Energetic barriers of Ecological
Systems
Ken Locey
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…
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
I = ioM3/4e-E/kt
M3/4 : based in delivery resources through
fractal-like networks
I = ioM3/4e-E/kt
• Boltzmann factor, e-E/kt based in the chemical
kinetics of biochemical reactions
Boltzmann factor, e-E/kT
• Increased temp. increases the fraction of
molecules with sufficient energy
• Effect on reaction rate is exponential
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
– (0.2-1.2 eV, Munch and Salinas 2009)
Clarke, Functional Ecology, 2006
Wang et al (2009) PNAs
McCain and Sanders (2010) Ecology
Algar et al. (2007) Global Ecol. Biogeogr.
Activation Energy
• Determines the rate of biochemical processes
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
Question
• Do changes in activation energy at the
biochemical level resemble changes at the
ecological level?
Prediction
• Higher activation energies (larger barriers)
occur at lower rates
Zang et al (2005) J Biol Chem
Carbon Monoxide from Composting
due to Thermal Oxidation of Biomass
Hellebrand and Schade (2006) J Env. Qual.
Estivation in the land snail Otala lactea
Ramnanan and Storey (2006) J Exp. Biol.
Soil Organic Carbon (SOC) Turnover
Knorr et al (2005) Nature
A strong trend for the more slowly
cycling pools to have a higher
activation energy
• Prediction appears to have some support
among studies where phenomena are the
direct product of metabolism
Question
• Do the dynamics of activation energy explain
the variation in species diversity that appears
to contradict MTE?
Prediction
• Lower richness accompanies higher activation
energy (larger barrier)
Zang et al (2005) J Biol Chem
Allen et al. (2007) Scaling Biodiversity
Allen et al. (2007) Scaling Biodiversity
Algar et al. (2007) Global Ecol. Biogeogr.
Want et al. (2009) PNAS
McCain and Sanders (2010) Ecology
Boltzmann factor
f = e-E/kT
Arrhenius equation
k = Aoe-E/RT
Gibbs free energy of activation, ∆G‡
k = kBT/h*e-∆G‡/RT
∆G‡ = ∆H‡ - T∆S‡
Mikan et al (2002) Soil Biology and Biochemistry
Mikan et al (2002) Soil Biology and Biochemistry
Algar et al. (2007) Global Ecol. Biogeogr.
• 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.
Activation energy as an energetic
barrier to ecological change
EA
ln (Rate)
EA
1/kT
Potential Energy
ATP Synthesis
ATP Synthesis
EA
EA
COLD
EA
HOT
EA
Thermal Adaptation
Potential Energy
COLD
EA
EA’
EA’
HOT
EA
Thermal Adaptation
Activation energy of metabolism as a
structuring force of diversity
EA
ln (Richness)
EA
1/kT
Irlich et al (2009) Am Nat.
Activation energy of metabolism as a
structuring force of diversity
EA
ln (Richness)
EA
1/kT
ln (Richness)
Activation energy of metabolism as a
structuring force of diversity
1/kT