Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics. (C) 2011 Elsevier B.V. All rights reserved.

Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

A new species of Leporinus Agassiz, 1829 from the upper Rio Paraná basin (Characiformes, Anostomidae) with redescription of L. elongatus Valenciennes, 1850 and L. obtusidens (Valenciennes, 1837)

Leporinus obtusidens Valenciennes, 1837 and L. elongatus Valenciennes, 1850 are redescribed based on the type specimens, including those of their junior synonyms, and recently collected specimens. Leporinus obtusidens is considered to be widespread, occuring in the river drainages of La Plata, São Francisco, and Parnaíba. Leporinus aguapeiensis Campos, 1945, described from the upper Rio Paraná, and L. silvestrii Boulenger, 1902, described from the Rio Paraguay, are considered junior synonyms of L. obtusidens. Leporinus elongatus is endemic to the Rio Jequitinhonha and Rio Pardo, two eastern Brazilian river basins, and the locality cited for the lectotype, Rio São Fransico, likely to be erroneous. Leporinus crassilabris Borodin, 1929, and L. crassilabris breviceps Borodin, 1929, both described from the Rio Jequitinhonha, are considered junior synynoms of L. elongatus. A new species of Leporinus, endemic to the upper Rio Paraná, very similar and sometimes mistaken with L. obtusidens, is formally described. In addition, comments on Leporinus pachyurus Valenciennes, 1850 and on L. bimaculatus Castelnau, 1855 are provided, and a lectotype for L. bimaculatus is selected.