observed empirically within many functional groups and trophic levels.
The theory can also be applied to understand the body-size structure of food
webs and the flow of energy and materials between trophic levels. Brownet al.
(2004) developed quantitative expressions for the ratios for consumer:producer
ratios of: (i) metabolic energy flux,F 1 /F 0 ; (ii) biomass,W 1 /W 0 ; and (iii) abundance,
N 1 /N 0 ; where the subscripts 0 and 1 denote any given trophic level and the next
highest level respectively. For aquatic ecosystems, we can usually assume that
all organisms (except for endotherms, which should be considered separately)
are operating at approximately the same temperature. Then these ratios are:
for energy flux:
F 1 =F 0 ¼i 1 N 1 M 13 =^4 =i 0 N 0 M 03 =^4 ¼ ( 1 : 7 )
wherei 0 andi 1 are the normalization constants for the field metabolic rates of
the producers and consumers organisms, respectively;
for biomass:
W 1 =W 0 ¼N 1 M 1 =N 0 M 0 / ðM 0 =M 1 Þ^1 =^4 ( 1 : 8 )
and for abundance:N 1 =N 0 / ðM 0 =M 1 Þ^3 =^4 ( 1 : 9 )
The ratio for energy flow,a, which must always be<1, is the traditional
Lindeman efficiency that has been the subject of so much discussion and inves-
tigation in ecology. It is apparent from inspection of the above equations that
theM3/4scaling of production is an important factor affectinga. If the body-mass
ratio of producer to consumer is large, and contributions to this symposium
suggest that it is often in the range of 100–500 in aquatic ecosystems (see also
Humphries, this volume;Woodward & Warren, this volume;Cohen, this vol-
ume), then a large component of the energy dissipated between trophic levels
will be due simply to the allometry of production rates. In addition to body sizeTHE METABOLIC THEORY OF ECOLOGY 11