Occurrence and abundance models of threatened plant species: Applications to mitigate the impact of hydroelectric power dams

Species occurrence and abundance models are important tools that can be used in biodiversity conservation, and can be applied to predict or plan actions needed to mitigate the environmental impacts of hydropower dams. In this study our objectives were: (i) to model the occurrence and abundance of threatened plant species, (ii) to verify the relationship between predicted occurrence and true abundance, and (iii) to assess whether models based on abundance are more effective in predicting species occurrence than those based on presence–absence data. Individual representatives of nine species were counted within 388 randomly georeferenced plots (10 m × 50 m) around the Barra Grande hydropower dam reservoir in southern Brazil. We modelled their relationship with 15 environmental variables using both occurrence (Generalised Linear Models) and abundance data (Hurdle and Zero-Inflated models). Overall, occurrence models were more accurate than abundance models. For all species, observed abundance was significantly, although not strongly, correlated with the probability of occurrence. This correlation lost significance when zero-abundance (absence) sites were excluded from analysis, but only when this entailed a substantial drop in sample size. The same occurred when analysing relationships between abundance and probability of occurrence from previously published studies on a range of different species, suggesting that future studies could potentially use probability of occurrence as an approximate indicator of abundance when the latter is not possible to obtain. This possibility might, however, depend on life history traits of the species in question, with some traits favouring a relationship between occurrence and abundance. Reconstructing species abundance patterns from occurrence could be an important tool for conservation planning and the management of threatened species, allowing scientists to indicate the best areas for collection and reintroduction of plant germplasm or choose conservation areas most likely to maintain viable populations.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.