Metabolic Allometry

Balanced Growth Equation

Ingestion = assimilation + excretion

Assimilation = somatic or individual growth + reproductive growth + respiration

Ingestion

represents the demands the organism puts on the environment

What you eat

Respiration

represents the rate of resource use to meet environmental demands

Breathing and using resources

Production

(new tissue) = assimilation - respiration

Quantifying Energy Flow

• Material budget

– Food in

– Feces etc. out

• Heat production

• O 2 or CO 2 exchange

– Measures aerobic

respiration

Metabolic Measurements

-BMR

-SMR (RMR)

-FMR

-Maximum metabolic rate - burst activity

-Sustainable maximum metabolic rate

BMR

Basal metabolic rate

– Minimal metabolic rate for fasting, non-reproducing, resting

animal under no thermal stress. Minimal cost of survival

SMR/RMR

Standard or resting metabolic rate

Minimal rate under specified thermal conditions

FMR/DEE

Field metabolic rate/Daily Energy Expenditure

—cost of life in real world

• Importance: estimate

Metabolic Rates Vary with Body Size

As body size increases, MR increases

Logarithmic Transformations of Power Functions

• MR = a M^b (a=constant, b=exponent, M=mass)

• Log MR = log a + b log M

• The exponent b becomes the slope of a straight line

• Transformation spreads out small values

• Make calculation of the best-fitting curve easier.

Why M^0.75? Could it be a “Surface Law”?

• Rate of heat loss ∝ surface area

• For objects of similar shape

– surface area ∝ volume 2/3 = volume 0.67

(Volume³ vs SA²)

– If density is constant, mass ∝ volume

• In resting mammal, heat production by metabolism = heat loss

• Therefore – BMR should be proportional to M0.67 , an ok fit to

measured data.

But the “Surface Law” has Problems

• Shapes and densities of animals differ

• Rates of heat loss vary across body surface, differ between

animals, and often change with adjustments in blood flow or

insulation.

• Measured exponents are usually higher than 0.67

• Metabolic scaling is similar in organisms that do not use

metabolic heat production to keep temperature constant.

Vertebrate Metabolic Scaling

Most vertebrates

near β = 0.75

(root of phylogeny

@ β = 0.78)

Why are Metabolic Rates ∝ M^0.75?

• The “surface law” is based on attractive but specious reasoning.

• Other hypotheses abound

– Within-species patterns @ 2/3 and between @ ¾? (NO!)

– Differences in body temperature?

– Nutrient supply through network of vessels (an energy flow model)

• WBE model best current explanation

What Does Metabolic Scaling Mean to Vertebrate Biology?

• Larger animals always use energy faster than smaller animals.

• Calculate mass-specific metabolic rate, by dividing animal’s

total metabolic rate by its body mass.

Mass-Specific Metabolic Rate

• For endotherms (birds and mammals)

– MR= 4.77M 0.75 where mass is in kg and MR in watts

• So mass-specific metabolic rate (W/kg)

• Mass-specific metabolic rate is the cost of supporting one

unit mass of tissue.

• Mass-specific metabolic rates get lower as body size

increases.

• Mice spend more per gram than rabbits, and rabbits more

per gram than cows.

• Of course, rabbits weigh more than mice, so the total

expenditure for a rabbit is more than that of the mouse, and

a cow uses a lot more energy than one rabbit.

Productivity = Assimilation - Respiration

• Small mammals utilize much more energy than an equal mass of a large mammal.(burning through energy quickly)

• HOWEVER, large mammals can survive without food for longer periods of time!

Assimilation Definition

Taking what you eat, digesting it and using it in body