Models of Diffusion-Mediated Gas Exchange in Animal Burrows

Abstract

Three mathematical models of gaseous diffusion were employed in order to investigate the gaseous environments in subaquatic and subterranean animal burrows. The results of these models for (a) simple cylindrical burrows in impermeable media, (b) spherical nest chamber and burrow(s) in impermeable media, and (c) spherical nest chamber and cylindrical burrow(s) in permeable media were evaluated using empirical data, and consideration of the physical and behavioral attributes of fossorial animals which promote forced convection through their burrows. Subaquatic, ectothermic animals in burrows constructed through impermeable media cannot rely upon diffusion to meet their metabolic requirements for O2 utilization and CO2 excretion unless they are of extremely small size. Subterranean ectotherms are predicted to be able to rely upon gaseous diffusion, except when they aggregate together in large numbers. Subterranean endotherms, because of their high mass specific metabolic rate, are likely to encounter low concentrations of O2 and high concentrations of CO2 in their burrows. Sensitivity analysis of the model for gas exchange from a nest chamber in a permeable medium indicates that the most significant parameters influencing the gaseous environment are soil porosity, soil moisture (because of its altering soil porosity), and the absolute metabolic requirements of the burrow occupant or occupants. The depth of the nest chamber and the burrow dimensions are, surprisingly, of little significance. A non-steady-state approximation for diffusion from a nest chamber in a porous medium demonstrated that the gaseous environment rapidly approaches equilibrium conditions, and the time required to approach to within 10% of the equilibrium values was inversely proportional to the absolute equilibrium gradient.