On the detection of dynamic responses in a drought-perturbed tropical rainforest in Borneo

The dynamics of aseasonal lowland dipterocarp forest in Borneo is influenced by perturbation from droughts. These events might be increasing in frequency and intensity in the future. This paper describes drought-affected dynamics between 1986 and 2001 in Sabah, Malaysia, and considers how it is possible, reliably and accurately, to measure both coarse- and fine-scale responses of the forest. Some fundamental concerns about methodology and data analysis emerge. In two plots forming 8 ha, mortality, recruitment, and stem growth rates of trees ≥10 cm gbh (girth at breast height) were measured in a ‘pre-drought’ period (1986–1996), and in a period (1996–2001) including the 1997–1998 ENSO-drought. For 2.56 ha of subplots, mortality and growth rates of small trees (10–<50 cm gbh) were found also for two sub-periods (1996–1999, 1999–2001). A total of c. 19 K trees were recorded. Mortality rate increased by 25% while both recruitment and relative growth rates increased by 12% for all trees at the coarse scale. For small trees, at the fine scale, mortality increased by 6% and 9% from pre-drought to drought and on to ‘post-drought’ sub-periods. Relative growth rates correspondingly decreased by 38% and increased by 98%. Tree size and topography interacted in a complex manner with between-plot differences. The forest appears to have been sustained by off-setting elevated tree mortality by highly resilient stem growth. This last is seen as the key integrating tree variable which links the external driver (drought causing water stress) and population dynamics recorded as mortality and recruitment. Suitably sound measurements of stem girth, leading to valid growth rates, are needed to understand and model tree dynamic responses to perturbations. The proportion of sound data, however, is in part determined by the drought itself.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.