Likelihood, entropy and species diversity; some comparisons in a Sumatran forest

In attempts to conserve the species diversity of trees in tropical forests, monitoring of diversity in inventories is essential. For effective monitoring it is crucial to be able to make meaningful comparisons between different regions, or comparisons of the diversity of a region at different times. Many species diversity measures have been defined, including the well-known abundance and entropy measures. All such measures share a number of problems in their effective practical use. However, probably the most problematic is that they cannot be used to meaningfully assess changes, since thay are only concerned with the number of species or the proportions of the population/sample which they constitute. A natural (though simplistic) model of a species frequency distribution is the multinomial distribution. It is shown that the likelihood analysis of samples from such a distribution are closely related to a number of entropy-type measures of diversity. Hence a comparison of the species distribution on two plots, using the multinomial model and likelihood methods, leads to generalised cross-entropy as the LRT test statistic of the null that the species distributions are the same. Data from 30 contiguous plots in a forest in Sumatra are analysed using these methods. Significance tests between all pairs of plots yield extremely low p-values, indicating strongly that it ought to been "Obvious" that the observed species distributions are different on different plots. In terms of how different the plots are, and how these differences vary over the whole study site, a display of the degrees of freedom of the test, (equivalent to the number of shared species) seems to be the most revealing indicator, as well as the simplest.

Vibrational spectroscopy and crystal structure analysis of two polymorphs of the di-amino acid peptide cyclo(L-Glu-L-Glu)

Cyclo(L-Glu-L-Glu) has been crystallised in two different polymorphic forms. Both polymorphs are monoclinic, but form 1 is in space group P21 and form 2 is in space group C2. Raman scattering and FT-IR spectroscopic studies have been conducted for the N,O-protonated and deuterated derivatives. Raman spectra of orientated single crystals, solid-state and aqueous solution samples have also been recorded. The different hydrogen-bonding patterns for the two polymorphs have the greatest effect on vibrational modes with N&bond;H and C&dbond;O stretching character. DFT (B3-LYP/cc-pVDZ) calculations of the isolated cyclo(L-Glu-L-Glu) molecule predict that the minimum energy structure, assuming C2 symmetry, has a boat conformation for the diketopiperazine ring with the two L-Glu side chains being folded above the ring. The calculated geometry is in good agreement with the X-ray crystallographic structures for both polymorphs. Normal coordinate analysis has facilitated the band assignments for the experimental vibrational spectra. Copyright © 2009 John Wiley & Sons, Ltd.