metabolic_scaling {metaRange}

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:

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 4 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}}

Value

⁠<numeric>⁠ The scaled parameter.

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

See Also

calculate_normalization_constant()

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
)