Browsing by Author "Gregorius, H. R."

Based on monoecious, diploid plant species, a model is constructed to determine genetic relationship within the seed production of an open-pollinated population, characterized by its rates of self-fertilization, population density and mode of pollen dispersal. Genetic relationship is measured by the coefficient of inbreeding of a seed produced by a mother plant located at a specified place, or by the coefficient of kinship between two seeds, produced from the same mother plant or produced from two different mother plants separated by a certain distance. The influence of the single parameters on these coefficients is demonstrated by some typical examples, which show that dimensionality of the habitat (one- or two-dimensional), as well as, range and type of pollen dispersal, has little influence on the relationship between seed produced from the same mother plant and, on the other hand, emphasize the important role of the rate of self-fertilization and population density. Some remarks on how to apply Wright's concept of neighbourhood to continuous plant populations close this paper.

Continuing a study of the average coefficient of kinship and inbreeding among offspring from specified mother plants belonging to a population of monoecious, diploid seed-plants, the variances of these coefficients have been computed. The variance in kinship was considered among offspring from a single mother plant and between offspring from two different mother plants. Special interest has been paid to the role played by the rate of self-fertilization and the effective size of neighbourhood and common neighbourhood. The graphical representation of some numerical examples indicates that it is impossible to predict general tendencies which hold true for the behaviour of all three types of variance if they are regarded as functions of the rate of self-fertilization; only the coefficient of inbreeding and kinship among offspring from the same parent showed similar tendencies. The influence of the effective size of neighbourhood and common neighbourhood on the respective variances proved to be of minor importance.

The development of an individual's phenotype is influenced by environmental factors (the modifying environment) which may differ from those factors (the adaptive environment) that decide on the adaptational value of the developed phenotype. The shapes of adaptationally optimal norms of reaction are therefore essentially determined by associations between these two environmental components together with the degree of adaptational sensitivity of the developed phenotypes. Two complementary aspects of optimality are accounted for: (a) environments can be optimal for a given norm of reaction and (b) norms of reaction can be optimal for a given environment. The results are obtained for random distribution of genotypes over environmental conditions and under the physiologically reasonable premise that fitness is a function of the costs of modification and adaptation. It turned out that the associations of adaptive and modifying environments are the primary sources of adaptational optimization. More specifically, it is shown that (i) independence between the two environmental components constitutes an adaptationally optimal environment only for norms of reaction in Which all phenotypes are adaptively insensitive; (ii) if costs of modification do not depend on the environment, and if the two environmental components are not associated, adaptationally optimal norms of reaction can always be realized through phenogenetic invariance; (iii) as a rule, adaptively sensitive phenotypes developed under strong environmental associations necessitate phenogenetic plasticity for the optimal norm of reaction; (iv) a norm of reaction which is adaptationally optimal in its adaptationally optimal environment can always be realized through phenogenetic invariance, if costs of modification do not vary with the environment. These results reveal an important role of patterns of adaptive sensitivity of phenotypes, which may even surpass that of shapes of norms of reaction in adaptational processes. (C) 2000 Academic Press.

To study the evolutionary role played by differential male and female fertility (sexual asymmetry) both between individuals and over the life span within single individuals, the terms "intrinsic male fertility" and "intrinsic female fertility" are introduced. With the help of these terms, the concept of sexual asymmetry can be made precise and its effect on the establishment and maintenance of genetic polymorphisms can be analyzed. The main conclusions are: (1) any mutant causing a modification of the male fertility parameters which result in an increased intrinsic male fertility becomes established; (2) a corollary of this is that age-specific sexual asymmetry, as results from alternating degrees of female and male flowering in successive reproduction cycles, for example, has only secondary effects on the initial growth rate; (3) under the biologically reasonable premise that modifications of life histories result from reallocation of fixed net reproduction resources (defined as constant total female and male net reproduction output), a shift of net reproduction (whether female, male, or both in arbitrary proportions) to earlier ages is evolutionarily successful in growing but not in declining populations; shifts of net reproduction to later ages have opposite consequences.

Biodiversity is a term that comprises the appearance, structure and function of all levels of biological organization, including genes, species and ecosystems. The vast majority of measures of biodiversity (usually termed 'diversity indices') considers only number, proportion and distribution of species which belong to a specified group and exist in a defined area or ecosystem. Genetic diversity as a part of biodiversity within species (or populations) was either not regarded in this respect or was treated (by geneticists) as a separate entity of diversity quantified with separate measures. Little attention has been given to the integration of both types of diversity, within and among species, in a single measurement (termed 'transspecific' diversity). In order to attain this integration on a general basis, an operational trait concept is developed which allows the determination of variation in traits observable in members not only of the same species but also of different species. The concept rests on methods of investigation that can be adapted to a broader range of organisms without modification of their characteristics. Once a trait is specified on this basis, any meaningful measure of diversity can be applied to assess biodiversity across levels of biological organization. The utility of the concept is demonstrated by application to the results of an earlier study on associations between species and genetic diversity in a forest tree community. Attributes of isozymes which are visible in electrophoresis are used as a transspecific genetic trait.

The assumptions for the model treated in this paper are based on a population of hypothetically infinite size, which has reached its optimum density within a limited habitat. The aim has been to derive sufficient conditions for the genetic composition of a population to converge to a limit if generations overlap and time is measured in discrete intervals. Trivially the genetic composition does not change if at the starting point of time the compositions within all age-classes are the same; otherwise global convergence of the age-class distributions implies uniform convergence of the genetic compositions within the single age-classes if mating takes place between at least two age-classes, or within the first age-class only. Excluding age-class 1 mating within one age-class only results in periodical change of genetic compositions.

Density-regulated selection is considered for a single, multiallele gene locus and separated generations. Characteristics resulting from the basic assumption that the average population fitness decreases with increasing density are derived. Under this assumption, it proves to be necessary to distinguish between regions of allelic frequencies which imply limited population growth, unlimited growth, or ultimate extinction when the population stays in the respective region. Particular attention is given to the investigation of the region of limited growth and the 'carrying capacity function' theta defined on it. Relationships between theta and the average fitness (adaptive surface) in the non-density dependent model are explained. Besides stability properties of equilibrium points, more general characteristics concerning the asymptotic behavior of population trajectories are treated. In this context, the problems of sudden loss of alleles and of population extinction as a result of large fluctuations in density are discussed.

Population genetic models, such as differential viability selection between the sexes and differential multiplicative fecundity contributions of the sexes, are considered for a single multiallelic locus. These selection models usually produce deviations of the zygotic genotype frequencies from Hardy-Weinberg proportions. The deviations are investigated (with special emphasis put on equilibrium states) to quantify the effect of selective asymmetry in the two sexes. For many selection regimes, the present results demonstrate a strong affinity of zygotic genotype frequencies for Hardy-Weinberg proportions after two generations, at the latest. It is shown that the deviations of genotypic equilibria from the corresponding Hardy-Weinberg proportions can be expressed and estimated by means of selection components of only that sex with the lower selection intensity. This corresponds to the well-known fact that viability selection acting in only one sex yields Hardy-Weinberg equilibria.

The present paper deals with a model of idiotype-environment interaction and its application to a tissue culture experiment with birch (Betula pendula ROTH.). The data of the experiment are characterized with respect to the physiological reactions and are discussed in the light of the model. The main results of the paper are: With respect to the environmental action one has to discriminate between the environment inside and outside the cell (external and internal environment). The environmental influences cause a differential gene activity which lead to transient differentiation states and to final states of differentiatedness. During mitosis two types of information transmission take place: transmission of genetic material (the "blueprint") and transmission of the milieu (the "experience" of previous events). They together give rise to differentiation. The data of the experiment show that differentiation is no one-way street: Because of the transmitted milieu it is sometimes easier to regain an earlier differentiation state than to reach a new one. Only the interaction of idiotype (sum of genetic information) and the milieu state (internal environment) causes parallel as well as divergent development of cell lines. The model is also used to reinterpret some selected papers in the literature.

An exact analysis of necessary and sufficient conditions for the establishment and protectedness of biallelic two-locus polymorphisms is developed for the classical model with constant, sexually symmetric fitnesses and random association of the successful gametes. To demonstrate application of the results to common model types, the model of symmetric viabilities depending on the degree of heterozygosity only is chosen as a paradigm. It is pointed out that a unique locally stable internal equilibrium may exist even though all marginal equilibria (including the fixation states) are locally attractive. This example is quoted as an indication of the priority that analyses of protectedness deserve over analyses of local stability or instability of internal equilibria. Further applications of broader appeal concern the role that recombination plays in protecting polymorphisms. Probably the most interesting finding is that with increasing recombination frequency the chances for protectedness of a polymorphism generally decline. Yet, if a certain hierarchic ordering of the fitnesses with respect to the degree of heterozygosity is realized, the polymorphism is protected for arbitrary amounts of recombination. If recombination is rare, heterozygote advantage is not a universal precondition for persistence of polymorphisms. This phenomenon is utilized to derive conditions under which deleterious recessive mutants can be maintained in a population.

A model has been constructed to investigate the consequences of the rate of self-fertilization, pollen-dispersal, population-size, and number of clones on the genetic structure of finite seed plant populations. Derivations have been performed for two different cases: A) Parental genetic structure explicitly given: inferences for the expected genetic structure of the resulting seed population; B) Extension of case A) to several non-overlapping generations. If random cross-fertilization is assumed for case A) the genetic composition does not change and the genetic distance between the corresponding Hardy-Weinberg-structure and the expected offspring-structure is 0 if the rate of self-fertilization is equal to 1/N (N = population-size); any deviation from 1/N causes an increase in genetic distance.in case B) the expected genetic structures have been derived for all generations and it was possible to establish a comparatively simple dependence on the coefficient of inbreeding. In addition the variance of the allele-frequency has been presented. All the above influential components can be summarized by a single quantity, called M. After proving that 1/M can be conceived as the effective population-size, all the results obtained could be presented depending on this effective size and the average rate of self-fertilization only.Applying the findings of the model to the situation realized approximately in a seed-orchard, the following statements can be made:Case A) Again assuming random cross-fertilization, a deviation of the parental population from the corresponding Hardy-Weinberg-proportions can, with increasing rate of self-fertilization, be exceeded by the respective deviation of the seed population. Case B) The influence of pollen dispersal on the effective population size has been investigated, assuming no variation of the individual rates of self-fertilization, pollen and seed production within the population. Only extremely small differences between effective and actual population size were obtained, which indicates that the influence of pollen dispersal is of minor importance in this case. For different rates of self-fertilization, significant differences in the increments per generation for the coefficients of inbreeding, as well as the frequency of homozygotes, were obtained for the first generation only. Decreasing number of clones influences the rate of self-fertilization and the effective population size simultaneously by increasing the first and decreasing the latter. This is transferred to the coefficient of inbreeding, frequency of the homozygotes and the variance of the allele frequency by an increase of increments for all generations.

In vitro culture experiments were carried out with three birch genotypes characterized by certain genealogical relationships which serve as indicators of genetic similarity or dissimilarity. Each genotype was grown in each of six different environments (medium types), and callus growth and colour were observed. The aim was to improve our understanding of the operation of genetic and environmental effects at the early stages of regeneration in vitro. For this purpose we tried to answer the question as to whether genetic differences exert effects that are consistently distinguishable under different environments or whether environmental differences exert effects that are consistently distinguishable between different genotypes. Since conventional analytical methods, such as the analysis of variance, are inappropriate for providing satisfactory answers to this question, we applied a new concept of interpretation. With the help of this concept we obtained the following results which appear to be unique among their kind. 1) For both characters, callus growth and callus colour, genetic differences are masked only slightly by the environments while environmental differences are almost completely masked by the genotypes. Thus, in the present experiment, interaction is one-sided in the sense that environmental effects interact strongly with genotypic effects but genotypic effects interact only slightly with the environmental ones. 2) Nuclear effects seem to be responsible for the differences observed in callus growth, while the differences in callus colour can be explained by the joint action of nuclear and extranuclear effects.

Different types of incompatibility systems were found to operate simultaneously in Alnus glutinosa in the course of numerous pollination experiments, including self-pollination and pollination with controlled pollen mixtures. Isozyme genetic markers were used to identify the pollen parent of each offspring from the mixed pollination experiments, thus allowing specification of the fertilization success of each pollen parent. In a first step, these results were compared with observations on in vitro pollen germination experiments. This comparison allows for exploration of the explanatory value of different germination media as models of germination conditions on stigmas. In most cases, the data suggest that the in vitro germination conditions resemble the fertilization conditions in vivo, at least in the sense that they favor the same pollen parents. By providing a generic and operable definition of the two basic types of incompatibility, eliminating (inability to fertilize ovules) and cryptic (resulting in lowered fertilization success of a pollen parent under competition), evidence was detected for the existence of both types of incompatibility in Alnus glutinosa, where eliminating incompatibility occurred as self-incompatibility only. However, since this incompatibility seems to act primarily via pollen elimination, seed production is not likely to be negatively affected in natural populations, even for comparatively large amounts of self-pollination.

The two most important components of biodiversity, species diversity and genetic diversity, have generally been treated as separate topics, although a coordination between both components is believed to be critical for ecosystem stability and resilience. Based on a new trait concept that allows for the assessment of genetic diversity across species, the relationship between species diversity and genetic diversity was examined in eight forest tree communities composed of different tree genera including both climax and pioneer species. It was intended to check whether a trade-off exists between the two diversity components as was found in a few studies on animal species. Using several isozyme-gene systems as genetic markers, the genetic diversity across species within each of the tree communities was determined by two measures, the commonly used intraspecific genetic diversity averaged over species and the recently developed transspecific genetic diversity per species. Both data sets were compared with the corresponding community-specific species diversity resulting in a positive relationship between the two diversity components. A statistically significant positive correlation was established between the transspecific genetic diversity per species and the species diversity for three isozyme-gene systems. Beyond that, consistent results were obtained using different parameters of the diversity measure which characterize the total, the effective and the number of prevalent variants. The number of prevalent variants reflected most significantly the non-randomness of the observed diversity patterns. These findings can be explained by the observation that the pioneer tree species reveal a by far higher genetic diversity than the climax tree species, which means that an increase in species diversity, due to the addition of several pioneer species at the expense of one or two climax species, goes along with an increase in the level of genetic diversity. Forest tree communities with the highest degree of species diversity exhibit therefore the highest transspecific genetic diversity per species. This result was discussed with regard to the particular composition and stability of forest tree communities.

A definition of jointly contributing genotypic and environmental effects is introduced, from which a new concept of genotype × environment interactions is derived. Interaction is defined to be the failure of genotypic or environmental response functions to be separable. For separable response functions, the contributions of the genotypic and environmental effects must be related in terms of an operator which can describe their joint actions. A scale-free method of determining the simplest operator is developed in terms of comparative norms of reaction and a characteristic of the operator is given for several operators. With a defined operator, the genetic and environmental contributions can be derived, and biologically interpreted. These methods are applied to published data on Pinus caribaea.

Populations differ not only in the frequency distributions of their traits. Differences between the states of traits may also be of relevance. Examples are genetic traits based on DNA fragment length polymorphisms, such as microsatellites. The new measure, Delta of the difference between two populations considers both types of difference. Delta quantifies the changes that must be made in the frequencies of the trait states in the one population in order to match the frequency distribution in the second population, under the requirement that trait states be shifted to the most similar trait state possible, in analogy to the transportation problem of operations research. The properties of Delta as a model-free, descriptive measure are contrasted to measures of population difference that apply the "F-ST-principle" to trait differences. Its applicability in phylogenetic analysis is demonstrated using isoenzyme and microsatellite marker data. (C) 2004 Elsevier B.V. All rights reserved.

The basis for measuring differentiation among subpopulations is discussed and a number of conditions formulated that are desirable for an appropriate measure. These conditions imply that each subpopulation is characterized by the difference in genetic composition between it and its complement. A direct method of determining this difference is described and shown to result from a known measure of genetic distance between populations. The weighted average of the genetic distances between subpopulations and their complements constitutes a measure of differentiation among subpopulations which fulfills all of the desirable conditions and has the additional advantage that its values are directly interpretable. This measure (δ) is equally applicable to gene (δ ge ), gametic (δ ga ) or genotypic (δ go ) frequencies, which guarantees an unequivocal multilocus treatment, provided that the sets of genetic entities to which the frequencies refer are properly defined. The general relationship δ ge ≤ δ ga ≤ δ go is consistent with the principle that increasing complexity of organization of genetic material results in increased opportunity for differentiation. It is demonstrated that Wright's F st (G ST in Nei's notation), which is often used to measure subpopulation differentiation, meets some but not all of the conditions formulated for a desirable measure.

A measure of difference between populations for a trait should reflect not only the differences in the relative frequencies of the trait states but also the trait differences between the states. Common approaches to measuring differences between populations rely on distance, probability, or variance concepts. To overcome conceptual problems of these approaches, a new difference measure Delta is presented that is based on both frequency and trait differences. For two populations, Delta expresses the degree to which the frequency distribution of the trait states within one population must be transformed in order to make it match the distribution in the other population. This is done by shifting the relative frequency excesses of trait states to other trait states of deficient frequency, where shifts occur between as similar states as possible. Delta equals the minimum sum of the shifted frequencies weighted by the respective trait differences. Its bounds are functions of the difference measure do, which considers only differences in relative frequency. The computer program DeltaS applies an algorithm from operations research to calculate Delta. The effect of including trait differences is demonstrated by the topological differences observed between Delta- and d(0)-dendrograms constructed from microsatellite allele frequencies in four riparian stands of black poplar (Populus nigra), where the trait difference between two alleles equals the difference in numbers of tandem repeats. A is applicable to all traits for which trait differences are measurable, and it is shown to have elementary linearity properties that considerably simplify its interpretation.