The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M^0.776 and MMR = 0.753M^0.785. The scaling exponents for RMR (b_r) and MMR (b_m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.

The metabolic-level boundaries (MLB) hypothesis proposes that metabolic level mediates the relative influence of surface area (SA) vs. volume related metabolic processes on the body-mass scaling of metabolic rate in organisms. The variation in the scaling of SA may affect how metabolic level affects the metabolic scaling exponent. This study aimed to determine the influence of increasing metabolic level at a higher temperature on the metabolic scaling exponent of the crucian carp and determine the link between metabolic scaling exponents and SA parameters of both gills and body. The SA of gills and body and the resting metabolic rate (RMR) of the crucian carp were assessed at 15oC and 25oC, and their mass scaling exponents were analyzed. The results showed a significantly higher RMR, with a lower scaling exponent, in the crucian carp at a higher temperature. The gills SA and the total SA of the fish (TSA) are reduced with the increasing temperature. The bRMR tends to be close to that of the TSA at a higher temperature. This suggests that temperature positively affects metabolic level but negatively affects the scaling exponent of RMR (bRMR). The findings support the MLB hypothesis. The lower scaling exponent at a higher temperature can be alternatively explained as that the higher viscosity of cold water impedes respiratory ventilation and oxygen uptake and reduces MR more in smaller individuals than in larger individuals at lower temperature, thus resulting in a negative association between temperature and bRMR.