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PS 88-80
The second law of thermodynamics predicts constraints on the size structure of plant communities

**Background/Question/Methods**

It has been difficult to conceptually link community and ecosystem ecology. We show that recent advances in the statistical physics of self replication lead to a new theoretical relationship between the size structure of plant communities and thermodynamic properties of primary productivity. The basic result is that the statistical order of the size distribution of biomass among species in a plant community must be less than the log odds of a carbon molecule being fixed by photosynthesis versus respired as carbon dioxide plus ratio of the work done by photosynthesis divided by the ambient temperature of the ecosystem. Statistical order is measured by the Shannon entropy of the size distribution of biomass among species subtracted from the maximum entropy of that biomass.

Ecosystems can be arrayed along gradients of factors that affect these two constraints on size structure. The rate of accumulation of carbon via photosynthesis is clearly determined by water availability and is also affected by temperature. Arraying ecosystems along moisture and temperature gradients produces predictions of which combinations of temperature and moisture should lead to the most ordered and speciose communities.

To test these theoretical conclusions we collected published data on biomass distributions of 32 tree communities along with moisture and temperature records for these communities. We calculated statistical order as log B - S, where S is the Shannon entropy of the biomass distribution among species and B is total biomass. We then plotted statistical order in a two dimensional space with 1/temperature (K) as one axis and precipitation as the other.

**Results/Conclusions **

We found that tropical communities with relatively high temperature and precipitation had the highest degree of statistical order when compared with temperate and boreal forests. Boreal forests had the lowest values for statistical order. These results are not surprising and are consistent with our understanding of the life history attributes of tree species in each community and the underlying edaphic conditions in which these communities exist. The significance of this approach is that the measure of statistical order is derived directly from the thermodynamic propertities of carbon dynamics in ecosystems. Plant communties belong to a class of replicating thermodynamic systems in which replication proceeds at a faster rate than degradation and hence, allows for the accumulation of order at steady state achieved far from thermodynamic equilibrium (i.e., maximum entropy).