1. Energetic barriers of Ecological Systems
Ken Locey

2. Metabolic Theory of Ecology MTE
Ecological phenomena are fundamentally influenced by metabolic rate
rates of development, population increase, times to extinction, variations in lifespan and elevational diversity, nutrient cycling…

3. Metabolic Theory of Ecology MTE
Ecological phenomena are fundamentally influenced by metabolic rate
Metabolic rate is fundamentally influenced by mass and temperature
Scaling relationships based on mass
I = ioM3/4
Exponential effect of temperature on metabolic rate
Boltzmann factor: e-E/kt

4. I = ioM3/4e-E/kt
M3/4 : based in delivery resources through fractal-like networks
While the scaling relationships of mass are based on the transport of resources through fractal-like networks

5. I = ioM3/4e-E/kt
Boltzmann factor, e-E/kt based in the chemical kinetics of biochemical reactions
The exponential effect of temperature on rate is based on theory governing the chemical kinetics of biochemical reactions. Though the theory governing this is based in statistical mechanics, the Boltzmann factor provides the relationship of temperature to metabolic rate that has been frequently reported for much of the last and current centuries.

6. Boltzmann factor, e-E/kT
Increased temp. increases the fraction of molecules with sufficient energy
Effect on reaction rate is exponential
Here, I will focus on the energy required to achieve and maintain a state of metabolism. More specifically, I will be focusing on the numerator in the exponent of the Boltzmann factor. This term is the activation energy for the process under study and is approximated as the slope of the graph relating the log of the rate to inverse temperature. These graphs are also known as Arrhenius plots, after Svante Arrhenius who defined the term activation energy, and determined that the linear slope of such plots approximates it.

7. Activation Energy, EA In MTE, EA is: activation energy of metabolism
Energy required to undergo cellular respiration, to drive the tricarboxylic acid cycle, reduce S,N, CH3, etc.
Suggested to be constant and narrowly constrained ( 0.6 to 0.8, Brown et al. 2004)
Considerable variation
( eV, Munch and Salinas 2009)
In metabolic theory, activation energy of metabolism is presumed to be the activation energy of the major rate limiting metabolic processes. The activation energies for these processes are assumed to be constant and have been shown to be confined to a narrow range.

8. Clarke, Functional Ecology, 2006 Wang et al (2009) PNAs
Support for predictions of metabolic theory often rest on these assumptions when demonstrating a linear relationship of temperature to metabolic rate or some ecological phenomenon, such as species richness.

9. McCain and Sanders (2010) Ecology
Algar et al. (2007) Global Ecol. Biogeogr.
However, some studies have revealed substantial variation and nonlinearity in the slopes interpreted as activation energy. These authors have suggested that the relationship is often curvilinear and that temperature does not drive species richness.
Besides acknowledging that activation energy sometimes varies from the predictions of MT, there is also good reason to investigate activation energy as more dynamic property.

10. Activation Energy Determines the rate of biochemical processes
First, activation energy is a barrier which determines the rate at which reactions proceed from one state to another. A large activation energy implies a large potential energy barrier. The larger the barrier, the slower the reaction.

11. Activation Energy Determines the rate of biochemical processes
Biological systems have evolved to decrease EA
General evolution of enzymes
Evolution of enzymes specific to cold climates
Second, biological systems have evolved to decrease activation energy. The evolution, and hence presence, of enzymes is evidence of this. Enzymes work by decreasing the activation energy of a reaction, and without them, life as we know it would not be possible.
In considering the importance of activation energy at the biochemical level, I was lead to the following question:

12. Question
Do changes in activation energy at the biochemical level resemble changes at the ecological level?
Do changes in activation energy at the biochemical level resemble changes in activation energy at the ecological level?

13. Prediction
Higher activation energies (larger barriers) occur at lower rates
As predicted from the Boltzmann factor, and as illustrated here in the Arrhenius plot for a set chemical reactions, higher rates accompany lower activation energies.
Zang et al (2005) J Biol Chem

14. Carbon Monoxide from Composting due to Thermal Oxidation of Biomass
Hellebrand and Schade (2006) J Env. Qual.
As you can see, the same relationship exists for Carbon Monoxide and Dioxide production by soil microbial communities.

15. Estivation in the land snail Otala lactea
Ramnanan and Storey (2006) J Exp. Biol.
And again, the same relationship is seen among estivating land snails. These snails lower their metabolic rates by suppressing rates of ATP related cell functions.

16. Soil Organic Carbon (SOC) Turnover
Knorr et al (2005) Nature
It has also been shown that soil organic carbon turnover rates are heavily influenced by activation energy, seen here to increase with time of turnover.
A strong trend for the more slowly cycling pools to have a higher activation energy

17. Prediction appears to have some support among studies where phenomena are the direct product of metabolism
Higher activation energies occur at lower rates when the phenomenon under study is the direct result of metabolism, that is, where y-axis of the Arrhenius plot is either metabolic rate or some proxy for it. However, even at this level, the predicted relationship could have been confounded by ecological factors that a simple Arrhenius relationship would not have captured.
This encouraged me to ask another question…

18. Question
Do the dynamics of activation energy explain the variation in species diversity that appears to contradict MTE?
Do the dynamics of activation energy explain the variation in species diversity that appear to contradict MTE?

19. Prediction
Lower richness accompanies higher activation energy (larger barrier)
A prediction that might follow stems from the logic used in MT to predict species richness. That is, as a result of the effects of temperature on biochemical reactions and mutation rates, and mutation rates on speciation, higher activation energies should produce lower rates of speciation and lower species richness.
Zang et al (2005) J Biol Chem

20. Allen et al. (2007) Scaling Biodiversity
Here, activation energies are approximated to be quite similar, 0.74 for amphibians and 0.70 for North American trees. However, if we could superimpose one graph onto the other we would see that the predicted relationship holds.

21. Allen et al. (2007) Scaling Biodiversity
That is, higher average richness is associated with lower activation energies. Hence, even the small amount variation in activation energy as seen here is predicted by the same chemical kinetics that produce the general predictions of the MTE. This is of course merely suggestive.

22. Algar et al. (2007) Global Ecol. Biogeogr.
Algar et al, using the same data as Allen et al, actually rejected the predictions of MT. However, superimposing the graphs for the predicted MT relationship reveals the variation as predicted here.

23. Want et al. (2009) PNAS
This relationship is predicted to disappear as the ranges of species richness become more highly overlapping. This is analogous to having highly overlapping distributions of metabolic rates whereby the activation energies would be expected to be similar.

24. McCain and Sanders (2010) Ecology
In some studies, the points from which activation energy is approximated take on highly varied distributions. For example, the distribution of points in some of these graphs hardly justifies an attempt to run a straight line through them. These authors concluded that several of the relationships are curvilinear and rejected temperature as a driving force of species richness.
At this point, I’ll introduce an important fact about activation energy.

25. Boltzmann factor Arrhenius equation f = e-E/kT k = Aoe-E/RT
Gibbs free energy of activation, ∆G‡
k = kBT/h*e-∆G‡/RT
∆G‡ = ∆H‡ - T∆S‡
The Boltzmann factor and the Arrhenius equation assume that the temperature dependence of activation energy is much less than the temperature dependence of the reaction rate.
However, activation energy can change when defined in terms of Gibbs free energy of activation. This term accounts for the changes in entropy and enthalpy in activation energy as a reaction proceeds. In these terms, temperature enters the reaction rate equation twice. The reaction still takes the Arrhenius form but as a slowly varying function of temperature, whereby decreased temperatures lead to even more greatly decreased rates than those predicted from the Arrhenius equation.

26. Here, red lines indicate the sharp downward turn in the distribution of points at decreased temperatures that would be predicted under this scenario.

27. Mikan et al (2002) Soil Biology and Biochemistry
This phenomenon is well-illustrated by Mikan et al. in their study of microbial respiration rates in the tundra.

28. Mikan et al (2002) Soil Biology and Biochemistry
We can see that activation energy takes a downward turn at zero degrees Celsius.

29. Algar et al. (2007) Global Ecol. Biogeogr.
Algar et al. have also concluded that the down-turned curvilinear relationships they observed were not in support of MT predictions. Again, the same effect of temperature on activation energy could apply here, but was not acknowledged by the authors.

30. Prediction is supported among studies where the phenomenon under study is the direct product of metabolism
Prediction appears to be supported when the phenomenon is fundamentally influenced by metabolic rate.
Both predictions of the effects of activation energy on ecological phenomena appear to have some support.
This completes my discussion for a more dynamic treatment of activation energy. Next, I would like to move on to developing the concept of activation energy as an energetic barrier at the macroecological and biogeographical levels.

31. Activation energy as an energetic barrier to ecological changeEA EA
ln (Rate)
A species that colonizes an environment sufficiently cold enough to affect metabolism, must overcome an increased activation energy while adjusting its thermal tolerance. This could be accomplished by developing strategies to deal with a higher activation energy or by evolving new pathways or enzymes that decrease it. This would not be accomplished in a vacuum, that is, outside the effects of competition with better adapted residents.
On the other hand, a species that colonizes an environment sufficiently warm enough to decrease activation energy and increase metabolic rate, must adjust its thermal tolerance while competing against species with higher metabolic rates and higher rates of population growth.
In this sense, activation energy becomes the basis for an energetic barrier to dispersal.
1/kT

32. EA Potential Energy Thermal Adaptation EA EA EA ATP Synthesis
COLD EA
Potential Energy
Given that activation energies are themselves measures of potential energy, and that changes from one activation energy adapted metabolic state to another requires metabolic reorganization, we can visualize the change from one activation energy to another as involving energetic barrier.
HOT EA
Thermal Adaptation

33. EA EA’ Potential Energy Thermal Adaptation EA’ EA COLD HOT
Here, the activation energy profile predicts that it is energetically easier to invade a relatively warm environment than a relatively cold one.
HOT EA
Thermal Adaptation

34. Activation energy of metabolism as a structuring force of diversityEA EA
ln (Richness)
Based on the activation energy required to adapt to a new thermal environment, species ranges should shift more readily to warmer climates than colder ones, resulting in greater richness with increased temperature.
Here, we potentially have the beginning for an additional hypothesis of the latitudinal and elevational gradients in biodiversity based on the tenets of MT. While other metabolic theory explanations of these phenomena are based on speciation, this one is based on dispersal.
1/kT

35. Irlich et al (2009) Am Nat.
There is already some evidence to support this within a study documenting an increase in activation energy of metabolism and development with latitude. Of course, the evolution of cold adapted enzymes to decrease the activation energies in higher latitudes is also evidence for this pattern.

36. Activation energy of metabolism as a structuring force of diversityEA EA
ln (Richness)
The addition of this hypothesis and the dynamic treatment of activation energy could strengthen MT in at least three ways. First, it contributes an additional level of explanation for a widely-known pattern that has been recently examined in MT studies. Second, it provides a way for MT to explain the variation that has caused some to reject its predictions. Third, accounting for dispersal in MT may facilitate the synthesis of MT and ecological neutral theory, wherein dispersal and dispersal limitation are crucial components.
1/kT

37. Activation energy of metabolism as a structuring force of diversity
ln (Richness)
Additional questions to be asked relate to the tendency of biological systems to decrease activation energy and the resulting effects on the distribution of diversity.
1/kT