Metabolic scaling

Description

A function to calculate the metabolic scaling of a parameter, based on the metabolic theory of ecology (Brown et al. 2004).

Usage

metabolic_scaling(
  normalization_constant,
  scaling_exponent,
  mass,
  temperature,
  E,
  k = 8.617333e-05
)

Arguments

• normalization_constant: <numeric> normalization constant.
• scaling_exponent: <numeric> allometric scaling exponent of the mass.
• mass: <numeric matrix> mean (individual) mass.
• temperature: <numeric matrix> temperature in kelvin (K).
• E: <numeric> activation energy in electronvolts (eV).
• k: <numeric> Boltzmann’s constant (eV / K).

Details

Equation:

The function uses the equation in the form of:

$\mathrm{parameter}=\mathrm{normalization\_constant}\cdot {\mathrm{mass}}^{\mathrm{scaling\_exponent}}\cdot e^{\frac{\mathrm{Activation\_energy}}{k\cdot \mathrm{temperature}}}$

Parameter:

Note the different scaling values for different parameter. The following is a summary from table 2 in Brown, Sibly and Kodric-Brown (2012) (see references).

Parameter	Scaling exponent	Activation energy
resource usage	3/4	-0.65
reproduction, mortality	-1/4	-0.65
carrying capacity	-3/4	0.65

Units:

$$1 \mathrm{electronvolt}=1.602176634 \cdot {10}^{-19} \mathrm{Joule}$$ $$\mathrm{Boltzmann} \mathrm{constant}=1.380649\cdot {10}^{-23} \mathrm{Joule}/\mathrm{Kelvin}$$ $$\mathrm{Boltzmann} \mathrm{constant} \mathrm{in} \mathrm{eV}/K=8.617333e-05=\frac{1.380649e-23}{1.602176634e-19}$$

References

Brown, J.H., Gillooly, J.F., Allen, A.P., Savage, V.M. and West, G.B. (2004) Toward a Metabolic Theory of Ecology. Ecology, 85 1771—1789. Brown, J.H., Sibly, R.M. and Kodric-Brown, A. (2012) Introduction: Metabolism as the Basis for a Theoretical Unification of Ecology. In Metabolic Ecology (eds R.M. Sibly, J.H. Brown and A. Kodric-Brown)

Seealso

calculate_normalization_constant()

Value

<numeric> The scaled parameter.

Examples

reproduction_rate <- 0.25
E_reproduction_rate <- -0.65
estimated_normalization_constant <-
    calculate_normalization_constant(
        parameter_value = reproduction_rate,
        scaling_exponent = -1/4,
        mass = 100,
        reference_temperature = 273.15 + 10,
        E = E_reproduction_rate
    )
metabolic_scaling(
    normalization_constant = estimated_normalization_constant,
    scaling_exponent = -1/4,
    mass = 100,
    temperature = 273.15 + 20,
    E = E_reproduction_rate
)

carrying_capacity <- 100
E_carrying_capacity <- 0.65
estimated_normalization_constant <-
    calculate_normalization_constant(
        parameter_value = carrying_capacity,
        scaling_exponent = -3/4,
        mass = 100,
        reference_temperature = 273.15 + 10,
        E = E_carrying_capacity
    )
metabolic_scaling(
    normalization_constant = estimated_normalization_constant,
    scaling_exponent = -3/4,
    mass = 100,
    temperature = 273.15 + 20,
    E = E_carrying_capacity
)