Reciprocal difference

Abstract: Self-incompatibility in passionfruit was studied in families originated from crosses among plants that presented differences in reciprocal crosses The three families, obtained by crossing S3 plants, exhibited one incompatible group; no reciprocal differences were observed The phenotype of the families was the same as the parent plants, S3 These results suggest the presence of a gene (G), gametophytic in its action, associated to the sporophytic gene S, modifying the incompatibility reaction in passionfruit The reciprocal difference exhibited in the crosses among the parents could be explained as a matching between plants homozygous for S, but homozygous and heterozygous for G Actually this would be a partially compatible cross, not detectable when the evaluation is done based on fruit set data As the family originated from this kind of cross is homozygous for S and heterozygous for G, no reciprocal differences are expected, and the phenotype should be the same as the parental plants, as observed in the present work

Abstract: We consider positive solutions of the following difference equation: We prove that every positive solution is eventually periodic.

Abstract: Procedures are described for efficient selection of: (1) homozygous and heterozygous S-allele genotypes; (2) homozygous inbreds with the strong self- and sib-incompatibility required for effective seed production of single-cross F1 hybrids; (3) heterozygous genotypes with the high self- and sib-incompatibility required for effective seed production of 3- and 4-way hybrids. From reciprocal crosses between two first generation inbred (I1) plants there are three potential results: both crosses are incompatible; one is incompatible and the other compatible; and both are compatible. Incompatibility of both crosses is useful information only when combined with data from other reciprocal crosses. Each compatible cross, depending on whether its reciprocal is incompatible or compatible, dictates alternative reasoning and additional reciprocal crosses for efficiently and simultaneously identifying: (A) the S-allele genotype of all individual I1 plants, and (B) the expressions of dominance or codominance in pollen and stigma (sexual organs) of an S-allele heterozygous genotype. Reciprocal crosses provide the only efficient means of identifying S-allele genotypes and also the sexual-organ x S-allele-interaction types. Fluorescent microscope assay of pollen tube penetration into the style facilitates quantitation within 24–48 hours of incompatibility and compatibility of the reciprocal crosses. A procedure for quantitating the reciprocal difference is described that maximizes informational content of the data about interactions between S alleles in pollen and stigma of the S-allele-heterozygous genotype. Use of the non-inbred Io generation parent as a ‘known’ heterozygous S-allele genotype in crosses with its first generation selfed (I1) progeny usually reduces at least 7 fold the effort required for achieving objectives 1, 2, and 3, compared to the method of making reciprocal crosses only among I1 plants. Identifying the heterozygous and both homozygous S-allele genotypes during the I1 generation facilitates, during subsequent inbred generations, strong selection for or against modifier genes that influence the intensity of self- and sib-incompatibility. Selection for strong self and sib incompatibility can be effective for both homozygous inbreds and also for the S-allele heterozygote, thus facilitating production of single-cross F1 hybrids and also of 3-and 4-way hybrids.