The respiratory ETS is a casual basis for the allometric relationship in Kleiber's law

THE RESPIRATORY ETS IS THE CASUAL BASIS FOR THE ALLOMETRIC RELATIONSHIP IN KLEIBER'S LAW Kleiber’s Law, relating an organism’s biomass (M) with its respiration rate (R), follows the allometric equation, R=aM0.75.It holds over 20 orders of magnitude for R and has gained increasing importance in recent years, because it serves as the basis for the Metabolic Theory of Ecology. (Brown et al, 2004). Why does the M-R relationship in Kleiber's Law work? We argue that because is the respiratory Vmax, because, through stoichiometry, potential respiration ()is equivalent to the activity of the respiratory electron transport system (ETS), and because the ETS is constitutive, both ETS and would track biomass better than R. To investigate this, zooplankton samples from the Canary Islands Transition Zone and from cultures of artemia (Artemia sp.), mysids (Leptomysis lingvura) and protozoa (Oxyrrhis marina) were analysed for agreement with Kleiber's Law. Conclusions: 1.- In well-nourished organisms (Upwelling and cyclonic eddy areas and mysids well fed) the slope of the log-log plots of -M is near 1, indicating a direct relationship. This means that and M are directly linearly related and do not follow the allometric equation and consequently do not require a logarithmic transformation. 2.- In coastal stations, in mysid cultures in standard conditions, and in fresh zooplankton samples (Packard and Gómez, 2008), the slope of log-log plots of -M is lower than in well-fed organisms and closer to Kleiber’s law (0.75). 3.- In starved organisms, in cultures maintained on low food levels, and in the offshore (oceanic) stations, the log-log -M slope is lower than Kleiber’s Law (b < 0.75). 4.- In general, considering all the pooled field data (lower right), the exponent in the - M relationship is closer to 1 than it is in Kleiber’s Law. M. Gómez, I. Fernández-Urruzola, A. Herrera, F. Maldonado-Uribe, I. Martínez, N. Osma and T. Packard Biological Oceanography Laboratory, Department of Biology. University of Las Palmas de Gran Canaria. FIELD EXPERIMENTS UPWELLING STATIONS y = 0,8862x + 0,1432 R2 = 0,5254 -1,5 -1 -0,5 0 0,5 1 1,5 2 -1,5 -1 -0,5 0 0,5 1 1,5 2 Biomass (Logmgprot) Log Φ (µmolO2h-1) Slope = 0.886 (n = 248) COASTAL STATIONS y = 0,7925x + 0,0832 R2 = 0,6425 -1,5 -1 -0,5 0 0,5 1 1,5 2 -1,5 -1 -0,5 0 0,5 1 1,5 2 Biomass (Log mg prot) Log Φ (µmolO2h-1) Slope = 0.797 (n = 64) OFFSHORE STATIONS y = 0,6441x - 0,0297 R2 = 0,3784 -1,5 -1 -0,5 0 0,5 1 1,5 2 -1,5 -1 -0,5 0 0,5 1 1,5 2 Biomass (L og mgprot) L og Φ (µmolO2h-1) Slope = 0.644 (n = 220) EDDY STATIONS y = 0,9787x - 0,1254 R2 = 0,4771 -1,5 -1 -0,5 0 0,5 1 1,5 2 -1,5 -1 -0,5 0 0,5 1 1,5 2 Biomass (L ogmgprot) L og Φ (µmolO2h-1) Slope = 0.978 (n = 30) Packard and Gómez (2008) y = 1,0078x - 0,0689 R2 = 0,6653 -1,5 -1 -0,5 0 0,5 1 1,5 2 -1,5 -1 -0,5 0 0,5 1 1,5 2 Biomass (Log mgprot) Log Φ (µmolO2h-1) ALL STATIONS Slope = 1.007 (n=672) Zooplankton samples Leptomysis lingvura Artemia sp. Oxyrrhis marina ALL MYSIDS WELL FED (200 ARTEMIA NAUPLII) MYSIDS, ARTEMIA & OXYRRHIS STARVED Slope = 0.49 (n=76) LABORATORY EXPERIMENTS MYSIDS FED 300 ARTEMIA NAUPLII MYSIDS FED 150 ARTEMIA NAUPLII MYSIDS FED 20 ARTEMIA NAUPLII Slope = 0.716 (n =34) Slope = 0.706 (n =36) Slope = 0.535 (n =35) MYSIDS IN STANDARD CULTURES MYSIDS WELL FED ARTEMIA IN LOW FOOD CONDITIONS Slope = 0.923 (n =32) Slope = 0.74 (n = 15) Slope = 0.255 (n = 16) Slope = 0.79 (n=47) EDDIE STATIONS UPWELLING STATIONS COASTAL STATIONS OFFSHORE STATIONS