Testing for clonal propagation.

The conceptual basis for testing clonal propagation is reconsidered with the result that two steps need to be distinguished clearly: (1) specification of the characteristics of multilocus genotype frequencies that result from sexual reproduction together with the kinds of deviations from these characteristics that are produced by clonal propagation, and (2) a statistical method for detecting these deviations in random samples. It is pointed out that a meaningful characterization of sexual reproduction reflects the association of genes in (multilocus) genotypes within the bounds set by the underlying gene frequencies. An appropriate measure of relative gene association is developed which is equivalent to a multilocus generalization of the standardized gametic disequilibrium (linkage disequilibrium). Its application to the characterization of sexually produced multilocus genotypes is demonstrated. The resulting hypothesis on the frequency of a sexually produced genotype is tested with the help of the (significance) probability of obtaining at least two copies of the genotype in question in a random sample of a given size. If at least two copies of the genotype are observed in a sample, and if the probability is significant, then the hypothesis of sexual reproduction is rejected in favor of the assumption that all copies of the genotype belong to the same clone. Common testing approaches rest on the hypothesis of completely independent association of genes in genotypes and on the (significance) probability of obtaining at least as many copies of a genotype as observed in a sample. The validity of these approaches is discussed in relation to the above considerations and recommendations are set out for conducting appropriate tests.

On a genetic assessment of the adaptedness of forest reproductive material.

Assessment of the adaptedness of forest tree populations and the reproductive material derived from them is largely based on historical records and observations on extant distributions of phenotypic traits. Genetic criteria are, if at all, usually considered only in the form of heuristic reasoning. A main reason for this situation lies in the lack of operational concepts that clearly distinguish between viability selection and adaptation. The present paper makes an attempt towards this aim by showing that the adaptational optimization of viability selection processes rests on three constituent features which allow minimization of the implied overall mortality at each relevant selection stage and across all of these stages. Indices are developed that measure the degree of adaptational optimization of viability selection. The concept and its indices are applied to an analysis of isozyme data obtained for an approved beech seed stand and reproductive material derived from this stand. An approved seed stand is required to be adapted, and this property is expected to be preserved in the derived reproductive material. Our observations revealed substantial degrees of overall reductions and suboptimal selection during the production process. Suboptimality is unevenly distributed over the stages of the production process, and stages of strongest suboptimality vary among gene loci. A preliminary explanation is given for a conspicuous effect on selective optimality that is consistently observable at the stage of seedling development across all loci.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The meaning of genetic variation within and between subpopulations.

Argumentation is presented which indicates that the additive decomposition of the total genetic variation of a population into variation within and between (among) its subpopulations suffers from conceptual inconsistency. While the measurement of variation between subpopulations can be shown to be identical to the measurement of subpopulation differentiation, the notion of variation within subpopulations, when viewed as a single measurement, cannot be derived as an independent and cogent concept. Rather, it appears to be merely technically defined as the arithmetic difference between the total variation and the variation between subpopulations, and this difference happens to be non-negative for concave measures of variation such as the (statistical) variance or certain measures of genetic diversity. In order to overcome the conceptual inconsistency, "variation between subpopulations" could be regarded as subpopulation differentiation and the notion of "variation within subpopulations" could be replaced by measurements of the degree to which the variation in the total population is represented within the subpopulations. A complementary situation with respect to total variation is thus realized once more, and appropriate measures can be directly derived from existing ones.

The relationship between the concepts of genetic diversity and differentiation.

Diversity as a measure of individual variation within a population is widely agreed to reflect the number of different types in the population, taking into account their frequencies. In contrast, differentiation measures variation between two or more populations, demes or subpopulations. As such, it is based on the relative frequencies of types within these subpopulations and, ideally, measures the average distance of subpopulations from their respective lumped remainders. This concept of subpopulation differentiation can be applied consistently to a single population by regarding each individual as a deme (subpopulation) of its own, and it results in a measure of population differentiation δ T which depends on the relative frequencies of the types and the population size. δ T corresponds to several indices of variation frequently applied in population genetics and ecology, and it verifies these indices as measures of differentiation rather than diversity. For any particular frequency distribution of types, the diversity ν is then shown to be the size of a hypothetical population in which each type is represented exactly once, i. e. for which δ T =1. Hence, the diversity of a population is its differentiation effective number of types. This uniquely specifies the link between the two concepts. Moreover, ν again corresponds to known measures of diversity applied in population genetics and ecology. While population differentiation can always be estimated from samples, the diversity of a population, particularly if it is large, may not be. In such cases, it is recommended that population differentiation is estimated and the corresponding sample diversity merely computed. Finally, a solution to the problem of measuring multi-locus diversities is provided.

Polymorphisms for purely cytoplasmically inherited traits in bisexual plants.

It is shown that cytoplasm polymorphisms transmitted only by the ovules can be maintained without gene-cytoplasmic interactions. The necessary prerequisites are asymmetry of the plasmotypes in production of ovules and pollen (sexual asymmetry), incomplete and frequency-dependent fertilization efficiency and differential selfing rates. These factors can generate the negative frequency dependence of cytoplasmic fitnesses required for a stable polymorphism. The model considered allows also for facultative fixation of either of two plasmotypes and, thus, may produce all of the dynamical characteristics known for nuclear selection with two alleles at one locus.Strong sexual asymmetry, which probably occurs frequently in bisexual plants, may facilitate stable cytoplasmic polymorphisms. However, these polymorphisms may also endanger survival of the whole population in the absence of nuclear interactions. Gene-cytoplasmic interactions avoid this risk and, at the same time, utilize the advantages of sexual asymmetry in maintaining genetic polymorphisms.

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.

Measurement of genetical differentiation among subpopulations.

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.

Joint analysis of genotypic and environmental effects.

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.

Genotype - environment interaction in tissue cultures of birch.

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.

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.