bluuebunny/crossref_metadata_2025 huggingface dataset:
Recircumscription of theLecythidaceae
Authors: Morton Cynthia M. , Prance Ghillean T. , Mori Scott A. , Thorburn Lucy G.
Published: April 2006

Morton, C. M., Prance, G. T., Mori, S. A. & Thorburn, L. G. : Recircumscription of theLecythidaceae.– Taxon 47: 817‐827. 1998. – ISSN 0040‐0262.

The phylogenetic relationships of the genera ofLecythidaceaeand representatives ofScytopetalaceaewere assessed using cladistic analysis of both molecular (rbcL andtrnL sequences) and morphological data. The results show that the pantropical familyLecythidaceaeis paraphyletic. Support was found for the monophyly of three of the four subfamilies:Lecythidoideae, Planehonioideae,andFoetidioideae.The fourth subfamily,Napoleonaeoideae,was found to be paraphyletic, with members of theScytopetalaceaebeing nested within it forming a strong clade withAsteranthos.Both families share a number of morphological features, including several distinct characters such as cortical bundles in the stem. The combined analysis produced three trees of 471 steps and consistency index CI = 0.71 and retention index RI = 0.70.Asteranthosand members ofScytopetalaceaeshould be treated as a subfamily ofLecythidaceae,whileNapoleonaeaandCrateranthus(the latter based solely on morphological features) should remain in the subfamilyNapoleonaeoideae.TheLecythidaceaeare recircumscribed, andAsteranthosand members ofScytopetalaceaeare included inScytopetaloideae.A formal taxonomic synopsis accommodating this new circumscription is presented.
Aucher‐Eloy's plant specimens from the Immamat of Muscat
Authors: Ghazanfar Shahina A.
Published: April 2006

Ghazanfar, S. A.: Aucher‐Eloy's plant specimens from the Immamat of Muscat. – Taxon 45: 609‐626. 1996. – ISSN 0040‐0262.

Aucher‐Eloy was the first to make a comprehensive collection of plants from northern Oman (then called the Immamat of Muscat). He collected mainly in the northern mountains and foothills during March and April 1838. These as well as his other collections from the Orient served as one of the main sources of information for Boissier's Flora orientalis, still a standard reference work for the flora of south‐west Asia. Aucher‐Eloy's collection from Oman is listed here insofar as specimens have been located in the herbaria at Paris, Geneva, and Kew. Identifications of the 143 species thus listed are revised. Collecting locations and a complete itinerary are reconstructed with the help of Aucher‐Eloy's published journal and his unpublished field note‐book (at the Muséum national d'Histoire naturelle, Paris).
Adapted to the rain forest floor: a remarkable new dwarfCoffea (Rubiaceae)from Lower Guinea (tropical Africa)
Authors: Stoffelen Piet , Robbrecht Elmar , Smets Erik
Published: April 2006

Stoffelen, P., Robbrecht, E. & Smets, E.: Adapted to the rain forest floor: a remarkable new dwarfCoffea (Rubiaceae)from Lower Guinea (tropical Africa). – Taxon 46: 37‐47. 1997. – ISSN 0040‐0262.

On the occasion of a taxonomic revision of western and central African herbarium material ofCoffea, a new Lower Guinean species was discovered in the unnamed material. It is here described and namedC. magnistipula.Several unusual features are discussed. The species is a monocaulous woody dwarf, such as one otherCoffeaspecies, the Upper GuineanC. humilis, but is peculiar in having adventitious roots on the stem and very large stipules which with the leaf‐bases form debris‐collecting cups. These adaptations presumably allow extra uptake of water and nutrients. As usual inCoffea, the calyx is reduced; inC. magnistipula, it is ‘replaced’ by a well developed bracteolar calyculus, resulting in a flower with a ‘pseudo‐superior’ ovary.C. magnistipulahas a distribution which is micro‐disjunct; it occurs in three postulated Ice Age refuge areas of the tropical African rain forest, viz. the Crystal Mountains and the Chaillu Massif in Gabon and the South Cameroon Plateau.
Arsenal for survival: secondary plant products
Authors: Harborne Jeffrey B.
Published: April 2006

Harborne, J. B.: Arsenal for survival: secondary plant products. ‐ Taxon 49: 435–449. 2000.‐ISSN 0040‐0262.

The rise and fall over the first fifty years of plant chemosystematics, employing secondary products, is outlined here. The retention of some degree of activity in this field is recommended, especially with the flavonoids that are of universal occurrence. This is not only to further refine systems of plant classification below the family level, but also to map the still largely uncharted territory of bioactive metabolites in plants. Almost every plant species has a unique collection of secondary constituents distributed throughout its tissues, a proportion of which is likely to respond positively to an appropriate medical bioassay. The success of the chemosystematic approach to the search for a renewable source of taxol, the anti‐cancer drug from Taxus brevifolia, is described.
Cytology and cytogenetics as a fundamental taxonomic resource for the 20th and 21st centuries
Authors: Stace Clive A.
Published: April 2006

Stace, C. A.: Cytology and cytogenetics as a fundamental taxonomic resource for the 20th and 21st centuries. ‐ Taxon 49: 451–477. 2000. ‐ ISSN 0040‐0262.

The status of cytological and cytogenetic data as evidence of value in taxonomic decisionmaking and biosystematic investigations over the past 50 years is surveyed. The main headings considered are chromosome number, genome size, chromosome morphology, chromosome staining characteristics, chromosome and genome disposition in the cell, and chromosome behaviour and homology. The main conclusions are that many of the exciting new developments at the borders of cytogenetics and molecular biology (molecular cytogenetics) are producing a wealth of new data of enormous taxonomic and evolutionary importance, but that for these to reach their full impact it is essential that they are fully integrated with traditional cytological data, the need for which remains as great as ever.
Lectotypification of names of Linnaean species of Scorzonera and Geropogon (Compositae, Lactuceae)
Authors: de la Guardia C. Díaz , Blanca G.
Published: April 2006

Díaz de la Guardia, C. & Blanca, G.: Lectotypification of names of Linnaean species of Scorzonera and Geropogon (Compositae, Lactuceae). – Taxon 46: 759‐762. 1997. – ISSN 0040‐0262.

Lectotypes are designated for Scorzonera hirsuta, S. purpurea, S. tomentosa, Leontodon lanatus [currently S. lanata], and Geropogon hirsutus.
Evolution and the genetic analysis of populations: 1950–2000
Authors: Bachmann Konrad
Published: April 2006

Bachmann, K.: Evolution and the genetic analysis of populations: 1950–2000. – Taxon 50: 7–45. 2001. – ISSN 0040–0262.

Population genetics had played a key role in the fusion of Mendelian genetics and Darwinian natural selection into the Synthetic Theory of Evolution. The realization that all basic processes of evolution occur in or among populations suggested that evolutionary processes at all levels could be extrapolated from observations on living populations. In plants, an active tradition in ecological genetics had prepared the ground for the Synthesis, and the new initiative of “biosystematics” made full use of experimental and analytical techniques for systematics, especially at the level of species. This development got caught up in the “hardening of the Synthesis”, the defensive persistence on a simplified core theory in the face of challenges from known facts and new discoveries, especially in molecular genetics. Enzyme electrophoresis was the first molecular method to be introduced into population biology. The new results revealed unexpectedly high levels of variation within populations and precipitated discussion about the selective neutrality of protein polymorphisms. This discussion distracted attention from the population genetic basis of organismic evolution. Together with the widespread adoption of molecular marker methods at the expense of other approaches, population genetics was in danger of losing its central relevance and its variety of experimental approaches. Since the end of the 1970s, calls for new initiatives have drawn attention to the importance of historical contingency in evolution, especially in the form of developmental constraints. A population genetic application of these ideas initially faced immense technical problems. A succession of new molecular marker systems suitable for the genetic analysis of populations added new resolving power, but introduced new problems with the inference of processes from basically static and descriptive data. Only very recently, methods have advanced to the point that molecular markers can help in the experimental analysis of morphological and physiological evolution. The coming challenge will be to adapt results from detailed analyses of individual plants to broadly comparative population genetic studies. The accumulated new insights of the last 50 years show that the pervasive influence of historical contingency has non–trivial consequences for evolutionary biology and taxonomy. These are strikingly exemplified by a completely changed picture of genome structure and evolution. The time seems to be right for a paradigm shift in evolutionary biology.
The biological reality of species: gene flow, selection, and collective evolution
Authors: Rieseberg Loren H. , Burke John M.
Published: April 2006

Rieseberg, L. H. & Burke, J. M.: The biological reality of species: gene flow, selection, and collective evolution. – Taxon 50: 47–67. – ISSN 0040–0262.

Some authors have claimed that species are passive end products of evolution and thus not substantially different than higher taxa. This claim is based on reports that (1) levels of intraspecific gene flow may be too low to account for species' integration, and (2) populations are likely to diverge rather than evolve in parallel when exposed to uniform selection pressures. These conclusions are premature. A review of the plant literature reveals that there is sufficient gene flow to enable the efficient spread of strongly favourable alleles (s> 0.05), the most likely agents of collective evolution. Moreover, estimates ofsfor major quantitative trait loci (QTLs) are sufficiently large to enable their spread across the range of a species, although minor QTLs seem more likely to evolve locally. In addition, evidence that intraspecific variation in genetic background affects the response of alleles to selection is rare, but examples of parallel genotypic evolution are becoming increasingly common. We conclude that, as traditionally believed, species are the most inclusive entities that directly participate in evolutionary processes. However, we also note that the traditional role of gene flow as a force that constrains differentiation due to genetic drift or local adaptation has been over‐emphasised relative to its creative role as a mechanism for the spread of advantageous mutations.
50 years of plant speciation
Authors: Levin Donald A.
Published: April 2006

Levin, D. A.: 50 years of plant speciation. – Taxon 50: 69–91. 2001. – ISSN 0040‐0262.

During the past fifty years our understanding of plant speciation has exploded due to the application of molecular techniques and to creative thinking and ingenious experiments. Some of the major advances regarding adaptive radiation, the lability of ecologically relevant traits, genetical and chromosomal changes associated with speciation, the tempo of speciation, recombinational speciation, and the geography of speciation are reviewed. It is apparent that the process of speciation may, but need not be, dependent on a small number of genetic and/or chromosomal changes and that speciation may occur rapidly, even without polyploidy. Speciation likely is a local phenomenon most likely involving a few local populations or a metapopulation. Polyploid taxa are dynamic entities, often by virtue of multiple origins and intragenome changes and intergenome rearrangements. The rate of evolution remains one of the most untractable issues.
Natural hybridisation and fitness
Authors: Arnold Michael L. , Kentner Edward K. , Johnston Jill A. , Cornman Scott , Bouck Amy C.
Published: April 2006

Arnold, M. L., Kentner, E. K., Johnston, J. A., Cornman, S. & Bouck, A. C.: Natural hybridisation and fitness. – Taxon 50: 93–104. 2001. – ISSN 0040‐0262.

There are several inferences that can be made from studies of the fitness of hybrid plants and animals. First, the fitness of hybrids varies. However, it is not possible to make a priori predictions concerning the relative fitness of a given hybrid genotype, or a series of genotypes. For example, plant hybrids are not more likely to have elevated fitness than animal hybrids. The variation in fitness for hybrids ranges from the highest fitness relative to parental genotypes to the lowest. The variation can be due to different environments or age classes. Furthermore, notwithstanding the paradigm that derived from the Neo‐Darwinian synthesis, some hybrid genotypes demonstrate elevated fitness relative to their parents.

To test the evolutionary importance of hybridisation in a given species complex, it is critical that findings from greenhouse/population cage experiments be tested in the field. This latter statement is easier for a botanist to argue, but even with plants, the field experimentation needed for a rigorous test of fitness (i.e., reciprocal transplants) is at the best risky, and costly in time and resources. Yet, these are the types of studies needed to test predictions concerning the likeliest circumstances under which hybridisation will be promoted.

The scientific literature over the past decade has seen a change in the tenor of papers describing natural hybridisation. Ten years ago, papers more often than not reported the use of natural hybridisation as a tool to understand divergent evolution. More recently, a majority of studies have discussed the evolutionary impact of natural hybridisation. We look forward to a continued increase in the frequency of studies that assume this process to have evolutionary importance per se.
Vestured pits: their occurrence and systematic importance in eudicots
Authors: Jansen Steven , Baas Pieter , Smets Erik
Published: April 2006

Jansen, S., Baas, P. & Smets, E.: Vestured pits: their occurrence and systematic importance in eudicots. – Taxon 50: 135–167. 2001. – ISSN 0040–0262.

The distribution of vestured pits in secondary xylem reveals interesting patterns that may bear on hypotheses of phylogenetic relationships within eudicots. Vestured pits are found to be relatively widespread at the base of the eurosids I, eurosids II, and euasterids I, but the feature probably has been lost or originated independently in several more derived branches of these clades. Vestured pits characterise ordersMyrtalesandGentianalessensu APG; other large monophyletic taxa that consistently show vestured pits includeMalpighiaceae, Polygonaceae, Brassicaceae,and mostFabaceae.Representatives from euasterids II always show nonvestured pits. The occurrence of the character implies numerous parallel origins in the following divergent, major taxa: (1)Proteaceae,(2)Polygonaceae(Caryophyllales), (3) eurosids I (Zygophyllaceae, Fabales,very fewRosales, Malpighiales), (4) eurosids II (Myrtales, Malvales, Brassicales), and (5) euasterids I (Gentianales, Lamiales, Solanales). It is demonstrated that vestured pits frequently support results from DNA data.
New hypotheses of phylogenetic relationships in Barnadesioideae (Asteraceae) based on morphology
Authors: Urtubey Estrella , Stuessy Tod F.
Published: April 2006

Urtubey, E. & Stuessy, T. F.: New hypotheses of phylogenetic relationships in Barnadesioideae (Asteraceae) based on morphology. ‐ Taxon 50: 1043–1066. 2001. — ISSN 0040–0262.

Previous molecular sequence and restriction site data have confirmed subfamily Barnadesioideae as basal within Asteraceae. The subfamily consists of 88 species in nine genera: Arnaldoa, Barnadesia, Chuquiraga, Dasyphyllum, Doniophyton, Duseniella, Fulcaldea, Huarpea, and Schlechtendalia. Two morphological cladistic analyses among genera or subgeneric groups within this subfamily have been completed previously, with contrasting results. Because of the importance of understanding relationships in this group of early Asteraceae, especially for insights on character evolution within the family, comprehensive morphological cladistic analyses were conducted at the specific level. Initial investigations utilising 31 characters with all 88 species led eventually to curtailed studies with 52 species. Five different outgroup hypotheses were employed: Acicarpha laxa, A. spathulata, Calycera leucanthema, C. spinulosa (all Calyceraceae), and Schlechtendalia luzulaefolia (Barnadesioideae; as functional outgroup). The results confirm Schlechtendalia as basal within Barnadesioideae. Monophyly is also confirmed for all genera, sections Chuquiraga and Acanthophyllae of Chuquiraga, and subgenus Archidasyphyllum of Dasyphyllum. All cladograms show two major groups (although statistical support values are low): (1) Chuquiraga, Doniophyton and Duseniella; and (2) Arnaldoa, Dasyphyllum, Fulcaldea, Huarpea and Barnadesia. Although bilabiate (4+1) corollas occur in Schlechtendalia, tubular corollas are believed plesiomorphic for the subfamily because they are pervasive in Calyceraceae as well as in all other basal Barnadesioideae. Pollen with no shallow depressions also are hypothesised as plesiomorphic for Barnadesioideae, even though one depression occurs in Schlechtendalia. A southern South American origin of Barnadesioideae (and the entire family) is re‐emphasised. The previously hypothesised ancient lineage of Dasyphyllum subg. Archidasyphyllum, consisting of large trees, appears more derived in the new analyses.
Entodon challengeri (Paris) Cardot, the correct name for E. compress us sensu Mizushima and Cru m and Anderson
Authors: Iwatsuki Zennoske , Tan Benito C.
Published: April 2006

Iwatsuki, Z. & Tan, B. C: Entodon challengeri (Paris) Cardot, the correct name for E. compressus sensu Mizushima and Crum and Anderson. ‐ Taxon 50: 1125–1128. 2001. – ISSN 0040–0262.

Entodon challengeri (Paris) Cardot is demonstrated to be the correct name for the taxon called E. compressus Müll. Hal. by Mizushima and by Crum and Anderson in their revisions and floristic account, respectively. Although validly published, Entodon compressus Müll. Hal. ex Cardot (1899) is shown to be an illegitimate later homonym of E. compressus (Hedw.) Müll. Hal. (1845), itself a synonym of Entodon cladorrhizans (Hedw.) Müll. Hal. (1845).
Lisianthius perkinsiae, a new name for Lisianthius acuminatus Perkins (Gentianaceae: Potalieae)
Authors: Struwe Lena , Weaver Richard E.
Published: April 2006

Struwe, L. & Weaver, R. E.; Lisianthius perkinsiae, a new name for Lisianthius acuminatus Perkins (Gentianaceae: Potalieae). – Taxon 50: 1161–1162. 2001. ‐ ISSN 0040–0262.

Lisianthius acuminatus Perkins from Veracruz, Mexico is a later homonym of Lisianthius acuminatus Desr., which is a synonym of Wurdackanthus frigidus (Sw.) Maguire & B. M. Boom from the Lesser Antilles. Therefore, Lisianthius acuminatus Perkins is here renamed Lisianthius perkinsiae Struwe & Weaver, nom. nov.
Name changes inPodostemaceae
Authors: Cook Christopher D. K. , Rutishauser Rolf
Published: April 2006

Cook, C. D. K. & Rutishauser, R.: Name changes inPodostemaceae. –Taxon 50: 1163–1167. 2001.‐ISSN 0040–0262.

While preparing a review of the familyPodostemaceae, we have found it necessary to change the name of some species. Following rules of priority,CreniasK. P. J. Sprengel replacesMniopsisMartius. No convincing reasons can be found to maintain the monotypic generaHydrobryopsis, Malaccotristicha, SynstylisandTorrenticola; they are merged in their sister generaZeylanidium, Tristicha, HydrobryumandCladopus, respectively. On morphological groundsPolypleurella micrantherais transferred toHydrobryumandPolypleurum submersais transferred toSaxicolella.
The Species Plantarum Project, an international collaborative initiative for higher plant taxonomy
Authors: Brummitt Richard K. , Castroviejo Santiago , Chikuni Augustine C. , Orchard Anthony E. , Smith Gideon F. , Wagner Warren L.
Published: April 2006

Brummitt, R. K., Castroviejo, S., Chikuni, A. C., Orchard A. E., Smith, G. F. & Wagner, W. L.: The Species Plantarum Project, an international collaborative initiative for higher plant taxonomy. – Taxon 50: 1217–1230. 2001. – ISSN 0040–0262.

Basic understanding of the higher plant resources of the world for the successful management of biodiversity requires international collaboration and the setting up of a global taxonomic database. Botanists at all levels should be involved in the taxonomic work, and biologists and conservationists need to be actively aware of the need for such work on a global basis. The database must include census, descriptive, and identification aspects. At present, existing available information is haphazardly distributed on library shelves and inadequately organised. Published data on threatened species have been shown to be hopelessly inaccurate. National and regional Floras may often portray a false perspective of the plants they include. The world's botanists have to organise themselves to pool their information, and substantial international funding is needed to support this. The Species Plantarum Project, set up in 1995 under the International Organisation for Plant Information affiliated to the International Union of Biological Sciences (IUBS), aims to overcome “the taxonomic impediment”, and is currently seeking appropriate funding. It responds to the priorities highlighted in the work programme being developed under the Global Taxonomy Initiative of the Convention on Biological Diversity. The project has an international Steering Committee representing all regions of the world, and aims to develop a further network of collaborators. Publication of data will be in both hard copy and electronic form. Instructions to contributors and accounts of five relatively small families have already been published in hard copy, and accounts of two further families totalling nearly 1000 species are in press. Future plans emphasise the need for capacity building in floristic work throughout the world. The project now invites the collaboration of taxonomists throughout the community, but the future of the project is dependent on funding being made available.
On controlled one-dimensional diffusion processes with unknown parameter
Authors: Dufková Věra
Published: April 2006

We consider a controlled diffusion process, the description of which depends on an unknown parameter α, and investigate the following control policy. To each α an optimal stationary control is associated. α is estimated recurrently from the trajectory by Bayes' method, and the optimal stationary control corresponding to the estimate is used. We establish the consistency of the estimate, and present asymptotic properties of the criterion function. They follow from the central limit theorem, from the law of large numbers and from the law of the iterated logarithm for local martingales.
Limit theorems in fluctuation theory
Authors: Bingham N. H.
Published: April 2006

We shall be concerned here with limit theorems arising in the fluctuation theory of random walks, processes with stationary independent increments, recurrent events and regenerative phenomena. In Section 1 on discrete time, we consider limit theorems for ladder-points (Theorem 1) and for maxima of partial sums of random variables (Theorem 2), and discuss some related questions. In Section 2 (Theorems 3 to 6) we consider the analogues of these results in continuous time.
The increase of balanced chromosome mutations in mammalian populations
Authors: Bengtsson Bengt Olle
Published: April 2006

Balanced, autosomal chromosome mutations do not change the genotype of animals that are hetero- or homozygotes for the mutation. However, in the gametes produced by a heterozygote animal, there normally exists a fraction with unbalanced chromosome complements. Such gametes are functionally effective in mammals and produce embryos with unbalanced genotypes, which leads to zygotic loss. The fertility of chromosomally heterozygote animals is thus lower than the fertility of homozygote animals. This fertility decrease of heterozygotes has been shown in a number of studies on translocations in mice, cattle and humans. The problem is, how such mutations can ever increase in a population until all animals are homozygotes for the chromosome change.
The coincidence approach to stochastic point processes
Authors: Macchi Odile
Published: April 2006

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.
Asymptotic distribution of a discrete transform of an arbitrarily sampled homogeneous random field
Authors: Swick David A.
Published: April 2006

Multidimensional sampling of real data, e.g., in space and time, often requires observations at non-uniformly spaced intervals. A discrete transform of a multidimensional stationary stochastic process transforms a multivariate problem into an asymptotically univariate one if the spacing is uniform in at least one dimension. For both uniform and non-uniform sampling and a model of ‘signal’ imbedded in a ‘noise’ process, asymptotic normality and independence justifies statistical testing in each cell of the transformed domain of the hypothesis ‘noise alone’ versus the alternate ‘signal plus noise’.
Quasi–stationary distributions in Markov population processes
Authors: Barbour Andrew D.
Published: April 2006

One way of analysing complicated Markov population processes is to approximate them by a diffusion about the deterministic path. This approximation alone may not, however, answer all the questions which might reasonably be asked. Many processes have phases, for example near boundaries, where a different approximation is required; such processes are better described by a succession of diffusion and special approximations alternately.

This paper looks at the special treatment required near a point where the deterministic equations are in equilibrium. When the equilibrium is unstable, the process will eventually wander off, and possibly follow a diffusion around another deterministic path. If the equilibrium is stable, the process will behave as if in stable equilibrium about it for a very much longer time, but may at last be trapped away from it, for instance in an absorbing state. The results presented describe the distributions of the time and place of leaving neighbourhoods of the equilibrium point. The neighbourhoods considered are large enough, in the unstable case, to make possible the link with the next phase of motion. In the stable case, exit times are shown to be so long that the possibility of exit can often be ignored in practice, and the quasi-equilibrium distribution treated as a true equilibrium. A more detailed result, showing how closely the normal approximation holds in this situation, is also provided.
Moment formulas for the Markov renewal branching process
Authors: Neuts Marcel F.
Published: April 2006

There are many queueing models in which there appears a semi-Markov matrix G(·), whose entries are absorption-time distributions in a Markov renewal branching process. The role of G(·) is similar to that of the busy period in the simple M/G/1 model. The computation of various quantities associated with G(·) is however much more complicated. The moment matrices, and particularly the mean matrix of G(·), are essential in the construction of general and mathematically well-justified algorithms for the steady-state distributions of such queues.

This paper discusses the moment matrices of G(·) and algorithms for their numerical computation. Its contents are basic to the algorithmic solutions to several queueing models, which are to be presented in follow-up papers.
Limit theorems for dissociated random variables
Authors: Silverman B. W.
Published: April 2006

Families of exchangeably dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj, …, Yz) for some function g of m arguments and some sequence Yn of i.i.d. random variables on any suitable space. A central limit theorem for exchangeably dissociated random variables is proved and some remarks on the closeness of the normal approximation are made. The weak convergence of the empirical distribution process to a Gaussian process is proved. Some applications to data analysis are discussed.
A continuous time Markov branching model with random environments
Authors: Kaplan Norman
Published: April 2006

A population model is constructed which combines the ideas of a discrete time branching process with random environments and a continuous time non-homogeneous Markov branching process. The extinction problem is considered and necessary and sufficient conditions for extinction are determined. Also discussed are limit theorems for what corresponds to the supercritical case.
Evolution in diploid populations by continuity of gametic types
Authors: Eshel Ilan
Published: April 2006

This work studies the long-term effects of mutation and selection pressures on a diploid population embracing many genetic types. A number of results previously established for the simpler asexual case (see [4]) are extended to the cases of random mating and complete inbreeding (Theorem 1), and then, under particular conditions, to certain circumstances of mixed random mating and inbreeding (Theorem 3 and Corollary 1). Several implications for sex and diploidity are drawn from Theorem 2 and its corollaries. Further biological interpretations of these findings, especially of Theorem 2, are given in [3].
The multitype Galton-Watson process with ρ near 1
Authors: Quine M. P.
Published: April 2006

The asymptotic behaviour of thosek-type (k≥ 1) Galton-Watson processes (both with and without immigration) with ρ close to unity is considered. The first principal result (Theorem 3) relates to the vector denoting the numbers of particles of each type at thenth generation in processes without immigration. It is shown that, when normed in a certain way and conditioned on non-extinction, this vector has approximately, for largen, a negative exponential distribution which is degenerate on a line. Theorem 4 is an analogous result for processes with immigration. In this case, no conditioning is required, and the limiting distribution is again degenerate on a line, although now it relates to the gamma rather than the negative exponential.
An age dependent branching process with variable lifetime distribution
Authors: Fildes Robert
Published: April 2006

A branching process with variable lifetime distribution is defined by a sequence of distribution functions {Gi(t)}, together with a probability generating function, h(s) = Σk∞= 0pksk. An ith generation particle lives a random length of time, determined by Gi(t). At the end of a particle's life it produces children, the number being determined by h(s). These offspring behave like the initial particle except they are (i + 1)th generation particles and have lifetime distribution Gi + 1 (t).

Let Zi(t) be the number of particles alive at time t, the initial particle being born into the ith generation. Integral equations are derived for the moments of Zi(t) and it is shown that for some constants Ni, γ, a, Zi (t)/(Nitγ-1eαt) converges in mean square to a proper random variable.
Limit theorems for stochastic growth models. I
Authors: Kesten Harry
Published: April 2006

We consider d-dimensional stochastic processes which take values in (R+)d. These processes generalize Galton-Watson branching processes, but the main assumption of branching processes, independence between particles, is dropped. Instead, we assume for some

Here τ: (R+)d → R+, |x| = Σ1d |x(i)| A = {x ∈ (R+)d: |x| = 1} and T: A → A. Under various assumptions on the maps τ and T it is shown that with probability one there exists a ρ > 1, a fixed point p ∈ A of T and a random variable w such that limn→∞Znρ−n = wp. This result is a generalization of the main limit theorem for super-critical branching processes; note, however, that in the present situation both p and ρ are random as well. The results are applied to a population genetical model for zygotic selection without mutation at one locus.
Stochastic models of grouping changes
Authors: Morgan Byron J. T.
Published: April 2006

Several simple stochastic models are given for a finite closed system of individuals existing in clusters which may come together to form larger clusters which may in turn split up. Some of these models are analysed and compared in equilibrium. Several of the models fit into a general framework established and investigated by Whittle (1965a); it is shown that these models have an equilibrium solution of a particularly simple form, deduced by Whittle, if and only if the models are stochastically reversible. A normal approximation to two of the models in equilibrium is found to give the same mean value as a deterministic approximation.
Recurrence criteria for multi-dimensional Markov chains and multi-dimensional linear birth and death processes
Authors: Kesten Harry
Published: April 2006

Criteria are established for a discrete-time Markov process {Xn}n≧0 in Rd to have strictly positive, respectively zero, probability of escaping to infinity. These criteria are mainly in terms of the mean displacement vectors μ(y) = E{Xn+1|Xn = y} – y, and are essentially such that they force a deterministic process w.p.1 to move off to infinity, respectively to return to a compact set infinitely often. As an application we determine of most two-dimensional birth and death processes with rates linearly dependent on the population, whether they can escape to infinity or not.
A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump-Mode-Jagers branching processes
Authors: Holte John M.
Published: April 2006

Let Z(t) be the population size at time t in a general age-dependent branching process (as defined by Crump and Mode, or Jagers) in which the number N of offspring of a parent has expected value 1 (critical case). Assuming positivity and finiteness of the second moments of N, of the lifespan distribution and of the expected number of births per parent as a function of age (also assumed to be strongly non-lattice), the distribution of Z(t)/t conditioned on non-extinction at time t is asymptotically exponential. The main step in the proof is a comparison lemma for the probability generating functions of Z(t) and of the embedded generation process.
Busy periods in time-dependent M/G/1 queues
Authors: Rosenlund Stig. I.
Published: April 2006

A single-server queue with batch arrivals in a non-homogeneous Poisson process and with balking is studied with respect to the busy period, using supplementary variables. A system of integral equations is obtained on the base of which the transforms are expressed in series. For the homogeneous case, assuming finite waiting room, the solutions are obtained via Cramer's rule. This gives asymptotic expressions for the expectations for large arrival intensity. An efficiency measure giving the long run loss probability is given. For a special case contour integral representations are given as solutions.
The asymptotic strength distribution of a general fiber bundle
Authors: Phoenix S. Leigh , Taylor Howard M.
Published: April 2006

The asymptotic statistical distribution of tensile strength of a bundle of parallel fibers is determined in terms of the statistical characteristics of the individual fibers as the number of fibers in the bundle grows indefinitely large.
On generalized shot noise
Authors: Rice John
Published: April 2006

A simple expression for the characteristic functional of generalized shot noise is developed. Through expansions in terms of functional derivatives this yields expressions for moment functions of all orders. A central limit theorem also follows. Several examples are discussed.
Stationary distributions for dams with additive input and content-dependent release rate
Authors: Brockwell P. J.
Published: April 2006

Conditions are derived under which a probability measure on the Borel subsets of [0, ∞) is a stationary distribution for the content {Xt} of an infinite dam whose cumulative input {At} is a pure-jump Lévy process and whose release rate is a non-decreasing continuous functionr(·) of the content. The conditions are used to find stationary distributions in a number of special cases, in particular whenand whenr(x) =xαand {At} is stable with index β ∊ (0, 1). In general ifEAt, < ∞ andr(0 +) > 0 it is shown that the condition supr(x)>EA1is necessary and sufficient for a stationary distribution to exist, a stationary distribution being found explicitly when the conditions are satisfied. If supr(x)>EA1it is shown that there is at most one stationary distribution and that if there is one then it is the limiting distribution of {Xt} ast→ ∞. For {At} stable with index β andr(x) =xα, α + β = 1, we show also thatcomplementing results of Brockwell and Chung for the zero-set of {Xt} in the cases α + β < 1 and α + β > 1. We conclude with a brief treatment of the finite dam, regarded as a limiting case of infinite dams with suitably chosen release functions.
A shot process by burst properties
Authors: Gilchrist James H. , Thomas John B.
Published: April 2006

A shot process with bursts of events is constructed using an occurrence time structure similar to that of clustering point processes. The characteristic function and a simple functional form for the power spectral density of the process are found. It is shown that the burst property might not be observable. Applications of a specific example of this process are given in modeling a 1/fnoise commonly found in some electronic components.
Finite non-homogeneous Markov chains: Asymptotic behaviour
Authors: Cohn Harry
Published: April 2006

The paper is concerned with aspects of the behaviour of the products of finite stochastic matrices, the methods used in the proofs being of a probabilistic nature. The main result of the paper (Theorem 1) presents a general picture of the asymptotic behaviour of the transition probabilities between various groups of states. A unified treatment of some results of non-homogeneous Markov chain theory pertaining to weak ergodicity is then given.
On fluctuation problems in the theory of queues
Authors: Takács Lajos
Published: April 2006

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.
Recent work in epidemiology at Sheffield
Authors: Gani J.
Published: April 2006

Recent research at Sheffield, which is briefly described below, has been concerned with chain-binomial models, and stochastic path integrals under infective curves.
The mathematical theory of epidemics: a study of the evolution of resistance in microorganisms
Authors: Krus V. P. , Rvachev L. A.
Published: April 2006

In modern medicine it becomes more and more urgent every year to solve new epidemiological problems. One of these is the evolution of resistance to antibiotics of a large spectrum of microorganisms; this resistance is a consequence of the mass administration of antibiotics. In this problem it becomes necessary to apply the mathematical methods of epidemic theory as here the key lies in a purely epidemiological factor, namely the mass character of the use of antibiotics. A first model of the phenomenon encountered is presented.
Malaria models
Authors: Dietz Klaus
Published: April 2006

There exists already a considerable literature about a mathematical approach to the description and control of malaria (see Ross (1911); Martini (1921); Lotka (1923); Moshkovskii (1950); Macdonald (1957), (1968)). This note gives an outline of the main assumptions of a simulation model which has been developed in close co-operation with epidemiologists, entomologists and immunologists in connection with a field project in Northern Nigeria where the necessary data for testing the model are being collected.
A note on perturbation techniques for epidemics
Authors: Daniels H. E.
Published: April 2006

This note is prompted by the papers of Weiss (this Symposium) and Bailey (1968). Weiss develops a technique for approximation to the moments of an epidemic process by regarding them as expandable in powers of N-1whereNis the size of the population, assumed constant. He first considers the simple stochastic epidemic with no removals and obtains explicit formulae for the terms of orderN-1, the zero order terms being the deterministic values. Bailey is concerned with a similar type of approximation and he derives explicit results to the same order. Bailey uses an eigenfunction approach whereas Weiss's method is more direct and perhaps easier to generalise. However, in attempting to extend the method to the case of a closed epidemic with removals Weiss is led to intractable difference equations.
A process by chain dependent growth rate. part II: The ruin and ergodic problems
Authors: Keilson Julian , Rao S. Subba
Published: April 2006

In the homogeneous process X(t) defined on a finite irreducible Markov chain R(t) was studied. The process was characterized by an overall transition rate v per unit time, a matrix β of transition probabilities for the chain and a linear growth for X(t) dependent on the chain; viz. dX(t)/dt|R(t) = i = vi. The central limit behavior of the process was exhibited in. For the case when the chain had only two states, the ruin and ergodic problems were considered in for the bounded process. The object of this paper is to investigate the ruin and ergodic problems for the process of in the presence of boundaries.
A model for character displacement based on competition between species
Authors: Bulmer M. G.
Published: April 2006

When two closely-related species have a partially-overlapping geographical range, it sometimes happens that populations of the two species are very similar in the non-overlapping parts of the range where only one species is present, but that they diverge and are easily distinguishable in the area of overlap where both species occur together. This phenomenon is known as character displacement. One of the best known examples occurs in two species of Rock Nuthatches (Sitta neumayer and S. tephronota) in their area of overlap in Iran (Vaurie (1951)). A plausible explanation of this phenomenon is that it is due to competition between the two species. The purpose of this paper is to construct a model for character displacement based on this idea. A full account of this work will be published elsewhere (Bulmer (1973)).
The continuity of queues
Authors: Whitt Ward
Published: April 2006

Kennedy (1972) showed that the standard single-server queueing model is continuous. These results are extended to the standard multi-server model here. Even when there is only one server, an additional condition is needed for the queue length process.
Markov renewal theory
Authors: Çinlar Erhan
Published: April 2006

Consider a stochastic processX(t) (t≧ 0) taking values in a countable state space, say, {1, 2,3, …}. To be picturesque we think ofX(t) as the state which a particle is in at epocht. Suppose the particle moves from state to state in such a way that the successive states visited form a Markov chain, and that the particle stays in a given state a random amount of time depending on the state it is in as well as on the state to be visited next. Below is a possible realization of such a process.
On estimating the variance of the offspring distribution in a simple branching process
Authors: Heyde C. C.
Published: April 2006

A single realization {Zn, 0 ≦n≦N + 1} of a supercritical Galton-Watson process (so called) is considered and it is required to estimate the variance of the offspring distribution. A prospective estimator is proposed, where , and is shown to be strongly consistent on the non-extinction set. A central limit result and an iterated logarithm result are provided to give information on the rate of convergence of the estimator. It is also shown that the estimation results are robust in the sense that they continue to apply unchanged in the case where immigration occurs. Martingale limit theory is employed at each stage in obtaining the limit results.
Critical branching processes
Authors: Ney Peter
Published: April 2006

This paper develops a comparison method for critical branching processes. The method is applied to prove the exponential limit law for the multi-type age-dependent process under second moment conditions.
The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models
Authors: Cannings C.
Published: April 2006

Haploid models of genetic drift in populations of constant size are considered. Generalizations of the models of Moran and Wright have been developed by Karlin and McGregor (for multiple alleles and non-overlapping generations), by Chia and Watterson (for two alleles and overlapping or non-overlapping generations) and by Chia (for multiple alleles and overlapping or non-overlapping generations), using conditioned branching processes. A new approach is developed which contains the models mentioned above and provides simpler expressions for the latent roots. A greater dependence between the birth events and death events can be permitted, and non-independent mutations treated.
An age dependent branching process with variable lifetime distribution: The generation size
Authors: Fildes Robert
Published: April 2006

In a branching process with variable lifetime, introduced by Fildes (1972) define Yjk(t) as the number of particles alive in generation k at time t when the initial particle is born in generation j. A limit law similar to that derived in the Bellman-Harris process is proved where it is shown that Yjk(t) suitably normalised converges in mean square to a random variable which is the limit random variable of Znm–n in the Galton-Watson process (m is the mean number of particles born).
Limit laws for maxima of a sequence of random variables defined on a Markov chain
Authors: Resnick Sidney I. , Neuts Marcel F.
Published: April 2006

Consider the bivariate sequence of r.v.'s {(Jn,Xn),n≧ 0} withX0= - ∞ a.s. The marginal sequence {Jn} is an irreducible, aperiodic,m-state M.C.,m< ∞, and the r.v.'sXnare conditionally independent given {Jn}. FurthermoreP{Jn=j, Xn≦x|Jn− 1=i} =pijHi(x) =Qij(x), whereH1(·), · · ·,Hm(·) are c.d.f.'s. SettingMn= max {X1, · · ·,Xn}, we obtainP{Jn=j, Mn≦x|J0=i} = [Qn(x)]i, j, whereQ(x) = {Qij(x)}. The limiting behavior of this probability and the possible limit laws forMnare characterized.

Theorem.Let ρ(x) be the Perron-Frobenius eigenvalue ofQ(x) for realx; then:

(a)ρ(x) is a c.d.f.;

(b) if for a suitable normalization {Qijn(aijnx+bijn)} converges completely to a matrix {Uij(x)} whose entries are non-degenerate distributions thenUij(x) = πjρU(x), where πj= limn→ ∞pijnand ρU(x) is an extreme value distribution;

(c) the normalizing constants need not depend oni, j;

(d) ρn(anx+bn) converges completely to ρU(x);

(e) the maximumMnhas a non-trivial limit law ρU(x) iffQn(x) has a non-trivial limit matrixU(x) = {Uij(x)} = {πjρU(x)} or equivalently iff ρ(x) or the c.d.f. πi= 1mHiπi(x) is in the domain of attraction of one of the extreme value distributions. Hence the only possible limit laws for {Mn} are the extreme value distributions which generalize the results of Gnedenko for the i.i.d. case.