Metabolic scaling

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).

Value

<numeric> The scaled parameter.

Details

Equation:

The function uses the equation in the form of: $$parameter = normalization\_constant \cdot mass^{scaling\_exponent} \cdot e^{\frac{Activation\_energy}{k \cdot temperature}}$$

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:

$$1 \ electronvolt = 1.602176634 \cdot 10^{-19} Joule$$

$$Boltzmann \ constant = 1.380649 \cdot 10^{-23} \frac{Joule}{Kelvin}$$

$$Boltzmann \ constant \ in \frac{eV}{K} = 8.617333e-05 = \frac{1.380649 \cdot 10^{-23}}{1.602176634 \cdot 10^{-19}}$$

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. doi:10.1890/03-9000

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) doi:10.1002/9781119968535.ch

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
)
#> [1] 0.6202913

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
)
#> [1] 40.30365