Elizabeth M. Gillet

Genetic analysis of isoenzyme phenotypes using single tree progenies

A method of genetic analysis is proposed for determination of the mode of inheritance of environmentally and ontogenetically stable isoenzyme phenotypes as expressed in angiospermous forest trees. This method also applies to higher plant and animal species characterized by multiple matings of single female parents. The modes of inheritance considered are codominance in the absence and the presence of a (recessive) null allele. The analyzed material consists of zymograms of single maternal trees and their progenies (as seeds or seedlings) from open pollination. Such data is more easily obtained than controlled crosses and can represent the total variation in the population. The genetic analysis requires only the basic assumptions of classical Mendelian analysis, which make use only of the elementary mechanisms of meiosis and fertilization. Additional assumptions on the mating system, such as those required by the mixed mating model, are not needed. The results confirm the need for explicit genetic analysis of zymograms.

Measuring differentiation among populations at different levels of genetic integration

BackgroundMost 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.ResultsTo 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 ΔSD. 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.ConclusionThis 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.

Phylogenetic relationships amongPinus species (Pinaceae) inferred from different numbers of 6PGDH loci

Electrophoretic examination of variousPinus species from both subgenera revealed that several taxa differ in the number of loci that control the enzyme system 6-phosphogluconate dehydrogenase (6PGDH). Based on inheritance analyses and published data, it was established that all species of subg.Pinus possess only two 6PGDH loci, whereas all stone pines of subg.Strobus exhibit four controlling loci. In order to trace the phylogenetic links at which one or two gene duplications occurred during pine evolution, several species of subsect.Strobi (sectionStrobus) and two species of sect.Parrya were additionally investigated. Based on conclusions about the uniqueness of gene duplications and the different numbers of 6PGDH loci, a phylogenetic tree of the pine taxa was constructed. This tree shows some new features not recognized in earlier studies and supports several novel assignments postulated in very recent pine classifications.

Maximum Likelihood Estimators of the Gametic Contributions to Single-Plant Progenies

Almost all population genetic studies of plant mating systems in natural populations are based on single-plant progenies from open pollination of each plants ovules. For estimation of the male and female gametic contributions to the unordered genotypes in the progeny of a heterozygous diploid plant, two types of closed-form maximum likelihood estimators (MLEs) are derived: conditional MLE of the allele frequencies in the pollen contribution for given ovule segregation proportions, and joint MLE of allele frequencies in the pollen and the ovule contributions. This provides estimates of the local pollen pool composition and ovule segregation proportions on a single-plant basis. The only assumption is random association among successful gametes. The analytical method predicts the non-global convergence of iterative methods by giving conditions under which the joint likelihood function possesses one, two, or three critical points, two of which can be of equal, maximal likelihood.

Classifying measures of biological variation.

Biological variation is commonly measured at two basic levels: variation within individual communities, and the distribution of variation over communities or within a metacommunity. We develop a classification for the measurement of biological variation on both levels: Within communities into the categories of dispersion and diversity, and within metacommunities into the categories of compositional differentiation and partitioning of variation. There are essentially two approaches to characterizing the distribution of trait variation over communities in that individuals with the same trait state or type tend to occur in the same community (describes differentiation tendencies), and individuals with different types tend to occur in different communities (describes apportionment tendencies). Both approaches can be viewed from the dual perspectives of trait variation distributed over communities (CT perspective) and community membership distributed over trait states (TC perspective). This classification covers most of the relevant descriptors (qualified measures) of biological variation, as is demonstrated with the help of major families of descriptors. Moreover, the classification is shown to open ways to develop new descriptors that meet current needs. Yet the classification also reveals the misclassification of some prominent and widely applied descriptors: Dispersion is often misclassified as diversity, particularly in cases where dispersion descriptor allow for the computation of effective numbers; the descriptor GST of population genetics is commonly misclassified as compositional differentiation and confused with partitioning-oriented differentiation, whereas it actually measures partitioning-oriented apportionment; descriptors of β-diversity are ambiguous about the differentiation effects they are supposed to represent and therefore require conceptual reconsideration.

DifferInt: compositional differentiation among populations at three levels of genetic integration

In many fields of study, it is important to know how different populations are genetically. Commonly used measures such as FST and its derivatives based on gene identity probabilities do not reliably reflect difference, as they can be maximal when almost all populations are identical and very small when populations are completely distinct. Compositional differentiation, in contrast, is maximal only for completely distinct populations. Moreover, underlying forces of fragmentation that act on single‐ and multilocus genotypes may be missed if only the allelic level is viewed. For these reasons, descriptive measures of compositional differentiation based on untransformed distributions of genetic types at different levels of genetic integration (alleles, single‐ and multilocus genotypes) were derived. Here, two measures of complementary differentiation and two new measures of dispersive differentiation are described. One of each considers genic differences between individuals, ensuring their consistency across integration levels. An increase from one level to the next indicates differences among the populations in their forms of gene association. The computer program DifferInt calculates these measures for one or more codominantly expressed gene loci at the gene‐pool, single‐locus and multilocus levels. Effects of gene pools and gene association on differentiation are compared by permutation analysis. Snail diagrams depict the contribution of each population to differentiation. Results are demonstrated using a numerical example. The applicability of the measures calculated by this program in conservation, phylogeography, mating system analysis and adaptation studies is discussed.

On the number of periodic sets for mappings on Hausdorff spaces

Abstract A sufficient condition is given for iterates of continuous mappings on Hausdorff spaces which guarantees the existence of at least Nt t-periodic sets for each t ϵ N , where the sequence (Nt)t ϵ N is an invariant of such mappings. Proof of existence yields a method of construction. The nontriviality of (Nt)t ϵ N is demonstrated by an example.

Stability in discrete dynamical systems containing independent subsystems

Motivated by problems frequently occurring in the analysis of evolutionary ecological and population genetic models, discrete dynamical systems on the product of compact topological spaces are considered which contain an independent subsystem on one component space. If this subsystem possesses an equilibrium point, then a dynamical system is defined on the other component space whenever the independent system is in equilibrium. It is shown that in the presence of global asymptotic stability in the two component systems, perturbation will result in a return of the entire system to equilibrium (i.e. in particular, the equilibrium is globally asymptotically stable). A weakening of these conditions to combinations of global attractivity and global asymptotic stability either no longer guarantees convergence, or else the equilibrium is globally attractive but unstable, and thus sensitive to further perturbation.

Detecting differential viability selection between environments by analysis of compositional differentiation at different levels of genetic integration

Abstract Viability selection can be detected directly in an environment when the genotypes of the individuals at one ontogenetic stage (e.g. seeds) and the genotypes of the survivors at a later stage are both known, but genotypes at the earlier stage often cannot be determined. In this case, differential viability selection between environments can be detected as differences in the distributions of genetic types among survivors growing in different environments, provided that the survivors stem from random samples of seeds from the same base population (e.g. seed lot). Since common FST-outlier methods for detecting selected gene loci use only allele frequencies, selection that affects the higher hierarchical levels of genetic integration (single- or multi-locus genotypes) without changing allele frequencies is not noticed. A new method for detecting differential viability selection at any level of genetic integration enables discovery of elementary mechanisms of selection that older methods miss. It is based on two measures of compositional differentiation between environments. δSD measures qualita-tive differences between distributions of genetic types at any given integration level without regarding differences in their constituent alleles, while ΔSD measures quantitative differences between the same distributions by additionally considering the genic differences. The difference between these measures expresses the degree to which the patterns of gene association in the genotypes differ between environments. The P-values of all measures are estimated by permutation analysis under the assumption that survivors were randomly assigned to environments. Significance indicates the occurrence of differential viability selection at the loci. As a case study, a field study of viability in juvenile beech (Fagus sylvatica L.) for twelve enzyme loci is reanalyzed. It turns out that the significant differential selection for genotypes detected at three loci can be attributed to three combinations of selective effects: on alleles only (SKDH-A), mostly alleles but also association patterns (LAP-A); interaction of effects on alleles and association patterns that are non-significant when viewed separately (AAT-B).

Selection in plant populations of effectively infinite size: IV. The maintenance of males among hermaphrodites for a biallelic model

Conditions for the maintenance of males in androdioecious populations (populations with both male and hermaphrodite individuals) have been derived for four different one-locus two-allele models of inheritance of androdioecy. The results are not in general accordance with those already known: depending on the mode of inheritance, males can be maintained irrespective of their fertilities. If males are sufficiently fertile, it may happen that they are maintained only for intermediate selfing rates of the hermaphrodites. A result already found for gynodioecy is confirmed for androdioecy, namely, that a 1∶1 sex ratio is immediately established among zygotes if hermaphrodites appear as heterozygotes only.