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

Spatiogenetic characteristics of beech stands with different degrees of autochthony

BACKGROUND: Autochthony in forest tree stands is characterized by a number of criteria, among which the range over which stands act as a population has been suggested to play a central role. Therefore, measures are needed for the delineation of populations or the detection of subpopulation structure. It is argued here that methods of population delineation must be based on the combined consideration of spatial distances and genetic differences between adult individuals. Conventional approaches and a set of newly developed methods are applied to seven isozyme loci in four beech stands which are distinguished by different types of forest management based on natural regeneration. RESULTS: Permutation analyses show that correlations between spatial distances and genetic differences vary only little in the studied beech stands. In view of the popularity of this and related descriptors of spatiogenetic covariation, this result came as a surprise. The newly developed methods lead to a different conclusion. Significant spatiogenetic structure is indicated in all stands when considering the mean and variance of spatiogenetic separation, where separation is measured by the smallest spatiogenetic difference of an individual from all others. Spatiogenetic difference is measured here by a combination of the spatial distances and genetic differences between individuals. This descriptor indicates the existence of spatiogenetic clusters in the beech stands. In order to arrive at an explicit representation of cluster structure as a representation of subpopulation structure, two types of cluster structure (primary and α-isolated) are distinguished, both of which reflect desirable characteristics of subpopulation structure. Particularly in the α-isolated structure, the proportion of individuals organized in clusters, the effective size, and the effective number of clusters clearly distinguish and consistently rank the four stands with respect to their types of forest management and the associated criteria of autochthony. CONCLUSION: The surprisingly high correspondence between our descriptors of spatiogenetic structure and forest management types confirms the appropriateness of the applied measure of cluster isolation and of the criterion for the choice of the level α of cluster isolation. The two types of cluster structure and their characteristic descriptors are thus suggested to be promising tools for the detection of subpopulation structure. To include the effects of long-distance gene flow, the presented methods can be extended as outlined to larger spatial scales in order to detect higher order population structure

Detecting local establishment strategies of wild cherry (Prunus avium L.)

BACKROUND: P. avium, a pioneer tree species that colonizes early forest successional stages, is assumed to require an effective strategy allowing stably repeatable rounds of local establishment, dispersal and local extinction. Consequently, the early replacement of cherry by climax tree species makes the establishment of several local generations very unlikely, especially in central European continuous cover forests. This has to be seen in connection with the mixed reproduction system involving asexual reproduction as a complementary adaptational strategy. Tests of the local establishment of wild cherry must therefore consider the possibility of first generation establishment via seedling recruitment potentially followed by an asexual generation (root suckering). Successful establishment can therefore be determined only among adult individuals with the option of detecting vegetative reproduction at these stages. To test the implied suggestion about local establishment strategies of wild cherry, nuclear microsatellites were used to analyse patterns of asexual propagation among adult stages that have been subjected to one of two major types of forest management. These management types, the historical "coppice with standards system" (CWS) and the "high forest system" (HFS), can be reasonably assumed to have affected the reproduction system of P. avium. RESULTS: Clear differences were found in the reproduction pattern between two stands representing the two forest management types: 1) Clonal propagation is observed in both management systems, but with a distinctly higher frequency in the CWS. Hence, sexual recruitment as a first local generation is followed by a second asexual generation in both, whereas in the CWS there is evidence for an additional clonal generation. 2) The estimation of amounts of clonal reproduction critically depends on the assumptions about multilocus gene associations. This is revealed by the application of newly developed methods of quantifying gene associations. 3) Haplotype diversities are higher in the CWS and found to be associated with a large degree of heterozygosity for the second largest clonal group. 4) Seed set was sparse over the last eight years of observation in the CWS stand. CONCLUSION: This study provides useful guidelines for more comprehensive investigations, particularly on the interrelationships between degrees of cloning and capacity of sexual reproduction, amounts of multilocus gene associations, effects of heterozygosity on cloning success, and sustainability of different forest management types

The concept of evenness/unevenness – Less evenness or more unevenness?

While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied evenness index. The latter approach, however, frequently leads to conceptual inconsistency due to the fact that the minimizing distribution is not specifiable or is monomorphic. The state of monomorphism, however, is indeterminate in terms of its evenness/unevenness characteristics. Indeed, the semantic indeterminacy also shows up in the observation that monomorphism represents a state of pronounced discontinuity for the established evenness indices. This serious conceptual inconsistency is latent in the widely held idea that evenness is an independent component of diversity. As a consequence, the established evenness indices largely appear as indicators of relative polymorphism rather than as indicators of evenness. In order to arrive at consistent measures of evenness/unevenness, it seems indispensable to determine which states are of maximal unevenness and then to assess the position of a given type distribution between states of maximal evenness and maximal unevenness. Since semantically, unevenness implies inequality among type representations, its maximum is reached if all type representations are equally different. For given number of types, this situation is realized if type representations, when ranked in descending order, show equal differences between adjacent types. We term such distributions "stepladders" as opposed to "plateaus" for uniform distributions. Two approaches to new evenness measures are proposed that reflect different perspectives on the positioning of type distributions between the closest stepladders and the closest plateaus. Their two extremes indicate states of complete evenness and complete unevenness, and the midpoint is postulated to represent the turning point between prevailing evenness and prevailing unevenness. The measures are graphically illustrated by evenness surfaces plotted above frequency simplices for three types, and by transects through evenness surfaces for more types. The approach can be generalized to include variable differences between types (as required in analyses of functional evenness) by simply replacing types with pairs of different types. Pairs, as the new types, can be represented by their abundances, for example, and these can be modified in various ways by the differences between the two types that form the pair. Pair representations thus consist of both the difference between the paired types and their frequency. Omission of pair frequencies leads to conceptual ambiguity. Given this specification of pair representations, their evenness/unevenness can be evaluated using the same indices developed for simple types. Pair evenness then turns out to quantify dispersion evenness

The Analysis of Association Between Traits When Differences Between Trait States Matter

Because of their elementary significance in almost all fields of science, measures of association between two variables or traits are abundant and multiform. One aspect of association that is of considerable interest, especially in population genetics and ecology, seems to be widely ignored. This aspect concerns association between complex traits that show variable and arbitrarily defined state differences. Among such traits are genetic characters controlled by many and potentially polyploid loci, species characteristics, and environmental variables, all of which may be mutually and asymmetrically associated. A concept of directed association of one trait with another is developed here that relies solely on difference measures between the states of a trait. Associations are considered at three levels: between individual states of two variables, between an individual state of one variable and the totality of the other variable, and between two variables. Relations to known concepts of association are identified. In particular, measures at the latter two levels turn out to be interpretable as measures of differentiation. Examples are given for areas of application (search for functional relationships, distribution of variation over populations, genomic associations, spatiogenetic structure)

Distribution of variation over populations

Understanding the significance of the distribution of genetic or phenotypic variation over populations is one of the central concerns of population genetic and ecological research. The import of the research decisively depends on the measures that are applied to assess the amount of variation residing within and between populations. Common approaches can be classified under two perspectives: differentiation and apportionment. While the former focuses on differences (distances) in trait distribution between populations, the latter considers the division of the overall trait variation among populations. Particularly when multiple populations are studied, the apportionment perspective is usually given preference (via FST/GST indices), even though the other perspective is also relevant. The differences between the two perspectives as well as their joint conceptual basis can be exposed by referring them to the association between trait states and population affiliations. It is demonstrated that the two directions, association of population affiliation with trait state and of trait state with population affiliation, reflect the differentiation and the apportionment perspective, respectively. When combining both perspectives and applying the suggested measure of association, new and efficient methods of analysis result, as is outlined for population genetic processes. In conclusion, the association approach to an analysis of the distribution of trait variation over populations resolves problems that are frequently encountered with the apportionment perspective and its commonly applied measures in both population genetics and ecology, suggesting new and more comprehensive methods of analysis that include patterns of differentiation and apportionment

Measuring differentiation among populations at different levels of genetic integration

<p>Abstract</p> <p>Background</p> <p>Most genetic studies of population differentiation are based on gene-pool frequencies. Population differences for gene associations that show up as deviations from Hardy-Weinberg proportions (homologous association) or gametic disequilibria (non-homologous association) are disregarded. Thus little is known about patterns of population differentiation at higher levels of genetic integration nor the causal forces.</p> <p>Results</p> <p>To fill this gap, a conceptual approach to the description and analysis of patterns of genetic differentiation at arbitrary levels of genetic integration (single or multiple loci, varying degrees of ploidy) is introduced. Measurement of differentiation is based on the measure Δ of genetic distance between populations, which is in turn based on an elementary genic difference between individuals at any given level of genetic integration. It is proven that Δ does not decrease when the level of genetic integration is increased, with equality if the gene associations at the higher level follow the same function in both populations (e.g. equal inbreeding coefficients, no association between loci). The pattern of differentiation is described using the matrix of pairwise genetic distances Δ and the differentiation snail based on the symmetric population differentiation Δ_<it>SD</it>. A measure of covariation compares patterns between levels. To show the significance of the observed differentiation among possible gene associations, a special permutation analysis is proposed. Applying this approach to published genetic data on oak, the differentiation is found to increase considerably from lower to higher levels of integration, revealing variation in the forms of gene association among populations.</p> <p>Conclusion</p> <p>This new approach to the analysis of genetic differentiation among populations demonstrates that the consideration of gene associations within populations adds a new quality to studies on population differentiation that is overlooked when viewing only gene-pools.</p

Meeting of the IUFRO Working Party “Ecological and Population Genetics”

When we consider the main object of forestry, the tree, it immediately becomes clear why experimental population geneticists have been so hesitant in making this object a primary concern of their research. Trees are very long-living organisms with generation intervals frequently exceeding those of their investigators by multiples. They virtually exclude, therefore, application of the classical methods of population genetics since these are based on observing genetic structures over generations. This situation, where the limits set to observation are so severe, particularly requires close cooperation between theory and experiment. It also requires careful consideration of results obtained for organisms other than trees, in order to gain additional insights by comparing the results for trees with those for other organisms. Yet, the greatest challenge to population and ecological genetics probably originates from the fact that forests are very likely to be the most complex ecosystems of all, even in some cases where they are subject to intense management. This complexity, which equally comprises biotic and abiotic factors varying both in time and space, makes extremely high demands on the adaptational capacity and thus flexibility of the carriers of such an ecosystem. Longevity combined with immobility during the vegetative phase, however, appears to contradict the obvious necessity of adaptational flexibility in forest tree populations when compared with short lived and/or mobile organisms