On the Theory of Partially Inbreeding Finite Populations. I. Partial Selfing

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is Ne = N'/(1 + FIS), where FIS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is found to be 2(N'/N)(FISS1 + (1 - FIS)S2), where S1 and S2 are the selective advantages of AA and AA in comparison with AA. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions Ne = N/(1 + 3FIS).     

On the Theory of Partially Inbreeding Finite Populations. II. Partial Sib Mating

It is assumed that a population has M males in every generation, each of which is permanently mated with c-1 females, and that a proportion beta of matings are between males and their full sisters or half-sisters. Recurrence equations are derived for the inbreeding coefficient of one random individual, coefficients of kinship of random pairs of mates and probabilities of allelic identity when the infinite alleles model holds. If Ft is the inbreeding coefficient at time t and M is large, (1-Ft)/(1-Ft-1)----1-1/(2Ne) as t increases. The effective population number Ne = aM/[1 + (2a-1)FIS], where FIS is the inbreeding coefficient at equilibrium when M is infinite and the constant a depends upon the conditional probabilities of matings between full sibs and the two possible types of half-sibs. When there are M permanent couples, an approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is proportional to FISs1 + (1-FIS)s2, where s1 and s2 are the selective advantages of AA and AA in comparison with AA. The paper concludes with a comparison between the results when there is partial selfing, partial full sib mating (c = 2) and partial sib mating when c is large.     

Exact Inbreeding Coefficient and Effective Size of Finite Populations under Partial Sib Mating

An exact recurrence equation for inbreeding coefficient is derived for a partially sib-mated population of N individuals mated in N/2 pairs. From the equation, a formula for effective size (N(e)) taking second order terms of 1/Ninto consideration is derived. When the family sizes are Poisson or equally distributed, the formula reduces to N(e) = [(4 - 3β)N/(4 - 2β)] + 1 or N(e) = [(4 - 3β)N/(2 - 2β)] - 8/(4 - 3β), approximately. For the special case of sib-mating exclusion and Poisson distribution of family size, the formula simplifies to N(e) = N + 1, which differs from the previous results derived by many authors by a value of one. Stochastic simulations are run to check our results where disagreements with others are involved.     

Evidence for the Partial Dominance of Viability Genes Contributing to Inbreeding Depression in Mimulus Guttatus

The relative importance of different modes of gene expression of viability genes contributing to inbreeding depression was investigated in the wild plant, Mimulus guttatus. Viability genes were identified by self-fertilizing 31 outbred plants, each heterozygous for three to nine unlinked allozyme markers, and analyzing segregation ratios of selfed progeny at maturity for deviations from 1:2:1 ratios. In this study, 24 linkages of viability genes to marker loci were detected. To infer the nature of gene action for these viability genes, a ``model-free' graphical method was developed that examines the ``space' of segregation ratios allowed by each of seven selection models (i.e., overdominance, complete recessivity, partial recessivity, additivity, partial dominance, complete dominance and underdominance). Using this method, we found that, of 24 linkages detected, 18 were consistent with either partial dominance, complete dominance or underdominance. Six were consistent with either partial recessivity, complete recessivity or overdominance. This finding indicates that, in these chromosomal segments identified by allozyme markers, partial dominance plays the predominant role in inbreeding depression. This is inconsistent with either the dominance or overdominance hypotheses proposed to account for inbreeding depression.     

The Exact Distributions of F IS under Partial Asexuality in Small Finite Populations with Mutation

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F_IS. Understanding how those mating systems impact the possible distributions of F_IS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of F_IS, the probabilities of positive and negative F_IS, the probabilities of fixation and the probabilities to observe changes in the sign of F_IS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive F_IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F_IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F_IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F_IS spectrum, including strong positive F_IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.     

On the Divergence of Alleles in Nested Subsamples from Finite Populations

Within-population variation at the DNA level will rarely be studied by sequencing of loci of randomly chosen individuals. Instead, individuals will usually be chosen for sequencing based on some knowledge of their genotype. Data collected in this way require new sampling theory. Motivated by these observations, we have examined the sampling properties of a finite population model with two mutation processes and with no selection or recombination. One mutation process generates new alleles according to an infinite-alleles model, and the other generates polymorphisms at sites according to an infinite-sites model. A sample of n genes is considered. The stationary distribution of the number of segregating sites in a subsample from one of the allelic classes in the sample conditional on the allelic configuration of the sample is studied. A recursive scheme is developed to compute the moments of this distribution, and it is shown that the distribution is functionally independent of the number of additional alleles in the sample and their respective frequencies in the sample. For the case in which the sample contains only two alleles, the distribution of the number of segregating sites in a subsample containing both alleles conditional on the sample frequencies of the alleles is studied. The results are applied to the analysis of DNA sequences of two alleles found at the Adh locus of Drosophila melanogaster. No significant departure from the neutral model is detected.     

Specificities of Electromagnetic Field Excitation in a Capacitive HF Discharge. III. Symmetric Discharge Partially Filling the Discharge Chamber

Plasma Physics Reports - Electrodynamic characteristics of a low-pressure (electron collision frequency much lower than the field frequency) capacitive HF discharge maintained by an electromagnetic...     

Transport and Fixation of Inorganic Carbon during Photosynthesis in Cells of Anabaena Grown under Ordinary Air: III. Some Characteristics of the HCO3--Transport System in Cells Grown under Ordinary Air

In cells of cyanobacterium Anabaena variabilis grown under ordinaryair (low-CO₂ cells), the transport of both CO₂ and HCO₃^–was significantly enhanced by Na⁺. This effect was pronouncedas the external pH increased. When low-CO₂ cells were treatedwith an inhibitor of carbonic anhydrase (CA), only CO₂ transportbut not HCO₃^– transport, was inhibited. The initial rateof photosynthetic carbon fixation as a function of the concentrationof internal inorganic carbon (IC) was practically the same irrespectiveof whether CO₂ or HCO₃^– was externally supplied. Theseresults suggest that IC is actively transported through theplasma membrane in a form of HCO₃^– probably by some transporterand that the transmembrane Na⁺ gradient is involved in thisIC transport system. Free CO₂ may be hydrated by CA to HCO₃^–and then transported to the cells by this transporter. On the other hand, CO₂ is actively taken up by cells grown withair containing 5% CO₂ (high-CO₂ cells) though the enhancingeffect of Na⁺ was much smaller in high- CO₂ cells than in low-CO₂cells. The initial rate of fixation as a function of internal IC concentrationindicated that the rate of the carboxylation reaction of accumulatedIC is higher in I0W-CO₂ cells than in high-CO₂ cells. The studieswith ethoxyzolamide indicated that even in low-CO₂ cells, CAdoes not function inside Anabaena cells. These results suggestthat inside the low-CO₂ cells of Anabaena, some mediator(s)facilitates the transport of IC to RuBPCase. (Received January 23, 1987; Accepted April 24, 1987)     

The sucrose carrier of the plant plasmalemma. III. Partial purification and reconstitution of active sucrose transport in liposomes.

The proteins from plasma membranes from sugar beet leaves were solubilized by 1% CHAPS and separated by size exclusion chromatography and by ion-exchange chromatography. The fractions enriched in sucrose transporter were monitored in three ways: differential labeling, ELISA, and reconstitution in proteoliposomes. When the plasma membranes were differentially labeled by N-ethylamaleimide in the presence of sucrose, a major peak of differential labeling was found at 120 kDa upon gel filtration. When this peak was recovered, denaturated by sodium dodecyl sulfate and reinjected on the gel filtration column, it yielded a peak of differential labeling at 42 kDa. When unlabeled membranes were used, the fractions eluted from the column were monitored by ELISA for their ability to recognize a serum directed against a 42 kDa previously identified as a putative sucrose carrier. The results paralleled those obtained by differential labeling, i.e. a major ELISA-reactive peak was found at 120 kDa upon gel filtration, and this peak yielded a peak most reactive at 40 kDa after denaturation. The 120 kDa peak prepared from unlabeled membranes was further separated on a Mono-Q column. The fractions were monitored by ELISA as described above, and reconstituted into proteoliposomes using asolectin. Active transport of sucrose, but not of valine could be observed with the reconstituted 120 kDa fraction. When the eluates from the Mono-Q column were reconstituted, the fractions exhibiting highest transport activity were enriched with a 42 kDa band. The data provide the first report concerning reconstitution of sucrose transport activity and confirm the involvement of a 42 kDa polypeptide in sucrose transport.     

Statistical Studies on Protein Polymorphism in Natural Populations. III. Distribution of Allele Frequencies and the Number of Alleles per Locus

With the aim of understanding the mechanism of maintenance of protein polymorphism, we have studied the properties of allele frequency distribution and the number of alleles per locus, using gene-frequency data from a wide range of organisms (mammals, birds, reptiles, amphibians, Drosophila and non-Drosophila invertebrates) in which 20 or more loci with at least 100 genes were sampled. The observed distribution of allele frequencies was U-shaped in all of the 138 populations (mostly species or subspecies) examined and generally agreed with the theoretical distribution expected under the mutation-drift hypothesis, though there was a significant excess of rare alleles (gene frequency, 0 ~ 0.05) in about a quarter of the populations. The agreement between the mutation-drift theory and observed data was quite satisfactory for the numbers of polymorphic (gene frequency, 0.05 ~ 0.95) and monomorphic (0.95 ~ 1.0) alleles.—The observed pattern of allele-frequency distribution was incompatible with the prediction from the overdominance hypothesis. The observed correlations of the numbers of rare alleles, polymorphic alleles and monomorphic alleles with heterozygosity were of the order of magnitude that was expected under the mutation-drift hypothesis. Our results did not support the view that intracistronic recombination is an important source of genetic variation. The total number of alleles per locus was positively correlated with molecular weight in most of the species examined, and the magnitude of the correlation was consistent with the theoretical prediction from mutation-drift hypothesis. The correlation between molecular weight and the number of alleles was generally higher than the correlation between molecular weight and heterozygosity, as expected.     

Viability of Clostridial Spores and the Requirements of Damaged Organisms III. The Effect of Delay in Plating after Exposure to the Bactericidal Influence

S ummary : Post-treatment recovery patterns of damaged spores of Clostridium welchii have been investigated. Heat damaged spores showed an early reactivation during storage but counts subsequently declined. Spores damaged by very low intensity γ-radiation showed a considerable degree of increased recovery during post-treatment storage. With radiation at higher intensities there was evidence only of a low rate of reactivation when storage was at 4°, and at 21° counts decreased. Progressive loss in viability was also shown in ethylene oxide treated spores on kaolin powders though in the presence of albumin this trend was arrested. A dependence of count on atmosphere of incubation, demonstrated also in 3 other species, was shown to develop during post-treatment storage.     

Physical training under the influence of beta-blockade in rats. III. Effects on muscular metabolism

Rats were trained by daily running exercises for 7 weeks. In addition, one group of rats was trained under the influence of propranolol, while another group received daily injections of propranolol only. None of the treatments used had influence on the activities of myocardial enzymes: 3-hydroxyacyl-CoA - dehydrogenase (HADH), succinate dehydrogenase (SDH), malate dehydrogenase (MDH), and citrate synthase (CS) which were assayed for estimating oxidative capacity, or lactate dehydrogenase (LDH) which was used as a measure of anaerobic capacity. Training without propranolol resulted in elevated activities of the oxidative enzymes in M. extensor digitorum and in M. soleus. The corresponding changes in the rat group trained with propranolol always were much smaller, despite an equal amount of training. Only the trend for lowered activity of LDH was observable in skeletal muscle of the rat groups trained both with and without propranolol. Long-term beta-blockade alone did not induce enzymatic changes. It is concluded that a functioning sympathetic nervous system is necessary for the adaptive responses of muscular metabolism to training. Blockade of the sympathetic influence during exercise periods also hampers the training-induced responses.     

On the mechanics of mucociliary flows. III. Flow-velocity profiles in frog palate mucus

Flow-velocity profiles over excised frog ciliated epithelium were obtained for the region within about 600 micron of the mucosa. Fluorescent particles were used as flow tracers. Both a control and an autologous mucus suspension were observed. The control culture medium was bounded by the walls of the observation chamber, and mucus was deposited on the epithelium as a blob after mixing it with tracers. In spite of the difference in boundary conditions the two profiles, normalized to maximum particle velocity and solution depth, were indistinguishable at heights over 60 micron from the mucosa. The near-mucosa profiles in contrast were unalike with mucus exhibiting a greater shear gradient than the control culture medium. It was concluded that ciliary contact is not necessary for generation of mucus flow provided the ciliary shear is not negated by the mucus "flake" or "slab" being in simultaneous contact with significant ciliostatic patches which would act as anchors.