Relationships between genotype x environment interactions and rank orders for a set of genotypes tested in different environments

Multilocation trials in plant breeding lead to cross-classified data sets with rows=genotypes and columns=environments, where the breeder is particularly interested in the rank orders of the genotypes in the different environments. Non-identical rank orders are the result of genotype x environment interactions. Not every interaction, however, causes rank changes among the genotypes (rank-interaction). From a breeder's point of view, interaction is tolerable only as long as it does not affect the rank orders. Therefore, the question arises of under which circumstances does interaction become rank-interaction. This paper contributes to our understanding of this topic. In our study we emphasized the detection of relationships between the similarity of the rank orders (measured by Kendall's coefficient of concordance W) and the functions of the diverse variance components (genotypes, environments, interaction, error). On the basis of extensive data sets on different agricultural crops (faba bean, fodder beet, sugar beet, oats, winter rape) obtained from registration trials (1985–1989) carried out in the Federal Republic of Germany, we obtained the following as main result: W ₂ ^g /( ₂ ^g + ₂ ^v ) where ₂ ^g =genotypic variance and ₂ ^v = ₂ ^ge + ₂ ^o /L with ₂ ^ge =interaction variance, ₂ ^o =error variance and L=number of replications.     

Genetic architecture of a heterotic cross between two populations of maize

Summary The nature and magnitude of variability in the interpopulation cross of Mezcla Amarillo Selection (MAS), an introduction from CIMMYT, Mexico, and J607, a population developed in India using indigenous, American, and Yugoslavian germplasm, were studied. Interpopulation progenies developed by following the North Carolina Design I were evaluated at two locations. The additive genetic variance component in interpopulation cross, _A(12) ² , and in one population assuming the other population as tester, _A12 ² and _A21 ² were significant for all the traits evaluated, namely ear length, ear girth, kernel rows and days to silk, with one exception. For kernel rows, the dominance variance component, _A(12) ² , was also significant but it was smaller than _A(12) ² . The variance component due to dominance X location interaction, _DL(12) ² , was significant for all traits except kernel rows. In the case of ear length and ear girth, _DL(12) ² was greater than the other components. _AL(12) ² , _AL12 ² and _AL21 ² were not significant for any trait. Expected genetic advance indicated a superiority of half-sib reciprocal recurrent selection over full-sib reciprocal recurrent selection.     

Genetic evaluation with autosomal and X-chromosomal inheritance

Summary At present, genetic evaluation in livestock using best linear unbiased prediction (BLUP) assumes autosomal inheritance. There is evidence, however, of X-chromosomal inheritance for some traits of economic importance. BLUP can accommodate models that include X-chromosomal in addition to autosomal inheritance. To obtain BLUP with autosomal and X-chromosomal additive inheritance for a population in which allelic frequency is equal in the sexes, and that is in gametic equilibrium, we write y _i = x_i + a_i + s_i + e_i, where y _i is the phenotypic value for individual i, x_i, is a vector of constants relating y _i to fixed effects, is a vector of fixed effects, a _i is the additive genetic effect for autosomal loci, S _i is the additive genetic effect for X-chromosomal loci, and e _i is random error. The covariance matrix of a _i's is A _A ² , where A is the matrix of twice the co-ancestries between relatives for autosomal loci, and _A ² is the variance of additive genetic effects for autosomal loci. The covariance matrix of s _i's is S _F ² , where S is a matrix of functions of co-ancestries between relatives for X-chromosomal loci and _F ² is the variance of additive genetic effects for X-chromosomal loci for noninbred females. Given the covariance matrices of random effects a _i, s_i, and e _i, BLUPs of autosomal and of X-chromosomal additive effects can be obtained using mixed model equations. Recursive rules to construct S and an efficient algorithm to compute its inverse are given.Dedicated to the memory of Dr. C. R. Henderson, whose encouraging comments stimulated the research in this paper. Supported in part by the Illinois Agricultural Experiment Station, Hatch Project 35-0367, Estimation of Genetic Parameters.     

Efficiency of check-plot designs in unreplicated field trials

Check-plot designs have a lower selection intensity than unreplicated non-check-plot designs if both the number of test lines to be selected (s) and of total plots in the trial (N) are kept constant. For a check-plot design to be more efficient, local control must effectively reduce the plot error variance and increase heritability to such a level that it compensates for the corresponding loss in selection intensity and makes the expected gain from selection at least equal to that in the non-check-plot design. To realize this goal, the required minimum reduction in plot error variance in a checkplot design (relative to that in a non-check-plot design) depends on (1) check-plot frequencyf _c , (2) fractionk = s/N, and (3) ratiow ₀= ₀ ² / _g ² of non-check-plot design plot error variance ₀ ² to genetic variance _g ² among test lines. Lowerw ₀ and higherf _c andk are found to require a relatively higher reduction in plot error variance in check-plot designs. A condition is derived to show when a check-plot design may never be more efficient.     

Theoretical studies on the necessary number of components in mixtures

Summary Theoretical studies on the optimal numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to phenotypic yield stability (measured by the parameter variance). For each component i, i = 1, 2,..., n, a parameter u_i with 0 u_i 1 has been introduced reflecting the different survival and yielding ability of the components. For the stochastic analysis the mean of each u_i is denoted by u ₁ and its variance by _i ² For the character total yield the phenotypic variance V can be explicitly expressed dependent on 1) the number n of components in the mixture, 2) the mean of the _i ² 3) the variance of the _i ² 4) the ratio and 5) the ratio _i ² /² where denotes the mean of the u _i and _u ² is the variance of the u _j. According to the dependence of the phenotypic stability on these factors some conclusions can be easily derived from this V-formula. Furthermore, two different approaches for a calculation of necessary or optimal numbers of components using the phenotypic variance V are discussed: A. Determination of optimal numbers in the sense that a continued increase of the number of components brings about no further significant effect according to stability. B. A reduction of b % of the number of components but nevertheless an unchanged stability can be realized by an increase of the mean of the u _i by 1% (with and _u ² assumed to be unchanged). Numerical results on n (from A) and 1 (from B) are given. Computing the coefficient of variation v for the character total yield and solving for the number n of components one obtains an explicit expression for n dependent on v and the factors 2.-5. mentioned above. In the special case of equal variances, _i ² = _o ² for each i, the number n depends on v, x = (₀/)² and y = (_u/)². Detailed numerical results for n = n (v, x, y) are given. For x 1 and y 1 one obtains n = 9, 20 and 79 for v = 0.30, 0.20 and 0.10, respectively while for x 1 and arbitrary y-values the results are n = 11, 24 and 95.This publication is an extended version of a lecture given at the 1984-EUCARPIA meeting (Section Biometrics in Plant Breeding) in Stuttgart-Hohenheim (Federal Republic of Germany)     

An integrated approach to oilseed rape cultivar selection using phenotypic stability

Summary Various methods of evaluating phenotypic stability have been proposed; however, no single method can adequately describe cultivar performance. The objectives of this study were to integrate a number of methods of evaluating stability and to use this approach for cultivar selection. These objectives were considered in the context of the broad-based oilseed rape cultivar (Brassica napus spp. oleifera) evaluation system currently used in western Canada. Regression analysis was used to assess cultivar response to environments. Cluster analysis was used to assemble cultivars into groups with similar regression coefficients (b _i ) and mean yield. Three parametric stability parameters, years within locations mean square (MS; Y/L), Shukla's stability variance ( _i ² ), and Francis and Kannenberg's coefficient of variability (CV _i ), were compared to determine which method would be most suitable for selection of oilseed rape cultivars from within clustered groups. Yield data from three cultivars and six breeding lines that had been tested for 2 years at 26 locations in the Western Canola Cooperative Test A were used for all calculations. The cluster analysis was successful in identifying commercially acceptable breeding lines. The parameter MS _i Y/L was considered to be more appropriate than either CV _i or _i ² , because it measured only the unpredictable portion of the genotype x environment interaction and was independent of the other cultivars in the test. The use of cluster analysis to group entries with similar b _i values and mean yields, followed by selection for stability within groups, was advocated.Contribution No. 846 of the Plant Science Department, University of Manitoba     

RNA polymerase sigma-related proteins in Escherichia coli: detection by antibodies against a synthetic peptide

Summary Antibodies were raised against a synthetic tetradecameric peptide with an amino acid sequence, DLIQEGNIGLMKAV, which corresponds to the most highly conserved region of bacterial RNA polymerase factors. In a Western-blot analysis of total Escherichia coli proteins, the antiserum reacted specifically with at least three proteins with apparent molecular weights of 75 kDa, 27 kDa and 23 kDa, in addition to the known factors (⁷⁰ and ³²). The majorities of ⁷⁰ and ³² were recovered as associated forms with the RNA polymerase on glycerol gradient centrifugation, while the other cross-reacting proteins were not. Unambiguous evidence was obtained which indicated that the intracellular level of ³² increased rapidly upon heatshock, at least in the strain containing high copy numbers of the rpoH gene.     

Foam behavior of biological media

Summary The surface tension and foaminess of (a) unlimited, (b) substrate limited, and (c) oxygen transfer limited growth media of Hansenula polymorpha were measured using methanol, ethanol or glucose as a substrate.The time dependence of can be described by the Avrami-Überreiter relationship: log (2.3 log V)=n log t+log b, where V = (_O – _eq/(_t – _eq, and _O, _t and _eq are at t_M=0, t_M=t and t_M (equilibrium value).The constants n and b are functions of the fermentation time t_F as long as the growth is unlimited but they are constant in the state of limited growth. With glucose substrate, the foaminess can be presented as a definite function of the time, t_DG, which is necessary to attain _eq. With alcohol as a substrate no definite (t_DG) function was found.Symbols b constant in Eq. (1) - n constant in Eq. (1) - S substrate concentration - T temperature - t_M time h (measured from the beginning of the determination of the surface tension ) - t_F cultivation time h (measured from the time of inoculation) - t_DG time (min) necessary to attain the equilibrium surface tension ) - X dry biomass concentration (gl^–1) - V (_O – _eq)/(_t – _eq) - V_S equilibrium volume of the foam (cm³) - V_G volumetric gas flow rate during the estimation of (cm³ s^–1) - vvm volumetric gas flow rate with regard to the volume of the medium (min^–1) - w_SG superficial gas velocity (cm s^–1) - _m maximum specific growth rate (h^–1) - V_S/V_G foaminess (s) - surface tension, mMm^–1 (milli Newton m^–1) - _O at t_M=0 - _eq equilibrium surface tension ( at t_M) - _t at t_M=t - HP probes from Hansenula polymorpha cultivation - NLG non limited growth - OTLG oxygen transfer limited growth - SLG substrate limited growth     

The<Emphasis Type="Italic"> ssgB</Emphasis> gene,encoding a member of the regulon of stress-response sigma factor σ<Superscript>H</Superscript>, is essential for aerial mycelium septation in<Emphasis Type="Italic"> Streptomyces coelicolor</Emphasis> A3(2)

The Streptomyces coelicolor A3(2) gene ssgB belongs to the regulon of stress-response sigma factor ^H. By integrative transformation via double cross-over, a stable null mutant of ssgB was obtained. This mutation had no obvious effect on vegetative growth, but critically affected aerial mycelium septation. The S. coelicolor ssgB mutant produced aerial hyphae without any signs of septation into spore compartments. The mutation was complemented in trans by wild-type ssgB including the ^H-dependent ssgBp promoter. The results proved that ssgB belongs a developmental branch of the ^H regulon.     

The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels

The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (²_g) and specific combining ability variance (²_s) had a large positive skewness. For ²_g and ²_s, a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121–128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Halls transformation methods (Zhou and Gao, Am Stat 54:100–104, 2000) had poor coverages. Coverage accuracy of Fiellers interval endpoint(J R Stat Soc Ser B 16:175–185, 1954) and t-interval endpoint were similar for both h² and r_B for sample sizes n10, but for n=30 the Fiellers method is much better.     

Highly polymorphic DNA markers to specify strains of the ectomycorrhizal basidiomycete Tricholoma matsutake based on σ marY1 , the long terminal repeat of gypsy-type retroelement marY1

The ectomycorrhizal basidiomycete Tricholoma matsutake produces commercially valuable fruit bodies—matsutake—in Pinus sp. forest. Here we report that PCR with outward facing primers designed based on sequences comprising _marY1, the long terminal repeat of the gypsy-type retroelement marY1, specifies strains of T. matsutake. PCR with a primer based on the 22-bp sequence conserved at the 5-end of _marY1 conferred 73 reliable bands overall whose profiles depend upon strains of T. matsutake and T. magnivelare, the latter known as American matsutake. This PCR system gave no detectable band in any other species of Tricholoma tested, including T. bakamatsutake and T. fulvocastaneum, symbionts closely related to T. matsutake, as well as a host plant, Pinus densiflora. Similarly, PCR with a set of primers based on 26-bp and 28-bp sequences at bp 48–73 and bp 281–308 of _marY1, internal regions that are mutated in a variant of marY1, conferred 90 reliable bands only in strains of T. matsutake. Theoretically, PCR with the 22-bp primer would allow generation of 2⁷³, or 9.4×10²¹, types of polymorphism, and PCR with a combination of 26- and 28-bp primers, 2⁹⁰, or 1.2×10²⁷ types. The probability of falsely specifying two different isolates as the same strain is <1/10²¹. While polymorphisms conferred by the primer based on the 5 end of _marY1 rather exhibit genetic conservation of a group of T. matsutake, those resulting from primers based on the internal sequences more clearly demonstrate intra-specific diversification. Both systems revealed that T. matsutake is divergent within the species. Ectomycorrhizas formed between P. densiflora and T. matsutake were identified by the PCR systems developed in the present study. This method, using _marY1 as a genetic marker, is useful in analyzing the diversity of T. matsutake, monitoring the behavior of individual mycorrhizas, and specifying the ecological background of fruit bodies traded in markets.     

Probabilities of negative estimates of genetic variances

Summary The probability of negative analysis of variance estimates of genetic variance components due to sampling error (Ps) was investigated. The objectives were to evaluate the magnitude of Ps, to compare Ps for estimates of _A ² and _D ² , and to compare Ps for genetic variance component estimates from the nested and factorial mating designs. Ps was defined in terms of ratios of mean squares and the F distribution was used to calculate probabilities of the negative estimates. The results indicated that Ps is often greater than 0.20 for _D ² . It is generally lower for _A ² than for _D ² , and lower for the factorial mating design than the nested mating design.Technical Contribution No. 2589 from the South Carolina Agricultural Experiment Station, Clemson University     

A study of the encoder properties of muscle-spindle primary afferent fibers by a random noise disturbance of the steady stretch response

Muscle spindle stretch responses (cat gastrocnemius muscles) were studied when bothsteady stretch andsmall near-threshold random stretch determined the Ia impulse sequence. Statistical properties of the inter-impulse-intervals gave some insight into the Ia encoder mechanism. Superimposed random stretch of mean velocities _vel below 5 mm s^–1 did not change the mean discharge rate, but the width of the Ia interspike interval distribution was clearly increased. Raising the stretch velocity further ( _vel > 5 mm s^–1) led to an additional increase in the distribution width, finally reaching values of 0.6 for the coefficient of variation. The shapes of the impulse interval histograms changed from symmetrical to positively skewed ones. The 1st order serial correlation coefficient of the interval sequence shifted to slightly more negative values with increasing _vel; on the average, ther _1,2-value varied between zero and –0.2. The data were discussed in relation to current ideas on the mechanism of impulse initiation in the Ia terminal ending. They provide evidence that a combination of multiple encoder sites located in the myelinated terminal branches and a separate pathway for large static and small-amplitude dynamic stretch is not very likely. A model is proposed as to how the whole tree of myelinated axons functions as a single encoder site.     

Selection studies in sugarcane (Saccharum sp. hybrids)

Summary An approximate method to determine sample size for the estimation of population variance, ², is given. The estimate of ² is denoted as s² . Based on the assumption of a normal distribution for (s²/²–1), the sample size is approximately equal to 20,000 z² _p,/k²; where z is a standard normal deviate, p is the probability that s² ( 100¦s² – ²¦/²) is less than, or equal to, a critical value k, and k (measured as gDs²) is the desired precision of s² .The expected value of s², with respect to sample size, and the expected cumulative frequencies of s² over sample size for various k values are given. Their goodness of fit to the observed results was satisfactory except for populations that were different from normal. The observed values were taken from a study on four yield components in five sugarcane polycross progenies, grown in two contrasting environments over 2 years in three selection stages.The expected s² was found to be independent of the population coefficient of variance.Research suppoted in part by USDA, ARS, grant #12-14-5001-34. Published with the approval of the Director as Paper No. 412 in the Journal Series of the Experiment Station, Hawaiian Sugar Planters' Association.     

Regression analysis of yield stability is strongly affected by companion test varieties and locations — examples from a study of Nordic barley lines

The suitability of regression analysis for studying the phenotypic stability of grain yield was investigated using a collection of 220 Nordic barley lines. Linear regression explained 26–52% of the genotype x environment (GE) interactions in different groupings of the material. The regression coefficient, b _i , measures the yield response of the i-th genotype to improved environmental conditions. Deviations from regression, S _di ² , have been used to estimate Tai's stability parameter, _i , which is a measure of the phenotypic yield stability in the agronomic sense. Repeatability of b _i , _i , and grain yield was studied by means of correlations between estimates obtained in each experimental year. Yield had the highest repeatability, with correlations between years ranging from 0.57 to 0.85. In this study, regression coefficients and _i -values were not repeatable, i.e. genotypes reacted differentially to the yearly climatic variations. Six-rowed (6r) barleys had higher responsiveness, but lower mean yields, than two-rowed (2r) barleys. This is partly due to the history of selection of 6r-barleys, which mainly originate from regions with low potential yield levels, i.e. Finland and Norway. In general, responsiveness and stability were not correlated with yield. The highest-yielding lines had b _i 1. The response pattern of the different types of barleys used in this study show that responsiveness can be changed by recombination.     

A mechanism for isotonic fluid flow through the tight junctions of Necturus gallbladder epithelium

During isotonic fluid flow, Necturus gallbladder epithelium mediates net fluxes of paracellular probes by a convective process. We show here that the paracellular system is modeled by permeation through three populations of channels: (i) convective parallel-sided ones of width 7.7 nm (ii) small diffusive ones of radius 0.6 nm, and (ii) large diffusive ones of radius exceeding 50 nm. The reflexion coefficient of the convective channels is very low and the calculated osmotic flow rate is close to zero when compared with the observed fluid absorptive rate of 2 x 10^–6 cm/sec. Analysis reveals that the convective channels behave as though closed to back-diffusion of probes; if this is due to solvent drag then very high fluid velocities are required, acting through minute areas. There are no transjunctional gradients that could drive the flow, and so the fluid must be propelled through the channel by components of the junction.We propose a mechanism based upon an active junctional peristalsis which allows discrimination on the basis of molecular size, in which the channels are always occluded at some point and so back-diffusion cannot occur. There is no local gradient of salt distal to the junctions and therefore the osmotic permeability of the membranes is irrelevant. High fluid velocities are not required, and the flow can occur over a substantial fraction of the junction. The mechanism must involve motile and contractile elements associated with the junction for which there is already considerable evidence.Symbols A _i filtration area of channel i;i=b (big), s (small) and c (convectional) - B constant for streamline flow - C _i concentration of probe at i - D diffusion coefficient - D ^o diffusion coefficient in free solution - d width of junction - F _i diffusive drag factor in channel i - g ionic conductivity - G _i convective drag factor in channel i - J _ij probe flux from i to j - J _net net probe flux - J _v volume flow per cm² of epithelium - l linear extent of junction per cm² epithelial plane - L length of junctional channel - L _p hydraulic conductivity - N Avogadro's number - q available filtration area fraction of channel - r _s probe molecular radius - r _c channel radius or half-width - S _i steric factor in channel i - V _w,s partial molar volume of water or salt - v _i fluid velocity in channel i - _w dynamic viscosity of water - specific conductivity - ratio of solute radius to channel radius or half-width - diffusive/pressure-driven flow ratio - reflexion coefficient     

Construction of spore mutants of Bacillus subtilis for the development as a host for foreign protein production

For the development of Bacillus subtilis as a host for foreign protein synthesis, three types of sigma factor deleted mutants (spoIIAC, spoIIIG and spoIIIC) were constructed by antibiotic marker insertion using plasmid vector-mediated method or LFH (Long Flanking Homology)-PCR. Mother cell specific sigma factor mutants of B. subtilis (^K), B. subtilis DB104 spoIIIC (km ^r)::pMK101, had two to three times higher subtilisin activity than the wild type DB104::pMK101. Subtilisin expression by the other two mutants, B. subtilis DB104 spoIIAC (km ^r)::pMK101 and DB104 spoIIIG (km ^r)::pMK101, which are pre-spore specific sigma factor (^F and ^G) deleted strains, was similar to, or less than that of the wild type.     

Influence of molecular variations of ionophore and lipid on the selective ion permeability of membranes: II. A theoretical model

Summary The steady-state electrical properties induced by neutral carriers of ions in lipid bilayer membranes and the time dependence of the membrane current for low applied voltages are described theoretically in terms of a model which allows for a voltage dependence of the interfacial reactions, as well as for a trapezoidal shape of the internal free energy barrier for translocation of the complex. The basic features of the model are closely related to those of others presented previously (J.E. Hall, C.A. Mead & G. Szabo, 1973,J. Membrane Biol. 11:75; S.B. Hladky, 1974,Biochim. Biophys. Acta 352:71; S.B. Hladky, 1975,Biochim. Biophys. Acta 375:327; Eisenman, Krasne & Ciani, 1975,Ann. N.Y. Acad. Sci. 264:34), but the analysis of its consequences on the steady-state and nonsteady-state electrical characteristics is given here in greater detail and is extended to provide the expression for the zero-current potential in ionic gradients. It is shown that parameters, such as the width of the trapezoidal barrier, the plane of the reaction and the ratio of the rate constant of translocation across the membrane interior to the rate constant of dissociation of the complex, can be deduced from steady-state analysis, whereas the individual values of these constants and the distance between the equilibrium positions of the complexes are deducible from relaxation measurements.Definition of the Symbols A _s ^* rate constant for translocation of the neutral carrier across the membrane interior - A _is ^* () defined by Eq. (18) - _is ^* defined by Eq. (24) - B defined by Eq. (9) - c _i , c _i aqueous concentrations of the ionic speciesi in the two bulk solutions - c _s ,c _s ^T ,c _s (0),c _s (d) concentrations of the neutral carrier in the bulk aqueous phases, in the membrane-surrounding torus, and at the ends of the unstirred layers near the membrane-solution interfaces - d membrane thickness - D _s diffusion coefficient of the carrier in the aqueous phase - D _is ^* diffusion coefficient of the complex in the membrane - E _A ,E _B ,E _C electric fields in the compartments shown in Fig. 2 - G(0) conductance near zero voltage - G() conductance at the normalized voltage - I electric current density - J _is flux of complexes across the membrane interior - k _s ^F ,k _s ^B rate constants for the transfer of neutral carriers across the interfaces - k _s ^TM ,k _s ^MT rate constants for the transfer of carriers from the torus into the membrane and vice versa - rate constants of the heterogeneous reaction describing the formation and the dissociation of the ion-carrier complexes - . - L _i () defined by Eq. (26) - N _i defined in Eq. (45) - N _s ^* (1),N _s ^* (2) surface densities of the neutral carrier at their equilibrium positions inside the membrane; note that the equilibrium positions for the neutral carrier, (1) and (2), do not coincide necessarily with the equilibrium positions, (1) _i , and (2) _i , of the complexis. - N _s ^* (st.) defined by Eq. (8) - N _is ^* (1) _i ,N _is ^* (2) _i surface densities of the ion-carrier complexes at their equilibrium positions inside the membrane - q, r fractions of membrane thickness defined in Fig. 1 - V, V ₀ transmembrane potential and potential at zero-current, respectively - defined by Eq. (35) - W _is ^* (x) defined by Eq. (14) - W _i free energy difference between the base and the top of the trapezoid in Fig. 1 - _i width of the flat top of the energy barrier, measured in membrane thickness units - _i distance of the interfacial peaks from the middle of the membrane, measured in membrane thickness units - distance between the two internal free energy wells for the complexes, measured in membrane thickness units (see Fig. 2) - relaxation amplitude - thickness of the unstirred layers - dielectric constant of the membrane phase - _is ^0* (x) standard chemical potential of the ion-carrier complex inside the membrane - transmembrane potential inRT/zF units, namelyzFV/RT=zF(V-V)/RT - (1) _i , (2) _i electric potential at the positions (1) _i , and (2) _i , respectively - ₀ membrane potential at zero current - , net charge of the diffuse double layers per unit membrane area. For small Debye lengths this charge can be viewed as distributed at the membrane-solution interfaces - ₁, ₂ surface charge due to the complexes located at their equilibrium positions - relaxation time - _i defined in Eq. (44)     

Studies of inheritance of reaction to common smut in corn

Summary Reaction to Ustilago maydis was studied in resistant and susceptible corn inbreds, their F ₁ hybrids and F ₂ and F ₃ segregants. Marked differences among inbreds in genetic prepotency were found. Segregation was polygenic. The concept of combining ability was applied and estimates of _G ^/2 and _S ^/2 were calculated. Both additive and non-additive gene action was found. Breeding for resistance based on crossing to special susceptible testers was suggested.

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Zusammenfassung An resistenten und anfälligen Mais-Inzuchtlinien, deren F ₁-Hybriden und deren F ₂- und F ₃- Generationen wurde die Reaktion auf Ustilago maydis untersucht. Bezüglich der genetischen Präpotenz zeigten sich bei den Inzuchtlinien deutliche Unterschiede. Die Spaltung war polygen. Es wurde die Methode der Prüfung der Kombinationsfähigkeit angewandt und die allgemeine ( _G ² ) und spezielle ( _G ^/2 ) Kombinationsfähigkeit geschätzt. Sowohl additive wie nicht-additive Genwirkung wurde gefunden. Für die Resistenzzüchtung werden Kreuzungen mit besonders anfälligen Testern vorgeschlagen.