Ecological Archives E092-131-A1

Wilco C. E. P. Verberk, David T. Bilton, Piero Calosi, and John I. Spicer. 2011. Oxygen supply in aquatic ectotherms: Partial pressure and solubility together explain biodiversity and size patterns. Ecology 92:1555–1572.

Appendix A. Boundary layer effect on the relationship between OSI and species richness.

We checked if the relationship between OSI and species richness was influenced by effects of a diffusion boundary layer. In streams animals are enveloped in a stationary laminar layer, which acts as a diffusion boundary layer, and the thickness of this layer affects diffusion distance and hence environmental oxygen supply. The thickness of the boundary layer will vary proportionally with the kinematic viscosity of water (Statzner and Holm 1989; Jacobsen 2000). With decreasing temperatures the thickness of the boundary layer increases, resulting in a greater diffusion distance which further decreases oxygen supply (since it is already lowered at low temperatures due to lower oxygen diffusivity). We adjusted both the OSI and rOSI for such an effect by dividing them by the temperature-dependent kinetic viscosity to check for a possible effect on oxygen supply. Unadjusted and adjusted indices yielded very comparable results (Table A1); in each case altitudinal clines in species richness were best explained by the OSI, whilst clines in species richness for the two datasets with organic pollution were sometimes better explained with the rOSI. As argued in the main paper, the better fit with rOSI in the latter two datasets is related to the constrained diversity in thermal physiologies, which makes the use of an overall Q10 value of 2.0 more appropriate to correct for changes in oxygen demand with temperature. In three instances where the adjusted and unadjusted indices differed significantly in explaining species richness, this was either a difference between adjusted and unadjusted OSI when the rOSI was the most appropriate index (both richness and rarefied richness in the Patagonian mountain streams) or a small improvement (species richness in the Colorado mountain streams). Furthermore, adjusting for the thickness of the boundary layer did not consistently improve or weaken the relationships with both indices.

A likely explanation for the similar relationships between adjusted and unadjusted indices is that species richness is too coarse a (response) measure to detect an effect of varying thicknesses in boundary layers. Differences between species in their basic physiology, behavior and morphology shape their efficiency and capabilities in meeting oxygen demand. Due to such interspecific differences, a general relationship is expected between oxygen supply and species richness, the latter being a measure which aggregates the response across individual species. In this respect, oxygen can be viewed as setting a physico-chemical ceiling, which precludes the occurrence of those species that are incapable of meeting their oxygen demand at the given oxygen supply. In addition, environmental variation in microhabitats with different flow regimes may further increase the available options for stream ectotherms to avoid low oxygen due to the effects of high viscosity in the cold by selecting patches with fast water currents, something which has been documented on a seasonal time scale (Genkai-Kato et al. 2005). By selecting microhabitats with faster currents, organisms are exposed to better conditions for oxygen diffusion (thinner boundary layer and a higher rate of refreshment), but at higher costs of maintaining position and increased abrasion by solid particles (Hynes 1970; Mérigoux and Dolédec 2004). Spatial variation in water current resulting from substrate heterogeneity may provide oxygen-rich patches where species can find refuge during periods of poor oxygenation. In this way, oxygen may underlie the positive effect of stream substrate heterogeneity on stream invertebrate diversity (Lancaster and Hildrew 1993; Brunke et al. 2003). Variation between species in their efficiency of meeting oxygen demand, and associated variation in microhabitat choice, may explain why accounting for the thickness of the boundary layer in the oxygen supply index yielded qualitatively similar results.

TABLE A1. Pearson R values for the relationships between species richness and the oxygen supply index (OSI) and relative oxygen index (rOSI). Results are shown separately for indices unadjusted and adjusted for the thickness of the laminar sub-layer. Significant relationships (P < 0.05) are in bold and significant differences due to such adjustment in the performance of the indices are indicated with asterisks (tested with pair-wise likelihood ratio tests). Note that unadjusted values are identical to those reported in Table 1, but are repeated here to facilitate comparison.

Unadjusted for laminar sub-layer Adjusted for laminar sub-layer
Oxygen supply
index1 (OSI)
Relative oxygen
supply index2 (rOSI)
Oxygen supply
index1 (OSI)
Relative oxygen
supply index2 (rOSI)
Higher species
richness at high
(low altitude)
(Jacobsen 2008) Rarefied
0.595 0.291 0.606 0.402
Ecuadorean Andes
(N = 30)
Richness 0.169 -0.161 0.214 -0.022
(Perry and
Schaeffer 1987)
0.560 -0.407 0.559 -0.363
Colorado mountains
(N = 12)
Richness 0.733* -0.735 0.851* -0.706
Lower species
richness at high
(high pollution)
(Jacobsen and
Marín 2008)
0.637 0.708 0.656 0.654
Bolivian Altiplano
(N = 12)
Richness 0.669 0.706 0.687 0.672
et al. 2008)
0.924* 0.899 -0.133* 0.905
Patagonian streams
(N = 6)
Richness 0.964* 0.927 0.034* 0.914

1 Calculations based on Tmin.
2 Calculations based on Tmax.


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