An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

An Unbalanced Two-way Model With Random Effects Having Unequal Variances

Consider the model y_ijk=u ± a_i ± b_i ± c_ij ± e_ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n_ij where μ is a constant and a_i, b_i, c_ij are distributed independently and normally with zero means and variances Δ₂ Δ2/bd_ij and δ₂ respectively. It is assumed that d_i's, and d_ij's are known (positive) constants (for all i and j). In this paper procedures for estimating the variance components (Δ₂, Δ²_b and Δ²_a) and for testing the hypothesis H_oc:Δ²_c/Δ² = y₃ and H_oa:Δ²_b/Δ² = y₄ (where y₂, y₃, and y₄, are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.     

On the Effects of Departure from Normality on the F-Ratios in a Nested Random Effect Model by Mixture of Normals

In this paper we consider the following nested random effect model where the α_i's, the β_ij's and the e_ijk are independent random variables. By assuming that these variables follow a mixture of two normal densities, we study the effects of departure from normality on the classical JT-tests for variance components. It is shown that the departure from normality has little effects on the type 1 error and the power function; this indicates that the classical F-tests are quite robust with respect to departure from normality.     

Chemically reacting systems of the type A + B ⇄ AB. II. Osmometry

The osmotic pressure equation for nonideal, associating systems of the type nA +mB ? A_nB_m, has been derived, by using the assumption yA _nB _m/yA ⁿyB ^m = 1. This treatment can also be applied to related associations such as nA + mB ? AB + AB₂ + A₂B + …. From osmotic pressure experiments on the pure reactants it is possible to obtain the molecular weights (M_A and M_B) of the reactants and also the virial coefficients (B_AA and B_BB) of the reactants. The osmotic pressure of a nonreacting mixture of A and B can be calculated from these measurements. It can be used along with osmotic pressure measurements on equilibrium mixtures of A and B to obtain expressions containing the equilibrium constant (or constants) and the cross-virial coefficients (B_AB and B_BA). Several procedures are described for the evaluation of the equilibrium constant (or constants) and the B_AB or B_BA terms. It appears that this procedure is a general one which is applicable to associations of the type nA + mB ? AB + A₂B + AB₂ + …. By correcting for nonideal behavior, one should then be able to apply it to any method available for analyzing ideal associations of the types considered here. In addition it is possible, subject to certain restrictions, to analyze associations of the type 3A + B ? A₂ + AB.     

Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors

Given independent multivariate random samples {X_ij: j = 1, …, n_i} from F_i, for i = 1,2, a test is desired for H₀: F₁ = F₂ against general alternatives. Consider the k · (n₁ + n₂) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let S_k be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed S_k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kS_k, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.     

Linked epistasis for six quantitative traits in Indian mustard (Brassica juncea (L.) Czern & Coss)

Summary Gene effects, and interactions, and associations between days-to-flower initiation and maturity, number of secondary branches and siliquae per plant, and 1,000-seed weight and yield per plant were studied in a cross of Indian mustard (Brassica juncea (L.) Czern & Coss) using the parents and F₁, F₂, F₃, B₁, B₂, B₁₁, B₁₂, B₂₁, B₂₂, B_1S, B_2S, B₁F₁, B₂F₁, B_1bip, B_2bip, F₂P₁, F₂F₁, and F_2bip generations. A linked digenic model was adequate for all characters studied. According to this model, the main effects, additive and interactions between linked pairs of genes, were present in varying proportions for days-to-flower initiation and maturity and number of siliquae per plant. The contribution of linked epistatic effects, however, was much greater than that of additive effects. Dominance effects contributed significantly to the inheritance of days-to-flower initiation. Duplicate epistasis was observed for all traits except 1,000-seed weight where epistasis was of the complementary type. A complete association among the genes of similar effect (increasing or decreasing) was observed for number of secondary branches and siliquae, and yield per plant. Coupling phase linkage was observed for days-to-flower initiation whereas repulsion phase linkage was observed for daysto-maturity and 1,000-seed weight.     

Direct Calculation of a Tree Length Using a Distance Matrix

Comparative studies of tree-building methods have shown minimum evolution to be in general an accurate criterion for selecting a true tree. To improve the use of this criterion, this paper proposes a method for rapidly and directly calculating a length of a dichotomous tree without having to resort to branch length calculations. This direct calculation (DC) method applies to the complete final topology, giving equal importance to each branch after a dichotomy. According to this method, the tree length S _DC is S _DC =∑ _i ∑ _j (D _ij /2 ^Bij ) = (∑ _i<j ∑D _ij 2 ^Bmax−Bij )/2 ^{Bmax −1} where D _ij is the observed distance between taxa i and j, B _ij is the number of branches connecting i and j, Bmax is the greatest B _ij in the tree, and the powers of two are due to the dichotomy of the tree. This tree length expression may be used as a rapid method for selecting the shortest tree from a set of hypothetical or subobtimal trees. Received: 2 March 2000 / Accepted: 24 March 2000     

Synergistic promotion of gibberellin and cytokinin on direct regeneration of floral buds from in vitro cultures of sepal segments in sinningia speciosa hiern

Summary This study reports the direct regeneration of flower buds from cultured sepal segments of Sinningia speciosa Hiern. Two types of floral bud regeneration were observed: regeneration of floral buds only (designed as B^F) and regeneration of both floral and vegetative buds (designed as B^F+V). The capacity of B^F regeneration was closely related to the location of sepal segments and the concentration of exogenous gibberellin (GA₃) and cytokinin in the medium. On the medium containing 1.0mgl^&#x2212;1 GA₃, the addition of 6-benzyladenine (BA) significantly increased the frequency of total flower bud (B^F+B^F+V) formation, with the frequency up to 91.5% in the presence of 0.4mgl^&#x2212;1 BA. On the medium containing 0.1mgl^&#x2212;1 BA, the addition of GA₃ also increased the frequency of total flower bud regeneration, with the frequency up to 74.3% in the presence of 1.0mgl^&#x2212;1 GA₃, but no further increase in regeneration was observed when the GA₃ concentration was higher than 1.0mgl^&#x2212;1. The capacity of B^F regeneration from different locations of sepal segments was differential. The adaxial part of sepal segments gave rise to the highest frequency of 56.7 and 84.3% for B^F and B^F+B^F+V, respectively.     

A testcross procedure for selecting exotic strains to improve pure-line cultivars in predominantly self-fertilizing species

Methods for identifying germplasm carrying alleles with the potential to improve a particular single-cross hybrid have been proposed and discussed in recent years. There is a need for similar methods to be used in breeding crops for which pure-line cultivars, rather than hybrids, are the goal. The objective of this research was to develop a method to identify germplasm lines with the potential to contribute favorable alleles not present in a specified pure line or set of pure lines. Given a set of adapted pure lines (A ₁, A ₂ ..., A _m) to be improved and a set of germplasm lines (P ₁ P ₂ ..., P _f), the procedure consists of producing all f x m possible hybrids and evaluating them along with the parents. The testcross statistic T _ij is defined by T _ij=(F _ij–A _j)+(1–) (F _ij–P _i), where A _j, P _i, and F _ij represent the performance of thej ^th adapted line, the i ^th germplasm line, and their hybrid, respectively. The statistic is the mean value of T _ij over all adapted parents A _j. If =(1/2)(1+d), where d = the mean degree of dominance, then T _ij measures the potential for alleles from P _i to improve A _j and measures the potential for alleles from P _i to improve the set A ₁, A ₂ ..., A _m. Use of data on soybean and peanut hybrids published by other researchers suggests that the value assumed for d has little effect on the P _i chosen. The ability of the T _ij and statistics to identify germplasm strains carrying rare favorable alleles should be assessed in empirical studies.Joint contribution: OARDC (Journal Articale No. 161-94), USDAARS, Iowa Agriculture and Home Economics Expriment Station (Journal Paper No. J-16109; Project 2985), and Agreculture and Agri-Food Canada. Salaries and research support for S. K. St. Martin Provided by state and federal funds appropriated to the Ohio Agricultural Research and Development Center, Ohio State University     

Contributions of the free oxidized and QB-bound plastoquinone molecules to the thermal phase of chlorophyll-a fluorescence

Variable chlorophyll a (Chl a) fluorescence is composed of a photochemical and a thermal phases of similar amplitudes. The photochemical phase can be induced by a saturating single turnover flash (STF) and reflects the reduction of the Photosystem II (PS II) Q_A primary electron acceptor. The thermal phase requires multiple turnover flash (MTF) and is somehow related to the reduction of the plastoquinone (PQ) molecules. This article aimed to determine the relative contributions of the Q_B-bound and the free oxidized PQ molecules to the thermal phase of Chl a fluorescence. We thus measured the interactive effects of exogenous PQ (PQex), of an inhibitor (DCMU) acting at the Q_B site of PS II and of an artificial quencher, 2-methyl-1,4-naphtoquinone, on Chl a fluorescence levels induced by STF (F_F) and MTF (F_M) in spinach thylakoids. We observed that: (1) the incorporation of PQex in thylakoids stimulated photosynthetic electron transport but barely affected F_F and F_M in the absence of DCMU; (2) DCMU significantly increased the amplitude of F_F but slightly quenched F_M; (3) 2-methyl-1,4-naphtoquinone quenched F_M to a larger-extent than F_F; (4) DCMU increased the quenching effects of PQex on F_F and F_M and also, of methyl-1,4-naphtoquinone on F_F. These results indicate that: (1) the Q_B-bound and the free PQ molecules contribute to about 56% and 25%, respectively, to the thermal phase Chl a fluorescence in dark-adapted thylakoids; and (2) the thermal phase of Chl a fluorescence is more susceptible than the photochemical phase to the non-photochemical quenching effect of oxidized quinones. This revised version was published online in June 2006 with corrections to the Cover Date.     

The falcifolia syndrome of Oenothera: III. The general pattern of its non-Mendelian inheritance

Summary The falcifolia (fal) syndrome is a malformation characterized by shoot sectors with sickle-shaped leaves, which appears in hybrids between Oenothera suaveolens and O. lamarckiana and shows a non-chromosomal inheritance of a previously undescribed type. The determinants, their location in the cell, and the mechanism of their expression are unknown. The defect is the result of a cross in which mixing of two different cytoplasms occurs, without the usual predominantly maternal inheritance. F₁ progeny of reciprocal crosses show a quantitative difference in the frequency and degree of expression of the fal character. When the F₁ progeny are backcrossed to the parents, the percentage of fal is high in crosses to O. suaveolens and low in those to O. lamarckiana. This manner of transmission is observed regardless of whether the hybrid is used as seed or pollen parent or shows a normal or fal phenotype. F₂ generations from F₁ plants having either a normal or a fal phenotype always include a certain percentage of fal plants, although the latter generally produce a higher percentage of fal progeny. If a second backcross is carried out, plants that produce normal progeny on self-pollination behave differently from those that produce some fal off-spring when selfed. The latter are similar to the F₁ with regard to the transmission of the fal trait. Plants of the F₁B₁ yielding normal progeny upon selfing produce normal progeny in the F₁B₂ if the parent to which they are backcrossed is the same as in the first backcross; if the parents of the first and second backcross differ, a high percentage of fal offspring is obtained. Again, whether the hybrid is used as seed or pollen parent is not relevant. Exceptions to this behaviour have been observed only rarely in that the character of the penultimate cross is retained. There is some evidence of somatic segregation of the fal determinants, since sister plants may react differently; this suggestion is supported by comparing the progenies of different branches of a self-pollinated fal plant of the F₁ generation.Abbreviations F₁, F₂, F₃, F₄ First through fourth filial generation, obtained by self-pollination - F₁B₁ First backcross generation, i.e. the F₁ was backcrossed to one of the original parents - F₁B₂ Second backcross generation, i.e. the F₁B₁ was backcrossed to one of the original parents - F₁B₃ Third backcross generation, i.e. the F₁B₂ was backcrossed to one of the original parents - (F₁B₁)D₁ Descendants obtained by self-pollination of a F₁B₁ plant; further generations obtained by self-pollination are designated as D₂, D₃, D₄ - (F₁B₁)D₁B₁ Descendant or generation obtained by a backcross of the D₁ of an F₁B₁. Backcrosses of the D₂ and D₃ are designated mutatis mutandis - (F₁B₁)D₁B₂ Generation obtained by a backcross of the (F₁B₁)D₁B₁     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Genetics of obesity in KK mouse and effects of A y allele on quantitative regulation

KK mouse is known as a polygenic model for non-insulin-dependent diabetes mellitus with moderate obesity. To identify the quantitative trait loci (QTLs) responsible for the body weight in KK, linkage analysis with 97 microsatellite markers was carried out into 192 F₂ progeny, comprising 93 mice with a/a genotype at agouti locus and 99 mice with A ^y /a genotype, of a cross between C57BL/6J female and KK-A^y (A^y congenic) male, thereby the influence of A ^y allele on the quantitative regulation of body weight was also examined. In F₂ a/a mice, we identified a QTL on Chromosome (Chr) 4, and two loci with suggestive linkage on Chrs 15 and 18. In F₂ A ^y /a mice, a QTL was identified on Chr 6, and two loci with suggestive linkage were identified on Chrs 4 and 16. That the QTL on Chr 4 was held in common between F₂ a/a and F₂ A ^y /a progenies implies that this locus may be a primary component regulating body weight in KK and KK-A^y. These results suggest that the body weight in KK is controlled by multiple genes, and the different combination of loci is involved in the presence of A ^y allele. The QTL on Chr 6 seemed to determine the body weight by controlling fat deposition, because the linkage was identified on body weight and adiposity, and is suggested to be a component involved in the metabolic pathway in obesity caused by the A ^y allele. Received: 16 December 1997 / Accepted: 16 March 1998     

Intergeneric hybridization between Brassica napus and Sinapis pubescens,and the cytology and crossability of their progenies

The cytological possibility of gene transfer from Sinapis pubescens to Brassica napus was investigated. Intergeneric hybrids between Brassica napus (2n = 38) and Sinapis pubescens (2n = 18) were produced through ovary culture. The F₁ hybrids were dihaploid and the chromosome configurations were (0–1) _III + (2–11) _II + (5–24) _I . One F₂ plant with 38 chromosomes was obtained from open pollination of the F₁ hybrid. Thirty-one seeds were obtained from the backcross of the F₂ plant with B. napus. Five out of seven plants had 38 chromosomes, and the pollen stainability ranged from 0% to 81.4%. In the B₂ plants obtained from the backcross of B₁ plants with B. napus, 66.7% of the plants examined had 38 chromosomes. S. pubescens may become a gene source for the improvement of B. napus.     

Identification of multiple quantitative trait loci affecting the size and shape of the mandible in mice

A quantitative trait locus (QTL) analysis was performed on the size and shape of the mandible in F₂ mice between KK-A ^y and C57BL/6 J strains and the effect of the A ^y allele on the morphology of the mandible was analyzed. A total of 13 measurements were taken on each right mandible. By means of discriminant and canonical discriminant analyses, KK-A ^y males and KK males were exactly discriminated from each other. In contrast to its known effects on body weight, the A ^y allele reduced the overall size of the mandible. QTL analysis of the 13 measurements and on three principal components extracted from these measurements identified multiple QTLs. When F₂ a/a and F₂ A ^y /a were analyzed separately, 11 significant main-effect QTLs were identified in F₂ a/a, whereas only two QTLs were identified in F₂ A ^y /a. Although four significant interactions were identified, all were in F₂ a/a. The A ^y allele thus made the difference in the size and shape of the mandible between strains obscure. Among mandible QTLs, those on Chrs 5 (Mssq6 and Mssq7) and 15 (Mssq14) were important. Mssq6 had an effect on the height of the posterior mandible. Mssq7 had an effect on mandible length. Mssq14 had an effect on the height of the anterior and posterior mandible. Mssq7 and Mssq14 also had an effect on the overall size. Thus, mandible QTLs have distinct and characteristic sites of action. Therefore, mandible morphology will be determined largely by the combination of these QTLs.     

Food resource utilization partitioning of fifteen fish species at Bukit Merah Reservoir,Malaysia

Statistical and mathematical models have been used to measure the subtle differences in food resources utilisation of fifteen (15) fish species at Bukit Merah Reservoir, Malaysia. The models employed are niche breadth, dietary overlap indices and discriminant analysis. A diet measure based on the relative importance index of food items was used for the analysis, to correct for biases of the single indices consisting of the volumetric, numerical and occurrence frequency. Niche breadth (B_i) indicating the diversity or breadth of the food resource gradient utilized by a fish classifies species as generalized feeders (B_i > 4.5), intermediate and specialized feeders (B_i < 2). Niche overlap (O_ij) quantifying the sharing of food resource between two species varies from 0.07 to 0.81 and describes high dietary overlap (O_ij > 0.60) for most fish at the reservoir; but Trichogaster pectoralis (Anabantidae) feeding on the plankton shows relatively low dietary overlap. A scatter plot and a territorial map of the discriminatory analysis on the dietary composition result in combination an objective basis for trophic classification of the fish community, and describe (1) Osteochilus hasselti and Puntius gonionotus as herbivores, (2) Oxyeleotris marmorata, Clarias batrachus, Ophicephalus striatus, Mystus planicep, and presumably Wallago leerii and Hampala macrolepidota as carnivores, (3) Puntius schwanenfeldii, Cyclocheilichthys apogon, and presumably Labiobarbus festiva as detritivores, (4) Notopterus notopterus as a generalist, and (5) Trichogaster pectoralis as a planktivore. This multivariate analysis is relatively superior to the traditional subjective method for trophic classification and discerning subtle differences objectively, though intermingling occur.     

Neutral stability in many-species food webs

The predator-prey systems of Lotka and Volterra are modified to include efficiencies e_ij of converting prey biomass to predator biomass. For three or more species, it is shown that neutral stability results if e_ik = e_ije_jk for all transfers. When the number of species is odd, consistency of the differential equation system for changes in logarithms of biomass is also required.     

Effects of stimulus timing on transmitter release and postsynaptic membrane potential at crayfish neuromuscular junctions

Summary Different synaptic terminals of the single excitor axon to the opener muscle of crayfish (Procambarus clarkii) often release transmitter in a very different manner when stimulated with the same equal-interval, doublet, or triplet patterns. Compared to synapses that show little facilitation (low F_e synapses), highly facilitating (high F_e) synapses show greater percentage increases in several measures of synaptic efficacy when stimulated with any of these patterns. Low F_e synapses usually show the greater absolute changes in these measures of synaptic efficacy. Changes in the span and pattern of doublets and triplets can independently affect both pre- and postsynaptic measures of synaptic efficacy at either low F_e or high F_e synapses.Abbreviations EJP excitatory junctional potential - MJP spontaneous miniature EJP - F _e ratio of EJP at 1 Hz to EJP amplitude at 10 Hz - F ₁ zero-time facilitation - A ₂,B ₂,C ₂ doubly corrected EJP amplitude of a particular pulse - average amplitude of doubly corrected EJPs in a train of equal-interval, doublets, and triplets, respectively - A_m, B_m, C_m maximum depolarization reached by a particular EJP - time constant of decay