Empirical biomass spectra in which biomass is measured in logarithmically equal body size intervals are different from those measured in linearly equal size intervals. Moreover, the scales of body size used by different authors may differ, e. g., length, volume, equivalent!sphere diameter and body mass. The discrete models derived to explain the regularity of the empirical spectra are dependent on the choice of size-scales and size!intervals. Hence, evaluating the effect of size scales and intervals on biomass spectra is helpful for understanding the size!structures of ecosystems. In the present contribution, we analyse the relationships between the size measures used frequently in expressing the empirical data and discuss the difference between the biomass spectra organized in logarithmically equal size intervals and those in linearly equal size intervals. On this basis, we present the distribution function of biomass spectral density and transformation to different size scales. After dexthe effect of size intervals on the distribution functions of biomass spectral density, we give an example of the calculation of this effect by assuming that the distribution function of biomass spectral density is an allometric relationship. Finally, we explore the influence of size intervals on the validity of three discrete models developed by Kerr, Sheldon and co!workers and Borgman.

In consequence of interactions between compartments, the matter or energy residence time in an econetwork is in nature distinct from that in a compartment. Based on the analysis of econetwork structure, a strategy is developed to calculate the matter or energy residence time in a general econetwork and the effects of self-, direct-and indirect interaction on econetwork residence time. Two typical examples are used to illustrate the strategy, the results show that total residence time equals the ratio of total standing stock to total system outflow or total system inflow instead of the ratio of total standing stock to total system throughput.

The paper analyzes the overall diversity of trophic structures and processes at the organizational level of ecosystems. The overall diversity based on Lindeman's trophic dynamics is considered as one-dimensional diversity. By unfolding ecosystems, trophic structures and processes of ecosystems are expressed in two-dimensional space along compartment and trophic level axes. By use of the Shannon-Weaver diversity index, the overall diversity of two-dimensional distributions of standing stocks or throughflows, which are significantly different from those defined in one-dimensional space, is determined. When flows between compartments are partitioned across trophic levels we can determine the overall diversity of three-dimensional distribution of throughflows over two compartment axes and a trophic level axis. The relationships between these overall diversity indexes defined in the different dimensional spaces are formulated by use of trophic niches and trophic functions as suggested by Higashi et al. (1992). The three-dimensional diversity of throughflows fall into three parts. The first identifies the overall diversity of two-dimensional distribution along compartment and trophic level axes. The second indicates the average diversity of resources utilized in an ecosystem. The third specifies the transfer efficiency of flows in an ecosystem. The three-dimensional diversity of throughflows may support a new framework to understand trophic structures and processes. Two real ecosystems are examined through the calculation of overall diversity indexes. The results confirm the differences between diversity indexes defined in different dimensions. Out of all the diversity indexes, those related to paths (to the third-dimension) are more powerful to reveal differences in trophic structures and processes between the two ecosystems.

Institute of Hydrobiology, Jinan University, Guangzhou 510632, People's Republic of China Three measures-total residence time, total ecosystem throughput, and ratio of total standing stock to total system throughput-are investigated on the basis of an analysis of two types of structure matrices (or transitive closure matrices). The quantitative expression of total residence time given by Han (Han, B. P., 1997. Total residence time of ecosystem at steady state. Ecol. Modelling 95, 301-310) is proved to be equal to the ratio of total standing stock to total system outflow, that is, total residence time does not depend on ecosystem structure. Whereas total system throughflow is explicitly dependent on ecosystem structure, the ratio of total standing stock to total system throughflow not only depends on system structure but also on system state. Therefore, total system throughflow and the ratio of total standing stock to total system throughflow may measure ecosystem maturity or complexity. The ratio of total system throughflow to total system inflow or total system outflow is defined as the flow multiplying index instead of average path length, for the throughflow which equals the difference between total system throughput and total system inflow results from the interaction between compartments, i. e. reutilization of total system inflow. By dividing two types of structure matrices (transitive closure matrices) into cycling matrices and noncycling matrices, which correspond to first and subsequent passage flows, respectively, the contribution of cycling paths and noncycling paths to the three measures can be understood.

In this study, a 1D model of reservoir hydrodynamics DYRESM has been applied to Sau Reservoir, a river valley reservoir in the North-Eastern Spain. Simulation is undertaken for 3 years (1995-1997). Meteorological input data measured at the dam are only available from May of 1997. In this case the simulation results fit measured temperatures very well. In the remaining periods, some meteorological data (radiation, wind and rainfall) were obtained from two nearby stations. Simulated temperature distribution in 1996 is close to the observed one. In 1995, however, the simulated result is far from the observed data. Inflows, outflow and local meteorological events such as storms and gusts of wind seem to be responsible for the differences. By changing some parameters, the effects of flow, light extinction coefficient and outlet elevation on thermal stratification are investigated. Simulations demonstrate that the inflow with high temperature is the main factor controlling the thermal structure in Sau Reservoir and demonstrate that the effect of residence time on thermal stratification is manifested mainly by the changes in the depth of thermocline.