Estimation of linkage in trisomic inheritance

 Based on F₂ families derived from selfed F₁ trisomic plants we have developed a genetic model to estimate linkage relationships between pairs of loci located on the extra chromosome. Genotypic frequencies of each class expected in a trisomic F₂ family have been calculated and the maximum-likelihood equations for recombination-fraction estimation have been derived for a variety of genetic situations. Morton’s test of homogeneity was used to compare recombination fractions estimated between loci exhibiting trisomic segregation to those obtained in families where the same loci showed Mendelian segregation. This method has been applied to an analysis of morphological, isozyme and RAPD data from faba bean (Vicia faba L.). Received: 11 October 1996 / Accepted: 21 March 1997     

AFLP genetic maps of Eucalyptus globulus and E. tereticornis

 Amplified fragment length polymorphism (AFLP) analysis is a rapid and efficient technique for detecting large numbers of DNA markers in eucalypts. We have used AFLP markers in a two-way pseudo-testcross strategy to generate genetic maps of two clones of different Eucalyptus species (E. tereticornis and E. globulus). Of 606 polymorphic fragments scored, 487 segregated in a 1 : 1 ratio, corresponding to DNA polymorphisms heterozygous in one parent and null in the other. In the maternal E. tereticornis map, 268 markers were ordered in 14 linkage groups (919 cM); the paternal E. globulus map had 200 markers in 16 linkage groups (967 cM). Results from PGRI software were compared with MAPMAKER. The average density of markers was approximately 1 per 3.9 cM. Framework markers were ordered with an average confidence level of 90%, covering 80–100% of the estimated Eucalyptus genome size. In order to investigate the homologies between the E. tereticornis and the E. globulus genetic linkage maps, we included 19 markers segregating 3 : 1 in the analysis. Some homeologous linkage groups were recognized. The linkage data developed in these maps will be used to detect loci controlling commercially important traits. Received: 17 July 1997 / Accepted: 13 October 1997     

A composite map of expressed sequences and phenotypic traits of the sunflower (Helianthus annuus L.) genome

 A map of the sunflower genome, based on expressed sequences and consisting of 273 loci, was constructed. The map incorporates data from seven F₂ populations, for a total of 1115 individuals. Two hundred and fourty five loci corresponding to 170 anonymous cDNA markers and four loci for morphological markers were mapped. We also mapped 18 loci corresponding to previously described genes or to sequences obtained through homology cloning. The unit maps vary from 774 cM to 1060 cM, with an average value of 14 major linkage groups. The integrated map is arranged in 17 major linkage groups including 238 loci, plus four small segments with 2–5 marker loci; and covers 1573 cM with an overall average marker interval of 7 cM. Thirty five percent of the markers were dominant in nature and 30% showed inter-linkage group duplication without any indication of homoeologous linkage groups. Evidence is provided for the independence of two distinct fertility restoration genes, for the presence of two loosely linked branching loci, and for marker tightly linked to the Rf1 restoration locus. This map provides an efficient tool in breeding applications such as disease-resistance mapping, QTL analyses and marker-assisted selection. Received: 27 August 1998 / Accepted: 28 December 1998     

An interspecific (Capsicum annuum ×C. chinese) F2 linkage map in pepper using RFLP and AFLP markers

We have constructed a molecular linkage map of pepper (Capsicum spp.) in an interspecific F₂ population of 107 plants with 150 RFLP and 430 AFLP markers. The resulting linkage map consists of 11 large (206–60.3 cM) and 5 small (32.6–10.3 cM) linkage groups covering 1,320 cM with an average map distance between framework markers of 7.5 cM. Most (80%) of the RFLP markers were pepper-derived clones, and these markers were evenly distributed across the genome. By using 30 primer combinations, we were able to generate 444 AFLP markers in the F₂ population. The majority of the AFLP markers clustered in each linkage group, although PstI/MseI markers were more evenly distributed than EcoRI/MseI markers within the linkage groups. Genes for the biosynthesis of carotenoids and capsaicinoids were mapped on our linkage map. This map will provide the basis of studying secondary metabolites in pepper. Received: 20 October 1999 / Accepted: 3 July 2000     

Exact sampling formulas for multi-type Galton-Watson processes

 Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction. Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA     

A discrete,size-structured model of phytoplankton growth in the chemostat: introduction of inhomogeneous cell division size

 We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification of several parameters of the system. Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002 RID="*" ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size     

Cattaneo models for chemosensitive movement

 We derive models for chemosensitive movement based on Cattaneo's law of heat propagation with finite speed. We apply the model to pattern formation as observed in experiments with Dictyostelium discoideum, with Salmonella typhimurium and with Escherichia coli. For Salmonella typhimurium we make predictions on pattern formation which can be tested in experiments. We discuss the relations of the Cattaneo models to classical models and we develop an effective numerical scheme. Received: 8 October 2001 / Revised version: 2 August 2002 / Published online: 19 November 2002 Key words or phrases: Chemotaxis – Aggregation – Cattaneo model – Numerical schemes Acknowledgements. We are very grateful for comments of S. Noelle concerning the numerical scheme. We thank K.P. Hadeler and C. Schmeiser for helpful remarks. The research was supported by the Deutsche Forschungsgemeinschaft, research project ANumE and the Austrian Science Foundation, grant no. W008.     

Development of RAPD and SCAR markers linked to the Russian wheat aphid resistance gene Dn2 in wheat

 RAPD (random amplified polymorphic DNA) analysis was used to identify molecular markers linked to the Dn2 gene conferring resistance to the Russian wheat aphid (Diuraphis noxia Mordvilko). A set of near-isogenic lines (NILs) was screened with 300 RAPD primers for polymorphisms linked to the Dn2 gene. A total of 2700 RAPD loci were screened for linkage to the resistance locus. Four polymorphic RAPD fragments, two in coupling phase and two in repulsion phase, were identified as putative RAPD markers for the Dn2 gene. Segregation analysis of these markers in an F₂ population segregating for the resistance gene revealed that all four markers were closely linked to the Dn2 locus. Linkage distances ranged from 3.3 cM to 4.4 cM. Southern analysis of the RAPD products using the cloned RAPD markers as probes confirmed the homology of the RAPD amplification products. The coupling-phase marker OPB10_880c and the repulsion-phase marker OPN1_400r were converted to sequence characterized amplified region (SCAR) markers. SCAR analysis of the F₂ population and other resistant and susceptible South African wheat cultivars corroborated the observed linkage of the RAPD markers to the Dn2 resistance locus. These markers will be useful for marker-assisted selection of the Dn2 gene for resistance breeding and gene pyramiding. Received: 1 July 1997 / Accepted: 20 October 1997     

Sequence-based genetic markers for genes and gene families: single-strand conformational polymorphisms for the fatty acid synthesis genes of Cuphea

 Gene sequences are rapidly accumulating for many commercially and scientifically important plants. These resources create the basis for developing sequence-based markers for mapping and tracking known (candidate) genes, thereby increasing the utility of genetic maps. Members of most of the gene families underlying the synthesis of seed oil fatty acids have been cloned from the medium-chain oilseed Cuphea. Allele-specific-PCR (AS-PCR) and single-strand conformational polymorphism (SSCP) markers were developed for 22 fatty acid synthesis genes belonging to seven gene families of Cuphea using homologous and heterologous DNA sequences. Markers were developed for 4 fatty-acyl-acyl carrier protein thioesterase, 2 β-ketoacyl-acyl carrier protein synthase I, 4 β-ketoacyl-acyl carrier protein synthase II, 3 β-ketoacyl-acyl carrier protein synthase III, 3 acyl carrier protein, 2 β-ketoacyl-acyl carrier protein reductase, and 4 enoyl-acyl carrier protein reductase loci. Eighty-eight percent (14 of 16) of the SSCP loci were polymorphic, whereas only 9% (2 of 22) of the AS-PCR loci were polymorphic. These markers were mapped using a Cuphea viscosissima×C. lanceolata F₂ population and produced linkage groups of 10, 3, and 2 loci (3 loci segregated independently). The 10-locus linkage group had every gene but one necessary for the synthesis of 2- to 16-carbon fatty acids from acetyl-CoA and malonyl-ACP (the missing gene family was not mapped). SSCP analysis has broad utility for DNA fingerprinting and mapping genes and gene families. Received: 3 May 1996 / Accepted: 30 August 1996     

Tomato chromosome 1: high resolution genetic and physical mapping of the short arm in an interspecific Lycopersicon esculentum × L. peruvianum cross

 A detailed map of part of the short arm of chromosome 1 proximal to the Cf-4/Cf-9 gene cluster was generated by using an F₂ population of 314 plants obtained from the cross between the remotely related species Lycopersicon esculentum and L. peruvianum. Six markers that cosegregate in an L. esculentum×L. pennellii F₂ population showed high recombination frequencies in the present interspecific population, spanning an interval of approximately 13 cM. Physical distances between RFLP markers were estimated by pulsed field gel electrophoresis of high-molecular-weight DNA and by identifying YACs that recognized more than one RFLP marker. In this region 1 cM corresponded to 55–110 kb. In comparsion with the value of 730 kb per cM averaged over the entire genome, this reflects the remarkably high recombination frequencies in this region in the hybrid L. esculentum×L. peruvianum progeny population. The present data underline the fact that recombination is not a process that occurs randomly over the entire genome, but can vary dramatically in intensity between chromosomal regions and among populations. Received: 20 May 1996 / Accepted: 10 September 1996     

Genetic diversity of Cryptomeria japonica using co-dominant DNA markers based on sequenced-tagged sites

 We have investigated the genetic diversity of 11 natural populations of C. japonica using 13 polymorphic STS markers. The average unbiased heterozygosities (H _e ), the average number of alleles per locus (N _a ) and the proportion of polymorphic loci (Pl) were 0.281, 1.93 and 76.92%, respectively. Coefficients of linkage disequilibrium were calculated, and no significant deviation was found except in four combinations – which might have occurred by chance alone. The fixation index (F _IS ) for 3 loci showed statistically significant values at the 1% level. The genetic differentiation between populations was only 0.047, and there were no clear geographical tendencies in the allele frequencies or the heterozygosities among populations. Consequently, the results from STS-based co-dominant DNA marker analysis were very similar to those from a previous allozyme study. However, the resolution of the technique is greater than allozyme analysis because many loci with high heterozygosities can be evaluated, and it is very simple. Therefore, the STS-based marker approach is very useful and convenient for population genetics and genome mapping of C. japonica. Received: 18 July 1998 / Accepted: 13 August 1998     

Ultrastructure of regions containing homologous loci in polytene chromosomes of Drosophila melanogaster and Drosophila subobscura

We have used a new approach involving in situ hybridisation and electron microscopy to establish ultrastructural homologies between polytene chromosome regions of Drosophila melanogaster and Drosophila subobscura. Twelve probes were chosen to cover all the chromosomal elements: the myospheroid gene, the collagen type IV gene, the collagen-like gene, the w26 homeobox gene, the β3 tubulin gene, the kinesin heavy chain gene, the tryptophan hydrolase gene, the Hsp82, Hsp22–26 and Hsp23–28, Hsp68, Hsp70 genes and the β unit of the F₀–F₁ ATPase gene. Most of these loci were previously undescribed in D. subobscura and imprecisely located in D. melanogaster. We have demonstrated here, by an ultrastructural analysis of each chromosomal region, that homologous genetic loci tend to show a similar ultrastructure in the two species. With a few exceptions, the structural homology extends to the chromosomal regions surrounding the loci. In some cases, however, no structurally recognisable homology can be seen either in the locus or in its flanking regions. Received: 15 December 1996; in revised form: 15 October 1997 / Accepted: 28 January 1998     

A nonlinear dynamical mechanism for bruit generation by an intracranial saccular aneurysm

 Intracranial saccular aneurysms have been clinically observed to emit a transient sound, a bruit, on each heartbeat. The mechanism causing the bruits has been a matter of contention. A qualitative analysis of the nonlinear dynamical properties of the Shah-Humphrey model for periodic pressure forcing of a thin-necked saccular aneurysm, using the Fung nonlinear constitutive model for the aneurysm material, shows that a small blood pressure jump on each beat, whether the pressure is weakly aperiodic or periodic, induces transients in the radial deformation response of the aneurysmal wall on each heartbeat. These transient vibrations, which have a component with frequency near the natural frequency of the system but are not resonant phenomena and which decay rapidly to a limit cycle during each distinct forcing pressure cycle, can generate the bruits. Received: 21 November 2000 / Revised version: 9 August 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): 92B99, 70K40, 70K05 Key words or phrases: Intracranial saccular aneurysm – Bruit – Spectrum – Nonlinear dynamics – Transients – Vortex shedding – Fung model     

Multicolor fluorescence in situ hybridization analysis of the spermatozoa of a male heterozygous for a reciprocal translocation t(11;22)(q23;q11)

A reciprocal translocation between chromosomes 11 and 22 is a site-specific translocation that has been seen in many families with no common ancestry. This translocation is of particular interest because balanced carriers have a 0.7–3.7% risk of having children with the supernumerary der(22), resulting from a 3:1 segregation. We have used a three color fluorescence in situ hybridization (FISH) with specific DNA probes to determine the chromosome segregation pattern of a male carrier of a translocation t(11;22)(q23;q11). The probes selected included a centromeric marker for chromosome 11, a marker closely linked to the centromere of chromosome 22, and a third probe distal to the translocation breakpoint of chromosome 22. The results showed that 3 : 1 segregation is preferential in this patient, with 40.1% of spermatozoa belonging to this segregation type. Alternate segregation followed with 27.4% of analyzed spermatozoa; 17.6% resulted from adjacent 1 and 12.5% resulted from adjacent 2 segregation. We detected 0.5% of presumably diploid spermatozoa. Complementary adjacent 1 products were observed at statistically different frequencies (P = 0.02). Complementary adjacent 2 products without recombination in the interstitial segments were also seen at different frequencies (P = 0.002). In 3 : 1 segregation, the products containing one chromosome were observed more frequently than those with three chromosomes (P = 0.0001). The 24,+der(22) gamete was seen more frequently than all of the other gametes combined which had 24 chromosomes resulting from 3 : 1 segregation. The results of this study demonstrate that in this t(11;22) carrier, 3 : 1 segregation is preferential but not exclusive. Received: 9 December 1998 / Accepted: 1 March 1999     

Progression age enhanced backward bifurcation in an epidemic model with super-infection

 We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one. Received: 11 October 2001 / Revised version: 17 September 2002 / Published online: 17 January 2003 Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801 This author was visiting Arizona State University when most of the research was done. Research partially supported by NSF grant DMS-0137687. This author's research was partially supported by NSF grant DMS-9706787. Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation – Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor     

A low-density genetic map of onion reveals a role for tandem duplication in the evolution of an extremely large diploid genome

 The bulb onion, Allium cepa L., is a diploid (2n=2x=16) plant with a huge nuclear genome. Previous genetic and cytogenetic analyses have not supported a polyploid origin for onion. We developed a low-density genetic map of morphological markers, randomly amplified polymorphic DNAs (RAPD), and restriction fragment length polymorphisms (RFLP) as a tool for onion improvement and to study the genome organization of onion. A mapping population of 58 F₃ families was produced from a single F₁ plant from the cross of two partially inbred lines (Brigham Yellow Globe 15-23 and Alisa Craig 43). Segregations were established for restoration of male fertility in sterile cytoplasm, complementary light-red bulb color, 14 RAPDs, 110 RFLPs revealed by 90 anonymous cDNA clones, and 2 RFLPs revealed by a cDNA clone of alliinase, the enzyme responsible for the characteristic Allium flavors. Duplicated RFLP loci were detected by 21% of the clones, of which 53% were unlinked (>30 cM), 5% loosely linked (10–30 cM), and 42% tightly linked (<10 cM). This duplication frequency is less than that reported for paleopolyploids but higher than for diploid species. We observed 40% dominant RFLPs, the highest yet reported among plants. Among duplicated RFLP loci, 19% segregated as two loci each with two codominant alleles, 52% segregated as one locus with codominant alleles and one locus with only a dominant fragment, and 29% segregated as two loci with only dominant fragments. We sequenced cDNAs detecting duplicated RFLPs; 63% showed homology to known gene families (e.g., chlorophyll binding proteins, ubiquitin, or RuBISCO), and 37% were unique clones showing significant homology to known genes of low-copy number or no homology to database sequences. Duplicated RFLPs showing linkage could be due to retroviral-like sequences in adjacent coding regions or intrachromosomal, as opposed to whole genome, duplications. Previous cytological analyses and this genetic map support intrachromosomal duplication as a mechanism contributing to the huge onion genome. Received: 3 July 1997 / Accepted: 8 August 1997     

Identification of DNA amplification fingerprinting (DAF) markers close to the symbiosis-ineffective sym31 mutation of pea (Pisum sativum L.)

 We demonstrate efficient genome mapping through a combination of bulked segregant analysis (BSA) with DNA amplification fingerprinting (DAF). Two sets of 64 octamer DAF primers, along with two PCR programs of low- and high-annealing temperatures (30°C and 55°C, respectively), appeared to be enough to locate molecular markers within 2–5 cM of a gene of interest. This approach allowed the rapid identification of four BSA markers linked to the pea (Pisum sativum L.) Sym31 gene, which is responsible for bacteroid and symbiosome differentiation. Three of these markers are shown to be tightly linked to the sym31 mutation. Two markers flanking the Sym31 gene, A21-310 and B1-277, cover a 4–5 cM interval of pea linkage group 3. Both markers were converted to sequence-characterized amplified regions (SCARs). The flanking markers may be potential tools for marker-assisted selection or for positional cloning of the Sym31 gene. Received: 2 July 1998 / Accepted: 8 October 1998     

Cloning and characterization of a centromere-specific repetitive DNA element from Sorghum bicolor

 A 823-bp Sau3AI fragment (pSau3A10) was subcloned from a sorghum bacterial artificial chromosome (BAC) clone, 13I16, that contains DNA sequences specific to the centromeres of grass species. Sequence analysis showed that pSau3A10 consists of six copies of an approximately 137-bp monomer. The six monomers were organized into three dimers. The monomers within the dimers shared 62–72% homology and the dimers were 79–82% homologous with each other. Fluorescence in situ hybridization (FISH) analysis indicated that the Sau3A10 family is present only in the centromeres of sorghum chromosomes. Sequencing, Southern hybridization, and Fiber-FISH analyses indicated that the Sau3A10 family is tandemly arranged and is present in uninterrupted stretches of up to at least 81 kb of DNA. Slot-blot analysis estimated that the Sau3A10 family constitutes 1.6–1.9% of the sorghum genome. The long stretches of Sau3A10 sequences were interrupted by other centromeric DNA elements. Southern analysis indicated that the Sau3A10 sequence is one of the most abundant DNA families located in sorghum centromeres and is conserved only in closely related sorghum species. Methylation experiments indicated that the cytosine of the CG sites in sorghum centromeric regions is generally methylated. The structure and organization of the Sau3A10 family shared similarities with centromeric DNA repeats in other eukaryotic species. It is suggested that the Sau3A10 family is probably an important part of sorghum centromeres. Received: 11 November 1997 / Accepted: 17 November 1997     

Early development and quorum sensing in bacterial biofilms

 We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm. The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum wave speed, determined by linearisation, is realised for a wide class of initial conditions. Received: 10 February 2002 / Revised version: 29 October 2002 / Published online: 19 March 2003 Key words or phrases: Bacterial biofilm – Quorum sensing – Mathematical modelling – Numerical solution – Asymptotic analysis – Travelling wave analysis