Emprirical Relationships - what affects Respiration ?
 
 


Individual respiration of ectotherm animals is affected by many different external and internal parameters. Body mass and temperature are the most distinctive forcing factors, but we can see effects of taxon, lifestyle, and habitat, too.

 
 


Respiration R scales exponentially with body mass M within species, but also across species:

R = a * Mb <=> R/M = a' * Mb-1

The exponent b of this formula ranges between 0.6 and 1.0 in most cases, i.e. repiration rate increases below 1:1 with body mass, and hence mass specific respiration rate R/M (= respiration rate per unit of body mass) decreases with body mass. There is much discussion about the underlying principles of this relationship. The most convincing theory has been brought forward by Brown abd co-workers (2004). They show that the fractal nature of the body internal "plumbing" which transports gases and matter to and from the cells leads to a scaling exponent of b = 0.75, which is about the average exponent we encounter in nature.

 
 
Metabolic activity increases exponentially with temperature. The Van't Hoff-Arrhenius relationship describes the kinetic of this process:
R = e-E/(k*T)

where E is activation energy (about 0.63 eV = 60.73 * 103 J/mol in metabolic processes), k is the Boltzmann constant (k = gas const / Avogardo const = 8,62 * 10-5 eV/K), and T is temperature (K).

 
 
Combining body mass and temperature effects leads to:
R = a * Mb * e-E/(k*T)

<=> log(R) = log(a) + b * log(M) + (-E/k) * (1/T)

<=> log(R) = log(a) + b1 * log(M) + b2 / T

and with R/M = a' * Mb-1

log(R/M) = log(a') + (b1-1) * log(M) + b2 / T

I.e., we would expect to see a linear decrease of log(mass specific respiration rate) with body mass as well as with 1/temperature, whereby the slopes should amount to about (b1-1) = -0.25 and b2 = -7300.

 
 

A really large data compilation of aquatic invertebrate respriation data (<22000 measurements, >900 species, > 440 references) confirms these considerations rather well, as the overall model is:
log(R/M) = 8.3732 - 0.2073 * log(M) - 2766.0235 / T [J/J/d, J, K]

See the plots of specific respiration rate versus body mass and temperature.