Analytical evaluation of the plasma dispersion function for a Fermi-Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

Functional traits of tree species with phylogenetic signal co-vary with environmental niches in two large forest dynamics plots

Aims While using phylogenetic and functional approaches to test the mechanisms of community assembly,functional traits often act as the proxy of niches.However,there is little detailed knowledge regarding the correlation between functional traits of tree species and their niches in local communities.We suggest that the co-varying correlation between functional traits and niches should be the premise for using phylogenetic and functional approaches to test mechanisms of community assembly.Using functional traits,phylogenetic and environmental data,this study aims to answer the questions:(i)within local communities,do functional traits of co-occurring species covary with their environmental niches at the species level?and(ii)what is the key ecological process underlying community assembly in Xishuangbanna and Ailaoshan forest dynamic plots(FDPs)?Methods We measured seven functional traits of 229 and 36 common species in Xishuangbanna and Ailaoshan FDPs in tropical and subtropical China,respectively.We also quantified the environmental niches for these species based on conditional probability.We then analyzed the correlations between functional traits and environmental niches using phylogenetic independent contrasts.After examining phylogenetic signals of functional traits using Pagel’sλ,we quantified the phylogenetic and functional dispersion along environmental gradients within local tree communities.Important Findings For target species,functional traits do co-vary with environmental niches at the species level in both of the FDPs,supporting that functional traits can be used as a proxy for local-scale environmental niches.Functional traits show significant phylogenetic signals in both of the FDPs.We found that the phylogenetic and functional dispersion were significantly clustered along topographical gradients in the Ailaoshan FDP but overdispersion in the Xishuangbanna FDP.These patterns of phylogenetic and functional dispersion suggest that environmental filtering plays a key role in structuring local tree assemblages in Ailaoshan FDP,while competition exclusion plays a key role in Xishuangbanna FDP.