scale_rate - Scales a physiological rate (absolute or
mass-specific) to a different mass, using a specified scaling exponent.
scale_rate(rate, mass, new.mass, b)
| rate | numeric. The physiological rate to be scaled. Also accepts
|
|---|---|
| mass | numeric. Original mass at which the |
| new.mass | numeric. The new mass the |
| b | numeric. Scaling exponent. Must be the correct one for the |
Physiological rates typically scale allometrically with body mass. Therefore, it is usually not appropriate to directly compare rates between individuals of different size. Instead, if the scaling exponent of the rate (either absolute or mass-specific) is known, this can be used to scale rates to a common mass for comparison or statistical testing.
scale_rate scales an absolute (i.e. whole animal) or mass-specific
physiological rate (e.g. metabolic, feeding) to a specified body mass,
using a specified scaling exponent. Important note: the scaling
exponent should be the correct one for the rate used. For example, in the
case of metabolism, absolute (whole animal) rates typically scale at values
between +0.67 to +1 (i.e. between two-thirds and one), and mass-specific
rates between -0.33 to 0. Therefore, make sure you use the correct scaling
exponent for the rate as entered, INCLUDING THE -/+ SIGN.
Multiple rates can be entered as a vector or as part
of a respR::convert_rate input. If mass is a single value, all rates
will be scaled to the new.mass. To scale multiple rates at different
masses (e.g. from different individuals), rate and mass should be of
equal length. The function is fully vectorised: all inputs accepts vectors,
but these should be single values or of the same length as rate. See
examples.
respR integrationFor the rate input the function accepts
objects saved (or piped) from the respR
(https://github.com/januarharianto/respR) convert_rate function. In
this case, the rate (absolute or mass-specific) is automatically extracted.
rateNOTE: both negative and positive rates can be
entered. In respirometry experiments, rates are typically reported as
positive values. These can be entered as is. In the case of
respR::convert_rate objects, extracted rates will typically be
negative, and these are left unchanged in the split_rate function. In
respR, to be mathematically consistent (since they represent oxygen
depletion), respiration rates are represented by negative slopes, and
therefore rates returned as negative. You can enter the `rate`` as the
usually reported postive value, or as a negative: the function will work
with either.
The scaled rate is calculated as: ((new mass/actual mass) ^ b) * rate.
## Scaling a whole animal metabolic rate. ## Here the rate is in mg/h, the metabolic scaling exponent is 0.72, and ## we are scaling the rate to 0.5g. scale_rate(0.1784, mass = 0.0847, new.mass = 0.5, b = 0.72)#> [1] 0.6405856## Result = 0.6406 mg/h at 0.5g ## Here the exact same calculation is done using the mass-specific ## metabolic rate (0.1784/0.0847 = 2.1063 mg/h/g), and the mass-specific ## metabolic scaling exponent (the negative difference from 1 of the ## absolute scaling exponent). scale_rate(2.1063, mass = 0.0847, new.mass = 0.5, b = -0.28)#> [1] 1.281197## Result = 1.2812 mg/h/g at 0.5g ## We can see this is the same result as in the first example if it is ## expressed as a mass-specific rate at the mass it is scaled to (0.5g): ## 0.6406/0.5 = 1.2812 mg/h/g ## Obviously, scaling a rate to the same mass will give the same rate. scale_rate(32.55, mass = 1, new.mass = 1, b = 0.75)#> [1] 32.55## And these demonstrate that isometric (i.e. purely linear) scaling of ## an absolute rate will do a simple multiplication/division. scale_rate(5, mass = 0.5, new.mass = 1, b = 1)#> [1] 10scale_rate(20, mass = 2, new.mass = 1, b = 1)#> [1] 10## Isometric scaling when the rate is expressed as a mass-specific rate ## is represented by a scaling exponent of zero. In this case the ## mass-specific rate will be the same at any other body mass. scale_rate(4.77, mass = 2.5, new.mass = 18.3, b = 0)#> [1] 4.77## To scale multiple rates from the same individual, or multiple rates ## from different individuals of different mass, use vectors. # Individual with multiple rates scale_rate(c(1,2,3), mass = 2.5, new.mass = 10, b = 0.75)#> [1] 2.828427 5.656854 8.485281# Multiple individuals of different mass scaled to same `new.mass` scale_rate(c(1,2,3), mass = c(10,9,8), new.mass = 5, b = 0.75)#> [1] 0.5946036 1.2869913 2.1087800## You can fully vectorise all inputs, as long as they are single values ## or vectors of equal length (though not sure why you would want to...) scale_rate(c(1,2,3), mass = c(10,9,8), new.mass = c(5,6,7), b = c(0.7,0.8,0.9))#> [1] 0.6155722 1.4459624 2.6602871