On the Maximum of a Branching Process Conditioned on the Total Progeny

The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

Some Theoretical Results on the Progeny of a Bisexual Galton-Watson Branching Process

A Superadditive Bisexual Galton-Watson Branching Process is considered and the total number of mating units, females and males, until the n-th generation, are studied. In particular some results about the stochastic monotony, probability generating functions and moments are obtained. Finally, the limit behaviour of those variables suitably normed is investigated.

Técnicas de criação em laboratório e dispersão do parasitóide de pupas Trichospilus diatraeae (Hymenoptera: eulophidae) no campo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A genetic linkage map of an apple rootstock progeny anchored to the Malus genome sequence

An apple rootstock progeny raised from the cross between the very dwarfing ‘M.27’ and the more vigorous ‘M.116’ (‘M.M.106’ × ‘M.27’) was used for the construction of a linkage map comprising a total of 324 loci: 252 previously mapped SSRs, 71 newly characterised or previously unmapped SSR loci (including 36 amplified by 33 out of the 35 novel markers reported here), and the self-incompatibility locus. The map spanned the 17 linkage groups (LG) expected for apple covering a genetic distance of 1,229.5 cM, an estimated 91% of the Malus genome. Linkage groups were well populated and, although marker density ranged from 2.3 to 6.2 cM/SSR, just 15 gaps of more than 15 cM were observed. Moreover, only 17.5% of markers displayed segregation distortion and, unsurprisingly in a semi-compatible backcross, distortion was particularly pronounced surrounding the self-incompatibility locus (S) at the bottom of LG17. DNA sequences of 273 SSR markers and the S locus, representing a total of 314 loci in this investigation, were used to anchor to the ‘Golden Delicious’ genome sequence. More than 260 of these loci were located on the expected pseudo-chromosome on the ‘Golden Delicious’ genome or on its homeologous pseudo-chromosome. In total, 282.4 Mbp of sequence from 142 genome sequence scaffolds of the Malus genome were anchored to the ‘M.27’ × ‘M.116’ map, providing an interface between the marker data and the underlying genome sequence. This will be exploited for the identification of genes responsible for traits of agronomic importance such as dwarfing and water use efficiency.

Development of a dense SNP-based linkage map of an apple rootstock progeny using the Malus Infinium whole genome genotyping array

Background A whole-genome genotyping array has previously been developed for Malus using SNP data from 28 Malus genotypes. This array offers the prospect of high throughput genotyping and linkage map development for any given Malus progeny. To test the applicability of the array for mapping in diverse Malus genotypes, we applied the array to the construction of a SNPbased linkage map of an apple rootstock progeny. Results Of the 7,867 Malus SNP markers on the array, 1,823 (23.2 %) were heterozygous in one of the two parents of the progeny, 1,007 (12.8 %) were heterozygous in both parental genotypes, whilst just 2.8 % of the 921 Pyrus SNPs were heterozygous. A linkage map spanning 1,282.2 cM was produced comprising 2,272 SNP markers, 306 SSR markers and the S-locus. The length of the M432 linkage map was increased by 52.7 cM with the addition of the SNP markers, whilst marker density increased from 3.8 cM/marker to 0.5 cM/marker. Just three regions in excess of 10 cM remain where no markers were mapped. We compared the positions of the mapped SNP markers on the M432 map with their predicted positions on the ‘Golden Delicious’ genome sequence. A total of 311 markers (13.7 % of all mapped markers) mapped to positions that conflicted with their predicted positions on the ‘Golden Delicious’ pseudo-chromosomes, indicating the presence of paralogous genomic regions or misassignments of genome sequence contigs during the assembly and anchoring of the genome sequence. Conclusions We incorporated data for the 2,272 SNP markers onto the map of the M432 progeny and have presented the most complete and saturated map of the full 17 linkage groups of M. pumila to date. The data were generated rapidly in a high-throughput semi-automated pipeline, permitting significant savings in time and cost over linkage map construction using microsatellites. The application of the array will permit linkage maps to be developed for QTL analyses in a cost-effective manner, and the identification of SNPs that have been assigned erroneous positions on the ‘Golden Delicious’ reference sequence will assist in the continued improvement of the genome sequence assembly for that variety.

Estimative of genetic parameters in progeny test of Pinus caribaea Morelet var. hondurensis Barret & Golfari by quantitative traits and microsatellite markers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

USE OF PROGENY TESTING IN BEEF-CATTLE - PREDICTION OF GENETIC GAIN IN A NELORE CATTLE-BREEDING PROGRAM

Genetic gains predicted for selection, based on both individual performance and progeny testing, were compared to provide information to be used in implementation of progeny testing for a Nelore cattle breeding program. The prediction of genetic gain based on progeny testing was obtained from a formula, derived from methodology of Young and weller (J. Genetics 57: 329-338, 1960) for two-stage selection, which allows prediction of genetic gain per generation when the individuals under test have been pre-selected on the basis of their own performance. The application of this formula also allowed determination of the number of progeny per tested bull needed to maximize genetic gain, when the total number of tested progeny is limited.

CHROMOSOMAL CONSTITUTION IN ROB (5/15) GOAT PROGENY

A total of 116 goats originating from three heterozygous bucks for rob (5/15) were cytogenetically studied at Botucatu, Brazil. In the mating 59,XY,t(5/15) x 60,XX, the offspring karyotype proportion did not differ significantly from the expected ratio of 1 normal:1 heterozygous. In the mating 59,XY,t(5/15) x 59,XX,t(5/15) the observed proportion was 1 normal:2 heterozygous:1 homozygous, and in the mating 59,XY,t(5/15) X 58,XX,tt(5/15) the observed proportion was 1 heterozygous:1 homozygous. No animals had unbalanced karyotypes and no differences in the weight at birth of normal, heterozygous and homozygous kids were observed (P > 0.10).

Use of progeny testing in beef cattle: Prediction of genetic gain in a Nelore Cattle Breeding Program

Genetic gains predicted for selection, based on both individual performance and progeny testing, were compared to provide information to be used in implementation of progeny testing for a Nelore cattle breeding program. The prediction of genetic gain based on progeny testing was obtained from a formula, derived from methodology of Young and Weiler (J. Genetics 57: 329-338, 1960) for two-stage selection, which allows prediction of genetic gain per generation when the individuals under test have been pre-selected on the basis of their own performance. The application of this formula also allowed determination of the number of progeny per tested bull needed to maximize genetic gain, when the total number of tested progeny is limited.

Lineage commitment in the progeny of murine hematopoietic preprogenitor cells: Influence of thrombopoietin and interleukin 5

Normal mouse marrow cells were stimulated by stem cell factor (SCF) to form dispersed or multicentric blast colonies containing progenitor cells committed to various hematopoietic lineages. Combination of the eosinophil-specific regulator interleukin 5 with SCF increased the frequency of colonies containing eosinophil-committed progenitor cells with multicentric but not dispersed blast colonies. Combination of thrombopoietin with SCF increased the frequency of colonies containing megakaryocyte-committed progenitor cells with both types of blast colony. Neither interleukin 5 nor thrombopoietin significantly altered the number or total cell content of blast colonies or progenitor cell numbers in blast colonies from those stimulated by SCF alone. No correlation was observed between total progenitor cell content and the presence or absence of either eosinophil or megakaryocyte progenitors in either type of blast colony. The data argue against a random process as being responsible for the formation of particular committed progenitor cells or the possibility that lineage-specific regulators merely enhance survival of such committed progenitor cells formed in developing blast colonies.

Chloroplast and total genomic diversity in the endemic Costa Rican tree Lonchocarpus costaricensis (J.D. Smith) Pittier (Papilionaceae).

In Mesoamerica, tropical dry forest is a highly threatened habitat, and species endemic to this environment are under extreme pressure. The tree species, Lonchocarpus costaricensis is endemic to the dry northwest of Costa Rica and southwest Nicaragua. It is a locally important species but, as land has been cleared for agriculture, populations have experienced considerable reduction and fragmentation. To assess current levels and distribution of genetic diversity in the species, a combination of chloroplast-specific (cpDNA) and whole genome DNA markers (amplified fragment length polymorphism, AFLP) were used to fingerprint 121 individual trees in 6 populations. Two cpDNA haplotypes were identified, distributed among populations such that populations at the extremes of the distribution showed lowest diversity. A large number (487) of AFLP markers were obtained and indicated that diversity levels were highest in the two coastal populations (Cobano, Matapalo, H = 0.23, 0.28 respectively). Population differentiation was low overall, F-ST = 0.12, although Matapalo was strongly differentiated from all other populations (F-ST = 0.16-0.22), apart from Cobano (F., = 0.11). Spatial genetic structure was present in both datasets at different scales: cpDNA was structured at a range-wide distribution scale, whilst AFLP data revealed genetic neighbourhoods on a population scale. In general, the habitat degradation of recent times appears not to have yet impacted diversity levels in mature populations. However, although no data on seed or saplings were collected, it seems likely that reproductive mechanisms in the species will have been affected by land clearance. It is recommended that efforts should be made to conserve the extant genetic resource base and further research undertaken to investigate diversity levels in the progeny generation.