The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Isolation and characterization of nine microsatellite loci from the Hawaiian grouper Epinephelus quernus (Serranidae) for population genetic analyses

The availability of variable genetic markers for groupers (Serranidae) has generally been limited to mitochondrial DNA. For studies of population genetic structure, more loci are usually required; particularly useful are those that are nuclear in origin such as microsatellites. Here, we isolated and characterized 9 microsatellite loci from the endemic Hawaiian grouper Epinephelus quernus using a biotin-labeled oligonucleotide-streptavidin-coated magnetic bead approach. Of the 20 repeat-containing fragments isolated, 15 had sufficient flanking region in which to design primers. Among these, 9 produced consistent polymerase chain reaction product, and 6 were highly variable. These 6 loci were all composed of dinucleotide repeats, with the number of alleles ranging from 6 to 18, and heterozygosities from 33.3% to 91.7%. The high levels of variability observed should make these markers useful for population genetic studies of E. quernus, and potentially other epinephelines.

The effect of a triclosan-containing dentifrice on the progression of periodontal disease in an adult population

Objectives: The aim of the present study was to determine the effect of unsupervised, long-term use of a 0.3% triclosan/2% copolymer dentifrice on the progression of periodontal disease in a general adult population. Methods: Five hundred and four volunteers were enrolled in a double-blind, controlled clinical trial. Participants were matched for disease status, plaque index, age and gender. At the baseline examination, probing pocket depths and relative attachment levels were recorded and participants were assigned to either the test or control group. Re-examinations took place after 6, 12, 24, 36, 48 and 60 months. Subgingival plaque samples were collected at each examination and assayed for Porphyromonas gingivalis , Actinobacillus actinomycetemcomitans and Prevotella intermedia . A generalised linear model was used to analyse the data, with a number of covariates thought to influence the responses included as the possible confounding effects. Results: The triclosan/copolymer dentifrice had a significant effect in subjects with interproximal probing depths greater than or equal to3.5 mm, where it significantly reduced the number of sites with probing depths greater than or equal to3.5 mm at the following examination, when compared with the control group (p

Single-nucleotide polymorphism in the CD14 promoter and periodontal disease expression in a Japanese population

It has been reported that there is a relationship between a single-nucleotide polymorphism (SNP) in the promoter region of the CD 14 gene at position -159 (C-->T) and infectious diseases. The aim of the present study was to test the hypthesis that expression of this SNP correlates with periodontal disease in a Japanese population. The CD14 genotype was determined in 163 subjects with periodontitis and in 104 age- and gender-matched control subjects without periodontitis. The genotype distribution and allele frequency within the periodontitis patients were not significantly different from those of control subjects. There was, however, a significant difference in the genotype distribution between young patients (< 35 yrs) and older patients (greater than or equal to 35 yrs). These findings suggest that CD14-159C/T polymorphism is not related to the development of periodontitis in a Japanese population, but that, within the periodontitis subjects, expression of the SNP may be related to early disease activity.

Quantitative trait loci for agronomic and seed quality traits in an F-2 and F-4 : 6 soybean population

Molecular breeding is becoming more practical as better technology emerges. The use of molecular markers in plant breeding for indirect selection of important traits can favorably impact breeding efficiency. The purpose of this research is to identify quantitative trait loci (QTL) on molecular linkage groups (MLG) which are associated with seed protein concentration, seed oil concentration, seed size, plant height, lodging, and maturity, in a population from a cross between the soybean cultivars 'Essex' and 'Williams.' DNA was extracted from F-2 generation soybean leaves and amplified via polymerase chain reaction (PCR) using simple sequence repeat (SSR) markers. Markers that were polymorphic between the parents were analyzed against phenotypic trait data from the F-2 and F-4:6 generation. For the F-2 population, significant additive QTL were Satt540 (MLG M, maturity, r(2)=0.11; height, r(2)=0.04, seed size, r(2)=0.061, Satt373 (MLG L, seed size, r(2)=0.04; height, r(2)=0.14), Satt50 (MLG A1, maturity r(2)=0.07), Satt14 (MLG D2, oil, r(2)=0.05), and Satt251 (protein r(2)=0.03, oil, r(2)=0.04). Significant dominant QTL for the F-2 population were Satt540 (MLG M, height, r(2)=0.04; seed size, r(2)=0.06) and Satt14 (MLG D2, oil, r(2)=0.05). In the F-4:6 generation significant additive QTL were Satt239 (MLG I, height, r(2)=0.02 at Knoxville, TN and r(2)=0.03 at Springfield, TN), Satt14 (MLG D2, seed size, r(2)=0.14 at Knoxville, TN), Satt373 (MLG L, protein, r(2)=0.04 at Knoxville, TN) and Satt251 (MLG B I, lodging r(2)=0.04 at Springfield, TN). Averaged over both environments in the F-4:6 generation, significant additive QTL were identified as Satt251 (MLG B 1, protein, r(2)=0.03), and Satt239 (MLG 1, height, r(2)=0.03). The results found in this study indicate that selections based solely on these QTL would produce limited gains (based on low r(2) values). Few QTL were detected to be stable across environments. Further research to identify stable QTL over environments is needed to make marker-assisted approaches more widely adopted by soybean breeders.

Dispersal patterns in a regional koala population in south-east Queensland

Koala dispersal was investigated as part of a detailed ecological study of a nationally significant koala population located 20 km south-east of Brisbane, Queensland. From 1996 to 2000, 195 koalas from three sites were captured and fitted with radio-collars. A total of 40 koalas ( 23 males and 17 females) dispersed from these sites. Most (93%) dispersing individuals were 20 - 36 months of age. Three adult females ( more than 36 months old) dispersed and no adult males dispersed during the study. A significantly higher proportion of young males dispersed than females. Dispersal occurred between June and December, with most dispersal of males commencing in July and August and that of females commencing between September and November prior to, and early in, the annual breeding season. The mean straight-line distance between the natal and breeding home ranges for males and females was similar and was measured at 3.5 km ( range 1.1 - 9.7 km) and 3.4 km ( range 0.3 - 10.6 km) respectively. Dispersing males and females tended to successfully disperse south and west of their natal home ranges and were generally unable to successfully disperse to urban areas within the study area, as a high proportion of the mortality of dispersing koalas was associated with attacks by domestic dogs and with collisions with vehicles on roads. Information from other studies indicates that most young koalas disperse from their natal areas. It is likely that the social behaviour and mating systems of koala populations provide mechanisms for young koalas to disperse. The potential role of dispersal in the dynamics of regional koala populations is discussed.

Genetic structure of a population of Ganoderma boninense on oil palm

Ganoderma boninense (the causal agent of basal stem rot of oil palm in Papua New Guinea) has a tetrapolar mating system with multiple alleles. Investigations into the population structure of G. boninense, using interfertility between isolates as a marker, revealed that the population on oil palm was comprised predominantly of genetically distinct individuals, although a number of isolates were found to share single mating alleles. No direct hereditary relationship was found between isolates on neighbouring or spatially separated diseased palms, indicating that outcrossing had probably occurred over several generations in the founder population prior to colonization of oil palm. In this study, a total of 81 A and 83 B mating type alleles (factors) were detected with 18 allelic repeats at the A locus and 17 at the B locus. Alleles appeared to be randomly dispersed throughout the population in each study block, although there was a significantly (P

Indirect evidence of density-dependent population regulation in Aponomma hydrosauri (Acari : Ixodidae), an ectoparasite of reptiles

The extent to which density-dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density-dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long-term dataset on the distribution of ticks among individual hosts. If density-dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host-parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re-analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density-dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population-scale increase in the aggregation coefficient is indirect evidence of a density-dependent process or processes sufficiently strong to produce a population-wide pattern, and thus also likely to influence population regulation. The direct observation of a density-dependent process is evidence of at least part of the responsible mechanism.

Oceanic interchange and nonequilibrium population structure in the estuarine dependent Indo-Pacific tasselfish, Polynemus sheridani

We assayed mtDNA haplotype [300 base pairs (bp) control region] geography and genealogy in the Indo-Pacific tasselfish, Polynemus sheridani from its contiguous estuarine distribution across northern Australia (n = 169). Eight estuaries were sampled from three oceanographic regions (Timor Sea, Gulf of Carpentaria and the Coral Sea) to assess the impact of Pleistocene sea level changes on the historical connectivity among P. sheridani populations. Specifically, we investigated the genetic consequences of disruption to Indian-Pacific Ocean connectivity brought about by the closure of the Torres Strait. Overall there was significant population subdivision among estuaries (F-ST = 0.161, (Phi(ST) = 0.187). Despite a linear distribution, P. sheridani did not show isolation by distance over the entire sampled range because of genetic similarity of estuaries greater than 3000 km apart. However, significant isolation by distance was detected between estuaries separated by less than 3000 km of coastline. Unlike many genetic studies of Indo-Pacific marine species, there was no evidence for an historical division between eastern and western populations. Instead, phylogeographical patterns were dominated by a starlike intraspecific phylogeny coupled with evidence for population expansion in both the Gulf of Carpentaria and the Coral Sea but not the Timor Sea. This was interpreted as evidence for recent west to east recolonization across of northern Australia following the last postglacial marine advance. We argue that although sufficient time has elapsed postcolonization for populations to approach gene flow-drift equilibrium over smaller spatial scales (< 3000 km), the signal of historical colonization persists to obscure the expected equilibrium pattern of isolation by distance over large spatial scales (> 3000 km).

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Ocular melanoma is not associated with CDKN2A or MC1R variants - a population-based study

Germline variants in the melanocortin 1 receptor gene (MC1R) and the p16 gene (CDKN2A) are associated with an increased risk of cutaneous melanoma. The frequency of these germline variants was examined in a population-based, incident series of 62 ocular melanoma cases and ethnicity-matched population controls. In both cases and controls, 59% of individuals carried at least one MC1R variant and there were no significant differences in the frequency of any of the five most common variants of MC1R. We also found no significant differences between cases and controls in the frequency of any of the four most common variants of CDKN2A, and no melanoma case carried a deleterious germline CDKN2A mutation. Our findings argue against an important predisposing effect of the MC1R and CDKN2A genes for ocular melanoma.

Chromosomal gains and losses in ocular melanoma detected by comparative genomic hybridization in an Australian population-based study

To define the location of potential oncogenes and tumor suppressor genes in ocular melanoma we carried out comparative genomic hybridization (CGH) analysis on a population-based series of 25 formalin-fixed, paraffin-embedded primary tumors comprising 17 choroidal, 2 ciliary body, 4 iris, and 2 conjunctival melanomas. Twelve (48%) of the 25 melanomas showed no chromosomal changes and 13 (52%) had at least one chromosomal gain or loss. The mean number of CGH changes in all tumors was 3.3, with similar mean numbers of chromosomal gains (1.5) and losses (1.8). The highest number of chromosomal changes (i.e., nine) occurred in a conjunctival melanoma and included four changes not observed in tumors at any other ocular site (gains in 22q and 11p and losses in 6p and 17p). The most frequent gains in all primary ocular melanomas were on chromosome arm 8q (69%), 6p (31%) and 8p (23%) and the most frequent losses were on 6q (38%), 10q (23%), and 16q (23%). The most common pairing was gain in 8p and gain in 8q, implying a whole chromosome copy number increase; gains in 8p occurred only in conjunction with gains in 8q. The smallest regions of copy number alteration were mapped to gain of 8q21 and loss of 6q21, 10q21, and 16q22. Sublocalization of these chromosomal changes to single-band resolution should accelerate the identification of genes involved in the genesis of ocular melanoma.