Ecological Archives E092-025-A3

Otso Ovaskainen and Janne Soininen. 2011. Making more out of sparse data: hierarchical modeling of species communities. Ecology 92:289–295.

Appendix C. Details of the diatom case study.

FIG. C1. Fifteen riffles were sampled in seven drainage systems (105 sites in total) in Finland, a latitudinal gradient between the southernmost and the northernmost sites being more than 1000 km (Supplementary Figure 2). The drainage systems were: (1) Kemijoki (68º), (2) Koutajoki (67º), (3) Muonionjoki (68º), (4) Kiiminkijoki (65º), (5) Upper Oulujoki (65°), (6) Tenojoki (70º) and (7) Vantaanjoki (60º).

Sampling and sample processing

The sites were sampled once in August either in 2001 or 2004. This sampling period should be optimal with regard to the presence of diatoms, which are known to be affected by discharge conditions. Thus, streams were sampled well after the snowmelt generated spring floods had leveled off, but before heavier autumn rainfalls. This should ensure that the discharge conditions were as stable as they could possibly be in boreal streams. With limited resources, we could not sample all the sites in one year without including considerable seasonal variability in the data. According to our experience on boreal streams, such inter-seasonal variability is much stronger than inter-annual for diatoms and other biotic communities (Soininen, unpublished data). Sampling was confined to near-pristine streams, except for the Vantaanjoki drainage system, where there are no near-pristine streams and sampling was restricted to the least-impacted sites.

Sampling was conducted by the same field crew using a strictly standardized field protocol at all sites. Each study site was divided into five or ten cross-sectional transects, depending on stream width. Ten stones were selected randomly along these transects, and diatoms were scraped off the stones for subsamples from a predefined area (3.1 cm2) using a plastic template. The subsamples were subsequently pooled into a composite sample at each site. The diatom samples from all sites were treated identically in the laboratory. Fresh samples were carefully checked to guarantee that most diatom frustules were alive before further processing. Almost all of the diatom cells had cytoplasmic contents and hydrogen peroxide was thus used to clean frustules of organic material. Cleaned diatoms were mounted in Naphrax. A total of 500 frustules per sample were identified and counted using phase contrast light microscopy (magnification 1000x). This number of frustules is typically identified in studies on stream diatom assemblages although it is likely that more species could be found with an increasing number of identified frustules, especially for the most diverse sites (Heino and Soininen 2005). Diatoms were identified to species level according to Krammer & Lange-Bertalot (1986-1991) and Lange-Bertalot & Metzeltin (1996).

Environmental covariates

Simultaneously to algal sampling, we measured several environmental characteristics that were expected to be the most important determinants of the local diversity and community structure of stream diatoms in our study area (Soininen et al. 2004, Heino and Soininen 2005). Shading (% canopy cover) was measured using a cylinder (diameter 7.5 cm) at 20 locations in evenly spaced cross-channel transects covering the whole study section. Current velocity (at 0.4 x depth), substratum size and moss cover were measured at 40 random locations along the same transects. To determine substratum size, we measured three perpendicular dimensions of each stone, 40 in total. Moss cover (%) was approximated based on amount of moss growing on 40 randomly picked stones. In the laboratory, water samples for color, conductivity, pH and total phosphorus were analyzed using Finnish national standards.

We used the first two principal components derived from Principal Component Analysis in further analyses. The analysis included the eight environmental variables described above (conductivity, total phosphorus, current velocity, water color, water pH, substratum size, moss cover and shading). The first PC axis explained 29.7 % of the total variance in environment and was most strongly related to variation in conductivity, total phosphorus and current velocity. The second PC axis in turn explained 24.6 % of the total variance and was most strongly related to water color and water pH.

Parameter values

The estimated parameter values (based on full diatom data) are given in Supplementary Tables C1-C5. Supplementary Figure C2 illustrates the model behavior with respect to the covariate PC2.

TABLE C1. Parameter estimates for the elements of the vector µ. The table shows for each element (7 region-specific intercepts and the linear and quadratic effects of PC1 and PC2) the 0.025, 0.5 and 0.975 quantiles of the marginal posterior.

Parameter 0.025 0.5 0.975
r1 -4,81102 -4,35083 -3,92685
r2 -3,45413 -3,10332 -2,78802
r3 -4,21406 -3,85378 -3,49394
r4 -4,14378 -3,65167 -3,20002
r5 -4,80232 -4,21467 -3,74585
r6 -5,21205 -4,69811 -4,26854
r7 -5,28181 -4,36828 -3,64759
PC1 0,018704 0,257778 0,488843
PC2 -0,28195 -0,08458 0,073958
PC12 -0,65172 -0,48066 -0,33246
PC22 -0,35785 -0,24963 -0,15053

TABLE C2. Parameter estimates for the diagonal elements of the matrix V. The table shows for each element (7 region-specific intercepts and the linear and quadratic effects of PC1 and PC2) the 0.025, 0.5 and 0.975 quantiles of the marginal posterior.

Parameter 0.025 0.5 0.975
r1 5,97468 7,779827 9,989204
r2 3,545194 4,483585 5,84829
r3 4,654161 5,847621 7,292074
r4 3,576062 5,134724 7,051198
r5 6,433021 8,352222 11,02183
r6 4,933614 6,453108 8,54075
r7 5,915997 8,659779 12,89632
PC1 0,215713 0,351981 0,552902
PC2 0,174965 0,257209 0,37464
PC12 0,077163 0,13515 0,209993
PC22 0,031805 0,047896 0,075305

TABLE C3. Median parameter estimates (0.5 quantile) for the off-diagonal elements of the matrix V (converted to correlations).

  r1 r2 r3 r4 r5 r6 r7 PC1 PC2 PC12 PC22
r1 1 0,91 0,88 0,89 0,91 0,79 0,75 -0,18 0,05 0,27 0,34
r2 0,91 1 0,85 0,87 0,84 0,84 0,72 -0,26 0,2 0,2 0,34
r3 0,88 0,85 1 0,86 0,77 0,89 0,89 -0,08 0,02 0,38 0,38
r4 0,89 0,87 0,86 1 0,87 0,91 0,64 -0,13 0,22 0,07 0,26
r5 0,91 0,84 0,77 0,87 1 0,69 0,51 0,05 -0,06 0,09 0,21
r6 0,79 0,84 0,89 0,91 0,69 1 0,77 -0,26 0,32 0,21 0,36
r7 0,75 0,72 0,89 0,64 0,51 0,77 1 -0,26 0,04 0,58 0,42
PC1 -0,18 -0,26 -0,08 -0,13 0,05 -0,26 -0,26 1 -0,57 -0,12 -0,24
PC2 0,05 0,2 0,02 0,22 -0,06 0,32 0,04 -0,57 1 -0,17 0,17
PC12 0,27 0,2 0,38 0,07 0,09 0,21 0,58 -0,12 -0,17 1 0,19
PC22 0,34 0,34 0,38 0,26 0,21 0,36 0,42 -0,24 0,17 0,19 1

TABLE C4. 0.025 quantiles for the off-diagonal elements of the matrix V (converted to correlations).

  r1 r2 r3 r4 r5 r6 r7 PC1 PC2 PC12 PC22
r1 1 0,87 0,83 0,81 0,86 0,72 0,64 -0,47 -0,21 0,01 -0,01
r2 0,87 1 0,79 0,77 0,76 0,77 0,6 -0,52 -0,07 -0,05 0,01
r3 0,83 0,79 1 0,76 0,68 0,84 0,82 -0,36 -0,24 0,15 0,05
r4 0,81 0,77 0,76 1 0,79 0,83 0,48 -0,41 -0,03 -0,19 -0,08
r5 0,86 0,76 0,68 0,79 1 0,58 0,35 -0,26 -0,32 -0,16 -0,16
r6 0,72 0,77 0,84 0,83 0,58 1 0,65 -0,5 0,07 -0,04 0,07
r7 0,64 0,6 0,82 0,48 0,35 0,65 1 -0,51 -0,21 0,33 0,14
PC1 -0,47 -0,52 -0,36 -0,41 -0,26 -0,5 -0,51 1 -0,75 -0,4 -0,5
PC2 -0,21 -0,07 -0,24 -0,03 -0,32 0,07 -0,21 -0,75 1 -0,41 -0,15
PC12 0,01 -0,05 0,15 -0,19 -0,16 -0,04 0,33 -0,4 -0,41 1 -0,09
PC22 -0,01 0,01 0,05 -0,08 -0,16 0,07 0,14 -0,5 -0,15 -0,09 1

TABLE C5. 0.975 quantiles for the off-diagonal elements of the matrix V (converted to correlations).

  r1 r2 r3 r4 r5 r6 r7 PC1 PC2 PC12 PC22
r1 1 0,95 0,92 0,94 0,94 0,86 0,83 0,15 0,32 0,48 0,61
r2 0,95 1 0,89 0,93 0,9 0,89 0,81 0,05 0,46 0,42 0,6
r3 0,92 0,89 1 0,92 0,83 0,93 0,93 0,22 0,28 0,58 0,62
r4 0,94 0,93 0,92 1 0,92 0,96 0,77 0,19 0,46 0,31 0,56
r5 0,94 0,9 0,83 0,92 1 0,78 0,63 0,37 0,23 0,3 0,49
r6 0,86 0,89 0,93 0,96 0,78 1 0,84 0,04 0,55 0,42 0,6
r7 0,83 0,81 0,93 0,77 0,63 0,84 1 0,06 0,29 0,75 0,64
PC1 0,15 0,05 0,22 0,19 0,37 0,04 0,06 1 -0,34 0,19 0,06
PC2 0,32 0,46 0,28 0,46 0,23 0,55 0,29 -0,34 1 0,11 0,44
PC12 0,48 0,42 0,58 0,31 0,3 0,42 0,75 0,19 0,11 1 0,45
PC22 0,61 0,6 0,62 0,56 0,49 0,6 0,64 0,06 0,44 0,45 1


FIG. C2. As Figure 2D in the main text, but shown for the covariate PC2.

LITERATURE CITED

Heino, J. and J. Soininen. 2005. Assembly rules and community models for unicellular organisms: patterns in diatoms of boreal streams. Freshwater Biology 50:567–577.

Krammer, K. and H. Lange-Bertalot. 1986–1991. Bacillariophyceae. Süßwasserflora von Mitteleuropa, 2 (1–4). Fischer, Stuttgart.

Lange-Bertalot, H. and D. Metzeltin. 1996. Indicators of oligotrophy. 800 taxa representative of three ecologically distinct lake types: carbonate buffered, oligodystrophic, weakly buffered soft water. Diatomologica 2:1–390.

Soininen, J., R. Paavola, and T. Muotka. 2004. Benthic diatom communities in boreal streams: community structure in relation to environmental and spatial gradients. Ecography 27:330–342.


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