Download Scaling

Simplifying Complexity – Scaling in Nature
Timothy Bonebrake – November 19, 2014
I. Arrhenius
1. Leave milk out of the fridge it goes bad, more reactions occur (due to heat)
2. Svante Arrhenius (1859-1927) Swedish scientist
3. Arrhenius perhaps best known for formulating activation energy
a. Energy required to start chemical reaction
b. Arrhenius equation quantifies the relationship between activation
energy, temperature and reaction rate.
c. Arrhenius plot shows relationship between temp and reaction rate.
4. Arrhenius also one of the first to quantify impact of greenhouse gases
a. Calculated that if CO2 ↑ 3 times then temp ↑ 8°C
b. Predicted “milder sky” given increase in global CO2
II. Climate change
1. NOT a new idea, known for a very long time.
2. Climate change science is a systems science, can’t be reductionist.
3. Models confirm that warming over past decades cannot be explained by
natural forcings, CO2 emitted by humans has caused the warming.
4. Many possible CO2 futures
5. Under worst case scenario (highest CO2) temp predicted to increase 4°C by
2100, best case scenario about 1°C.
a. Globally warming will be heterogeneous (vaired) geographically
b. Could be as much as 10°C in high latitudes (not TOO far off from
Arrhenius calculations)
6. One world, n=1 => can we look at climate change scientifically?
7. Reasons for hope – recent US/ China climate deal!
III. Metabolic theory
1. Body size (e.g. in animals) is a key trait in life.
2. Metabolism is the processing of energy for life.
a. Metabolic pathways are generally well known, but complicated.
b. Basal metabolic rate (BMR) is the metabolic energy consumed at rest.
3. How does metabolic rate scale with body size?
a. Surface area is important as this is how organisms dissipate heat
generated by metabolism.
b. SA=V2/3
c. If metabolic rate scaled linearly with body size, big animals would get
really hot because SA would not be sufficient to dissipate heat.
4. Kleiber’s law or the ¾ law
a. Metabolic rate = body size3/4 (empirically determined)
b. This is a power law
c. Solves the problem of heat dissipation.
d. Note that metabolic rate does NOT scale to the 2/3 power – thus large
animals are more efficient in a sense.
5. Many of these relationships use “spherical cow” calculations
6. Why ¾ ?
a. West, Enquist and Brown sought to use complex systems science to
determine why metabolic rate = body size3/4.
b. They used fractals to do so. Recall bodies are largely fractal in nature.
c. Using the geometry of veins and organismal systems West et al.
determined theoretically that metabolic rate = body size3/4.
7. Metabolic theory of ecology (MTE)
a. Focuses on power law relationship between body size and metabolic
rate. Examines all scales in nature (from single cells to hippos).
b. James Brown generally thought of as “father” of MTE
c. Hugely influential in ecology over the past decade but controversial.
d. MTE has been compared to as the modern synthesis of ecology.
IV. Power of power laws
1. Recall that Google works due to scale-free structure of the internet.
2. Species area curves = power law crucial for conservation.
3. Stefan–Boltzmann law = temp and black body radiation.
4. Zipf’s law = power law describing word frequencies of texts.
a. Empirically determined word freq = rank-1.
b. Why -1? Lots of debates. Miller found typing monkeys generally
followed word freq = rank-1.
5. Features of power laws: “more normal than normal”, no average, scale free.
V. Climate change and the metabolic theory of ecology (MTE)
1. MTE has also uncovered power law relationship of temp and metabolic rate.
2. Titanoboa (huge snake!) shows how body size, temp and metabolism scale.
3. Similar scaling law between temp and population growth r (fitness).
a. Relationship between temp and fitness could shift evolutionarily.
b. Insects have clear temp/fitness “curves”.
c. These fitness curves can change depending on environmental
conditions, e.g. seasonality.
4. Frazier study demonstrated that empirical insect temp and fitness
relationship was steeper than predicted by MTE, thus “higher activation
energy” and thermodynamics constrains insect evolution.
5. Tropical insects have narrow performance curves.
6. Bonebrake and others demonstrated that this relationship (between temp
and fitness) could be used to project climate change impacts on insects.
Though warming smaller in tropics, potential impacts bigger.
7. Tropical biodiversity is great! MOST species in the world live in the tropics.
Environmental impacts there are huge and include climate change and
habitat destruction.