Supplemental Information:
Testing the metabolic theory of ecology
Level 4 - Evaluating MTE’s Extended predictions
Here we consider three areas that have built on the basic MTE foundation to yield additional
predictions. The three areas are ontogenetic growth, size-frequency distributions and
biodiversity gradients.
Extended Prediction, Ontogenetic Growth: One of the earliest extensions of Model A was
the development of a model of ontogenetic growth (West et al. 2001). As in the case of the
scaling of metabolic rate, WBE were building on a field with a rich modelling history (von
Bertalanffy 1957; Ricklefs 1969; Reiss 1989; Kooijman 1993). WBE assume that the total
metabolic rate of an organism (B) is the sum of the metabolic expenditure devoted to growth
(i.e., the synthesis of new biomass) and the metabolic expenditure devoted to maintaining
existing biomass,
B  Em
dm
 Bm m
dt
(1)
where Em is the energy required to synthesize a unit of biomass (e.g., in J g-1), and Bm is the
power required to maintain 
a unit of biomass (e.g., in W g-1) , and m is the total mass of the
organism at time t. Further, they assumed the ¾-power allometry for total metabolic rate, i.e.,
B = B0 m3/4 where B0 is a coefficient that depends on taxa, temperature, and metabolic state.
Solving for the rate of growth in mass yields the relationship
3
dm
 am 4  bm
dt
,
(2)
B
where m is the mass of the growing animal, a  B0 and b  m . Thus, a is the ratio of the

Em
Em
metabolic scaling coefficient (B0) to the energetic cost of biomass synthesis, while b is the

 energy to create it.
ratio of the power to maintain tissue relative to the
Interestingly, and perhaps not surprisingly, this model produces a similar-shaped
prediction as earlier efforts in modelling the generally sigmoid pattern of ontogenetic growth
trajectories (von Bertalanffy 1957; Ricklefs 1969; Reiss 1989), but differs from its
predecessors in its underlying assumptions and in explicitly linking the parameters of the
equation to basic cellular and tissue properties. As a result, several authors noted that while
the fits of the model to data from a wide variety of animal species were quite impressive,
support for the details of the model, and especially for the universality of the ¾ metabolic
exponent, could not be concluded from statistical fits of growth trajectories alone (Banavar et
al. 2002; Ricklefs 2003).
In the case of the original growth model, the authors rely on the assumption that the
¾-power scaling across species applies equally well to developmental size changes. Glazier
questioned this assumption (Glazier 2005), and while the overall average of the scaling
exponent is around ¾, especially for organisms growing over a substantial size range (Moses
et al. 2008), there is considerable variation present across intraspecific metabolic scaling
relationships (von Bertalanffy 1957; Glazier 2005). Later versions of the model have been
generalized to incorporate both variation in the metabolic scaling exponent (Moses et al.
2008) and a more thorough partitioning of energy assimilation and allocation (Hou et al.
2008) that together may provide more flexible and robust predictions.
Summary: While the simplicity of the original WBE growth model combines MTE with a
theory of ontogenetic growth, it has limitations that are being addressed with additional
research. The considerable phylogenetic, ecological, and ontogenetic variation present across
intraspecific metabolic scaling relationships suggests that applying the MTE to patterns of
ontogenetic growth will require a flexible theory that relaxes many of the original
assumptions. Further ontogenetic studies of growth and metabolism in model organisms
(Yagi et al. 2010; Sears et al. 2012) will help to provide stronger tests of the underlying
model assumptions and to adapt the generalized theory to more specific biological contexts.
Extended prediction, size-frequency distributions: Enquist et al. (1998) applied MTE to
the size-abundance relationship within plant communities. By assuming resource limited
growth, a steady state in resource flux, and scaling of metabolic rate with body mass to the ¾
power, Enquist et al.(1998) predicted that maximum abundance should scale with mean body
mass to the -3/4 power. These authors found good empirical support for this prediction and
indirectly tested their assumed size scaling of metabolism. MTE has also been applied to
size-abundance relationships within mixed-age, mixed-species forest stands (Enquist &
Niklas 2001) by estimating the scaling exponent for a large number of within-stand sizeabundance relationships. Later models derived that the key prediction is that abundance
declines with stem diameter to the -2 power. This prediction actually corresponds to a
decline of abundance with mean body mass to the -7/8 power, and reasonable support was
found for this prediction (see also, Stegen & White 2008; Enquist et al. 2009; West et al.
2009).
Summary: Reanalysis of the global data from Enquist and Niklas (2001) and several tropical
sites (Muller-Landau et al. 2006) has revealed that size-frequency distributions are often not
straight lines on log-log axes (Coomes et al. 2003) and show extensive covariation in both the
scaling exponent and allometric constant of forest self-thinning (Niklas et al. 2003).
Furthermore, size-distributions within populations undergoing stand development are better
described by Weibull distributions than power functions (Mohler et al. 1978; Muller-Landau
et al. 2006; Coomes & Allen 2007). Hence, the use of mechanistic models that incorporate
species level information on allometric dependencies of growth and mortality may provide a
potential route to develop simplified models that can explain observed forest data (e.g., see
the work of Purves et al. (2008)).
Extended Prediction, Biodiversity Gradients:
Metabolic influence over species packing. The first formal link between MTE and diversity
gradients was developed in Allen et al. (2002). These authors started with the (Boltzmann)
assumption for metabolic rate dependence on temperature and predicted that the number of
individuals of a given species within a given area will decrease exponentially with
temperature. Three further assumptions underlie this approach: namely that the limiting
resource supply, population-level energy use per area, and the number of individuals per area,
all do not vary with temperature. The model then predicts that at higher temperatures each
species is represented by fewer individuals, but the whole community contains the same
number of individuals, so that the number of species must increase with temperature. Allen et
al. (2002) assume that limiting resource supply does not vary with temperature so that energy
use across all individuals at the population- or community-level should not vary with
temperature. However, the model also assumes that total community abundance and average
body size do not vary with temperature. In this case community-level energy use must
increase with temperature. As such, the model does not appear to be internally consistent
(Storch 2003; Stegen et al. 2009). However as Allen et al. (2002) point out, the model may
be robust to violations of some assumptions, an issue that warrants further investigation.
Metabolic influence over mutation and speciation rates. A separate line of enquiry explores
the influence of metabolic rates on rates of genetic mutation (Gillooly et al. 2005; Gillooly et
al. 2007) and speciation (Allen et al. 2006). Allen et al. (2006) assume the following: that
both the number of mutations, and the number of generations per time increase with
metabolic rate, and thus both increase exponentially with temperature; that the number of
genetic changes required for speciation, effective population size, and selection strength are
all independent of temperature; that speciation is proportional to overall mutation rate,
avoiding the need for a causal link with species ecology. Combining these assumptions leads
to the prediction that speciation rate will increase exponentially with temperature.
Correlations of speciation rate with temperature can thus be used to support the models
predictions, but do not directly validate the models’ underlying assumptions or mechanism
(Davies et al. 2004; Stegen et al. 2009). Some assumptions have been tested (e.g. the
temperature dependence of mutation rate, Gillooly et al. 2005), while others are yet to be
directly evaluated (e.g. the temperature independence of effective population size, Stegen et
al. 2009).
Summary: Meta-analyses of global datasets for plant, invertebrate and ectothermic
vertebrate groups uncovered a broad range of relationships between species richness and
environmental temperature (Hawkins et al. 2007). The majority of these patterns depart
significantly from the pattern predicted by Allen et al. (2002), suggesting that there is little
support for current extensions of MTE as a predictor of global diversity gradients and a need
for further modelling (e.g. Stegen et al. 2012).
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