Asian rice, Oryza sativa, consists of two major subspecies, indica and japonica, which are physiologically differentiated and adapted to different latitudes. Genes for photoperiod sensitivity are likely targets of selection along latitude. We examined the footprints of natural and artificial selections for four major genes of the photoperiod pathway, namely PHYTOCHROME B (PhyB), HEADING DATE 1 (Hd1), HEADING DATE 3a (Hd3a), and EARLY HEADING DATE 1 (Ehd1), by investigation of the patterns of nucleotide polymorphisms in cultivated and wild rice. Geographical subdivision between tropical and subtropical O. rufipogon was found for all of the photoperiod genes in plants divided by the Tropic of Cancer (TOC). All of these genes, except for PhyB, were characterized by the existence of clades that split a long time ago and that corresponded to latitudinal subdivisions, and revealed a likely diversifying selection. Ssp. indica showed close affinity to tropical O. rufipogon for all genes, while ssp. japonica, which has a much wider range of distribution, displayed complex patterns of differentiation from O. rufipogon, which reflected various agricultural needs in relation to crop yield. In japonica, all genes, except Hd3a, were genetically differentiated at the TOC, while geographical subdivision occurred at 31°N in Hd3a, probably the result of varying photoperiods. Many other features of the photoperiod genes revealed domestication signatures, which included high linkage disequilibrium (LD) within genes, the occurrence of frequent and recurrent non-functional Hd1 mutants in cultivated rice, crossovers between subtropical and tropical alleles of Hd1, and significant LD between Hd1 and Hd3a in japonica and indica.

Summary• Outcrossing Arabidopsis species that diverged from their inbreeding relative Arabidopsis thaliana 5 million yr ago and display a biogeographical pattern of interspecific sympatry vs intraspecific allopatry provides an ideal model for studying impacts of gene introgression and polyploidization on species diversification.• Flow cytometry analyses detected ploidy polymorphisms of 2· and 4· in Arabidopsis lyrata ssp. kamchatica of Taiwan. Genomic divergence between species ⁄ subspecies was estimated based on 98 randomly chosen nuclear genes. Multilocus analyses revealed a mosaic genome in diploid A. l. kamchatica composed of Arabidopsis halleri-like and A. lyrata-like alleles.• Coalescent analyses suggest that the segregation of ancestral polymorphisms alone cannot explain the high inconsistency between gene trees across loci, and that gene introgression via diploid A. l. kamchatica likely distorts the molecular phylogenies of Arabidopsis species. However, not all genes migrated across species freely. Gene ontology analyses suggested that some nonmigrating genes were constrained by natural selection.• High levels of estimated ancestral polymorphisms between A. halleri and A. lyrata suggest that gene flow between these species has not completely ceased since their initial isolation. Polymorphism data of extant populations also imply recent gene flow between the species. Our study reveals that interspecific gene flow affects the genome evolution in Arabidopsis.

This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied. (c) 2007 Elsevier Inc. All rights reserved

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This paper studies the interrelationship between the -N policy M/G/1/K queue and the -F policy G/M/1/K queue. The -N policy queuing problem investigates the most common issue of controlling service. The -F policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the -N policy M/G/1/K queue with startup time. We have demonstrated that the -N policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the -F policy G/M/1/K queue with startup time. The interrelationship between the -N policy and the -F policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.