A probabilistic approach to estimating species pools from large compositional matrices

Abstract. Species pools are increasingly recognized as important controls of local plant community structure and diversity. While existing approaches to estimate their content and size either rely on phytosociological expert knowledge or on simple response models across environmental gradients, the proposed application of phytosociological smoothing according to Beals exploits the full information of plant co‐occurrence patterns statistically. Where numerous representative compositional data are available, the new method yields robust estimates of the potential of sites to harbour plant species. To test the new method, a large phytosociological databank covering the forested regions of Oregon (US) was subsampled randomly and evenly across strata defined by geographic regions and elevation belts. The resulting matrix of species presence/absence in 874 plots was smoothed by calculating Beals' index of sociological favourability, which estimates the probability of encountering each species at each site from the actual plot composition and the pattern of species co‐occurrence in the matrix. In a second step, the resulting lists of sociologically probable species were intersected with complete species lists for each of 14 geographical subregions. Species pools were compared to observed species composition and richness. Species pool size exhibited much clearer spatial trends than plot richness and could be modelled much better as a function of climatic factors. In this framework the goal of modelling species pools is not to test a hypothesis, but to bridge the gap between manageable scales of empirical observation and the spatio‐temporal hierarchy of diversity patterns.     

Spectral Estimation by Variable Span Log Periodogram Smoothing: An Application to Annual Lynx Numbers

Spectral estimation is commonly based on smoothing the periodogram or its logarithm. In such a smoothing exercise, it is not entirely sensible to use the same bandwidth for all frequencies, since the smoothness of the underlying spectrum may vary. This note describes the use of a variable span smoother in estimating the log spectrum. An application to annual lynx data is presented.     

Parametric and Parametrically Smoothed Distribution-Free Proportional Hazard Models with Discrete Data

This paper discusses discrete time proportional hazard models and suggests a new class of flexible hazard functions. Explicitly modeling the discreteness of data is important since standard continuous models are biased; allowing for flexibility in the hazard estimation is desirable since strong parametric restrictions are likely to be similarly misleading. Simulation compare continuous and discrete models when data are generated by grouping and demonstrate that simple approximations recover underlying hazards well and outperform nonparametric maximum likelihood estimates in term of mean squared error.     

Non‐parametric habitat models with automatic interactions

Questions: Can a statistical model be designed to represent more directly the nature of organismal response to multiple interacting factors? Can multiplicative kernel smoothers be used for this purpose? What advantages does this approach have over more traditional habitat modelling methods? Methods: Non‐parametric multiplicative regression (NPMR) was developed from the premises that: the response variable has a minimum of zero and a physiologically‐determined maximum, species respond simultaneously to multiple ecological factors, the response to any one factor is conditioned by the values of other factors, and that if any of the factors is intolerable then the response is zero. Key features of NPMR are interactive effects of predictors, no need to specify an overall model form in advance, and built‐in controls on overfitting. The effectiveness of the method is demonstrated with simulated and real data sets. Results: Empirical and theoretical relationships of species response to multiple interacting predictors can be represented effectively by multiplicative kernel smoothers. NPMR allows us to abandon simplistic assumptions about overall model form, while embracing the ecological truism that habitat factors interact.     

On partial local smoothing rules for curve estimation

We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma ‘half-way house’ between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals.