The role of migration in the genetic structure of populations in temporally and spatially varying environments II. Island Models

The Island Model introduced by Sewall Wright (1951) has proven to be a useful construction for studying the interaction of genetic drift, population subdivision, and mutation. Interest in the model has recently increased because of its relevance to certain questions involving the rate of differentiation of sub-populations under the neutral allele hypothesis (e.g., Smith, 1970; Latter, 1973). It is perhaps the only realistic population structure in which the test for neutrality proposed by Lewontin and Krakauer (1973) is valid (Lewontin and Krakauer, 1975). If data from natural populations is to be compared to the predictions of the Island Model, it is desirable to have an alternative model with the same migration pattern but with natural selection operating. In this paper one such model will be introduced where the stochastic element comes from random fluctuations in the environment rather than from genetic drift. The model is a direct extension of the one in the previous paper in this series (Gillespie, 1975) which dealt with a population which is subdivided into two patches with restricted migration between them.     

A note on the sampling theory for infinite alleles and infinite sites models

This note considers sampling theory for a selectively neutral locus where it is supposed that the data provide nucleotide sequences for the genes sampled. It thus anticipates that technical advances will soon provide data of this form in volume approaching that currently obtained from electrophoresis. The assumption made on the nature of the data will require us to use, in the terminology ofKimura (Theor. Pop. Biol.2, 174–208 (1971)), the “infinite sites” model of Karlin and McGregor (Proc. Fifth Berkeley Symp. Math. Statist. Prob.4, 415–438 (1967)) rather that the “infinite alleles” model of Kimura and Crow (Genetics49, 174–738 (1964)). We emphasize that these two models refer not to two different real-world circumstances, but rather to two different assumptions concerning our capacity to investigate the real world. We compare our results where appropriate with corresponding sampling theory of Ewens (Theor. Pop. Biol.3, 87–112 (1972)) for the “infinite alleles” model. Note finally that some of our results depend on an assumption of independence of behavior at individual sites; a parallel paper byWatterson (submitted for publication (1974)) assumes no recombination between sites. Real-world behavior will lie between these two assumptions, closer to the situation assumed by Watterson than in this note. Our analysis provides upper bounds for increased efficiency in using complete nucleotide sequences.     

An approach to a physico-chemical model of olfactory stimulation in vertebrates by single compounds

During recent years, numerous attempts have been made to correlate both quantitative (Davies &; Taylor, 1959; Engen, 1962; Beck, 1964; Engen, Cain &; Rovee, 1968; Cain, 1969; Dravnieks &; Laffoit, 1970; Laffort, 1969a,b) and qualitative (Davies, 1965; Amoore &; Venstrom, 1965; Döving, 1966a,b; Wright &; Michels, 1964; Leveteau &; MacLeod, 1969) odorous properties of single compounds to their molecular properties. These attempts have been only partially successful.In the present paper we will try to explain the several odorous properties of single compounds on the basis of the non-specific properties of odorants involved in solubility.This model is a first approach, and although it gives statistically highly significant relations, it is not as accurate as those advanced with respect to the physical and sensory dimensions of stimuli in the fields of vision and audition.We will first give the present definitions of the most suitable physicochemical parameters, and then advance quantitative and qualitative models for single compounds. Quantitative odorous properties are: odour threshold, rate of change of odour intensity with odorant concentration in the suprathreshold region, and the somewhat controversial upper odour intensity. Qualitative properties refer to odour character.     

Trehalose-6-phosphate synthetase activity in extracts of Dictyostelium discoideum.

Trehalose-6-phosphate (T-6-P) synthetase activity in extracts of Dictyostelium discoideum has been reexamined in an effort to resolve discrepancies between the results of previous studies (R. Roth and M. Sussman (1966). Biochim. Biophys. Acta, 122, 225; K. A. Killick and B. E. Wright (1972). J. Biol. Chem., 247, 2967). We find that T-6-P synthetase is not cold sensitive as reported by Killick and Wright (1972), is not present in bacterial-grown vegetative cells (though subject to some modulation by other nutritional conditions), and is not in our hands unmasked or activated by ammonium sulfate fractionation. We conclude that the pattern of T-6-P synthetase accumulation and disappearance during fruiting body construction in D. discoideum is as originally described by R. Roth and M. Sussman (1968). J. Biol. Chem., 243, 5081) and confirmed elsewhere (P. C. Newell et al. (1972). J. Mol. Biol., 63, 373; R. W. Brackenbury et al. (1974). J. Mol. Biol., 90, 529; B. D. Hames and J. M. Ashworth (1974). Biochem. J., 142, 301).     

Is the most frequent allele the oldest?

Exact and approximate expressions are obtained for the probability that the most frequent allele is oldest, in neutral allele models in which all mutations produce new alleles. The higher the mutation rate, the less likely is it that the most frequent allele would be oldest. The results are in agreement with simulation studies by Ewens and Gillespie (1974) (Theor. Popul. Biol.6, 35–57), and limit the range of validity of a suggestion made by Crow (1972) (J. Hered.63, 306–316) with respect to the statistical testing of the neutral allele hypothesis.     

Theory of radiation dose-survival curves for the case where organism lethality is defined as loss of reproductive capacity. II. Application to cells and physical interpretation

The general theory of survival curves (Craig, 1971) is applied to the case of cells and sub-cellular organisms with a physical interpretation via gene or chromosome damage as the terminal lesion.It is indicated how the proposed terminal lesion is consistent with the salient features of cellular response to radiation and analytical expressions for reactivity and sensitivity in terms of a damage, or mutation, cross section are obtained.The probability of a complex cross section and conditions under which it reduces to simple approximations are discussed and the influence of various factors on the cross section are indicated.Acceptable fits are obtained to the data of Barendsen, Beusker, Vergroesen &; Budke (1960), McCulloch &; Till (1962) and Puck &; Marcus (1956) with simple forms of cross section.     

Proteolysis in eucaryotic cells: Aminopeptidases and dipeptidyl aminopeptidases of yeast revisited

Using nine different l-aminoacyl-4-nitroanilides and four different dipeptidyl-4-nitroanilides, aminopeptidases and dipeptidyl aminopeptidases active at pH 7.5 and (or) pH 5.5 in logarithmically growing and stationary-phase cells of Saccharomyces cerevisiae were searched for. Ion-exchange chromatography was used to separate the proteins of the soluble cell extract. Besides the three already-characterized aminopeptidases—aminopeptidase I (P. Matile, A. Wiemken, and W. Guyer (1971) Planta (Berlin)96, 43–53; J. Frey and K. H. Röhm (1978) Biochim. Biophys. Acta527, 31–41), aminopeptidase II (J. Frey and K. H. Röhm (1978) Biochim. Biophys. Acta527, 31–41; J. Knüver (1982) Thesis, Fachbereich Chemie, Marburg, FRG), and aminopeptidase Co (T. Achstetter, C. Ehmann, and D. H. Wolf (1982) Biochem. Biophys. Res. Commun.109, 341–347)—12 additional aminopeptidase activities are found in soluble cell extracts eluting from the ion-exchange column. These activities differ from the characterized aminopeptidases in one or more of the parameters such as charge, size, substrate specificity, inhibition pattern, pH optimum for activity and regulation. Also, a particulate aminopeptidase, called aminopeptidase P, is found in the nonsoluble fraction of disintegrated cells. Besides the described particulate X-prolyl-dipeptidyl aminopeptidase (M. P. Suarez Rendueles, J. Schwencke, N. Garcia-Alvarez and S. Gascon (1981) FEBS Lett.131, 296–300), three additional dipeptidyl aminopeptidase activities of different substrate specificities are found in the soluble extract.     

Quantitative dependence of mitochondrial oxidative phosphorylation on oxygen concentration: a mathematical model.

The model of Wilson and co-workers (2., 3., Arch. Biochem. Biophys. 182, 749–762) for the regulation of mitochondrial oxidative phosphorylation has been extended to include the dependence on oxygen tension. The derived rate expression correctly describes the observed dependence of cellular energy metabolism on oxygen tension, including the oxygen dependence at “normoxic” physiological values. Experimental evidence is presented that oxidative phosphorylation by suspensions of isolated rat liver mitochondria is also dependent on oxygen concentration up to values of at least 100 μM.     

Xylidine isomers. VII. Structure-hepatotoxic activity relationships of some xylidines

Hepatotoxic studies of xylidines differ with regard to the animal species and type of isomer. The aim of the present paper is to correlate electronic structure data and physical-chemical properties, studied by the authors during a few previous papers (Sahini & Weinberg, 1973; Sahini, Weinberg & Vasilescu 1976, Weinberg & Sahini, to be published; Weinberg & Sahini, 1980), with the hepatotoxic activity of xylidines. Two possible biochemical mechanisms are advanced by help of correlation equations.     

Cotranslational cleavage of immunoglobulin light chain precursors by plasmacytoma microsomes.

Murine plasmacytoma endoplasmic reticulum which has been freed of ribosomes by EDTA treatment is capable of the cotranslational proteolytic processing of representative λ₁,λ₂, and k immunoglobulin light chain precursors. Messenger RNA fractions from the MOPC-104E, MOPC-315, and MOPC-46B tumor lines were used to direct the synthesis of the light chain precursors in a cell-free system derived from Krebs II ascites cells. The precursor cleavage activity of the plasmacytoma membranes is comparable in activity and in characteristics to that of two well-defined membrane preparations: Krebs II ascites intracellular membranes (E. Szczesna and I. Boime, 1976, Proc. Nat. Acad. Sci. USA73, 1179–1183) and EDTA-treated rough endoplasmic reticulum from canine pancreas (34., 35., J. Cell Biol.67, 852–862). The efficiency of the cleavage reaction appears to be dependent upon the precursor being utilized as a substrate. An assay suitable for a preliminary characterization of the plasmacytoma membrane preparations is described.     

Complexity-stability relationship of two-prey-one-predator species system model: Local and global stability

Parrish & Saila (1970), motivated by the experiments of Paine (1966), constructed a simple mathematical model for a two-prey-one-predator system. They were unable to find, in their model, a set of parametric values with which the three-species system can be stable, whereas a twoprey species system without a predator is unstable. Cramer & May (1972) showed that, in fact, such parametric values exist, and gave the necessary mathematical condition. I have investigated the complete conditions for the stability of the system around the equilibrium point, and show that the conditions must be more stringent than given by Cramer & May (1972). Also, it is shown that the present model can have a globally stable limit cycle in three species even when the equilibrium point is locally unstable.     

Local mate competition and the sex ratio

Hamilton (1967) pointed out that Fisher's (1930) argument predicting an equality of the sex ratio may break down when there is local competition for mates. He considered in particular a model in which the environment consists of a number of isolated patches, each of which is colonized by a number of inseminated females; the offspring breed within the patch before dispersal. The present paper provides a careful derivation of the equilibrium sex ratio under this model in both diploid and haplo-diploid populations, and extends the model to consider the effects of having a finite number of patches.We suggest that the equilibrium sex ratio is not simply a function of the amount of inbreeding or sib-mating, as suggested by Maynard Smith (1978), but that the detailed breeding structure of the population must be taken into account.     

Kinship and covariance

Price's (1970) covariance theorem can be used to derive an expression for gene frequency change in kin selection models in which the fitness effect of an act is independent of the genotype of the recipient. This expression defines a coefficient of relatedness which subsumes r(Wright, 1922), b(Hamilton, 1972), ρ (Orlove &; Wood, 1978), and R(Michod &; Hamilton, 1980). The new coefficient extends the domain of Hamilton's rule to models in which the average gene frequency of actors differs from that of recipients.     

Spontaneous frequency of a developmental mutant in Volvox

Two types of mutants, those resistant to the base analog 5-bromo-2′-deoxyuridine (BrdU) and somatic regenerator (SR) mutants, have been analyzed in Volvox carteri. In somatic regenerator mutants, the somatic cells which are normally terminally differentiated dedifferentiate and regenerate gonidia [Sessoms, A., and Huskey, R. J. (1973). Proc. Nat. Acad. Sci. USA70, 1335–1338; Starr, R. C. (1970). Develop. Biol. Suppl.4, 59–100]. The SR phenotype allows recovery of SR mutations arising in somatic cells, since such somatic cells would regenerate gonidia and give rise to mutant clones. Mutants of any phenotype other than SR can only be recovered if the mutation first appears in a gonidium. Since the somatic cells are 100-fold more numerous than reproductive cells (gonidia), we have determined the spontaneous frequency of both somatic regenerator mutants and mutations to BrdU resistance in order to determine if the SR mutation exerts its effect in the gonidium or in the somatic cell. The two frequencies were found to be nearly identical, suggesting that the SR mutation must first appear in a gonidium in order to be expressed.     

Does a functional relationship exist between the polymerization and catalytic activity of beef liver glutamate dehydrogenase?

The recent work of Cohen &; Benedek (1976) and Cohen et al. (1975, 1976) on the apparent interdependence of beef liver glutamate dohydrogenase catalytic activity and degree of polymerization is examined in the light of previously published equilibrium and kinetic results. It is shown that some of the hypotheses central to the Cohen &; Benedek (1976) model are in contradiction with existent data. Consideration of all available information leads to the conclusion that effector-induced depolymerization may simply be an incidental side reaction in the events leading to inhibition.     

A general theory of chromosome pairing based on the palindromic DNA model of Sobell with modifications and amplifications

A model for chromosome pairing is presented. It is based on the presence of segments of symmetric sequences of bases (palindromes) in the DNA at specific places in the chromosome. Palindromic DNA has been characterized by Wilson &; Thomas (1974), who state that these sequences are a regular feature of eukaryotic DNA. Sobell (1972) has suggested that they may be involved in synapsis and genetic recombination. Sobell's model is modified and amplified in an attempt to develop a general theory of chromosome pairing that explains congressional pairing, synapsis, non-homologous pairing, the initiation of crossing over, and interference.     

Equilibrium frequencies of α-globin genes

A mathematical model has been developed to study the mechanism of the maintenance of variable numbers of α-globin genes in human populations. The model incorporates both selection and unequal crossing-over. The selection is formulated so that a homozygous individual with a double deletion is lethal and a heterozygous individual with a deletion or addition of an α-globin gene in a chromosome has decreased fitness. This differs from the previous models of stabilizing selection studied by Ohta (1981) and Takahata (1981). The effect of random genetic drift on the α-thalassemia polymorphims has also been studied.It has been shown that, although the results obtained are compatible with the observation of the low frequency of triple α-globin loci, it cannot explain the high frequency of single and double deletions in Asian populations. For the latter case, some type of heterozygote advantage may be operating.     

Warfare and hominid brain evolution.

This paper reviews literature on the evolutionary effects of warfare upon the hominid brain. Alexander &; Tinkle (1968) and Bigelow (1969) are found to be the first to propose that warfare was the principle evolutionary pressure that created the novel substance of the human brain, and that it acted at least from the early Pleistocene. These writers are distinguished from Darwin (1871), Keith (1947) and Wilson (1975) who saw warfare influencing the development of the brain only in historical or near-historical times.The warfare hypothesis of Alexander &; Tinkle is found to be an excellent explanation of the evolution of the human brain, but to be unsatisfactory from a biological viewpoint because they do not explain how warfare evolved in the first place, nor do they attempt to account for the apparent absence of warfare as a behavioral adaptation in species other than some eusocial insects.This author underpins the warfare hypothesis, arguing that it evolved as a necessary consequence of the circumstances of early hominids. Proficient tool use gave domination over predators and opened up new food resources, thereby diminishing two population controls. A population explosion resulted and, at critical densities, when starvation threatened, warfare was the genetically most successful behavioral adaptation. Alternative hypotheses are shown to be inadequate. Finally, the author asks why such an important hypothesis has been ignored for almost a decade.