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A procedure is developed for obtaining approximate thermodynamic properties of statistical models, based on a well known variational principle for the free energy. The procedure involves the choice of a suitable parametrized trial Hamiltonian which contains some elementary interactions. The free trial Hamiltonian leads to the usual mean-field approximation. When the trial Hamiltonian includes a certain number of pair interactions only, the results are regained of the constant-coupling approximation for the Ising model if the number of interacting pairs is conveniently chosen b y a comparison with the first few terms of the exact high-temperature expansion. This procedure is simpler than existing approximations and can be easily generalized. Besides treating the Ising model, some applications are presented to the spin-l/2 antiferromagnetic Heisenberg model, and to the spin-1 Heisenberg model with uniaxial anisotropy.

1. Streams in the seasonal wet and dry tropics have highly dynamic discharge regimes. Our study stream, located in mid‐western Brazil, drains into the Pantanal, South America’s largest wetlands, and is characterized by frequent spates in the rainy season and several weeks of interrupted flow in the dry season. 2. In order to understand how these seasonal flow patterns influence the aquatic fauna, floating litter was studied because: (i) this habitat is exposed to the current, and thus is likely to be most affected abiotically and biotically by changes in flow; and (ii) this habitat is abundant in unaltered tropical streams. Studies were conducted in a third‐ and a fourth‐order reach. Mayflies were chosen as study organisms because they were frequent and species‐rich on floating litter, and because they should to be responsive to changes in current velocity. 3. In the course of 15 months, covering one rainy and two dry seasons, mayflies showed pronounced seasonal patterns at family and genus level, which were evidently driven by discharge. Two periods of high mayfly densities were observed in the course of one year. One maximum coincided with the peak of the rainy season, the other with the peak of the dry season, and both were distinct in faunistic composition. At high current velocities the leptophlebiid Farrodes sp. was dominant and Leptohyphes sp., Acerpenna sp. and Paracloeodes sp. were frequent. In the dry season, when the river was reduced to isolated standing waters, 86–93% of all mayflies were Caenis sp. 4. Altogether sixteen mayfly genera from the families Baetidae, Caenidae, Leptohyphidae, Leptophlebiidae and Oligoneuriidae were recorded. Two genera are new to science, the baetid Aturbina was recently described (among others, from material from our study river), Acerpenna and Paracloeodes are new records for South America, and Miroculis and Terpides are recorded for the first time south of the Amazon.