Metabolic scaling
Description
Section titled “Description”A function to calculate the metabolic scaling of a parameter, based on the metabolic theory of ecology (Brown et al. 2004).
metabolic_scaling( normalization_constant, scaling_exponent, mass, temperature, E, k = 8.617333e-05)
Arguments
Section titled “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
Section titled “Details”Equation:
Section titled “Equation:”The function uses the equation in the form of:
parameter = normalization_constant * mass^{scaling_exponent} * e^{{Activation_energy} / {k * temperature}}
Parameter:
Section titled “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:
Section titled “Units:”1 \ electronvolt = 1.602176634 * 10^{-19} Joule``Boltzmann \ constant = 1.380649 * 10^{-23} {Joule} / {Kelvin}``Boltzmann \ constant \ in {eV} / {K} = 8.617333e-05 = {1.380649 * 10^{-23}} / {1.602176634 * 10^{-19}}
References
Section titled “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
Section titled “Seealso”calculate_normalization_constant()
<numeric>
The scaled parameter.
Examples
Section titled “Examples”reproduction_rate <- 0.25E_reproduction_rate <- -0.65estimated_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 <- 100E_carrying_capacity <- 0.65estimated_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)