A case study: River bryophytes

In his response, Grime (Journal of Ecology 85, 97-98; 1997) says that an article by Muotka T & Virtanen R (Freshwater Biology 33, 141-160; 1995) gives evidence against the no-interaction model. I analyse these data in more detail here, and I will show, that their data give support to the no-interaction model.

The data are taken from the article by Muotka & Virtanen. Biomass data were roughly estimated from their Figure 6. Species richness, total cover and cover of large bryophyte species were taken directly from their Table 3 (Fig. 6 has wrong species richness for one site, cf. their Table 3).

Species richness

The no-interaction model fits the data very well [Fig: jpeg, 18K], and certainly better than the original second degree polynomial forced through the origin which was used by Muotka & Virtanen. The maximum species richness was estimated to be at 32 g per plot (0.1 m²); however, the biomass data were visually estimated from Fig. 6 of Muotka & Virtanen, and were thus not very accurate.

Even a good fit proves nothing about the mechanisms, since there are several alternative models which may produce well fitting curves. However, the article gives some data which can be used to directly evaluate hypotheses 1 and 2 of the no-interaction model.


The no-interaction model assumes that at low biomass the increase in species number is caused by the increase in the number of plants. In other words, at low biomass the cover should increase linearly until the stand reaches the biomass with maximum species richness (in this case 32 g per plot). At this stage, the stand is crowded, and so the cover should remain constant when the biomass increases over this limit. Exactly this response was observed [Fig: jpeg 16K]: Cover increased with increasing biomass, and then stabilized to ca. 73% at biomass 32 g per plot with maximum predicted species richness. This parametric model was reasonably similar with a 4 d.f. generalized additive model, but used only 1 d.f. and was clearly significant.

Plant size

The second assumption in the no-interaction model is that decreasing species richness at high biomass is due to increasing plant size so that there are fewer, larger plants with high biomass in plots of fixed size. According to Muotka & Virtanen, Fontinalis antipyretica, F. dalecarlica, Hygrohypnum ochraceum and Rhyncostegium riparioides are big "canopy" species. The proportion of these big species of the total cover should increase with increasing biomass. Exactly this response was observed [Fig: jpeg, 18K]: The logit of the proportion of big "canopy" species increased linearly with increasing biomass, indicating that the average plant size increases with biomass. The logit-linear increase was confirmed with 4 d.f. generalized additive model which produced nearly identical response. The response used only 2 d.f. and was significant.


Muotka & Virtanen do not give any data in their article that would justify the use of fixed plot size of 0.1 m²: Actually, they hardly discuss the subject. It seems that their data support the no-interaction model: The hump was produced as an artefact of fixed plot size. Below the maximum, the increase in richness is seemingly caused by increase of cover until the vegetation becomes crowded. At high biomass, the proportion of large species increases, and so the increasing average plant size is responsible both for the decreasing species richness and for increasing biomass.

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Updated 29/4/97