On the density of intracellular water

The density of individualArtemia cysts has been determined by sedimentation velocity measurements at unit gravity. Dried cyst (< 0.02 g H₂O/g dry weight) densities, _s were obtained by successive sedimentation in two nonpenetrating organic solvents. This removes geometric terms from the equation relating density to sedimentation velocity. Hydrated cysts ( 1.68 g H₂O/g dry weight) were sedimented in 0.0750 m NaCl to obtain their density ( _c). Values of _s, _c, and their ratios were found to be independent of cyst volume; therefore, the weight fraction of water in hydrated cysts is very nearly the same in cysts of greatly different size. It can be concluded that measurement of the water content of large populations of these cysts accurately reflects the water content of individual cysts, a point which has been assumed in previous work on this system. If _s does not change appreciably when dried cysts are fully hydrated then the density of their water, _w, can be calculated to be 1.022 g/cm³ (±0.0011 ). That value is significantly higher than the density of pure water and is very close to estimates of _w in skeletal muscle and amphibian oocytes obtained by others. However, the assumption that _s is independent of hydration is open to serious criticism, for all these studies. Consequently, conclusions and interpretations derived from such measurements must be considered to be tentative and uncertain.     

Isolation of pea nodule bacteroids utilizing silica sol (Percoll) density gradient centrifugation

Isolation of bacteroids from effective (Fix⁺) and ineffective (Fix^–) pea nodules, inoculated withRhizobium leguminosarum K, were performed by a density gradient centrifugation method using silica sol (Percoll). Only one zone (=1.064–1.072; n-zone) was recognized in the Fix⁺ nodule which contained typical Y-shaped bacteroids while two zones (n-zone and =1.125–1.145; n'-zone) were obtained from the Fix^– nodule. The cells in the n'-zone, which are long rods differed morphologically from free-living cells at any growth phase (=1.108–1.125; f-zone and =1.074–1.078; f'-zone), and differed from Y-shaped bacteroids by cell density. The esterase isozyme pattern of bacteroids in the n-and n'-zones also showed clear differences from that of f-and f'-zone of free-living cells.     

Fusion of mitochondria with protoplasts in Saccharomyces cerevisiae.

Summary Protoplasts prepared from a neutral petite haploid BO60AF-1 (a ade2 arg4 leu2 trp C ^O E ^O O ^{O O O}) were mixed with mitochondria isolated from an oligomycin resistant respiring haploid AN^ROR 12D (a his4 leu2 thr4 C ^S E ^S O _II ^{R + +}) and treated with 30% polythylene glycol and CaCl₂. When the treated protoplasts were spread and incubated on selective agar plates, oligomycin resistant respiration-sufficient colonies appeared with low frequency. All of these colonies carried the mitochondrial genotype of C ^S E ^S O _II ^{R + +} and showed the same mating type and nutritional requirements as did BO60AF-1, thus evidencing the mitochondrial transfer into protoplasts. Recombination and transmission of the mitochondrial drug resistance markers were studied in crosses involving the strains issued from mitochondria accepted protoplasts.     

Salinity-temperature tolerance of two closely related triclad species,Dugesia lugubris and D. polychroa (Turbellaria), in relation to their distribution in The Netherlands

The tolerance of adult specimens of Dugesia lugubris and D. polychroa for 13 different chlorinities ranging from 15.0–3.8 and for two temperatures, viz. 4 and 23 °C, was tested.At chlorinities of 7.5 and lower, the survival time of both species was considerably longer than at higher chlorinities (a few hours at 7.5, one to several days at 6.6 and lower concentrations). It is assumed that this is determined by the osmoregulatory capacity of the planarians.It was found that at low chlorinities combined with a high temperature D. polychroa survived longer than D. lugubris, while at the same chlorinities the opposite was true for a low temperature. The effect of temperature on survival at low chlorinities was more drastic for D. lugubris than for D. polychroa.The results correlate with data on the distribution of both species in The Netherlands. Outside areas with an average chlorinity below 2 the two species were rarely found.     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

Electric phenomena in the habitat of the catfishIctalurus nebulosus LeS

Summary The biotic and abiotic electric phenomena in the habitat of the electrosensitive catfish,Ictalurus nebulosus LeS were investigated. Fish, insect larvae, tadpoles and snails proved to possess electric fields that can be described as stationary fields of the dipole type, upon which fluctuations, due to respiration or other movements, are superimposed. The frequency components of these fields fall within the DC to 10 Hz range, whereas the potential gradients are in the order of magnitude of 10 mV/m. The maximal potential differences found were several millivolts. These measurements were carried out in tap water with a specific resistance = 20 · m. Further, hydroelectric fields were measured in some find-localities ofIctalurus. Potential gradients up to 15 mV/m have been recorded in water with a specific resistance = 110 · m. These fields proved to be stationary, fairly constant in direction and strength, and strongly dependent on the structure of the bottom of the pool and the depth of the water. The possible significance of these biotic and abiotic fields toIctalurus is discussed.     

Fluorescence studies of normal and sickle beta apohemoglobin self-association

The acrylamide quenching of the intrinsic tryptophanyl fluorescence of normal and sickle apohemoglobins has been studied in 0.05 M potassium phosphate buffer,pH 7.5, at 5°C over a protein concentration range from 1 to 50M. Analysis of quenching dynamics revealed a strong dependence on acrylamide concentration for the intrinsic fluorescence of both normal and sickle apohemoglobins, suggesting that one tryptophanyl residue [presumably that at position 37(C3)], was more accessible to collisional quencher than the other tryptophanyl residue [15(A12)]. Additional studies, which altered viscosity and subunit assembly experimental parameters, supported the assignment of residue 37 as the more dynamically accessible residue. Finally, the quenching data were also found to be dependent on protein concentration, implying that this difference in the mobility between the two residues is a sensitive probe of self-aggregation. Extrapolated dynamic quenching constants at low concentration of acrylamide were used to estimate the dimer-monomer equilibrium dissociation constants of normal and sickle apohemoglobins, and were found to be 5.6 and 2.4M, respectively, thus demonstrating distinct self-association properties of _A and _S apohemoglobins.     

Detection of specific DNA sequences in yeast by colony hybridization

Summary A procedure is described for the detection of specific DNA sequences in Saccharomyces cerevisiae. This method allows a rapid screening of a large number of yeast colonies. The yeast cells of each colony, grown on nitrocellulose filters, are converted, in situ, to protoplasts by snail enzyme, and are then lysed and their DNAs are denatured and fixed on the filter. The presence of the specific DNA sequence is detected directly on the filter by hybridization with a radioactive cRNA.We have used successfully this technique to detect the presence or the absence of specific mt DNA sequences, in ⁺, ^- and ⁰ strains, and to detect the presence or the absence of the 2 m DNA sequences in different strains.     

Identification of Slow Motions in the Reduced Recombinant High-potential Iron Sulfur Protein I (HiPIP I) from Ectothiorhodospira Halophila via 15N Rotating-frame NMR Relaxation Measurements

Rotating-frame 15N relaxation rate (R1) NMR experiments have been performed in order to study the dynamic behavior of the reduced recombinant high-potential iron-sulfur protein iso I (HiPIP I) from Ectothiorhodospira halophila, in the s to ms time range. Measurements of R1 were performed as a function of the effective spin-lock magnetic field amplitude by using both on and off-resonance radio frequency irradiation. The two data sets provided consistent results and were fit globally in order to identify possible exchange processes in an external loop of the reduced HiPIP I. The loop consists of residues 43-45 and the correlation time of the exchange process was determined to be 50 ± 8 s for the backbone nitrogen of Gln 44.     

Growth analysis of the self-thinning stands of Pinus densiflora Sieb. et Zucc

The competition-density (C-D) effect for self-thinning Pinus densiflora Sieb. et Zucc. stands was analyzed. The relationship between biological time and physical time t followed a hyperbolic curve. The coefficients A_t and B included in the reciprocal equation of the C-D effect in self-thinning stands (i.e. 1/w=A_t+B), where w and , respectively, represent the mean stem volume and the realized stand density, were calculated at each time. With increasing , the coefficient A_t increased abruptly up to a maximum value, and then decreased gradually to a constant level, whereas the coefficient B decreased exponentially. The relationship between the realized stand density and the initial stand density _i was confirmed to follow the equation: 1/=1/_i+, where 1/ represents the asymptotic stand density at a given time. The - relationship was represented by the equation: =p(e–1), where p and are constants. The density in the self-thinning stands tended to converge to the same density level after a sufficient lapse of time, irrespective of the difference in initial stand density. The time-trajectory of the mean stem volume and asymptotic stand density on logarithmic coordinates moved gradually toward the self-thinning line with a slope of approximately –3/2, whereas the time-trajectory of the mean stem volume and full stand density moved initially along the self-thinning line with a slope of approximately –3/2, and then changed to move along the maximum yield line with a slope of –1.0.     

Establishment and characterization of Rubus tissue culture systems for in vitro bioassays against phytotoxins from Rubus fungal pathogens

The Rubus species R. parviflorus, R. spectabilis and R. strigosus interfere with conifer seedling establishment on forest regeneration sites in Canada and the United States. As a first step towards microbial metabolite-based control, callus and cell suspension cultures of the Rubus species were developed as a bioassay system to detect phytotoxic compounds that may have relevance in a vegetation control context. Rapidly growing friable callus and suspension cultures were obtained from leaf disks of the three weedy Rubus species using similar culture media conditions (modified Murashige and Skoog) but required different plant growth regulators (R. parviflorus, 4.5 M 2,4-D; R. spectabilis, 26.9 M NAA/0.5 M zeatin; and R. strigosus, 12.4 M picloram). Cell growth and health attributes including callus circumference, degree of browning and suspension culture cell viability as measured by the TTC vital stain assay were developed and were rapid and convenient to use. We have established Rubus tissue culture systems that will make it possible for large scale screening of phytotoxic metabolites.     

Conservation and chromosomal localization of DNA satellites in balenopterid whales

DNA satellites were isolated from three balenopterid species, viz. the minke, sei, and fin whales. In each of them at least two DNA satellites were recognizable with buoyant densities in neutral CsCl of =1.702/1.703 and =1.710/1.711, respectively. cRNAs from each satellite group were used for filter and in situ hybridisations. Homo- and heterologous DNA-cRNA hybrids within each satellite group yielded virtually identical melting curve profiles showing conservation of at least a considerable part of the DNA satellite sequences. There was no evident sequence homology between the =1.702/1.703 and the =1.710/1.711 satellites by filter hybridisation. — The in situ hybridisation showed that in each species the =1.702/1.703 satellite was located in centromeric-paracentromeric C-bands in a few pairs, whereas the =1.710/1.711 satellite was located in terminal C-bands throughout the karyotypes. — The data on the whale DNA satellites indicate that the quantitative evolution of the satellite DNA sequences preceded species divergence of the balenopterids and that the satellite sequences have remained relatively unaltered since the divergence took place. The function of satellite DNA is considered to imply the introduction of both chromosomal and genic polymorphisms and thus being of great importance in speciation. Based upon these concepts a model is postulated for the function of satellite DNA. According to this model at meiotic pairing euchromatin-heterochromatin overlapping between homologous chromosomes is considered to be of a general occurrence. This overlapping is presumed to be accentuated by the size heteromorphism frequently observed between homologous heterochromatic segments (C-bands). In the region of such euchromatin-heterochromatin overlapping, crossing-over would be excluded. The overlapping is suggested to be rectified progressively in the chromosome arms, leaving unaffected crossing-over distant to the euchromatin-heterochromatin junctions. The consequence of this will be that genes in the proximity of the junctions are collectively inherited and selected, whereas genes distant to the heterochromatin will be independently assorted and selected.     

Site of synthesis of spinach chloroplast ribosomal proteins and formation of incomplete ribosomal particles in isolated chloroplasts

Chloroplast ribosomal proteins from spinach have been prepared in the presence of a protease inhibitor and some modifications have been introduced to the previous characterization of the 50S subunits (Mache et al., MGG, 177, 333, 1980): 33 ribosomal proteins are detected instead of 34. No change has been observed for the 30S subunits.Using a light-driven system of protein synthesis it is shown that up to ten ribosomal proteins of the 30S and eight proteins of the 50S subunits are made in the chloroplast.Newly synthesized ribosomal subunits have been analysed on CsCl gradients after sedimentation at equilibrium, allowing the separation of fully assembled subunits from incomplete ribosomal particles. Most of the newly made 50S subunits are fully assembled (=1.634). A small amount of incomplete 50S particles (=1.686) is detectable. Newly made 30S subunits (=1.598) and incomplete 30S particles (=1.691) are also observed. The ribosomal proteins of the incomplete 30S have been determined. They contain eight or nine of the 30S-proteins, seven of which are synthesized within the chloroplast. It is suggested that incomplete ribosomal particles resulted from a step in the assembly of ribosomal subunits.     

Die Aktivit?tsperiodik bei V?geln mit und ohne dunklem Schlafkasten

Zusammenfassung In 2 Versuchsserien wurden Kohlmeisen(Parus major) und japanische Möwchen(Lonchura striata var.domestica) einzeln und schallisoliert gehalten. In der ersten Versuchsserie, in der alle Vögel einen dunklen Schlafkasten hatten, wurde der Einfluß der Beleuchtungsstärke auf die Periode () der Hüpfaktivität und auf das Verhältnis von Aktivitätszeit zu Ruhezeit ( : -Verhältnis) untersucht. Sowhol Kohlmeisen als auch japanische Möwchen folgen der Regel, daß mit wachsender Beleuchtungsstärke die Periode kürzer und das : -Verhältnis größer wird.In der 2. Serie wurde der Einfluß Ruhe im dunklen Schlafkasten auf die Periodenlänge und auf das : -Verhältnis untersucht. Es wurden die Messungen aus Bedingung 1 (der Vogel hat einen dunklen Schlafkasten zur Verfügung) mit den Messungen aus Bedingung 2 (der Vogel hat keinen oder einen hellen Schlafkasten zur Verfügung) verglichen. Das Ergebnis bei Kohlmeisen entspricht den Befunden bei konstantem Licht verschiedener Intensität. Unter Bedingung 1 ist länger und das : -Verhältnis kleiner als in Bedingung 2. Das Ausmaß der Änderung von nach Fortnahme des dunklen Kastens ist unabhängig von der Periodenlänge in Bedingung 1. Das Ausmaß der änderung von : ist unabhängig von a : in Bedingung 1, jedoch schwach negativ korreliert mit der Periodenlänge in Bedingung 1.Bei japanischen Möwchen entsprechen die Ergebnisse dieser Versuchsserie nicht der Regel für tagaktive Vögel. Mit Benützen des dunklen Schlafkastens ist kürzer als ohne den Schlafkasten. Ohne den Schlafkasten ist etwa 24 Std. Das : -Verhältnis ist in Bedingung 1 unter bestimmten Voraussetzungen kleiner als in Bedingung 2. Das Ausmaß der Änderung von nach Fortnahme des Kastens ist mit der dazugehörigen Periode in Bedingung 1 hochsignifikant korreliert (Regressionskoeffizient b=-1.01, Korrelationskoeffizient r=0.89). Ebenfalls ist das Ausmaß der Änderung von : nach Fortnahme des Kastens mit : aus Bedingung 1 korreliert; es scheint, als würde ein bevorzugtes : -Verhältnis von etwa 2.0 eingeregelt.Die Ergebnisse werden im Hinblick auf 4 Punkte diskutiert: 1) Das circadiane System arbeitet innerhalb eines engen Bereiches von - und : -Werten optimal. 2) Der Optimalbereich wird bevorzugt unter ungünstigen Bedingungen angestrebt. 3) Der Entzug des dunklen Schlafkastens belastet japanische Möwchen mehr als Kohlmeisen. 4) Bei japanischen Möwchen wird in Bedingung 1 durch fortplfanzungsphysiologischen Einfluß verkürzt.

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Circadian activity rhythms of birds with and without a dark nest box

Summary Perch-hopping activity of Great tits(Parus major) and Bengales finches(Lonchura striata domestica), housed individually in soundproof boxes, was studied in two series of experiments. In the first series all birds had access to a dark nest box, in which they retired during their subjective night. In this experiment the effect of light intensity on the freerunning circadian activity rhythm was investigated. Both Great tits and Bengalese finches obey the circadian rule by responding to an increase in light intensity with shortening the circadian period () and with an increase of the ratio of activity time and rest time ( : ).In the second series of experiments the influence of sleeping in the dark nest box on both circadian period and : -ratio was studied. The results of two experimental conditions — without and with access to a dark nest box — were compared. In the Great tits, the results are in agreement with the effect of light intensity: when a dark nestbox is available, is longer and the : -ratio is smaller than in the absence of a nest box. The magnitude of the change in free-running period after removal of the nest box is independent of the original value of ; the amount of change : -ratio is likewise independent of the original : -ratio, but is weakly correlated to the original .InLonchura striata var. domestica, removal of the dark nest box leads to a lenghtening of the free-running period to about 24 hours; the : -ratio is smaller in the presence of a dark nestbox, if certain other conditions are fulfilled. The magnitude of the change in after removal of the nest box is highly correlated to the original free-running period (r=-0.89) in such a way that, without nest box, the period approaches a value of 24 hours. Also, the amount of change in : -ratio due to nest box removal is negatively correlated to the original : -ratio. A probably preferred : -ratio of 2.0 is adopted.These results are discussed in the view of 4 points: 1) The circadian system operates at its optimum within a narrow range of - and : -values. 2) This optimal range is especially adopted when conditions become adverse. 3) Removal of the dark nest box results in a more stressful situation for Bengalese finches than for Great tits. 4) In the Bengalese finches, is shortened in the presence of a nest box due to effects on reproductive physiology.

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Herrn Prof. Dr. JürgenAschoff zum 60. Geburtstag gewidemt.     

Mode of uptake of sterol by Arthrobacter simplex

The mechanism of uptake of water-insoluble -sitosterol by a newly isolated strain of Arthrobacter simplex SS-7 was studied. The production of an extracellular sterol-pseudosolubilizing protein during growth of A. simplex on -sitosterol was demonstrated by isolating the factor from the cell-free supernatant and its subsequent purification by Sephadex G-150 column chromatography. The M _r of the purified sterol-pseudosolubilizing protein determined by SDS–PAGE was 19kDa. The rate of sterol pseudosolubilization (5.2×10^–3g l^–1h^–1) could not adequately account for the rate of sterol uptake (72×10^–3g l^–1h^–1) and the specific growth rate (56×10^–3 h^–1). However in the unfavourable growth condition, when the cells were treated with sodium azide at the level of 30–60% of MIC, the sterol pseudosolubilization accounted for nearly 74% of the total growth containing 96% free cells. Cellular adherence to substrate particles was found to play an active role in the normal growth of the strain on -sitosterol. Unlike sodium acetate-grown cells, whose surface activity was negligible (60mNm^–1), the sterol-grown cells had strong surface activity (40mNm^–1). The high lipid content and long chain fatty acids in the cell-wall of -sitosterol-grown cells probably contribute to the high sterol adherence activity of the cells.     

Comparisons of the Genomes of New Giant Phages Isolated from Environmental Pseudomonas aeruginosa Strains of Different Regions

To study the genome diversity of bacteriophages from geographically distant natural populations, new giant KZ-like Pseudomonas aeruginosa phages isolated in two different regions were compared with earlier known phages of three species (KZ, Lin68, EL). A broad spectrum of lytic activity was demonstrated for all KZ-like phages. Phages of the KZ species proved to be common in natural populations of various regions, while EL- and Lin68-related phages were extremely rare. Most KZ-related phages had unique DNA restriction patterns, but the differences between these were only minor, and the genomes did not contain nonhomologous fragments. The spectrum of capsid polypeptides proved to be conserved in each species, and was proposed as a character necessary and sufficient for express classification of phages with an accuracy of species. Phages isolated in different geographical regions showed no substantial difference. Some phages only slightly differing in DNA restriction pattern from KZ may be used to study the origin of KZ genes coding for orthologs of proteins of unrelated species (other phages, pathogenic bacteria, eukaryotes).     

Enzymic synthesis of the trisaccharide core region of the carbohydrate chain ofN-glycoprotein

Transmannosylation from mannotriose (Man1-4Man1-4Man) to the 4-position at the nonreducing end N-acetylglucosaminyl residue ofN,N-diacetylchitobiose was regioselectively induced through the use of -d-mannanase fromAspergillus niger. The enzyme formed the trisaccharide Man1-4GlcNAc1-4GlcNAc (3.7% of the enzyme-catalysed net decrease ofN,N-diacetylchitobiose) from mannotriose as a donor andN,N-diacetylchitobiose as an acceptor. Mannobiose (Man1-4Man) was also shown to be useful as a donor substrate for the desired trisaccharide synthesis.Abbreviations Man d-mannose - (M _n) (n=1–5) -linkedn-mer of mannose - GlcNAc₂ 2-acetamido-2-deoxy--d-glucopyranosyl-(1–4)-2-acetamido-2-deoxy-d-glucose     

The role of tree sprouts in the restoration of stand structure and species diversity in tropical moist forest after slash-and-burn agriculture in Eastern Paraguay

The contribution of tree sprouts to the recovery of tropical moist forest in Eastern Paraguay after swidden agriculture was examined in 2–15 yr old forest fallows and compared with sprouting in mature forest. The proportion of stems of sprout origin, as individuals arising from stumps or lower parts of live stems ( 1 m), in the stem density declined from 59.5% (stems 1–4.9 cm DBH) and 21.0% (stems 5 cm DBH) in the young regrowth stands (2–5 yr old) to 32.9% and 19.6%, respectively in the older regrowth stands (10 and 15 yr old). Sprouts were absent in the mature forest. Out of 58 species sampled in the regrowth stands, 28 occured both as resprouts and seed regeneration, 7 were only found as resprouts, and 23 were only present as seed-established individuals. No significant relationship was found between the successional status or the growth form of species and apparent resprouting capacity. Seed-established individuals of Trema micrantha were predominant in the two and three-year old regrowth stands. In the more advanced successional stages, T. micrantha was replaced by Cecropia pachystachia and other secondary species. Species richness increased during succession. Species-abundance distribution in the successional stands followed a log series pattern, whereas the mature forest showed a log normal distribution. Floristic similarity to the mature forest, calculated with the qualitative Soerensen index, increased from 0.45 (1–4.9 cm DBH) in the young regrowth stands to 0.52 in the older regrowth stands. In the tree stratum ( 5 cm DBH), however, floristic composition approached only 0.28 in the younger regrowth stands and 0.44 in the older regrowth stands, respectively that of the mature forest.     

Modelling of predator–prey trophic interactions. Part I: two trophic levels

A class of lumped parameter models to describe the local dynamics in a controlled environment of a two-trophic chain is considered. The class is characterized by a trophic function (functional response of predator to the abundance of prey) depending on the ratio of prey biomass x and a linear function of predator biomass y: f(qx/[(1-)k+y]), where q is the efficiency of the predation process, k is a reference biomass, and (01) specifies the predation model. The trophic function is defined only by some properties determining its shape. A stability analysis of the models has been performed by taking the parameters q and as bifurcation parameters: the regions in the (,q) plane of existence and stability of nonnegative equilibrium states and limit cycles are determined. This analysis shows that the behaviour of the models is qualitatively similar for 0<1 (in particular the null state is always a saddle point), while the value =1 gives rise to some kind of structural instability of the system (in particular the null state becomes an attractor for sufficiently high predation efficiency).     

Equilibria in structured populations

The existence of a stable positive equilibrium state for the density of a population which is internally structured by means of a single scalar such as age, size, etc. is studied as a bifurcation problem. Using an inherent birth modulus n as a bifurcation parameter it is shown for very general nonlinear model equations, in which vital birth and growth processes depend on population density, that a global unbounded continuum of nontrivial equilibrium pairs (n, ) bifurcates from the unique (normalized) critical point (1, 0). The pairs are locally positive and conditions are given under which the continuum is globally positive. Local stability is shown to depend on the direction of bifurcation. For the important case when density dependence is a nonlinear expression involving a linear functional of density (such as total population size) it is shown how a detailed global bifurcation diagram is easily constructed in applications from the graph of a certain real valued function obtained from an invariant on the continuum. Uniqueness and nonuniqueness of positive equilibrium states are studied. The results are illustrated by several applications to models appearing in the literature.This research was done while the author was on leave at the Lehrstuhl für Biomathematik, Universität Tübingen, Auf der Morgenstelle 10, 7400 Tübingen 1, Federal Republic of Germany