In various fields of science 'equilibrium' refers to a balance between opposing forces: positive and negative values in an equation, reactants and products in a chemical reaction, production and respiration in an ecosystem, and supply and demand in a market. An equilibrium will be stable or unstable, steady state or dynamic, depending on both the stability of the interacting forces and the control and retro-control mechanisms of the interactions. Since forces are spatially and temporally defined, equilibrium is also spatially and temporally defined, or scale dependent.

The concept of equilibrium was introduced in those fields that are now known as community and ecosystem ecology in the late nineteenth/early twentieth centuries by Stephen A. Forbes and F. E. Clements. These authors had defined ecological communities as organisms interacting with each other (i.e., predator-prey, competitor-competitor, etc.), and had described community evolution toward an ordered stage or condition, which was formalized by Clements through the climax concept. A climax was defined as a community equilibrium stage that is persistent, self-sustaining, and at which further 'change' is limited if at all possible. It has a mass balance component that is described by the thermodynamic equilibrium between gross production and respiration at the ecosystem level, and a food web stability component, which is described by the interacting population equilibrium between gains and losses of individuals at the community level. Stable or dynamic equilibrium conditions correspond to the assumption of perfect fitness equivalence among coexisting species in a certain time interval.

Numerical (or biomass) abundance and taxonomic composition are two major components of every guild and community, which, taking into account average individual body size and metabolic rates, give information on the overall energy and matter flow and on its apportionment among species. However, since the early definitions of climax and community persistency, community ecology has mainly used the term equilibrium to refer to a situation characterized by little variability in species composition over time or by the indefinite coexistence of a single species in a mixture.

Focusing on primary producers in terrestrial ecosystems, where producers are large and long-living trees, the temporal scale of the equilibrium conditions can be measured in terms ofhundreds ofyears: the primary succession established on the Lake Michigan sand dunes spans over 11 000 years. In contrast, in aquatic and deep-water ecosystems, where producers are microscopic phytoplankton species, dynamic equilibrium conditions can be described on temporal scales of days, weeks, or months.

Phytoplankton are phototrophs, able to reproduce and build up populations utilizing sources of CO2, inorganic nitrogen, sulfur and phosphorous compounds, and a number of other elements (Na, K, Mg, Ca, Si, Fe, Mn, B, Cl, Cu, Zn, Mo, Co, and V), most of which are required in small concentrations and not all of which are known to be required by all groups. In addition, several phytoplankton species are known to require vitamins, namely, thiamine, the cobalamines, and biotin.

When light is available, the processes of absorbing light and nutrients to build up biomass and reproduce are carried out at a very high rate by the small phytoplankton cells, measuring between 0.5 mm and c. 200 mm as linear dimension. In oligotrophic conditions, ranging from atoll lagoons to coastal marine and open ocean environments, phytoplankton biomass has an average turnover rate of 1.4-2.0 d_1; in eutrophic conditions phytoplankton biomass has a much higher turnover rate, up to 10 times per day in shallow, enclosed, brackish ecosystems (e.g., Mediterranean lagoon ecosystems - such as Lake Alimini Grande, Puglia, Italy).

The high turnover rate of phytoplankton cells has different implications for the equilibrium concept of phy-toplankton communities depending on whether it is applied to numerical and biomass abundance or to species interaction and community taxonomic composition. As regards numerical and/or biomass densities, a high turnover rate confers high resilience on phytoplankton communities with respect to spatial and temporal variation of those forces determining phytoplankton production, respiration, and predatory loss. Spatial and temporal patterns of numerical and/or biomass densities in phytoplankton communities are commonly observed at the ecosystem level in lake, lagoon, and marine ecosystems as a result of the equilibrium between phytoplankton requirements and both abiotic and biotic conditions. As regards taxonomic richness and species composition, a well-known tradeoff occurs between turnover rates and population stability, which also holds for phytoplankton communities. The dynamics of phytoplankton populations and the coexistence of a number of species on a limited amount of inorganic and organic resources distributed in a relatively isotropic and unstructured environment has challenged phytoplankton community ecologists over the last 50 years, representing a classic paradox of ecology: that is, the plankton paradox.

The dichotomy between (1) the balance between phytoplankton (numbers and biomass) and limiting factors and (2) the apparent lack of competitive equilibria among species has long been the subject of debate on the equilibrium concept in phytoplankton communities. The critical aspect of phytoplankton communities, which is difficult to explain in the context of the equilibrium concept, is their taxonomic richness, the number of species being much higher than the number of factors limiting phytoplankton numerical and biomass densities.

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