BIOL3045 Lecture Notes - Lecture 15: Isometry, Allometry, Power Law
3 Jul 2018
School
Department
Course
Professor
Animal Ecological Physiology BIOL3045 460381099
Lecture 15: Metabolic ecology.
The metabolic rate of the individual is dependent on the mass (increasing with mass) and
temperature (increasing with temperature, to optimum, then a dramatic drop) of the individual.
Start predicting how the metabolic flux will change at different levels of organisation.
Body size and energy:
Body mass and metabolic rate tends to follow a universal curve.
Isometry: true linear relationship on a natural scale.
Allometry: for every unit of body mass (X), the growth in Y is smaller. Can be divided by mass, to give
per unit gram. Shows that a bigger organism has smaller metabolic rate per unit gram. If your system
has this, then the society needs varying amounts of energy to sustain all individuals.
What is the value of alpha? 2/3, Rubner found that the metabolic rate and body mass increased in a
power law. As the body mass becomes bigger, the volume increases more than the surface area.
Thus, this is proportional to 2/3.
Kleiber retested this, measuring metabolic rate of mammals. Uses many more species than just dogs
(i.e. like Rubner). He realised that this scaling relationship was much closer to ¾. He, however, didn’t
have an explanation for this.
Other scientists West, Brown and Enquist discovered a universal reason for this ¾:
Assumes that animals have a heart and arteries and have a fractal-like branching pattern.
The final branch of the network is size-invariant the radii of all capillaries are the same.
The energy required to distribute resources is minimized in transporting fluids through this network.
Put this together with fluid dynamics, it would show that this is a value of ¾.
Works in networks in animals, as well as, plants.
Formalizes things in terms of mathematics, predictions were very close to observed values.
However, these ideas ignored lots of real life (i.e. what if they are exercising). Nothing is still,
everything is interacting and moving.
There’s no actual answer to this, and improvements of the theory are still needed.
Sponges don’t have hearts, how does this apply? Need something to explain deviations from ¾.
Application: Circulation time vs body mass – how much anticancer drug to administer.
Growth rate vs body mass – fisheries to determine better profit, greatest yield.
How much carbon is being recycled per year in a particular ecosystem.
This approach, gives you so much predicative power.
Document Summary
The metabolic rate of the individual is dependent on the mass (increasing with mass) and temperature (increasing with temperature, to optimum, then a dramatic drop) of the individual. Start predicting how the metabolic flux will change at different levels of organisation. Body mass and metabolic rate tends to follow a universal curve. Isometry: true linear relationship on a natural scale. Allometry: for every unit of body mass (x), the growth in y is smaller. Can be divided by mass, to give per unit gram. Shows that a bigger organism has smaller metabolic rate per unit gram. If your system has this, then the society needs varying amounts of energy to sustain all individuals. 2/3, rubner found that the metabolic rate and body mass increased in a power law. As the body mass becomes bigger, the volume increases more than the surface area. Kleiber retested this, measuring metabolic rate of mammals. Uses many more species than just dogs (i. e. like rubner).
