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).     

Drone bees fixate the queen with the dorsal frontal part of their compound eyes

Summary Free flying drone bees (Apis mellifera carnia () were filmed from the side while chasing the honey bee queen or landing on a hive.Drones use the upper frontal part of the field of view of their eyes while chasing the queen. They fixate with the lower frontal part of the field of view of their eyes during landing. Drones keep a particular distance from the queen while chasing her.The diameter of ommatidial lenses in drones shows a maximum in the region where the queen is fixated.Niedersächsisches Landesinstitut für Bienenforschung und Bienenwirtschaftliche Betriebslehre, Wehrstrasse 4, D-3100 Celle, Federal Republic of GermanyLehrstuhl Entwicklungsphysiologie, Fakultät für Biologie, Universität Tübingen, Auf der Morgenstelle, D-7400 Tübingen, Federal Republic of GermanyWe thank Walter F. Gelinski for kind cooperation and Professor W. Engels for support.     

Die Wirkungen des Lichtes auf einige Pilze und ihre spektrale Grenze zum Langwelligen hin

Ohne ZusammenfassungTeil der Dissertation: Die Wirkungen des unpolarisierten und polarisierten Lichtes auf einige Pilze, Tübingen 1959.     

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.     

Aggregative effects for a reaction-advection equation

The time course of a single population subject to logistic growth and drift towards regions of increasing population density is modelled by a quasilinear differential equation of the first order. The stationary solutions and the travelling waves are investigated. The existence of travelling waves with compact support is used to prove, among other properties, that populations initially concentrated in a finite region preserve this property for all future times.Visiting A. von Humboldt Fellow at the Universität Tübingen, Lehrstuhl für Biomathematik, Auf der Morgenstelle 28, D-7406 Tübingen 1     

Aufbau, Variabilit?t und m?gliche Funktionen des Rufduetts beim ThermometerhuhnLeipoa ocellata

Zusammenfassung Beim ThermometerhuhnLeipoa ocellata tragen die Partner eine Paares ein Rufduett vor. Der Anteil des besteht aus einer Rufreihe, die sich aus einer Folge von 2–7 identischen, zweisilbigen Rufen zusammensetzt. Das trägt einen einzelnen, obertonreichen und langgezogenen Ruf vor. Sowohl der Ruf des als auch die Rufreihe des wird in Serien vorgetragen. Innerhalb einer solcher Ruf- bzw. Rufreihenserie können mehrere Duette auftreten. Die Rufe sind jedoch nicht ausschließlich an das Duett gebunden. Die Variabilität im Aufbau des Duetts äußert sich im Zeitpunkt des Einsatzes des antwortenden Vogels, in der Anzahl der -Rufe während des Duetts und in der Anzahl der Einheiten, aus denen sich der Duettanteil des zusammensetzt. Das beginnt signifikant häufiger als das eine Serie, in der ein oder mehrere Duette vorkommen. Ebenso ist es häufiger der Initiator des ersten in dieser Serie liegenden Duetts. Das Duett dient wohl hauptsächlich zur Festigung des Zusammenhalts zwischen den Paarpartnern. Es erfüllt jedoch von seinen physikalischen Eigenschaften her auch die Bedingungen, die für ein territorial wirksames Signal gelten.

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Structure, variability and possible functions of duetting in the Mallee FowlLeipoa ocellata

Summary In the Australian Mallee Fowl,Leipoa ocellata, both and of a pair are involved in a call duet. The part of the consists of a sequence of 2–7 identical two-syllable calls. The contributes a single long-drawn-out call rich in harmonics. The call of the as well as the call sequence of the are presented in series. Within a series of calls () or call sequences () several duets can occur. The respective vocalizations, however, do not exclusively occur during the duet.The variability in the details of the duet expresses itself in the lag period after which the mate responds, in the number of -calls during the duet, and in the number of calls within the call sequence of the . The begins a series during which one or several duets occur significantly more frequently than the . The circumstances under which duetting occurs indicate that duet calling mainly serves to maintain the pair bond. Moreover, due to its physical characteristics the duet also seems to be suited to serve as a territorial signal.

     

The Hopf bifurcation in some biochemical control loops

Conclusions By working with inequality theory it is possible to check the sign of the local nonlinearity at a Hopf bifurcation in much more general circumstances than previous work has done. In particular, any bifurcation in the Goodwin equations when the Hill coefficient is at least 2 and the ratio ¦G(i₀)/G(0)¦ at the bifurcation point is at least 1/2, produces an attracting orbit, existing when the equilibrium is unstable.In a multiple loop system there can be bifurcations of the opposite type, and then there are likely to be certain parameter ranges in which there can be two attracting sets in the state space: one steady state and one periodic orbit. Which of these the system converges to will depend on its past history, so there is the possibility of hysteresis.This research was financed by a research studentship from the Science Research Council     

Equilibria in systems of interacting structured populations

The existence of a stable positive equilibrium density for a community of k interacting structured species is studied as a bifurcation problem. Under the assumption that a subcommunity of k–1 species has a positive equilibrium and under only very mild restrictions on the density dependent vital growth rates, it is shown that a global continuum of equilibria for the full community bifurcates from the subcommunity equilibrium at a unique critical value of a certain inherent birth modulus for the kth species. Local stability is shown to depend upon the direction of bifurcation. The direction of bifurcation is studied in more detail for the case when vital per unity birth and death rates depend on population density through positive linear functionals of density and for the important case of two interacting species. Some examples involving competition, predation and epidemics are given.     

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.     

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.     

Competition between two annual herbs,Atriplex gmelini C.A. Mey and Chenopodium album L., in mixed cultures irrigated with seawater of various concentrations

Summary Atriplex gmelini and Chenopodium album were grown in mixed stands with various combinations of plant density and mixing ratio, and irrigated with seawater of different concentrations (f) to formulate the effect of changing concentration on the competitive relationship between the species.In single-species stands, the mean plant weight (w)plant density () relation for each level of seawater concentration could well be described by Shinozaki-Kira's reciprocal equation of crowding effect. On the other hand, the response of w to f followed Hozumi-Shinozaki's formulation for an optimum growth factor at respective levels of .By introducing the density conversion factor (q) that enabled the conversion of the density of one species to that of the other species on the basis of their effects on growth of respective species, the results of mixed culture experiments could be successfully formulated by similar reciprocal equations. The dependence of q and coefficient values of the equations on seawater concentration was also formulated in a way similar to the case of pure stands.Based on all these quantitative relations, a comprehensive formulation was developed to describe the effects of plant density and seawater concentration on the growth of two species in mixed stands. The behavior of species biomass in mixed stands was then examined by means of the formulation.It was thereby demonstrated that the relative dominance of two species in a mixed stand was strongly affected not only by total plant density and density ratio between the two species but also by concentration of irrigated seawater. Even the optimum seawater concentration that resulted in the maximum species biomass differed between pure and mixed cultures.     

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.     

Studien zum L-Cyclus der Bakterien

Ohne ZusammenfassungAuszug aus dem ersten Teil einer Dissertation Studien zum Gestaltwandel der Bakterien. (Nach Untersuchungen an Proteus vulgaris und einem gram-negativen unbeweglichen Stäbchen) der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Tübingen 1956.     

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.     

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.     

Globally asymptotic properties of proliferating cell populations

This paper presents a general model for the cell division cycle in a population of cells. Three hypotheses are used: (1) There is a substance (mitogen) produced by cells which is necessary for mitosis; (2) The probability of mitosis is a function of mitogen levels; and (3) At mitosis each daughter cell receives exactly one-half of the mitogen present in the mother cell. With these hypotheses we derive expressions for the and curves, the distributions of mitogen and cell cycle times, and the correlation coefficients between mother-daughter (_md) and sister-sister (_ss) cell cycle times.The distribution of mitogen levels is shown to be given by the solution to an integral equation, and under very mild assumptions we prove that this distribution is globally asymptotically stable. We further show that the limiting logarithmic slopes of (t) and (t) are equal and constant, and that _md0 while _ss0. These results are in accord with the experimental results in many different cell lines. Further, the transition probability model of the cell cycle is shown to be a simple special case of the model presented here.     

Electrical characteristics of mollusk giant neurons

The following electrical parameters of giant neurons of the molluskPlanorbis corneus were determined: the time constant , the ratio between the input conductance of the axon membrane and the conductance of the soma membrane , the input resistance of the neuron R_N and axon r_a, the total r_s and specific R_s resistance of the soma membrane. To determine and the course of the transition process during membrane polarization by a square pulse of input current was analyzed. R_N was estimated from the electrotonic potential V after the end of the transition process; r_s and r_a were calculated by the equations r_s=R_N·(1+) and r_a=r_s/. The surface area of the soma membrane (for calculating R_s) was estimated from its capacitance. It was assumed that the specific capacitance of the membrane is 1 µ F/cm². According to these calculations the surface area of the soma may be more than ten times greater than the surface area of a sphere of the same diameter. The results showed that R_s can vary appreciably in different neurons from 20·10³ to 200·10³ ·cm². The time constant of the different neurons varies from 20 to 200 msec; usually the value of did not exceed 1.0 and it varied from nearly zero to 1.5. Changes in temperature and ionic composition of the external solution led to changes in the parameters r_a and r_s and also of and . Various responses of the soma and axon membranes to changes in the composition of the external solution were noted and they can be regarded as an index of some properties of the membrane in these regions of the cells.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 4, No. 6, pp. 651–658, November–December, 1972.     

Alternative pathway activities in aged potato tuber slices measured by three methods

To find a simple and reliable oxygen electrode-based method to estimate the values of alternative pathway activity (V _alt) and its contribution to total respiration V _alt/V _t) in aged potato (Solanum tuberosum L.) tuber slices, we compared conventional hydroxamate-inhibiting method, improved hydroxamate-inhibiting method with 2,6-dichlorophenol indophenol (DCPIP), and the oxygen isotope discrimination (OID) method. The values of V _alt and V _alt/V _t obtained with an improved hydroxamate-inhibiting method with DCPIP in 12-h- and 24-h-aged slices were about twice higher than those with the conventional hydroxamate-inhibiting method. Only a relatively small difference in the values of V _alt and V _alt/V _t obtained by the OID method and the improved hydroxamate-inhibiting method with DCPIP in 12-h and 24-h-aged slices was observed. These results indicated that the improved hydroxamate-inhibiting method with DCPIP could be considered as a new, simple, and reliable technique for the noninvasive assay of the AP activity.From Fiziologiya Rastenii, Vol. 52, No. 2, 2005, pp. 311–315.Original English Text Copyright © 2005 by Hou, Zhou, Kong, Liang, Zhang.This article was submitted by the authors in English.This revised version was published online in April 2005 with a corrected cover date.     

Temperatursensitive Mutanten des Tabakmosaikvirus

Ohne ZusammenfassungVerwendete Abkürzungen TMV Tabakmosaikvirus - ts temperatursensitiv - tr temperaturresistent - def defekt - HP Hüllprotein - RNS Ribonukleinsäure - RNase Ribonuklease - EDTA Äthylendiamintetraessigsäure Dissertation der Math.-Naturw. Fakultät der Universität Tübingen.     

The functional significance of synchronization of cortical potentials in humans

The dependence between the level and the topography of spatial synchronization of cortical potentials and the manifestation of motor reactions to light stimuli was studied in humans. To evaluate the spatial synchronization of potentials the correlation coefficients () were calculated between three points of the motor area and each of three occipital points of the cortex. The calculation was made using a computer with direct input of the potentials. At a definite level of the machine switched on a light stimulus and a mechanism recording the motor reaction. The experiments have shown that the higher the number of pair derivations giving a high value of , the more often movements are caused. Moreover it became apparent that the pattern of correlation ratios between the derivations depends on the motor reactions. In the case of movements a significant constancy of the ratios between individual derivations was found. It is shown that the spatial synchronization of potentials in the human cerebral cortex has a functional significance. However, this synchronization does not reflect the realization of movements but only the conditions required for them.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 2, No. 2, pp. 166–172, March–April, 1970.