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H R Gregorius

Publications and source records attributed to H R Gregorius.

At least 19 recordsLinked to original sources
PubMed2001

Reinforcement of genetic coherence in a two-locus model.

BACKGROUND: In order to maintain populations as units of reproduction and thus enable anagenetic evolution, genetic factors must exist which prevent continuing reproductive separation or enhance reproductive contact. This evolutionary principle is called genetic coherence and it marks the often ignored counterpart of cladistic evolution. Possibilities of the evolution of genetic coherence are studied with the help of a two-locus model with two alleles at each locus. The locus at which viability selection takes place is also the one that controls the fusion of gametes. The second locus acts on the first by modifying the control of the fusion probabilities. It thus acts as a mating modifier whereas the first locus plays the role of the object of selection and mating. Genetic coherence is enhanced by modifications which confer higher probabilities of fusion to heterotypic gametic combinations (resulting in heterozygous zygotes) at the object locus. RESULTS: It is shown that mutants at the mating modifier locus, which increase heterotypic fusions but do not lower the homotpyic fusions relative to the resident allele at the object locus, generally replace the resident allele. Since heterozygote advantage at the object locus is a necessary condition for this result to hold true, reinforcement of genetic coherence can be claimed for this case. If the homotypic fusions are lowered, complex situations may arise which may favor or disfavor the mutant depending on initial frequencies and recombination rates. To allow for a generalized analysis including alternative models of genetic coherence as well as the estimation of its degrees in real populations, an operational concept for the measurement of this degree is developed. The resulting index is applied to the interpretation of data from crossing experiments in Alnus species designed to detect incompatibility relations.

Alleles↗
PubMed2000

Adaptation to spatially heterogeneous modifying and adaptive environments.

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.

Adaptation, Physiological↗
PubMed2000

Qualified testing of single-locus codominant inheritance using single tree progenies.

In forest trees, classical techniques of studying modes of inheritance are usually not feasible due to the difficulty of performing controlled crosses. The limited information on inheritance extractable from readily available data, such as the large progenies collectable from single seed trees, must be compensated by the design of appropriately parameterized models. For this purpose, a system analytic approach is used to develop a new inferential framework for testing a single-locus codominant mode of inheritance of genetic traits using the inferred genotypes within progenies of single trees of inferred heterozygous genotype. Model assumptions are random gametic fusion between the local gamete pools and absence of postzygotic selection; ovule segregation distortion is allowed. The method yields estimates of the allele frequencies in both local gamete pools. Since tests of modes of inheritance must be tests of models rather than of parameters, the utility of the classical statistical testing procedures is limited, particularly concerning the qualification of a sampling method to attain a preassigned level of precision. Consistent application of this principle makes it possible to design qualified sampling methods prior to the actual experiment as well as to specify qualification levels for tests of completed experiments.

Alleles↗
PubMed1999

Incompatibility and pollen competition in Alnus glutinosa: Evidence from pollination experiments.

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.

Journal Article↗
PubMed1997

The adaptational system as a dynamical feedback system.

The characteristics of biological systems of adaptation are developed from the principle that the manifestations of life are modified by and must conform with their environment in order to enable organismic persistence. The two roles of the environment, termed "modifying" and "adaptive", give rise to the distinction of three elementary and sequentially coupled subsystems characterizing the adaptational system: the modifying system, comparator system, and state regulation system. The third system determines which state alterations are required for adaptation of manifestations (responses) to the demands of the adaptive environment. Adaptational valuation is introduced as a measure of adaptedness of response to adaptive environment. The dynamical aspect of adaptation is shown to be completely described by the timing of feedback. Discrete and continuous forms of adaptation can thus be treated on the same conceptional basis. All steps of the generic system formulation are illustrated with the help of a simple model with additive effects and linear state regulation. The system representation is used to demonstrate how basic intuitive conceptions, such as adaptational lag or adaptational capacity, can be made amenable to precise analysis. Another demonstration concerns recognition of adaptational clues resulting from the distinction between the two environmental classes, modifying and adaptive. Among these clues are challenges of low correlation between the two classes to adaptational systems and the specification of questions of the evolution of phenotypic plasticity.

Adaptation, Biological↗
PubMed1997

Reinforcement of genetic coherence: a single-locus model.

Genetic coherence and genetic separation are the outcome of evolutionary mechanisms which maintain genetic variation within populations through recombination on the one hand, and which divide this variation via speciation between reproductively (recombinatorically) more or less isolated populations on the other. While mechanisms of speciation have received considerable attention in biology, their counterpart, mechanisms of genetic coherence, are addressed only implicitly, if at all. Usually, genetic coherence is intuitively associated with the forces maintaining genetic polymorphisms and thus potential for flexible adaptational reaction of populations. However, so far no models seem to exist which explain the evolution of genetic coherence as the natural counterpart of genetic separation or speciation. In this paper a single-locus model is analyzed, in which a mutant allele is introduced into a resident stable diallelic polymorphism, and where this allele is equivalent to one of the resident alleles in all respects with the exception of mating relations. The conditions for replacement of the resident allele by its selectively equivalent mutant are obtained with reference to the associated mating relations. It turned out that for heterozygote advantage the mutant replaces the selectively equivalent resident allele if it increases the mating preferences for carriers of other alleles. The evolution of lower such preferences requires heterozygote inferiority, which confirms the Wallace effect of speciation (by reinforcement). It is argued that this observation suggests that non-selective constituents of the mating system form the section of the genetic system that is responsible for moderating the genetic load implied by adapting selection while simultaneously securing the adaptational potential embodied in the resident allelic variation. Mating systems thus serve the preservation of adaptability.

Adaptation, Physiological↗
PubMed1992

A two-locus model of speciation.

Speciation is considered as the evolution of partial or complete cross-incompatibility between the carriers of genes (at a locus called "object locus") that distinguish the prospective species populations. The mating relations at the object locus are modified by the alleles at a second mating modifier locus. Based on a widely applicable concept of fitness and mating preference, it is shown that heterozygote disadvantage in fitness at the object locus is necessary for speciation, which corroborates Wallace's hypothesis. It is pointed out that the difference between sympatric and parapatric speciation essentially lies in the mechanisms stabilizing the polymorphism required at the object locus as a prerequisite for speciation. In the presence of recombination between the object and mating modifier locus speciation may be prevented by forces maintaining gametic phase imbalance between these loci such as can result from unidirectional gene flow between parapatric populations.

Adaptation, Physiological↗
PubMed1991

Establishment of allelic two-locus polymorphisms.

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.

Alleles↗
PubMed1991

On the concept of effective number.

A generalized conceptual basis for Wright's notion of effective size is presented. The concept is applied to the calculation of effective numbers based on the rate of change of genetic variability. With particular reference to the inbreeding, the eigen value, and the newly introduced "diversity" effective size, the use of the concept as a means for discrimination between and identification of various effective sizes is demonstrated.

Biometry↗
PubMed1991

Age-dependent sexually asymmetric selection: the use of intrinsic values.

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.

Age Factors↗
PubMed1986

The significance of over- and underdominance for the maintenance of genetic polymorphisms. II. Overdominance and instability with random mating.

Part I of the present series demonstrates that globally stable polymorphic equilibria may show underdominance in Darwinian fitness. Hence, overdominance in fitness can no longer be conceived of as a necessary condition for the stability of a polymorphism. In the present paper, the question is posed as to whether overdominance is at least sufficient for this stability. A population of randomly mating individuals is considered, where selection operates uniquely through differential fecundities of particular mating types and may generate either a heterozygote excess or deficit relative to Hardy-Weinberg proportions. It turns out that both unstable central overdominance and stable central underdominance are possible and that their occurrence is strongly related to an excess or a deficiency of heterozygotes in the vicinity of the regions of instability or stability. As one consequence, the above suggested sufficiency of heterozygote superiority is not valid, even in random mating populations. Based on the results of both papers of this series, which demonstrate the inadequacy of over- and underdominance as indicators of stability or instability, a modified overdominance principle is discussed. This principle states that a biallelic polymorphism is maintained if the heterozygote is superior in its degree of "heterogamous self-replication" to the degrees of "autogamous self-replication" of the corresponding homozygotes. It is derived with the help of fractional fitnesses, and it is pointed out that certain ratios of these may be more useful for finding evolutionary constants which govern the maintenance of genetic polymorphisms than are ratios of total fitnesses.

Animals↗
PubMed1985

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability.

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.

Animals↗
PubMed1984

Differentiation--a consequence of idiotype-environment interaction.

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.

Cell Differentiation↗
PubMed1980

The probability of losing an allele when diploid genotypes are sampled.

Given the genotypic frequencies for a single gene locus with an arbitrary number of alleles in a hypothetically infinite population, the probability of losing at least one of the alleles in a sample of genotypes from this population is derived. The sensitivity of this probability to changes in the population frequencies of heterozygotes and of alleles has been investigated and has proved to be in accord with intuitive expectations. Least upper bounds for this probability, in cases where only the allelic frequencies or the minimum allelic frequency of alpha is known, have been found and the correspondence of these bounds to the situation of sampling of gametes rather than genotypes has been pointed out. It has been proved that the latter bound is also the least upper bound of the probability of losing at least one of the alleles with frequencies greater than or equal to alpha in a sample of genotypes or gametes if neither the number of alleles in the population nor the genotypic frequencies are known. This result has been used for the compilation of a table of the minimum sample sizes required to assure that all alleles with frequencies greater than or equal to alpha are detected with probability 1-sigma for the different values of alpha or sigma.

Alleles↗
PubMed1979

Deterministic single-locus density-dependent selection.

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.

Alleles↗
PubMed1976

Convergence of genetic compositions assuming infinite population-size and overlapping generations.

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.

Age Factors↗