A Novel Nonparametric Density Estimator

We present a novel nonparametric density estimator and a new data-driven bandwidth selection method with excellent properties. The approach is in- spired by the principles of the generalized cross entropy method. The pro- posed density estimation procedure has numerous advantages over the tra- ditional kernel density estimator methods. Firstly, for the first time in the nonparametric literature, the proposed estimator allows for a genuine incor- poration of prior information in the density estimation procedure. Secondly, the approach provides the first data-driven bandwidth selection method that is guaranteed to provide a unique bandwidth for any data. Lastly, simulation examples suggest the proposed approach outperforms the current state of the art in nonparametric density estimation in terms of accuracy and reliability.

Marine macroalgal biodiversity hotspots: why is there high species richness and endemism in southern Australian marine benthic flora?

The southern Australian marine macroalgal flora has the highest levels of species richness and endemism of any regional macroalgal flora in the world. Analyses of species composition and distributions for the southern Australian flora have identified four different floristic elements, namely the southern Australian endemic element, the widely distributed temperate element, the tropical element and a cold water element. Within the southern Australian endemic element, four species distribution patterns are apparent, thought to largely result from the Jurassic to Oligocene fragmentation of East Gondwana, the subsequent migration of Tethyan ancestors from the west Australian coast and the later invasion of high latitude Pacific species. Climatic deterioration from the late Eocene to the present is thought responsible for the replacement of the previous tropical south coast flora by an endemic temperate flora which has subsequently diversified in response to fluctuating environmental conditions, abundant rocky substrata and substantial habitat heterogeneity. High levels of endemism are attributed to Australia's long isolation and maintained, as is the high species richness, by the lack of recent mass extinction events. The warm water Leeuwin Current has had profound influence in the region since the Eocene, flowing to disperse macroalgal species onto the south coast as well as ameliorating the local environment. It is now evident that the high species richness and endemism we now observe in the southern Australian marine macroalgal flora can be attributed to a complex interaction of biogeographical, ecological and phylogenetic processes over the last 160 million years.

Species richness in agamid lizards: chance, body size, sexual selection or ecology?

Why does species richness vary so greatly across lineages? Traditionally, variation in species richness has been attributed to deterministic processes, although it is equally plausible that it may result from purely stochastic processes. We show that, based on the best available phylogenetic hypothesis, the pattern of cladogenesis among agamid lizards is not consistent with a random model, with some lineages having more species, and others fewer species, than expected by chance. We then use phylogenetic comparative methods to test six types of deterministic explanation for variation in species richness: body size, life history, sexual selection, ecological generalism, range size and latitude. Of eight variables we tested, only sexual size dimorphism and sexual dichromatism predicted species richness. Increases in species richness are associated with increases in sexual dichromatism but reductions in sexual size dimorphism. Consistent with recent comparative studies, we find no evidence that species richness is associated with small body size or high fecundity. Equally, we find no evidence that species richness covaries with ecological generalism, latitude or range size.

Testing the link between the latitudinal gradient in species richness and rates of molecular evolution

Numerous hypotheses have been proposed to explain latitudinal gradients in species richness, but all are subject to ongoing debate. Here we examine Rohde's (1978, 1992) hypothesis, which proposes that climatic conditions at low latitudes lead to elevated rates of speciation. This hypothesis predicts that rates of molecular evolution should increase towards lower latitudes, but this prediction has never been tested. We discuss potential links between rates of molecular evolution and latitudinal diversity gradients, and present the first test of latitudinal variation in rates of molecular evolution. Using 45 phylogenetically independent, latitudinally separated pairs of bird species and higher taxa, we compare rates of evolution of two mitochondrial genes and DNA-DNA hybridization distances. We find no support for an effect of latitude on rate of molecular evolution. This result casts doubt on the generality of a key component of Rohde's hypothesis linking climate and speciation.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

The Thelastomatoidea (Nematoda : Oxyurida) of two sympatric Panesthiinae (Insecta : Blattodea) from southeastern Queensland, Australia: taxonomy, species richness and host specificity

The thelastomatoid fauna of two species of wood-burrowing cockroach (Blattodea, Blaberidae), Panesthia cribrata and Panesthia tryoni tryoni, from Lamington National Park, Australia, is described. The following eight new species and three new genera of thelastomatid are proposed: Bilobostoma exerovulva n. g., n. sp.; Cordonicola gibsoni n. sp.; Coronostoma australiae n. sp.; Desmicola ornata n. sp.; Hammerschmidtiella hochi n. sp.; Malaspinanema goateri n. g., n. sp.; Travassosinema jaidenae n. sp.; and Tsuganema cribratum n. g., n. sp. Additional data are given for Blattophila sphaerolaima and Leidynemella fusiformis. Of the 11 species reported, nine were found in P. cribrata and ten in P. tryoni tryoni. Such levels of thelastomatoid species richnessness in single host species are exceptional. Only the mole cricket, Gryllotalpa africana (23), and the domestic cockroach, Periplaneta americana (20), have higher reported richness. Three species, T jaidenae, C. australiae and D. ornata, were found either exclusively or significantly more prevalently in P tryoni tryoni than in R cribrata. Species of Travassosinema, Coronostoma and Desmicola have been found previously only in millipedes (Diplopoda), a fact that suggests that there is a greater degree of niche overlap between R tryoni tryoni and millipedes than for R cribrata.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Substructure and Dynamics of the Fornax Cluster

We present the first dynamical analysis of a galaxy cluster to include a large fraction of dwarf galaxies. Our sample of 108 Fornax Cluster members measured with the UK Schmidt Telescope FLAIR-II spectrograph contains 55 dwarf galaxies (15.5 > b(j) > 18.0 or -16 > M-B > -13.5). H alpha emission shows that of the dwarfs are star forming, twice the fraction implied by morphological classifications. The total sample has a mean velocity of 1493 +/- 36 kms s(-1) and a velocity dispersion of 374 +/- 26 km s(-1). The dwarf galaxies form a distinct population: their velocity dispersion (429 +/- 41 km s(-1)) is larger than that of the giants () at the 98% confidence level. This suggests that the dwarf population is dominated by infalling objects whereas the giants are virialized. The Fornax system has two components, the main Fornax Cluster centered on NGC 1399 with cz = 1478 km s(-1) and sigma (cz) = 370 km s(-1) and a subcluster centered 3 degrees to the southwest including NGC 1316 with cz = 1583 km s(-1) and sigma (cz) = 377 km s(-1). This partition is preferred over a single cluster at the 99% confidence level. The subcluster, a site of intense star formation, is bound to Fornax and probably infalling toward the cluster core for the first time. We discuss the implications of this substructure for distance estimates of the Fornax Cluster. We determine the cluster mass profile using the method of Diaferio, which does not assume a virialized sample. The mass within a projected radius of 1.4 Mpc is (7 +/- 2) x 10(13) M-., and the mass-to-light ratio is 300 +/- 100 M-./L-.. The mass is consistent with values derived from the projected mass virial estimator and X-ray measurements at smaller radii.

The diversity of the Digenea of Australian animals

The Digenea is one of five major helminth assemblages represented in Australian animals. History of the study of digeneans in Australia is reviewed briefly to show that it has never been subjected to the kind of sustained study needed to reach an understanding of it. The Australian vertebrate fauna comprises over 5500 species. These have so far been shown to harbour just over 70 families, about 306 genera and 566 species of digeneans. Digeneans occur in all classes of vertebrates in Australia but are distributed very unevenly; aquatic hosts are generally most heavily infected, but many terrestrial species are also infected. Particular weaknesses in knowledge of the fauna concern the bats, cetaceans and teleosts. Another weakness is in knowledge of life-cycles; representative life-cycles are known for only about 20 of the 70 families known in Australia. Estimates of the overall size of the fauna are dependent on an understanding of sampling strategies, the heterogeneity of distribution of the fauna, and the nature of host-specificity. These subjects are reviewed briefly and an estimate of the total fauna is made. There may be as many as 6000 species of digeneans in Australia. (C) 1998 Australian Society for Parasitology. Published by Elsevier Science Ltd.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.