Based on a model of light lindted growth, Huisman and Weissing found that in a well mixed water column with constant light supply (energy reaching the water surface), equilibrium growth and competition of phytoplankton for light can be characterised by a critical light intensity at the base of the colunm (I*out). The present study attempts to give a further insight into this model. We first analyse the dependence of the critical light intensity on four parameters: initial slope of the photosynthesis-inntensity (p-I) curve, maxinaal photosynthetic rate, the light-saturated parameter Ik and specific carbon loss rate. Increases in the first two parameters tend to reduce the critical light intensity and increases in the last two tend to increase the critical light intensity. Then we analyse the performance of the model under variable light supply with a time-scale of 1 day (24hr). Within this time-scale, the critical light intensity changes with time. However, the equilibrium growth and the outcome of competition for light can be adequately characterised by critical light extinction defined as the upper lindt of total light extinction due to both biomass and non-living matter in the water column. Under constant light supply, a critical light intensity uniquely corresponds to a critical light extinction. Therefore, critical light extinction can be utilised to predict the equilibrimn growth and the outcome of competition under both constant and variable light supply. By changing the maximal light supply at noon, seasonal succession of species composition of conmmnities is investigated. The possible effect of two typical photoresponses, photoadaptation and photoinhibition, on growth and competition are discussed.

A mechanistic model is developed to present the photosynthetic response of phytoplankton to irradiance at the physiological level. The model is operated on photosynthetic units (PSU), and each PSU is assumed to have two states: reactive and activated. Light absorption that drives a reactive PSU into the activated state results from the e!ective absorption of the PSU. Transitions between the two states are asymmetrical in rate. A PSU in the reactive state becomes activated much faster than it recovers from the activated state to the reactive one. The turnover time for an activated PSU to transit into the reactive one is defined by the turnover time of the electron transport chain. The present model yields a photosynthesis-irradiance curve (PE-curve) in a hyperbola, which is described by three physiological parameters: effective cross-section (σPSII), turnover time of electron transport chain (τ) and number of PSUs (N). The PE-curve has an initial slope of σpus×N, a half-saturated irradiance of 1/(τσPSII), and a maximal photosynthetic rate of τN/at the saturated irradiance. The PE-curve from the present model is comparable to the empirical function based on the target theory described by the Poisson distribution.

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.

We explore control mechanisms underlying the vertical migration of zooplankton in the water column under the predator-avoidance hypothesis. Two groups of assumptions in which the organisms are assumed to migrate vertically in order to minimize realized or effective predation pressure (type-I) and to minimize changes in realized or e!ective predation pressure (type-II), respectively, are investigated. Realized predation pressure is defined as the product of light intensity and relative predation abundance and the part of realized predation pressure that really affects organisms is termed as effective predation pressure. Although both types of assumptions can lead to the migration of zooplankton to avoid the mortality from predators, only the mechanisms based on type-II assumptions permit zooplankton to undergo a normal diel vertical migration (morning descent and evening ascent). The assumption of minimizing changes in realized predation pressure is based on consideration of DVM induction only by light intensity and predators. The assumption of minimizing changes in effective predation pressure takes into account, apart from light and predators also the effects of food and temperature. The latter assumption results in the same expression of migration velocity as the former one when both food and temperature are constant over water depth. A significant characteristic of the two type-II assumptions is that the relative change in light intensity plays a primary role in determining the migration velocity. The photoresponse is modified by other environmental variables: predation pressure, food and temperature. Both light and predation pressure are necessary for organisms to undertake DVM. We analyse the effect of each single variable. The modification of the phototaxis of migratory organisms depends on the vertical distribution of these variables.