Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

Mendelian segregation: a choice between “order” and “chaos”

Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and by NIH grants GM 28016 and GM 10452     

Heterogeneous selection in subdivided populations

The dynamics of allele frequencies changing under migration and heterogeneous selection in a subdivided population are investigated. Using perturbation techniques, a stationary state is obtained when migration and selection are both small. Heterogeneous selection leads to a positive correlation between values of F-statistics and heterozygosities when these are compared among sets of subdivided populations. This contrasts with a negative value of the correlation obtained under Wright's classical model of homogeneous selection, and with the absence of correlation in the completely neutral situation.Research supported in part by NIH grants GM 28016 and GM 10452 and a grant from the John D. and Catherine T. MacArthur Foundation     

Peroxidase isozyme patterns in primary trisomics of pearl millet

Summary The peroxidases zymogram phenotypes of seven primary trisomics of pearl millet (Pennisetum typhoides) and their disomic sibs were determined. It was found that each of the trisomics can be differentiated from its disomic sib and from other trisomics on the basis of the isozyme band intensities.This research was supported in part by the USDA under grant PL-480     

Tutorial on large deviations for the binomial distribution

We present, in an easy to use form, the large deviation theory of the binomial distribution: how to approximate the probability ofk or more successes inn independent trials, each with success probabilityp, when the specified fraction of successes,a≡k/n, satisfies 0<p<a<1. Supported by NIH grant GM 36230 and NSF grant DMS 8601986. Supported by NIH grant GM 36230 and a grant from the System Development Foundation.     

Pattern recognition in several sequences: Consensus and alignment

The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themes are examples of these problems. Previously proposed methods, such as dynamic programming, are not adequate for solving problems of realistic size. This paper gives a new and practical solution for finding unknown patterns that occur imperfectly above a preset frequency. Algorithms for finding the patterns are given as well as estimates of statistical significance. This author supported by a grant from the System Development Foundation. This author supported by NSF grant MCS-8301960 and by a grant from the System Development Foundation. This author supported by NIH grant GM19036.     

Assignment of the gene for dipeptidase 2 to Mus musculus chromosome 18 by somatic cell hybridization

Evidence is presented for the assignment of the gene for dipeptidase 2 to Mus musculus chromosome 18 by synteny testing and karyotypic analysis of Chinese hamster × mouse somatic cell hybrid clones. DIP-2 and chromosome 18 were expressed concordantly in 24/24 clones examined (ten primary clones and 14 secondary clones). Synteny testing indicated that DIP-2 was not expressed concordantly with the expression of any marker enzymes.This work was supported by NIH grant USPHS GM 09966.     

Actin acetylation in Drosophila tissue culture cells

In a permanent cell line derived from Drosophila embryos, cytoplasmic actin is produced as an unstable precursor, which is subsequently converted to a stable form. This conversion results in a reduction in isoelectric point, with no apparent change in molecular weight. The conversion involves an enzymatic acetylation, and results in an insensitivity to aminopeptidase digestion, suggesting N-terminal blockage. Both the acetylated and unacetylated actins can participate in the assembly of F-actin, but with different efficiencies.This work was supported by a grant from the NIH (GM 22866).     

The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

On the probability of loss of new mutations in the presence of linkage disequilibrium

A new selectively neutral mutation occurs in a multilocus genetic background that has achieved a stable equilibrium at which there is a linkage disequilibrium. Perturbation techniques are applied to an extension of the branching process formulation of Fisher in order to address the question of extinction probabilities. We show that under appropriate conditions the probability of extinction of the new mutant is increased by the existence of linkage disequilibrium in the genetic background.Research supported in part by NIH grant GM 28016     

Family composition and the characteristics of parental care during the nursing phase of captive common marmosets (Callithrix jacchus)

Cooperative care of the young by the father, older siblings, and unrelated group members is observed in a number of species, but inCallithrix jacchus parental care by the father is considered to be part of the reproductive behavior of the species. Nevertheless, the way the presence of potential helpers influences the costs of caring for the parents is not well understood. In this study we describe the suckling phase of youngC. jacchus, in families with and without older siblings, assessing the effect of siblings on the amount of care given by the father and mother. Six family groups were observed: three consisting of the mated pair and two newborn infants, and three with one or two additional sub-adult siblings. Our results suggest that the presence of older siblings as helpers affects the parents' participation in caregiving by altering maternal investment through the control of nursing and by reducing the costs of carrying for the father.     

Genes involved in mating type expression of fission yeast

Summary Mutations of Schizosaccharomyces pombe are described, which change homothallism to heterothallism without affecting the mating type locus itself. The genetic block was effective at the level of agglutinated cells in two instances, or before that in two other cases. Mutations of particular interest affected meiosis as well, when homozygous diploid strains were constructed. In these strains azygotic meiosis was inducible by the addition of h ⁺ cells, even in the absence of cellular fusion.This work was supported by NIH grant GM 13234 initially, and by DFG (SFB 46).     

The effect of fetal bovine serum on polyene macrolide antibiotic cytotoxicity and antifungal activity

Summary The relationships between fetal bovine serum (FBS) concentration and polyene macrolide antibiotic cytotoxicity to animal cells and to fungi were evaluated. The toxicity of amphotericin B (AB) and its derivative, amphotericin B methyl ester (AME), toward KB cells was found to be directly related to fetal bovine serum concentration. At higher FBS levels, increased concentrations of AB and AME were required to reduce 72-hr KB viable cell numbers to 50% of control values. Similarly, polyene macrolide antibiotic levels required to inhibit the growth ofSaccharomyces cerevisiae to 50% of controls, and for obtaining minimum fungicidal concentrations (MFC), were greater when higher levels of FBS were used. In addition, AME was less toxic than AB toward KB cells grown in media containing 2, 5, 10, 15 or 20% FBS, whereas the antifungal activities of AB and AME were similar. AME was also capable of eliminatingCandida albicans, Saccharomyces cerevisiae, Aspergillus niger orFusarium moniliforme from KB cultures at antibiotic levels which exhibited less cell toxicity than did the concentrations of AB required for a similar response. These findings indicate that AME may be a potentially useful antifungal antibiotic for tissue culture systems. Portions of this paper were presented at the 25th Annual Meeting of the Tissue Culture Association at Miami, Florida, 1974. This investigation was supported in part by contract NIH 69-2161, NIH grant no. AI-02095 and NIH training grant no. GM 507 from the National Institute of General Medical Sciences.     

Ionic mechanisms of electrical activity in somatic muscle of the nematodeAscaris lumbricoides

Summary The ionic dependence of the myogenic spike potentials and slow waves recorded fromAscaris lumbricoides somatic muscles has been investigated. Spikes appear to be mediated exclusively by calcium ions; the spike active potential varies with calcium concentration as expected for a calcium electrode and spikes persist in sodium-free media (Fig. 2). Slow waves can be mediated either by sodium or calcium; they persist when calcium or sodium are removed separately, but not when both are removed together (Figs. 3, 4, 6).In rhythmically active preparations, a burst of slow waves and spikes accompanies each contraction. Two phenomena may be related to the mechanism of this modulation:1) TEA, although it does not prolong slow waves or spikes, induces rhythmic bursts of activity similar to spontaneous modulation (Fig. 5). This TEA-induced modulation appears to be myogenic. 2) Under conditions where calcium influx is reduced (either by addition of EGTA to the bath or by replacement of calcium with barium or strontium), very long-duration square waves are observed (Figs. 4. 7. 8). The square waves resemble slow waves in their ionic dependence, but differ in their sensitivity to TEA and to variation in the external potassium concentration. It is suggested that modulation and square waves involve the same channels. The significance of these results in understanding the role of myogenic activity in nematode locomotion is discussed.We thank Mr. Mac McGlaughlin for help in obtainingAscaris. This work was supported by a Sloan Foundation grant in Neuroscience and a U.S. Public Health Service grant (NS 09654) to R.L.R., by an NIH Traineeship on grant BCH Tol GM 01262-12 to D.A.W., and by an NIH Postdoctoral Fellowship (1 FO2 GM55347) to L.B.     

Estimation of inbreeding by random walks in pedigrees

Summary Wright and McPhee (1925) suggested a method of estimating the inbreeding coefficient of an individual based on the probability that a pair of lineages traced randomly, one through the maternal line and one through the paternal line, both contain a common ancestor. (One-half of this probability is an unbiased estimate of the inbreeding coefficient). In their procedure, maternal and paternal lines are chosen in pairs, and comparisons are made only between the lines in a pair. A more efficient procedure is to compare every maternal line with every paternal line, a procedure used by Robertson and Mason (1954). In this paper we provide estimates of the sampling variance of the inbreeding coefficient as estimated by the multiple comparison method, and we examine the relative efficiency of this method and the Wright-McPhee procedure. Formulae are also provided for ascertaining the optimal sampling method for estimating the average inbreeding coefficient of a group or herd.Work supported by NSF grant GB43209, NIH grant GM21732 and by Research Career Award GM0002301.     

Physiological effects of an allozyme polymorphism: Glutamate-pyruvate transaminase and response to hyperosmotic stress in the copepod Tigriopus californicus

In order to regulate cell volume during hyperosmotic stress, the intertidal copepod Tigriopus californicus, like other aquatic crustaceans, rapidly accumulates high levels of intracellular alanine, proline, and glycine. Glutamate-pyruvate transaminase (GPT; EC 2.6.1.2), which catalyzes the final step of alanine synthesis, is genetically polymorphic in T. californicus populations at Santa Cruz, California. Spectrophotometric studies of homogenates derived from a homozygous isofemale line of each of the two common GPT alleles indicated that the GPT^F allozyme has a significantly higher specific activity than the GPT^S allozyme. Under conditions of hyperosmotic stress, individual adult copepods of GPT^F and GPT^F/S genotypes accumulated alanine, but not glycine or proline, more rapidly than GPT^S homozygotes. When young larvae were subjected to the same hyperosmotic conditions, GPT^S larvae suffered a significantly higher mortality than GPT^F or GPT^F/S larvae. These results suggest that the biochemical differences among GPT allozymes result in specific physiological variation among GPT genotypes and that this physiological variation is manifested in differential genotypic survivorships under some naturally occurring environmental conditions.This work was supported in part by a grant from the Lerner Fund for Marine Research of the American Museum of Natural History, an NIH Training Grant in Integrative Biology, and NIH Grants GM 28016 and GM 10452.     

Isozyme variability in species of the genus Drosophila. III. Qualitative comparison of the esterases of D. aldrichi and D. mulleri

Two closely related species, Drosophila aldrichi and D. mulleri, are compared on the basis of their esterase isozyme patterns after starch gel electrophoresis. Comparable esterases between the two species are identified by substrate specificity, inhibition, and enhancement of esterase activity by various agents. The extensive electrophoretic variability of most of the esterases in nature is described and data relating to the inheritance of the various enzyme forms are presented.This work was supported (in part) by a U.S. Public Health Service research grant (GM 11609 to W. S. Stone and M. R. Wheeler) and a training grant (2 T1-GM 337-07 to R. P. Wagner et al.) from the National Institutes of Health.     

Mid-prophase human chromosomes. The attainment of 2000 bands

Summary Human mid-prophase chromosomes exposed to amethopterin, actinomycin D, and bromodeoxyuridine display more than 2000 bands per haploid set and show a remarkable resemblance to the fine chromomeric structures of early pachytene.Supported in part by grant No. 1-568 from the National Foundation and by NIH grant GM26800     

Two-locus inbreeding measures for recurrent selection

Summary For a population undergoing recurrent selection, a method is presented for determining the average inbreeding coefficients at the end of each breeding cycle. The coefficients are derived in terms of probability measures that genes are identical by descent. For the one-locus case, two digametic measures are defined and employed in the derivation of a recurrence formula for the inbreeding coefficient. Two further classes of measures, trigametic and quadrigametic, are required for transition from one cycle to the previous one to allow the calculation of the inbreeding function for the two-locus case. Numerical values of the average probability of double identity by descent for populations with various imposed assumptions are listed to illustrate the effects of linkage and population size on the accrual of inbreeding and hence of homozygosity.Paper number 5018 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, North Carolina. This investigation was supported in part by NIH research grant number GM 11546 from the National Institute of General Medical Sciences.     

Age-dependent allozymic variation in a natural population of lizards

An analysis of allozymic variation at 17 loci in a population of the sagebrush lizard (Sceloporus graciosus) in southern Utah yielded an estimate of genic heterozygosity of 0.028. Seven of the loci were variable, but only one, Est-1, was strongly polymorphic. The observation that the frequency of the common genotype (MM) at the Est-1 locus declined monotonically in successive age classes from 0.74 in hatchlings to 0.58 in adults 4 years old or older suggests that allele frequencies at this locus are not independent of selective influences.This research was supported by NSF grant GB-29141 to D.W.T. and NIH grant GM-15769 to R.K.S.