The study was done in the geothermal Hengill region of Iceland (64°03′N, 021°18′W, 350–420 metres above sea level). The area contains multiple indirectly heated streams that are tributaries to the same main stem and which all lie within 2 km of one another, such that dispersal constraints are negligible across the whole system (Fig. 2; see O'Gorman et al. 2012 for a more detailed site description). Stream water temperatures are altered by geothermal warming from deep below the streambed. Temperature is the major determinant of the taxonomic composition of assemblages of both primary and secondary producers across the streams (Woodward et al. 2010b; Gudmundsdóttir et al. 2011). These features enable us to isolate the effects of temperature on diatom community composition and size structure. Fourteen streams in the system were used for this study (Fig. 2), spanning about 5–25 °C. This stream system was the subject of previous work (Woodward et al. 2010b; Gudmundsdóttir et al. 2011; O'Gorman et al. 2012), in which the streams were named numerically. We have changed notation slightly so readers can more easily distinguish between warm and cold streams. Streams we used are labelled with the letters a-n in order from the coldest to the warmest stream, followed by the number used in the original system, so that readers can easily compare with previous work.
Environmental variables other than temperature
A broad suite of physical and chemical variables was measured in the streams in August 2008, concurrently with the diatom sampling (see Woodward et al. 2010b; Demars et al. 2011; O'Gorman et al. 2012 for detailed methods). These variables included the major macronutrients (e.g. nitrate, ammonium, orthophosphate), ions (e.g. Ca2+, K+, Na+, Cl−), trace elements (e.g. Si), pH and conductivity (see Table S1). Besides temperature and a few variables directly linked to it by physico-chemical processes, all water chemistry and environmental variables were broadly similar among the streams and not strongly related to temperature (Friberg et al. 2009; Woodward et al. 2010b; Demars et al. 2011; O'Gorman et al. 2012; Table S2). Among those that are driven by physical laws that apply to all systems, dissolved oxygen concentrations declined with temperature, but the % saturation was independent of temperature across the gradient. The other two exceptions are silicon (Si) and K+ concentrations, which increased with temperature, reflecting the increased chemical weathering of rocks. These two abiotic variables are unlikely to have ecological significance for the diatom assemblages at Hengill because Si is found in concentrations at least one order of magnitude above what is typically considered limiting in freshwaters (White et al. 1999; Dalai et al. 2002; Dupré et al. 2003) and potassium (K) is thought to be unlikely to limit growth in natural waters (Hynes 1970; Jaworski et al. 2003; Talling 2010). Algal production in these streams is (co)limited by N and P (Friberg et al. 2009), as is typical of freshwater ecosystems, but concentrations of these macronutrients were not strongly related to temperature and there was very little variation across the catchment: total variation was <0.1% of the range for European streams (Woodward et al., 2012 and also Figure S1).
Diatom identification and measurements
Diatom species that accounted for the top 95% of abundance in each stream were measured for size: the remainder species were grouped together and designated as a single group, ‘other’, for later use in resampling schemes. There were several species outside the 95% abundance group but these were always very rare. Within each stream, for every species and for the ‘other’ group, ten individuals per group were selected for size measurement along a transect starting at the centre of the slide, using an Olympus BH2 microscope. Samples for the ‘other’ group were taken as the first ten individuals found on a slide that were outside the top 95% for that stream. For some groups, 10 samples could not be found; in those cases as many were found as possible. Samples from ‘other’ were also identified to species level. Broken or obscured valves were not used. Individuals selected for size measurement were photographed in valve view with a high resolution Canon digital SLR camera. Any individuals that were lying out of focus had multiple images taken and were rendered in Helicon Focus (Helicon Soft Ltd, 2011). Images were taken at a magnification of ×1000, except for a few very large individuals where ×400 was used. Diatoms were identified using the species definitions and nomenclature of Krammer and Lange-Bertalot (1986–1991). Classifications beyond the species level were not used.
Measurements were taken in Image J (Abramoff et al. 2004) for valve length and maximum valve width. Diatom size is sometimes estimated using cell volume, using dimensions taken from diatoms in both valve view and girdle view (Hillebrand et al. 1999). In this study, projected (cross-sectional) valve area was used because measurements of individual diatoms were required, and because each single diatom was lying in either valve or girdle view. This is a reliable measurement of body size as diatom cell volume is strongly correlated with valve length (Snoeijs et al. 2002; Finkel et al. 2009b) and valve area incorporates valve length as well as the additional information of valve width, and hence is likely to be even better correlated with volume. Valve area (μm2) was calculated using a standard geometric shape for each genus as described in Hillebrand et al. (1999), with a few exceptions where the shape of the species in the Hengill region was distinctly different from the described shape for the genus. Table S3 and Figure S2 justify the exceptions, showing that our shape modifications improved accuracy.
Statistical analysis: intraspecific patterns
To determine the relationship between temperature and body size within individual species, we considered every species that was present in two or more streams. Linear regressions were carried out for each species, of temperature against body size of individuals. A Bonferroni correction for multiple tests was applied: P-values were multiplied by 31, the number of tests. Size data were log10-transformed for this and all analyses.
During the asexual part of their life cycle, diatom cells progressively reduce in size (Edlund & Stoermer 1997). Since we have used a natural experiment where the sampled individuals could be at any stage of their life cycle, this phenomenon could potentially be contributing to any cell size differences we observe. However, this vegetative cell size reduction is not uniform and in pennate diatoms the width of the valve decreases proportionally far less than the length (Round et al. 1990). Thus, we repeated the intraspecific analysis using only valve width as the measure of body size, as a way of determining whether the diatom life cycle could have confounded our results.
Statistical analysis: whole-community analysis
Average diatom size for each stream was calculated using a simple weighted mean. If kα is the number of species present in stream α (including the ‘other’ group as a single ‘species’ for this count), nαi is the number of samples taken of species i (cells measured, usually 10), aαi is the relative abundance of species i in stream α, sαij is the log10 size measured for individual j of species i and is the average log10 size of species i in α, then the abundance-weighted mean size for α is . The aαi are relative abundances, so they sum to 1 across all species (including ‘other’ as a species). Confidence intervals of the abundance-weighted mean were calculated using a resampling method (Crowley 1992); for each stream, we calculated Mα for a resampled data set 10 000 times and from those took 95% confidence intervals, as follows. The resampled data set was obtained by first resampling the original size data for each species nαi times with replacement (including ‘other’ as a species), and second, recalculating the relative abundance of each species by resampling, with replacement, the original diatom count data C times using multinomial trials with probabilities proportional to the ci for the species (including ‘other’).
Statistical analysis: partitioning the causes of community size change
We partitioned the causes of community size change in two ways: first, by determining whether intraspecific effects or compositional shifts are the main contributor to whole-community size differences; and second by determining if compositional shifts are mostly due to differences in relative abundances of species or species turnover.
We determined the proportional contribution of intraspecific effects to whole-community size differences by calculating the size difference we would expect between any two streams, α and β, if there were no differences in community composition, and comparing this to the observed size differences between α and β in average diatom size (computed as described above). To remove compositional effects, we first considered only species that were present in both α and β. To remove effects of differences in the relative abundance of species between α and β, which is a compositional effect, aαβi was calculated as , the average relative abundance of species i in α and β. Then, if kαβ is the number of species in common between α and β, the size difference we would expect due only to intraspecific effects is
To provide illustration of the methods using simplified two-species examples, Table 1 gives calculations of and for comparisons between a reference stream (α) and other streams (βi); the three outcomes described above are shown. In all cases, the average community body size decreases from stream α to stream βi and is negative, but the causes of the decrease are different. Examples (a) and (b) show the simplest examples, where only one cause of community size change is contributing. In (a), there is no change in the relative abundance of species between streams, only changes in the log10 size, therefore only intraspecific effects are contributing to the community size difference and and . In (b), there is no change in the log10 size of species, only in the relative abundances of the species; therefore, only compositional effects are contributing and and . Examples (c) to (f) illustrate a mixture of causes contributing to the difference in average community size between the streams. In (c), there is a decrease in the log10 size of each species, and also a shift in the relative abundance towards species 1, the smaller species. Therefore, both intraspecific and compositional effects are occurring in the same direction. , so intraspecific effects are responsible for 91% of the average size difference between streams. In (d), there is the same decrease in log10 size as in (c) but the shift in the relative abundance is in the opposite direction towards species 2, the larger species. In this case, intraspecific effects and compositional effects are acting in opposite directions, so : intraspecific effects overcame compositional effects and are the only cause of the overall size decrease. In (e), there is an increase in log10 size of species 2, and a shift in relative abundance towards species 1. This is the opposite of example (d): , and compositional effects overcame intraspecific effects. Example (f) shows the same outcome from the analysis as (e) with but in this case the compositional effects are due to species 3, a smaller species, replacing species 1. Turnover is the cause of the size decrease between the streams, rather than relative abundance shifts as in (e).
Table 1. Examples of calculations for and between streams α and βj. Each example illustrates a difference from stream α in either (i) a change in log size for one or both species; (ii) a shift in the relative abundances of the species; (iii) a different species being present or (iv) a combination of these. is calculated for a two–species system as , where aαi and aβi are the relative abundances of species i in streams α and β. is calculated as . There is only one species in common between α and β6 so
| ||Stream||Species 1||Species 2||Species 3|| || || ||Result|
|abundance||log10 size ()||abundance||log10 size ()||abundance||log10 size ()|
| || α ||7||2||3||3||–||–|| || || || |
|(a)|| β 1 ||7||1||3||2||–||–||−1||−1||1||ALL INTRA|
|(b)|| β 2 ||8||2||2||3||–||–||0||−0.1||0||ALL COMP|
|(c)|| β 3 ||8||1||2||2||–||–||–1||−1.1||0.91||91% INTRA|
|(d)|| β 4 ||6||1||4||2||–||–||–1||−0.9||1.11||ALL INTRA|
|(e)|| β 5 ||9||2||1||4||–||–||0.2||−0.1||−2||ALL COMP|
|(f)|| β 6 ||–||–||3||4||7||1||0.3||−0.4||−0.75||ALL COMP|
To assess the types of compositional shift that may be contributing to differences in body size we considered the presence and absence of species (all species found in the streams, including those in the ‘other’ group) between streams and their relative abundances in the streams. We calculated the proportion of compositional change from stream α to stream β that was represented by species turnover, as opposed to species relative abundance shifts, as the sum of the relative abundances of the species that were present in α but not detected in β. If the main compositional difference between streams is mostly because of species turnover, then these values will be close to 1. If the main compositional differences are due to relative abundance shifts, then the values will be close to 0.
Intraspecific effects are the main contributor to changes in overall community size differences from one stream to another when the index is greater than 0.5, and species turnover is the main contributor to compositional shifts when the index of the previous paragraph is greater than 0.5. Thus, the total fraction of all possible pairwise comparison values among streams that were greater than 0.5 in each analysis indicates the number of cases in which intraspecific effects or species turnover, respectively, are relatively more important, and characterizes the importance of these effects in the whole system. We calculated confidence intervals for these measures using a resampling method. Data were resampled 1000 times according to the same scheme used for calculating confidence intervals for average community size, and all pairwise comparisons between streams were re-calculated for each surrogate data set created in this way. For each resampling, the total number of comparisons that showed a >50% contribution of , or species turnover, was counted, and 95% confidence intervals for these numbers were taken as quantiles from the resulting distributions. All computations were carried out in the R programming language (version 2.14.1; R Development Core Team 2010).