A controlled-nutrient (CN) experiment was conducted to test three heterosis hypotheses with reference to tomato yield, and its components, for a set of two inbred lines and their hybrid that had previously exhibited considerable heterosis under field conditions. The CN treatments consisted of periodic applications of differential doses of nutrient solution to plants reared individually in containers filled with vermiculite. Ripe fruit were harvested, counted and weighed over a period of 340 days. The data permitted the partitioning of yield into a closed system of five component variables. Heterosis was not exhibited by yield, nor yield components, at any of the four nutrient levels. Hence the total heterosis phenomenon was classified as nutrient-dependent: heterosis occurring under field conditions, but not under the nutritional restrictions of the CN experiment. Three heterosis hypotheses were examined for their ability to explain all of the nutrient-dependent aspects of the heterosis phenomenon. Hypothesis 1: Heterosis is a consequence of a more efficient hybrid metabolic system in that it can produce more product with equal input. Hypothesis 2: Heterosis is a consequence of the somatic multiplication of additive component traits. Hypothesis 3: Heterosis is a consequence of a faster hybrid growth rate. Although none of the hypotheses are rejected by the field data, the first two are rejected by the CN experimental results. The third hypothesis fits all aspects of the nutrient-dependent heterosis phenomenon remarkably well. It is speculated that the indeterminate pattern of plant development responsible for yield and its components is due to two major gene systems: genes that determine morphogenetic, and genes that determine growth rate manifestations of growth. Under this hypothesis, the CN technique permits separation of the responses due to these two gene systems.

Plant mixtures are difficult to analyze genetically because of possible interactions between neighboring plants (i.e., between plants in the same biological group). However, a genetic modeling scheme has been devised which, theoretically, can accommodate such interactions. This study was an attempt to put the theoretical modeling procedure to an experimental test. To this end an experimental procedure was devised that generated biological groups from a well defined base population. A cultural system was used which permitted growing plant mixtures in controlled environmental facilities. This allowed the experiment to be conducted over a wide range of temperature and nutrient conditions. Application of the theoretical gene model to the experimental data permitted identification of those classes of gene effects that were responsible for genetic variation exhibited by the mixtures. Adequacy of the genetic modeling description was corroborated by precise prediction of an independent genetic response. The genetic analyses also identified statistically significant temperature-and nutrient-dependent forms of heterosis. It was concluded that the study demonstrated the suitability of the theoretical group gene model for describing complexities inherent in plant mixtures.

This paper and the previous member of the series, deal with genetical mechanisms responsible for the evolution of eusociality (a level of social organization that includes differentiated sterile castes) among the “social” insects. Eusociality has evolved in a number of different species. Two different types of genetic systems are represented among these species: diplodiploidy (both sexes diploid) and haplodiploidy (haploid males and diploid females). The previous paper examined the evolution of a sterile caste system in the context of diplodiploidy, and the present paper considers the evolution of eusociality in the context of haplodiploidy.

The previous paper, (VII), in this series dealt with a group structure that consisted of a single mating pair. It was demonstrated that selection operating on such groups produced optimum short- and long-term results. The present study extends this group structure to include a single sire and several, (n − 1), dams. The objective of the present study is to determine whether or not the optimum evolutionary results inherent with groups consisting of a single mating pair extend to groups consisting of multiple matings.

This paper and the next member of the series, deal with genetical mechanisms responsible for the evolution of eusociality (a level of social organization that includes differentiated sterile castes) among the “social” insects. Eusociality has evolved in a number of different species. Two different types of genetic systems are represented among these species: diplodiploidy (both sexes diploid) and haplodiploidy (haploid males and diploid females). The present paper examines the evolution of a sterile caste system in the context of diplodiploidy, and the next paper considers the evolution of eusociality in the context of haplodiploidy.

Short- and long-term consequences of natural selection, operating in accordance with the classical (non-interaction) model, are reviewed. This review provides the basis for comparisons of the optimum results of the classical model with the results from interaction models. Then as a first step, the simplest interaction modeling system (Model I) is developed subject to the following conditions: (i) The natural selection model is constructed so that it is compatible with the one that already exists for artificial selection theory. This condition ensures that an overall theory is formulated which embraces both natural and artificial selection with a single modeling system and a common notation. (ii) The interaction theory is developed so that it is an extension of the classical theory. This condition ensures that the generalized theory includes the classical results as a special case when interaction is absent.

The present series of papers attempts to accommodate interaction among individuals in evolutionary theory. The interaction phenomenon is genetically characterized by two dimensions (direct and associate) of gene activity. For optimal selection results, a balance between the two dimensions must occur. In the first paper of the series, it was shown that random interactions resulted in an unbalanced selection response in that the direct, but not associate, effects were included in the expression for gene frequency change. The next three papers of the series (II, III and IV) were designed to determine whether or not selection with life-history models that involved non-random interactions would be useful in ameliorating the problem of selection balance.

Races of a C3 plant species, Arabidopsis thaliana, were screened for time of survival when enclosed in an air-tight chamber with a C4 plant species (Zea mays L.). This has been suggested as a method of detecting and selecting for increased photosynthetic efficiency among C3 genotypes. The C4 plant should, in such conditions, reduce the atmospheric CO2 concentration below the compensation point of the C3 plant, resulting in its eventual death. Significant differences were found among the A. thaliana races for survival time; some races survived only one week in competition with corn while others survived more than two weeks. Two races, chosen for contrasting survival in closed chambers, were hybridized and compared to their F2 progeny for survival time. Substantial genetic segregation occurred among the F2, and a number of transgressive segregates having survival times superior of both parents were identified. Also significant heterosis was observed in the F2 population.

Previous studies in this series have dealt with the consequences of truncation selection operating with respect to random groups within which geno-full-sib group structure. The objective is to compare the results of individual and group selection as these methods operate on populations of random versus typic interaction may exist. The present study deal with a non-random, full-sib groups. In almost all comparisons individual selection is found to be qualitatively and quantitatively superior when used in conjunction with full-sib groups. This is due to the fact that the change in gene frequency for full-sib groups is a function of both direct and associate effects, whereas with random groups it is a function of direct effects only. With regard to group selection the efficiency is invariably superior when selection operates on non-random, full-sib rather than random groups.

The strategy of using non-random groups to increase the efficiency of truncation selection is discussed. The present study, which considers extreme forms of non-rnadom groups, complements a previous study involving full-sib groups. It is shown that of the two kinds of non-randomness, i.e. that due to homozygosity or that due to homogeneity (as represented by cloning), the latter is the most effective. This suggests that with those plant crops in which intense competition among plants exists, use of clonal propagation to produce non-random groups should be investigated.

Journal Article Growth of Arabidopsis thaliana in miniature containers Get access P. MIKOLAJ, P. MIKOLAJ The authors are affiliated with the Academic Faculty of Genetics of the Ohio State University, Columbus, Ohio 43210. This investigation was supported by the Atomic Energy Commission grant (AT11-1)-1761. The authors would like to acknowledge the competent assistance of Mrs. Ruth Kersteter. Search for other works by this author on: Oxford Academic PubMed Google Scholar B. GRIFFING B. GRIFFING The authors are affiliated with the Academic Faculty of Genetics of the Ohio State University, Columbus, Ohio 43210. This investigation was supported by the Atomic Energy Commission grant (AT11-1)-1761. The authors would like to acknowledge the competent assistance of Mrs. Ruth Kersteter. Search for other works by this author on: Oxford Academic PubMed Google Scholar Journal of Heredity, Volume 62, Issue 1, January 1971, Pages 54–57, https://doi.org/10.1093/oxfordjournals.jhered.a108125 Published: 01 January 1971

SE of hybrid vigor is of great importance in terms of present-day agricultural production. For example GARDNER (1968) states: ". . . Development and use of heterosis has been the most important practical achievement of genetics so far. The monetary value of the increase in corn production due to use of heterosis for a single year has been estimated to exceed the total cost of federal research for plant improvement since 1900." Even though the importance of hybrid vigor is well recognized, the underlying phenomenon, heterosis, remains an enigma of quantitative genetics. Various hypotheses have been developed on purely genetic grounds. In our laboratory we have adopted a different approach-one which views heterosis as not entirely the result of genetic stimuli but rather as the result of the interaction between genetic and environmental stimuli. Such a view is not without precedent, as each of the studies in the following partial list have implicated the environment as a significant factor in the manifestation of heterosis: HANEY, GARTNER and WILSON 1953; GRIFFING 1954; LEWIS 1954; BARNETT and COLEMAN 1960; SHANK and ADAMS 1960; GRIFFING and LANGRIDGE 1963; MCWILLIAM and GRIFFING 1965; PEDERSON 1968; also see LANGRIDGE (1962) far a detailed review of temperature-dependent heterosis. In order to examine the effects of the total stimulus pattern on the manife1tation of heterosis, experiments must be designed so that genetically related 01"ganisms are reared in different but quantitatively related and exactly controlled environmental regimes. Such factorial types of experiment permit a genetic analysis, an environment analysis, and most important of all, an analysis of the contributions of the interactions between ger?etic and environmental stimuli to the observed heterosis. In view of the complexities of the experimental design which requires controlled cultural regimes, it is important to choose a biological system which yields a maximum amount of data while utilizing a minimum amount of time and space in the controlled-environmevt facility. The biological system chosen for this study was that in which the flowering plant Arabidopsis thaliana was grown aseptically in test tubes on nutrient solution solidified with agar. The advantages of this system are: (i) the plants grow in test tubes and hence occupy little space; and (ii) the plants grow quickly,

Index theory is applied to selection methods which use individuals or ran-domly associated groups of individuals as basic units of selection. An index is developed which combines "direct" and "associate" phenotypic values in such a way as to invariably ensure a maximum, non-negative change in the population mean. The theory is applicable to populations of groups in each of which individuals may interact in any arbitrary manner, whether such interaction be cooperative or competitive in nature.

Index theory is applied to selection methods which use individuals or ran-domly associated groups of individuals as basic units of selection. An index is developed which combines direct and associate phenotypic values in such a way as to invariably ensure a maximum, non-negative change in the population mean. The theory is applicable to populations of groups in each of which individuals may interact in any arbitrary manner, whether such interaction be cooperative or competitive in nature.

Consequences of individual and group selection are examined for the case in which selection operates with regard to groups of one size and its effects are measured with regard to groups of a different size. In such a situation neither selection procedure can ensure that positive selection will result in a non-negative change in the population mean.

Transference of the model-building unit from that of the gene to that of the entire genotype permits the consequences of individual and group selection to be given in terms of parent-offspring covariances. This, in turn, solves two basic problems: (1) extending the genetic analysis to any arbitrary level of complexity; and (2) formulating the prediction equations of genetic advance in terms of parameters which are directly estimable

A selection theory designed to accommodate interactions among genotypes is presented. This involves defining unordered groups of genotypes among which interactions may occur, and describing populations of groups generated as combinatorial products of base populations. Gene models are developed which consist not only of direct contributions of the genotypes they represent but also of associate effects from other genotypes in the group.

The joint contributions of sex-linked and autosomal genes to mass and general combining ability selection procedures are examined. Detailed results are given for n consecutive cycles of selection, and for relaxation from selection, with regard to a twolocus model which involves both sex-linked and autosomal loci. This model permits (1) an arbitrary number of alleles at each locus; (2) an arbitrary system of dominance parameters; (3) an arbitrary system of sex-linked-autosomal epistatic parameters; and (4) different genotypic values for the same autosomal genotype in the two sexes. This last condition implies that the model incorporates "sex-influenced" as well as "sex-linked" inheritance.