No-interaction model does not mean that interactions should not be studied

It is best to see the 'no-interaction' model as a null model. Only deviations from the null-model are worth explaining. So the model does not say that there are no interactions, you just don't need any interactions to produce the hump. The model says that biomass and species richness are confounded, circular parameters. If you observe a hump in species richness against biomass, you can say nothing about ecological interactions or diversity. Instead, you should study directly those interactions, or diversity. Studying interactions is a whole field of experimental ecology, but we can concentrate here on parameters related to diversity.


Diversity is not the same as species richness. Diversity is determined by species abundance relations as well. Species richness increases with increasing sample size. If sample size is unknown, it is impossible to compare two communities. Plants are often difficult to count, since it is difficult define the sampling unit (often called 'individual' though it need not be individual in biological sense). Species number increases with sample size [Fig: jpeg, 9K], and for a given species number, we cannot know whether it is from a small sample with high diversity, or from a large sample with low diversity. Some field observations (Condit et al. Journal of Ecology, 84, 549-562; 1996), and my stand simulations indicate that diversity could be less scale dependent than species richness. Therefore, if we observe a pattern in diversity, it is more credible than pattern in species richness.

Plant shape and size

My basic model discussed only plants of equal size, though stand simulations found the same pattern with variable plant sizes. However, it may be that systematic changes in plant shape can contribute to the hump. For instance, Al-Mufti et al. (1977), Journal of Ecology, 65, 759-791 found the species richness peak at grassland, and lower richness in forest understorey and in tall herbs. Grasses may be narrower and higher, and so it is possible to have a larger number of plants in a unit area.

It is difficult to say how to measure plant shape directly, though it is related to parameters like plant height, plant density, and plant weight.

Though the 'no-interaction' model was based on plants of constant size, it survives simulation tests with variable plant sizes. However, it should be noted that species richness - productivity measures with constant plot size will produce a humped pattern and so hide possible variability in plant size hierarchies. As such, these would be interesting to study directly.

Abundance relations

Plant abundance relations are related both to diversity and to plant shape and size. Wilson, J.B. (1991) Journal of Vegetation Science, 2, 35-46, and Wilson, J.B et al. (1996) Journal of Ecology, 84, 527-538, give methods to evaluate the shape of abundance patterns and to interpret the results in ecological context.

Nested quadrats and species-area relation

In principle, we can have the hump in species richness when we are comparing quadrats which have different number of plants. So the hump should be generated at all sample quadrat sizes. On the other hand, the rate at which new species are added to the species list with increasing quadrat area can be independent of scale, like suggested by Rapson et al. (1997) Journal of Ecology, 85, 99-100, and confirmed by my stand simulation. This approach may be related to pattern diversity as well (at least to so-called spatial pattern diversity).

Neighbour diversity

A completely scale-independent and non-spatial way of assessing diversity is to see the diversity of neighbours of each plant species (Oksanen, J. 1997, Journal of Vegetation Science, 8, 255-258). However, this is so non-spatial that it does not give any stand level statistics. The approach is related to the tradition where species association is studied with plotless sampling based on neighbourhood (Yarranton, G.A. 1966 Journal of Ecology, 54, 229-237; de Jong,et al. 1983 Journal of Ecology, 71, 545-559).

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Updated 15/8/97 Jari Oksanen