ALBERT

Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.

Notes: Abstract The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.

Notes: Abstract In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given.

Notes: Abstract The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.

Notes: Abstract A performance criterion and weighting factors for the optimal cardiac assistance are investigated by applying Tellegen's network theorem and tolerance analysis on animal experimental data for left ventricular (LV) bypass on the failing heart. Two major factors with respect to cardiac assistance (total power delivered to the peripheral circulatory system, and changes in temporal pattern of ventricular contraction) are represented by two performance criteria,J 1 andJ 2 whereJ 1 relates to the sum of LV and pump power, andJ 2 relates to the “peakedness” factor of LV power. The total performance index (J) is determined as the weighted sum ofJ 1 andJ 2;J=w 1J1+w2J2. The weighting factors,w 1 andw 2, are computed as inverses of the tolerance in the performance contours with respect to improvement of stroke work per minute from pre- to post-bypass condition.

Notes: Abstract In treating the Volterra-Verhulst prey-predator system with time dependent coefficients, we ask how far this deterministic system represents or approximates the dynamics of the population evolving in a realistic environment which is stochastic in nature. We consider a stochastic system withsmall Gaussian noise type fluctuations. It is shown that the higher moments of the deviation of the deterministic system from the stochastic approach zero as the strength δ of the perturbation decays to zero. For any δ〉0 and allT〉0, ε〉0, the sample population paths that stay within ε distance from the deterministic path during [0,T] form a collection of positive probability. In comparing the stationary distributions of the two systems, we show that the weak limits of those of the stochastic system form a subset of those of the deterministic system. This is in analogy with a result of May connected with the stability of the two systems. Plant and rodent populations possess periodic parameters andexhibit periodic behaivor. We establish theoretically this periodicity under periodicity conditions on the coefficients and perturbing random forces. We also establish a central limit property for the prey-predator system.

Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.

Notes: Abstract A setQ(n) of noncongruent connected shapes, constructed from a fixed numbern of congruent regular hexagons laid edge to edge, is defined. Various measures of shape are applied toQ(n) and the results are numerically analyzed in the special casesn≦9. The concept of spatial entropy is introduced which affords a measure of the “complexity” of shape. Possible biological applications include the analysis of ecological cover,stigmergy or the complex nest-building activities of social insects and morphogenesis. Essentially any comparative study of shape, regardless of the specific application, might be carried out along the lines suggested in the paper.

Notes: Abstract This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.

Notes: Abstract Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.

Notes: Abstract A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.

Notes: Abstract A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.

Notes: Abstract The global flow equations of nonequilibrium thermodynamics for a single nonelectrolyte solute and water passing through a membrane are obtained by solving the local equations of motion. The method follows that developed for the general,n-solute case in the previous paper (Mikulecky, 1978). It is easily seen in this simple case that the passage from local interactions, formulated as position dependent frictional interactions in the equations of motion, to ghe global result involves a loss of any simple way of identifying particulars about local information. Two particular cases are analyzed in further detail: the case of no interaction within the pore and the case of constant interaction for both solute and solvent across the pore. In the former case, Onsager reciprocity survives in the global result if a self-consistent definition of the partial viscosity coefficients is used, while in the latter case, reciprocity is lost. Since, in many biologically interesting cases, the presence of interaction of the type considered here is likely to occur, the reciprocity condition should not automatically be assumed to hold.

Notes: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.

Notes: Abstract Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.

Notes: Abstract The basis of an analytical description of the behaviour of large random nets of binary elements of the type first investigated in detail by S. A. Kauffman is presented. It is shown that information about the network dynamics can be deduced from quite general considerations of the properties of the state transition graph and matrix. An expression for the matrix elements of the state transition matrix in terms of the Boolean function specification of the net is derived. Using these ideas the distribution of limit cycle lengthsl for a completely random net is calculated and shown to bex 1/l, a result which agrees well with experimental data.

Notes: Abstract The state-transition matrix description of Kauffman binary networks described in the previous paper is further developed to obtain an analytical expression for the fraction of states involved in limit cycles as a function of the network size and connectivity. The result obtained for totally connected networks agrees with that derived from quite different considerations by other workers. For low connectivity networks the results are in qualitative agreement with the experimental data of Kauffman but there is a quantitative discrepancy which remains to be resolved.

Notes: Abstract Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.

Notes: Abstract Oxygen consumption of the left ventricle (MVO 2) was evaluated theoretically under the condition that the ventricle pumps a constant stroke volume against a constant arterial pressure, hence producing a constant external mechanical stroke work, with a widely varied contractility.MVO 2 was calculated by an empirical equation which had been inferred previously. Theoretical results indicated that the ventricle has a contractility at whichMVO 2 is minimal in spite of constant external work and therefore the mechanical efficiency as a pump is maximal. Such a contractility can be considered to be optimal from a standpoint of metabolic economy. The optimal contractility fell within the physiological range of contractility which had been observed experimentally. The result suggests a possibility that the contractility of a normal heart might be physiologically adapted to such an optimal level.

Notes: Abstract Diffusion problem with variabale diffusion coefficient in a spherical biological system is investigated. Also included in this study is the biological reaction of the Michaelis-Menten type. The problem formulated consists of a highly nonlinear differential equation which, however, can be efficiently solved by the orthogonal collocation method on a digital computer. The effects of the dimensionless governing parameters on the transient and steady state concentration responses are parametrically examined for the diffusion system with and without biological reaction.

Notes: Abstract The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ e , occupying the same overall volume, coupled to the first via the resistanceR m and capacitanceC m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR a, and capacitanceC a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ ia/R a and β=ρ i /ρ e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.

Notes: Abstract The model developed in an earlier paper using two coupled partial differential equations for calculating the intracellular and extracellular electric potentials in a syncytium is applied here to cylindrical geometry. Eigenfunction expansions are obtained for the potentials resulting from an intracellular point source of current. The required orthogonality relations for the two sets of coupled radial eigenfunctions are derived. The model is applied to the structure composed of the interior and the transverse tubules of a muscle fiber. Asymtotic expansions for ζ and β→0 are obtained, where ζ is the product of the effective intracellular resistivity, the fiber radius and the outer surface membrane admittance per unit area, and β is the ratio of the effective intracellular resistivity to that of the tubular lumen. Earlier results from the distributed circuit model of a muscle fiber are recovered when ζ and β are small, and for a nerve axon when β=0.

Notes: Abstract Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, πK, of the potassium conducting system ≃59 the permeabilityP Ks, of the periaxonal barrier of the squid giant axon for K+ ions≃(1.2±0.44)×10−4 cm sec−1 and the thickness of the periaxonal space ≃477±168 Å. Using a value (10−4 cm sec−1) ofP Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ϕ, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K+ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ≃70mV along the voltage axis in the hyperpolarization direction. By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ϕ curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K+ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K+ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.

Notes: Abstract Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.

Notes: Abstract A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.

Notes: Abstract It is shown that the Weber-Fechner law. which relates the response of a sensory biosystem to the intensity of the input stimulus, can be derived from a teleological principle of minimum transentropy (maximal noise reduction) provided the relative mean fluctuation (coefficient of variation) of the input intensity can be assumed to be (approximately) constant for all feasible mean input intensities. A law is then deduced from experimental results which quantifies the relationship existing between the relative amount of activated muscle mass and the “size” (which term is clearly defined) of a newly recruited motor unit. This law is found to be formally equivalent to the Weber-Fechner law when applied to motor unit recruitment. It is then shown that, in general, the ratio of the force increment upon recruitment, to the present force output does not obey Weber's law. Finally, it is proved that the “motor unit size law” as derived in this paper implies a fixed sequential order in the recruitment of motor units and that it may be viewed as the realization, by the mammalian neuromuscular system, of a general principle of maximum grading sensitivity.

Notes: Abstract In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.

Notes: Abstract A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.

Notes: Abstract We analyze under different environmental conditions the occurrence of bistability, i.e. of two simultaneously stables steady states, in a biological model system which describes the immunological interactions of neoplastic-target cells and cytotoxic-effector cells. As a result of environmental fluctuations such complex biological systems may undergo drastic modifications of their steady state properties. In particular, when the variance of fluctuations increases around a well defined mean value, transition phenomena appear which are absent in the usual bifurcation diagrams. The properties of the non-fluctuating systems can no longer be considered as a first approximation of the properties of the real system. Interestingly, in the case of the model, these transitions correspond to a rejection of tumor cells.

Notes: Abstract Two results on light penetration of an absorbing medium are presented in this paper: (1) It is shown, using the general light penetration law of Mannet al. (1977), that a random distribution of absorbing bodies (cells, leaves, etc.) is most efficient at intercepting direct beam (parallel) light. (2) A transmission coefficient is added to the general law in a manner similar to Monteith's (1965). This leads to the partitioning of the radiation regime beneath an absorbing medium into unintercepted, once intercepted, twice intercepted, etc., components. We are thus enabled to calculate the mean radiation intensity beneath the absorbing medium.

Notes: Abstract Previous stochastic compartmental models have introduced the primary source of stochasticity through either a probabilistic transfer mechanism or a random rate coefficient. This paper combines these primary sources into a unified stochastic compartmental model. Twelve different stochastic models are produced by combining various sources of stochasticity and the mean value and the covariance for each of the twelve models is derived. The covariance of each model has a different form whereby the individual sources of stochasticity are identificable from data. The various stochastic models are illustrated for certain specified distributions of the rate coefficient and of the initial count. Several properties of the models are derived and discussed. Among these is the fact that the expected count of a model with a random rate coefficient will always exceed the expected count of a model with a fixed coefficient evaluated at the mean rate. A general modeling strategy for the onecompartment, time invariant hazard rate is also proposed.

Notes: Abstract A new equation for the growth rate of photosynthetic microorganisms is derived. It is based on a series formulation of the mechanism of photosynthesis and it has the form of a functional of the spectral qualities of light. Using this functional to model their growth it is shown that populations of photosynthetic microorganisms can coexist in the same homogeneous environment even though they compete for the available light.

Notes: Abstract The formalism and results of the theory of random evolutions are used to establish and investigate a model for two randomly interacting populations. The asymptotic stability of the expected solution is studied and contrasted to that of the associated deterministic system.

Notes: Abstract In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.

Notes: Abstract A branching processZ(t) which behaves as Markov branching processesZ 1(t) andZ 2(t) during the free and dead times of a counter process is considered. Expression forE[Z(t)] is given.

Notes: Abstract The spontaneous electrical rhythms recorded from the gastro-intestinal tract of humans and animals have been successfully modelled by an array of interconnected van der Pol oscillators. To account for asymmetry in the recorded waveforms (with particular reference to the human small intestine) an additional term in the van der Pol dynamics has been included. It is shown that the method of harmonic balance can be used to give analytical results for this asymmetrical condition. The non-linear algebraic equations are solved by hill-climbing to give values of d.c., fundamental and second harmonic amplitudes together with the entrained frequency. The results correlate well with actual measurements made on an analogue simulation by three different methods for waveshape factors of 0.1 and 1.0

Notes: Abstract In view of the increasing evidence that multicomponent diffusion effects could be significant in biological gas exchange systems, a non-equimolar film model of multicomponent diffusion was derived. “Osmotic” ternary diffusion was studied for the gas systems He−N2−O2, He−SF6−O2, and N2−SF6−O2. Diffusional fluxes and concentration profiles were calculated under both the “square-root” and the “product” flux conditions. Results were also compared with those obtained using the equimolar flux condition. It was found that the greater the difference of the diffusibilities between the two active components in a system, the greater the osmotic fluxes, and also the more alinear the concentration profiles. These results support the suggestion that the “product” condition applies to molecular diffusion in free space, the “square-root” condition to molecular diffusion in pores, and the equimolar flux condition to closed diffusion systems.

Notes: Abstract This communication contains a proof of the fact that the coefficient of variation of the contents of a compartment of a stochastic compartmental model with deterministic rate parameters is small for large populations. We can therefore conclude that the use of stochastic compartmental models is not of great consequence in the case of systems involving large populations when only the randomness of the transfer mechanism is considered.

Notes: Abstract A system of arbitrarily many nonlinear ordinary differential equations which can be interpreted as describing competition between populations is studied here. It is found that limits exist for the system given specified constraints on the “signal function” which describes input-output relations at the level of single populations. Existence of limits is shown by means of a function which records which variable in the system is growing fastest at a given time i.e. who is winning the competition. Generalizations are discussed to sigmoid signal functions which appear in models of pattern discrimination by neuron populations.

Notes: Abstract The cumulant generating function and first two moments are derived for the stochastic distribution of units in a general irreversiblen-compartment model with time-dependent transition probabilities. In this model, a unit in the first compartment can transfer to any one of the remainingn−1 compartments and a unit in the second compartment can transfer to any of the remainingn−2 compartments and so on. In addition, a unit can enter or leave the system through any compartment. The work is related to previous research and a numerical example is given.

Notes: Abstract Many ecological and biological systems can be studied in terms of a bivariate stochastic branching process, {X 1 (t), X 2 (t)}, each of whose components (or populations) varies in magnitude according to the laws of a generalized birth-death process. Of particular interest is such a model in which the birth and death rates of the first population,X 1, are constant while those of the second population,X 2, exhibit a functional dependence upon the magnitude of the first. It is shown, first, that the existence of the stochastic mean of a birth death process implies the existence of all higher moments. The values of all the factorial moments of such a process are then determined. The moments of the dependent population of the bivariate process are given in terms of its expectation and the joint probability density function of the process is determined. It is possible, therefore, to use Bayesian techniques to infer conclusions about the independent population, given information about the variation of the dependent one.

Notes: Abstract Only a fraction of the total number of equilibrium solutions of the differential system which describes the populations of species in an ecosystem are feasible: that is only a fraction of the solutions give non-negative values for all the populations. The feasible equilibrium solutions of a generalized logistic equation are considered for the limiting cases of strongly and weakly interacting species. It is found that only about one third of all the possible species are generally expected to be present (i.e. to have non-zero populations) at any given equilibrium solution.

Notes: Abstract We consider a method for selection among a collection of self-reproducing macromolecular information carriers. The information carriers are assumed subject to the general constraint in which the fluxes of the energy rich monomers used in the syntheses of the information carriers are controlled externally. The constraint forces a competition among the various macromolecular species and a Darwinian like selection takes place. We show that the overall selective behaviour is independent of the specific form of the constraint. A general criteria for selection is given and we show that the selection process may generally be characterized by an optimization principle.

Notes: Abstract The bifurcation equations of a general reaction-diffusion system are derived for a circular surface. Particular attention is directed to the deformation of the circular boundary into an elliptic shape. This leads to a new bifurcation diagram which may involve secondary bifurcation, but which retains however the basic characteristics of the solutions for the circular case. Numerical simulations of the various coexisting, time-periodic and space-dependent solutions, are presented for a simple model reaction and circular geometry.

Notes: Abstract The dynamics of a self-organizing molecular system is described in terms of its normal modes. Each normal mode is associated with a certain eigenvalue, the average of which reflects most directly the overall process of self-organization. For the temporal change of this quantity a maximum principle holds.

Notes: Abstract The purpose of this study is to investigate the relationship between the structure of muscle and its function, especially with regard to the influence of the internal pressure when a muscle contracts. A model is constructed based on the anatomy of muscle. For difference shapes of muscle, but of equal volume, the muscle features (i.e. force exerted etc.) are computed after every contraction step. A function for the internal pressure is also calculated. The internal pressure influences the structure of the muscle which also depends in a certain way upon the function of the muscle.

Notes: Abstract Experimentally induced auto-immune hemolytic anemia (AIHA) in rabbits is characterized either by constant depressed erythrocyte numbers, or by oscillatory erythrocyte numbers about a depressed level (periodic auto-immune hemolytic anemia). Here the experimetallys observed characteristics of AIHA are satisfactorily accounted for by a simple model for erythropoiesis, assuming only the peripheral erythrocyte destruction rate is elevated with all other parameters normal. The onset of periodic AIHA is identified with the occurrence of a Hopf bifurcation in the model dynamics for certain values of the erythrocyte destruction rate.

Notes: Abstract Gating current is considered to be due to the transition of dipoles, which are coupled with the membrane matrix. Based on previous theory of nerve excitation, the equation for gating current is derived; the charge displacement equation and the time constant of the gating current are also derived. Agreement with experimental data is good.

Notes: Abstract The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds $$c = \pm 5/\sqrt {(6)} $$ . In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.

Notes: Abstract A system involving two kinds of sliding filaments is analysed with special attention to the actomyosin system. Rigorous results are obtained about the statistical effect originating from many active sites distributed on both filaments. It is necessary for the occurrence of smooth motion in sliding filament that the spatial periods of active sites on both filaments are relatively incommensurable, and that the number of active sites on each filament is large enough. Sufficient conditions for smooth contraction are derived under the assumption that both filaments are rigid; this is called rigid rod approximation in the present paper. The elastic mode of the filaments, during the sliding process, is analysed by perturbation theory based on the rigid rod approximation. A stochastic theory is briefly discussed in reference to the cooperative generation of contractile force, which is concerned in Hill's relation of muscle contraction.

Notes: Abstract We consider some models for selection in self-reproducing macromolecular systems subject to time varying environmental constraints. We show that many of the results concerning selection obtained previously for stationary constraints may be generalized and that the over-all selective behaviour even in complex enzyme coupled systems is basically the same under the time varying external conditions as it is in the stationary case.

Notes: Abstract Standard results relating to the stability of autonomous first order difference equations are restated here with slight modifications so as to apply directly to equations in which the state variable remains positive. Some simple and effective tests for both local and global stability of these first order difference equations are presented. The main results are illustrated with examples drawn from population biology.

Notes: Abstract An analytical procedure is used to derive a class of functions for the shapes of the cross section of the human red cell during its osmotic swelling.

Notes: Abstract The ecology and distribution of the polychaetes inhabiting the rocky interidal zone of the island of Helgoland (German Bight, North Sea) were studied at five ecologically different stations.Scolelepis squamata, Microphthalmus sczelkowii andOphryotrocha gracilis were the only typical intertidal polychaetes observed. Of the 53 polychaete species documented, eight were recorded for the first time in the German Bight. Two species and one subspecies had not been described previously. The following invironmental variables were measured and, where possible, related to the occurrence of the polychaetes: pH, redox potential, O2 diffusion rate, temperature, salinity, particle-size distribution, and amount of organic particles. In the investigation area the number of species and their frequency maxima increase horizontally from east to west. This appears to be due to the increasing diversity of microhabitats in the substratum, as well as to conditions of O2 supply or H2S presence. Vertically, the number of species increases with water depth. The potential effects of temperature and salinity on the distribution patterns are discussed.

Notes: Abstract The response surface method was used to study the effects of temperature, salinity and Cd contamination on the development of fertilized eggs ofMytilus edulis from the western Baltic Sea to the veliger stage as well as on growth and cumulative mortality of a veliger population. The reactions observed differ considerably with reference to temperature and salinity. This is discussed in respect to the mode of life of the larvae and to the environmental conditions of the western Baltic Sea. Cd only slightly influences various temperature-dependent life functions, but strongly modifies those depending on salinity. The development optimum is shifted to higher salinities with increasing Cd concentrations of the medium, while that of survival and growth is shifted to lower salinities. These factor interactions modify the tolerance limits. In addition, the rates of factor interactions on the larval stages change with the degree of development. The trochophora stage proves to be most sensitive to the factors studied. A significant influence of cadmium on different life functions is found from concentrations of about 50 ppb on.

Notes: Abstract In the sessile barnacleBalanus balanus L. the relationship between stimulus duration and reaction intensity varies considerably. Investigations on the light reactions (increased cirral activity per unit time) and shadow reactions (decreased cirral activity per unit time) showed that increase of stimulus duration at a temporal range of 1–5 min and 30–360 min causes an increased response intensity, whereas, at a range of 5–30 min, the response intensity decreases. Two adaptive systems are assumed to be responsible for this behaviour. The peculiarities of the light and shadow reactions are interpreted as a result of interactions of central and peripheral components, but the unusual relationship between stimulus duration and reaction intensity is probably based on a greater influence of central components. The biological significance of the light and shadow reactions is discussed in relation to the larval and adult life: By means of the central variation of stimulus threshold in the described protective shadow responsesB. balanus seems to compensate for extreme environmental conditions. The light responses observed in the adults are considered as resulting from metamorphosis of larval swimming activity.

Notes: Abstract Investigations on the influence of daylength, light intensity, inundation and accretion tolerance on the morphological and ecological characteristics ofPuccinellia maritima in connection with the role of increasing salinity and temperature (results of former investigations) lead to a deeper understanding of the role this species plays in land reclamation and preservation of coastal areas. The results obtained indicate that the species exhibits a temperature — related seasonal dimorphism with short-stem growth at daylengths up to about 12 h light/day (vernal and autumnal types, caespitose growth) and a long-stem growth at daylength of about 16 h and more light/day (aestival type, stoloniferous growth). Increasing salinity (above 10‰ S) and inundation with artificial sea water (25‰ S) reduce stem and leave development. Accretion of long-stems with sand +3% peat-mixture up to 30 cm yields in 5‰ S further development of runners under long-day conditions and longation of short-stems (up to 10 cm) up to the new soil-surface level. Three shortstem types and two long-stem types can be distinguished. These results explain the natural responses of the species, the forming of the Puccinellietum maritimae within the allogene succession and its role in land preservation. The species is a facultative halophyte which occupies, due to competition from other species, the lower part of its inundation amplitude, utilising its high-salt tolerance. Its aestival long-stem and its autumnal/vernal short-stem production increases the sedimentation rate of soil particles during inundation; the following accretion leads to an elongation of short-stems up to the new soil level, and to an increased production of adventitious roots; the latter results in soil fixation.

Notes: Abstract The adhesive systems ofNematoplana coelogynoporoides Meixner, which are almost indiscernible in live animals, were examined with scanning and transmission electron microscopes. There are conformities with the fine structure of the adhesive systems in other Proseriata. However, there are also some special characteristics: the position of the adhesive systems in the epidermis; the number of anchor cells pro adhesive system; and the coexistence of intra-epithelial and insunk anchor cells in each adhesive system.

Notes: Abstract Experiments have been carried out on the duration of larval development of the spider crabHyas araneus L., in relation to temperature, food quality, and individual variation. A graphical model is presented which predicts larval occurrence and settlement in the field (Helgoland waters, North Sea). Preliminary observations are reported on predator-prey interactions with larvae of the spionid polychaetePolydora ciliata. Cannibalism and necrophagy during starvation experiments with zooplankton are considered: In larvae which are not kept in individual confinement, maximum survival time doubles due to feeding on living or dead sibling larvae. Analyses are presented revealing elemental and biochemical composition of starved and fed larvae as well as energy equivalents calculated from these data. During starvation, early larvae lose carbon, nitrogen, and hydrogen. Their main metabolic substrate is protein; lipid is utilized to a much lesser extent. Exoskeleton formation is, apparently, independent of nutrition: Zoea-1 larvae starved for 8 days contain the same amount of chitin as larvae fed well over this period of time. Energy calculations suggest an extremely low respiration rate and a very effective reconstruction of body material in starved larvae.

Notes: Zusammenfassung In 13 aufeinanderfolgenden Jahren wurden 65 Bruten des Schreiadlers und 28 (davon zwei Nachgelege) des Kaiseradlers registriert. 47 Schreiadlergelege enthielten im Mittel 1,68 Eier (15×1, 32×2). Aus 78 Eiern schlüpften 56 Junge. Der Verlust an Nestlingen durch Kainismus hätte ohne unser Eingreifen 38% ausgemacht, nur 32,8% von 78 abgelegten Eiern hätten flügge Adlerjunge und 61 durchbeobachtete Bruten eine Fortpflanzungsrate von 0,53 Jungen je Paar und Jahr ergeben. 13 Kaiseradlergelege enthielten durchschnittlich 2,46 Eier (7×2 und 6×3). Aus 40,6% von 32 Eiern kamen Küken aus. In 10 Bruten schlüpften im Mittel 1,8 Junge (2×1 und 8×2). 31,2% von 32 abgelegten Eiern ergaben flügge Jungadler. 12 von 27 Brutversuchen waren erfolgreich; im Durchschnitt kamen 1,6 Junge je geglückte Brut zum Ausfliegen. Darunter befanden sich zwei Bruten aus Nachgelegen eines Paares, mit einem und zwei flüggen Nestlingen. Der Reproduktionserfolg bei 25 Brutversuchen (plus zwei Nachgelegen) betrug 0,76 ausgeflogene Nachkommen je Paar und Jahr. Die Verlustursachen werden, soweit möglich, aufgeführt und die Ergebnisse mit denen anderer Autoren bei beiden Arten verglichen.

Notes: Zusammenfassung Ein Paar des HonigsaugersNectarinia kilimensis wurde in der Brutzeit beim Nestbau 21 Stunden beobachtet. Über die Bauaktivität gibt Abb. 2 Aufschluß. 140 von 144 Anflügen mit Nistmaterial waren auf 8 Stunden von 8h–16h konzentriert. Das Nistmaterial bestand fast ausschließlich aus Halmen, Pflanzenwolle und Spinnweben; dieses Material wurde von Anfang an abwechselnd verwendet. Nur das ♀ hat gebaut. Die Baumethoden werden beschrieben, ebenso verschiedene Balzhandlungen des ♂. Der Nestbau dauerte 4 1/2, beim folgenden Nest 3 1/2 Tage. Beim Brüten waren Schnabel und Oberkopf des ♀ sichtbar. Während der Bauzeit wurde ein ausgeflogenes juv. nur vom ♂ gefüttert. Als es mindestens 17 Tage alt war, wurde es vom ♂, 6 Tage später auch vom ♀ aggressive gejagt, doch war dieses juv. mehr als 3 Wochen nach dem Ausfliegen noch im Revier.

Notes: Zusammenfassung 1. Der Wert von Rasterkartierungen zur Erfassung des Vogelbestands auf Probeflächen liegt hauptsächlich in der Möglichkeit, schnell und großflächig arbeiten zu können. Wegen des geringen Zeitaufwands können sie auch öfters wiederholt und zu Trendanalysen herangezogen werden. 2. Da Kartierungen des Brutbestands von Vogelarten nachträglich mit einem Raster versehen werden können, lassen sich deren Ergebnisse ähnlich Rasterkartierungen verarbeiten, wenn Raster und Probefläche nicht zu klein gewählt wurden. 3. Die Rasterfrequenz des Brutbestands kann durch die probeflächenspezifische Antreffwahrscheinlichkeit einer Art bei sogenannten Relativmethoden (Linien-, Punkttaxierung) ersetzt werden. 4. Da neben der Abundanz einer Art auch deren Verteilung in die Rasterfrequenz eingeht, ist die Rasterfrequenz von der Rastergröße nicht unabhängig. Gleichmäßig verteilte Arten erreichen schon bei kleineren Rastern höhere Frequenzen als Arten mit stark geklumpter Verteilung. Rasterfrequenzen bei einer Rastergröße von 1 km2 können am zweckmäßigsten zur Beurteilung des Werts einer Landschaft für eine Vogelart verwendet werden. Bei von dieser Rastergröße abweichenden Kartierungen sollten also immer auch die Rasterfrequenzen für 1 km2-Raster angegeben werden. 5. Mit Rasterkartierungen lassen sich auch ökologisch relevante Siedlungsdichteparameter über Vogelarten mit großen oder fehlenden Territorien gewinnen, die durch Revierkartierung bzw. Nestersuche nur schwer zu erhalten sind (Greifvögel, Rabenvögel, Schwalben etc.). 6. Rasterkartierungen sollten nur mit Rastergrößen über 1 Hektar und einer Rasterzahl über 100 durchgeführt werden, da sonst die Territoriengröße der meisten Kleinvogelarten unterschritten wird (Revierkartierung günstiger!) bzw. Fehler bei der Erfassung sich zu stark auf die Rasterfrequenzen auswirken. Die Mindestfläche für Rasterkartierungen ist also 1 km2. 7. Das Verhältnis von Rasterzahl zu Rastergröße in Hektar sollte mind. 1 betragen. Bei kleineren Quotienten besteht der Nachteil, daß einzelne Arten Rasterfrequenzen von 100 erreichen können. Solche Werte verlieren viel von ihrer ökologischen Aussagekraft und können höchstens noch in übergeordneten Atlasprojekten Verwendung finden. 8. Bereits bei Bearbeitung von nur 5–10% gleichmäßig oder zufällig über eine Probefläche verteilten Einzelrastern können die Rasterfrequenzen der Einzelarten annähernd bestimmt werden. Bei seltenen Arten mit Frequenzen unter 5% ist die Unschärfe allerdings (z. B. nach Wiederholung für Trendanalysen) zu groß. 9. Durch Kombination von Rasterkartierung auf großen Flächen und Revierkartierung, Nestersuche etc. auf Einzelrastern kann die Größenordnung der Vogelbestände einer Landschaft abgeschätzt werden. Das Produkt Rasterfrequenz und mittlerer Bestand der Einzelraster dürfte genauere Werte liefern als die Revierkartierung kleinflächiger Biotope und die Hochrechnung auf das Umland (Randeffekte, Strukturunterschiede äußerlich „gleicher“ Biotope).

Notes: Zusammenfassung Auftriebs- und Profilwiderstandsbeiwerte von Flügelmodellen, die nach Vogelflügelprofilen gefertigt waren, werden als Funktion des Anstellwinkels bei Geschwindigkeit zwischen 4 und 12 m pro Sekunde (Reynoldszahlen zwischen 2,7 · 104 und 8,1 · 104) bestimmt. Die glatten technischen Flügelprofile wurden in exakter geometrischer Ähnlichkeit Flügelprofilen der Haustaube in Gleitflugstellung nachgebildet. Deren Geometrie war mittels einer zerstörungsfreien Abtastmethode bestimmt worden. Die Profilgeometrie ist sehr unterschiedlich, je nachdem ob man basale oder distale Profile des Flügels betrachtet. Der maximale Auftriebskoeffizient wurde zu 1,27, der minimale Widerstandskoeffizient zu 0,05 bestimmt, und zwar bei einem Profil mittlerer Lage. Die physiologischen Gleitfluggeschwindigkeiten entsprechen dem Bereich kritischer Reynoldszahlen der Flügelprofile. Damit übereinstimmend waren die aerodynamischen Polaren und Gleitzahlen stark abhängig von Änderungen der Reynoldszahlen. Der — in dieser Mitteilung meßtechnisch noch nicht behandelte — mögliche Einfluß der Oberflächenrauhigkeit wird diskutiert.

Notes: Zusammenfassung Ein Buntspecht(Dendrocopos major) wurde beim Bearbeiten von Lärchenzapfen(Larix decidua) beobachtet; verschiedene Verhaltensweisen wurden gemessen. Die Bearbeitungsdauer ist bei trockener Witterung länger als bei nasser (Abb. 2). Während des Bearbeitens wird der Zapfen in regelmäßigen Zeitabständen gedreht (Abb. 3 unten); das heißt, daß mit zunehmender Bearbeitungsdauer die Häufigkeit des Drehens linear anwächst (Abb. 4). Für das Heranholen eines neuen Zapfens benötigt der Specht durchschnittlich 43 sec. Die Daten werden mit solchen vom Fichtenkreuzschnabel(Loxia curvirostra) verglichen.

Notes: Zusammenfassung Eine unter extrem starkem Feinddruck stehende Population von Wacholderdrosseln wurde im schweizerischen Mittelland untersucht. Dabei zeigte sich, daß die Vögel ihren Brutplatz verließen, wenn ihr Nest ausgeraubt wurde. Ersatzbruten erfolgten vermutlich noch innerhalb des etwa 360 ha umfassenden Untersuchungsgebietes, doch kann weitere Abwanderung und Ersatz der Brutpaare durch Einwanderung nicht ausgeschlossen werden. Für die Wacholderdrossel dürfte die Möglichkeit, dank der Abwanderung in ein Gebiet mit geringerem Feinddruck zu gelangen, besonders wichtig sein. Der generell in einem Gebiet herrschende Feinddruck läßt sich offenbar nicht im voraus feststellen. Dabei beeinflußt der Feinddruck die Bruterfolgswahrscheinlichkeit mehr als die Güte des Nestverstecks. Die für die Wacholderdrossel obligat scheinende Brutplatzverschiebung nach Nestverlust wird verglichen mit Angaben von territorialen Vogelarten. Bei letzteren kommen solche Verschiebungen zwar regelmäßig vor, sie sind aber art- und wohl auch ortsspezifisch verschieden, und niemals sind solche Abwanderungen der Normalfall. Die Diskussion befaßt sich vor allem mit den evolutions-ökologischen Aspekten, die zum beobachteten Verhalten geführt haben dürften. Dabei ergibt sich als Schlußfolgerung: Eine Brutplatzverschiebung nach Nestverlust ist um so zweckmäßiger und also um so eher zu erwarten, je häufiger ebenso günstige andere Nistgelegenheiten zur Verfügung stehen.

Notes: Zusammenfassung Von 1968–1978 wurden auf sechs Probeflächen im Bodenseegebiet zwei- bis dreimal je Winter Greifvögel gezählt. Seit 1973 wurde außerdem der Wühlmausbestand durch Auszählen der Löcher auf Testflächen von je 100 m2 geschätzt. In den feuchten Niederungswiesen hielten sich überwiegend junge, nicht reviergebundene Mäusebussarde auf. Die Bestände schwankten von Winter zu Winter synchron mit dem 3- bis 4-Jahre-Rhythmus der Feldmauspopulationen im Verhältnis 1 : 7 bis 1 : 22 (in einem Brutgebiet mit adulten Reviervögeln nur 1 : 2). Der Turmfalke erreichte in 50 % der Fälle sein Maximum bereits ein Jahr vor dem Feldmaus- bzw. Mäusebussardgipfel. Er konnte seine Mäusefang-Erfolgsquote bei hohen Feldmausdichten wegen intra- und interspezifischer Konkurrenz nicht mehr steigern. Die Turmfalkenzahlen schwankten von Winter zu Winter stärker als die Bussardzahlen zwischen 1 : 10 und 1 : 28. Im Dezember 1976 zogen etwa 3000 Mäusebussarde als Winterflüchter am Bodensee entlang. Nach anfangs hohen Verlusten wurden nach einer Presseaktion über 500 kg Fleisch an 80 Plätzen ausgelegt, was fast ausschließlich den Bussarden zugute kam.

Notes: Summary Our observations on Barnacle geese in Spitsbergen permit the following conclusions: The non-breeding geese molted at about the same time as hatching occurred in the nesting colonies, about 16 days before the breeders' molt began. The non-breeders came together into large groups along the coast. Pair bond displays (cackling and triumph ceremonies) were infrequent in non-breeder molting flocks. Families formed small flocks after hatching and migrating to the breeding areas. The flocks grew in number as the summer progressed and the parental molt occurred. The non-breeder flocks and the family flocks were both extremely cohesive. The families in a particular flock were normally synchronized in their activities. A flock of three families was studied in detail. An analysis of activity patterns showed that no diurnal fluctuations in resting, grazing and travelling were present. One gander initiated place changes more successfully than the other two. No geese or goslings were preyed upon during our observations. Gulls and skuas were threatened by individual geese. Arctic foxes caused flightless geese to take refuge in water. Full-winged adults mobbed the foxes.

Notes: Zusammenfassung Die Rückkehr von Zugvögeln ins Heimatgebiet ist ein von vielen Arten aufgrund zahlreicher Ringwiederfunde gut bekanntes Phänomen, das als „Geburtsortstreue“ bezeichnet wird. Am Beispiel des in Zentralafrika überwinternden TrauerschnäppersFicedula hypoleuca untersuchten die Verfasser, ob die Kenntnis des Geburtsortes angeboren ist oder durch Prägung bzw. Lernen erworben werden muß. Zur Prüfung dieses Fragenkomplexes wurden 1975 und 1976 Eier, Nestlinge und bis 3 Wochen über den potentiellen Ausfliegetermin im Geburtsgebiet gekäfigte Jungvögel 250 km weit in ein anderes vom Trauerschnäpper bewohntes Gebiet verfrachtet (Versuchsgebiete im westlichen bzw. östlichen Niedersachsen). Da die Brut-Ansiedlungen, welche 1976, 1977 und 1978 von diesen Versuchsvögeln nachgewiesen werden konnten, ausnahmslos im jeweiligen Ausfliege- bzw. Freilassungsgebiet erfolgten, kann die Kenntnis der Heimat nicht genetisch festgelegt sein. Vielmehr erfolgt die Fixierung des Geburtsortes während einer Jugendphase innerhalb kurzer Zeit und in sehr stabiler Weise. Daher halten es die Verfasser für berechtigt, die Erscheinung der „Geburtsortstreue“ auf einen prägungsartigen Vorgang zurückzuführen. In der zusammenfassenden Diskussion wird versucht, einen schematisch-hypothetischen Überblick über das Zug- und Heimkehrverhalten eines Trauerschnäppers innerhalb seines crsten Lebensjahres zu geben.

Notes: Summary Observations on the nest construction of the White-browed Purpletuft,Iodopleura isabellae, in Pará, Brazil; note on the nest site of the White-winged Cotinga,Xipholena atropurpurea, in Espirito Santo.

Notes: Zusammenfassung 1. In zwei südwestdeutschen Populationen wurden an individuell markierten Jungvögeln von Kohlmeise und Blaumeise Beziehungen zwischen brutinterner Altersstruktur und Nestlingsentwicklung untersucht. 2. Mit fortschreitender Brutsaison tritt zunehmend asynchrones Schlüpfen innerhalb einer Brut auf. Dies resultiert aus vorgezogenem Brutbeginn (vor Erreichen des Vollgeleges) bei späten Bruten. 3. Spätgeschlüpfte Jungvögel sind prädestinierte Nesthäkchen. In der Nestlingsmortalität existiert eine Sterbefolge nach dem Gewicht „von klein nach groß“. Diese differentielle Mortalität ist in ungünstigen Ernährungssituationen krasser ausgeprägt als in günstigen. 4. In gutgenährten Bruten gleichen Nesthäkchen ihr Gewicht besser an die Geschwister an als in schlechtgenährten, dort verringert sich der Abstand nur wenig, vergrößert sich oder/und die Nesthäkchen sterben. 5. Spätgeschlüpfte Jungvögel erreichen unter nahrungsökologisch günstigen Bedingungen ihr individuelles Gewichtsmaximum als Folge eines differentiellen Wachstums 1–2 Tage früher als die zuerst geschlüpften, das bedeutet, gleichzeitig mit diesen. Die Maxima liegen absolut dabei im wesentlichen auf gleicher Höhe. 6. Aus den Ergebnissen ist ein Selektionsdruck auf die Produktion von Nesthäkchen in einer Periode unsicheren Nahrungsangebots abzuleiten. Dadurch sind die Meisen in der Lage, auch noch nach einer groben adaptiven Modifikation der Gelegegröße ihre Jungenzahl mit Hilfe mehrerer Mechanismen an die aktuellen Verhältnisse optimal anzupassen.

Notes: Zusammenfassung Bei drei Durchquerungen der Tanezrouft-Wüste im März und April 1973 und 1977 wurden durchziehende paläarktische Vögel beobachtet, gezählt und Verluste erfaßt. FürStreptopelia turtur, Merops apiaster, Calandrella brachydactyla, Oenanthe oenanthe, Cercotrichas galactotes wird die Möglichkeit regelmäßiger Zwischenlandungen diskutiert. 20 erschöpft gegriffene oder tot gefundene Durchzügler sowie 18 Kontrolltiere wurden u. a. auf Fettgehalt, Wassergehalt und Rückstände chlorierter Kohlenwasserstoffe untersucht. Kleinvögel waren in der Tanezrouft am aufgezehrten Fettdepot gescheitert, größere Vögel am Wasserverlust bei hohen Fettreserven. Biozidrückstände waren ohne nachweisbaren Einfluß auf die Mortalität. Die Wasserindices aller untersuchten Durchzügler aus der Wüste waren erniedrigt. Von 1062 beobachteten Zugvögeln (das ist nur ein Bruchteil der dort in der Beobachtungszeit zu erwartenden Durchzügler) hatten 42 (4 %) versagt. Die tatsächlichen Mortalitätsraten bei der Überquerung der Westsahara dürften gewöhnlich weit unter diesen 4 % liegen, besonders niedrig bei manchen Arten, wieMerops apiaster, Calandrella brachydactyla, Cercotrichas galactotes, Grasmücken- und Laubsängerarten.

Notes: Zusammenfassung Voous (1947) meinte, der BlutspechtPicoides syriacus und eine gut gekennzeichnete nordafrikanische Unterart des BuntspechtsP. m. numidus seien die Nachfahren von Rückzugs-populationen des Buntspechtes während der Mindel-Eiszeit. Alle morphologischen Merkmale, die sonst zur Unterscheidung von Blut- und Buntspecht herangezogen werden, zeigen, daßP. m. numidus ein Buntspecht ist. Dasselbe trifft für die Lautäußerungen zu. Im Gegensatz zu europäischen Rassen weistP. m. numidus einen ökologischen Sexualdimorphismus auf. ♀ gehen öfter in der Kronenschicht der Nahrungssuche nach. Sie halten sich dabei auch öfter an dünnen Zweigen auf als ♂. Kein deutlicher Unterschied besteht bezüglich der Tätigkeiten des Nahrungserwerbs. Ökologisch ist die nordafrikanische Rasse mitteleuropäischen Buntspechten ähnlicher als Blutspechten. In der Erörterung des ökologischen Sexualdimorphismus wird auf das inselartige Vorkommen, die Eintönigkeit des Lebensraumes, das offensichtliche Fehlen einer Nahrungsspezialisierung im Winter, Merkmalsfreisetzung und die Rolle der Geschlechter im Fortpflanzungsgeschehen eingegangen. Die Auffassung wird vertreten, daßP. m. numidus keine unmittelbaren historischen Beziehungen zuP. syriacus hat.

Notes: Zusammenfassung Bei der südamerikanischen KolibriartOcreatus u. underwoodii (2.7 g±0.09 SD, n=3) wurde der Ruhe- und Flugstoffwechsel in Abhängigkeit von der Umgebungstemperatur (3° bis 34° C) bei Licht und ohne Nahrungsentzug untersucht, sowie der stündliche Energieverbrauch ermittelt. 1. Der Ruhestoffwechsel stieg linear bei fallender Umgebungstemperatur (r=0.95±0.04 SD, n=3). 2. Der Flugstoffwechsel zeigte eine dem Ruhestoffwechsel entsprechende Abhängigkeit von der Umgebungstemperatur. 3. FürOcreatus u. underwoodii wurden für Sitzen bzw. Fliegen mit 199.2 mW/g bzw. 325.3 mW/g die höchsten für homöotherme Tiere bisher ermittelten Wärmeproduktionsraten gemessen. 4. Im getesteten Umgebungstemperaturbereich schwankte die Körpertemperatur bei den drei Individuen zwischen 38.8° und 39.9° C. 5. Der für 25° C Umgebungstemperatur berechnete Energieverbrauch betrug ca. 1030 J/h. 6. Zur Deckung des Energiebedarfs mußOcreatus u. underwoodii stündlich z. B. 205Salvia-Blüten besuchen.

Notes: Summary On 23.7. 1977a colour-ringed first-year Meadow Pipit was observed feeding nestlings of a third brood of more than two-year-old parent Meadow Pipits for at least three times. The first-year Meadow Pipit had hatched about 1.5. 1977 in a nest about 3100m off the place where it helped feeding. On 27. and 28.6. 1978 another first-year Meadow Pipit was observed feeding nestlings of a brood some four times. This first-year Meadow Pipit had hatched about 8.5. 1978 nearly 3400m off the place where it helped feeding. The only adult parent that was seen feeding the brood was a colour-ringed adult male. On 14.6. 1978 a copulation was observed between the adult male and the first-year Meadow Pipit — obviously a female. Evidently there were no close relationships between the first-year Meadow Pipits and the parents of the broods they helped.

Notes: Zusammenfassung Im März 1978 und Juni 1978 konnten am Dj. Babor im E-Atlas (Nordalgerien) 54 Reviere des KabylenkleibersSitta ledanti nachgewiesen werden. Die Gesamtpopulation wurde für 1978 auf gut 70 Reviere geschätzt, ihr gesamter Lebensraum auf höchstens 1100 ha. DaVielliard, Ledant und Mitarbeiter in den beiden Vorjahren nur 12 bzw. 20 Paare festgestellt haben, befindet sich die Population momentan anscheinend in einer Aufwärtsbewegung ihres Bestandes. Vorkommen außerhalb des Babor-Massives sind bis jetzt noch nicht bekannt geworden; sie sind aus ökologischer Sicht auch nicht zu erwarten. Die höchste Siedlungsdichte von 4 Paaren/10 ha wird im artenreichen Mischwald der Gipfelregion des Massives mit den bestandsbildenden BaumartenCedrus atlantica, Abies numidica, Quercus faginea undAcer obtusatum erreicht. Die tieferen Bergstufen sind wesentlich dünner besiedelt; das am tiefsten gelegene Revier wurde bei 1500 m ermittelt. 1978 gelangen 9 Nestfunde. Die selbstgeschlagenen Höhlen sind 3–13 m hoch in morschem Holz angelegt (5mal in Tanne, 3mal in Zeder, 1mal in Eiche) und besitzen ein auffallend großes Flugloch, von denen entgegen dem Verhalten der Verwandtschaftsgruppe dieser Kleibersippe ein Loch sehr stark verklebt war (Abb. 3). Der Kabylenkleiber weist weiterhin entgegen anderen Angaben einen deutlichen Geschlechtsdimorphismus auf (Abb. 4). Das im Optimalbiotop nur knapp 3 ha große Revier wird von beiden Partnern an der sehr genau festgelegten Grenze verteidigt; das Drohverhalten wird beschrieben. Die Kabylenkleiber ernähren sich im Winter vor allem von den in dichten Flechten- und Moospolstern versteckten Sämereien der Koniferen und der Eiche, vermutlich auch des Ahorns. Zur Brutzeit bevorzugen sie zur Nahrungssuche die Eiche wegen ihres Insektenreichtums, jedoch werden auch die Koniferensamen an die Jungen verfüttert. Es gibt nahrungsökologisch keinen Hinweis, daß die Numidische Tanne (ebenfalls Endemit am Dj. Babor) für den Kabylenkleiber von besonderer Bedeutung ist. Vielmehr dürfte es die Vielfalt des Mischwaldes sein, der dem Kabylenkleiber das Überleben auf einem einzigen Bergmassiv ermöglichte. Da hier 4 samenliefernde, bestandbildende Baumarten zusammen vorkommen, stehen dem Kabylenkleiber anscheinend jeden Winter genügend Sämereien zur Vorratshortung zur Verfügung. Im wesentlichen dürften der Ahorn und die Tanne die starken Schwankungen in der Fruktifikation von Zeder und Eiche ausgleichen. Der algerische Staat sollte in seinen Schutzbestrebungen um dieses einzigartige Gebiet möglichst viel Unterstützung erhalten.

Notes: Abstract Tisbe clodiensis andT. holothuriae females and males were maintained at different densities, from sexual maturity to the extrusion of the first egg sac, in order to study the effect of crowding on the number of nauplii produced by the first egg sac. They were tested in pure cultures at densities of 1, 2, 4, 6 and 8 couples per 20 ml of sea water, and in mixed cultures (half of the individuals belonging to each of the two species) with 2, 4, 6 and 8 couples per 20 ml, without food limitation. At the highest crowding level, and forT. holothuriae only, the effect of daily renewal of the culture water was examined. The mean number of nauplii per female decreases with increased density. A significant linear regression of number of nauplii on number of couples was found. The regression slopes appear to be the same for both species, regardless of whether they are cultured singly or together. The daily renewal of water diminishes the effect of crowding. The possibility that a complex chemical compound, produced by the animals, which enables the latter to perceive and to react to crowding, is discussed.

Notes: Abstract The larval development ofPhoronis psammophila Cori is divided into 6 phases (on the basis of increasing pairs of larval tentacles); furthermore an initial and a ripe phase are distinguished. Specific aspects of the development are described: Formation and structure of larval tentacles; anlage of adult tentacles as a thickening in the larval tentacle base; late development of the metasome (larva with 4–6 tentacles); formation of the metasome pouch in the larva with 8 tentacles; enlargement of the apical plate; differentiation of the gut; differentiation of larval nephridia; formation of pigment particles in the larva with 6 tentacles (storage function of pigments and its significance for larval identification); different types of discoflagella in various regions of the body. The larval development shows the following tendencies: Improvement of locomotion; intensification of food filtration; anlage of adult organs in the larva leading to a shortening of metamorphosis duration. The larva ofP. psammophila is compared with those ofP. pallida, P. hippocrepia, andP. vancouverensis. Earlier larval determinations ofP. psammophila (e.g.Actinotrocha sabatieri, A. hatschekii) are shown to have been mistakes. Termination of the postembryonic phase (metamorphosis) can be induced experimentally by bacteria and also by cations. Pure or mixed bacteria cultures must be present at the beginning exponential growth phase. The bacteria density required is 20–94×106 bact.ml−1 for pure cultures and on the average 28×106 bact. ml−1 for mixed cultures. Metamorphosis initiation by cations can be induced with CsCl (0.06 M) and RbCl (0.035 M). Metamorphosis ofP. psammophila occurs in 6 phases: larva, ready for metamorphosis; larva, activated by bacteria or ions; evagination of the metasome diverticle, dislocation of gut; losing and swallowing of episphaere and larval tentacles; formation of the youngP. psammophila. All developmental phases are described and compared with those ofP. muelleri; imperfect metamorphosis is characterized and the youngP. psammophila compared with older stages and the adult Phoronis.

Notes: Abstract The effects of light and darkness on chromatophore arrangements inFucus vesiculosus thalli exposed to air with one side (half dry) or with both sides (dry) were investigated. Low-intensity arrangement, high-intensity arrangement and dark arrangement were induced in submerged thalli. Then the thalli were exposed to air while light conditions were either kept constant or were changed. Independently of the light conditions, in all thalli exposed to air the chromatophores arranged more or less in the inner area of the cells, in epidermal cells as well as in cortical cells. Thus the chromatophore arrangements observed in submerged thalli differ in some respect from those exposed to low-tide conditions. Based on these observations the physiological and ecological role of chromatophore displacements in seaweeds is discussed.

Notes: Abstract Following previous investigations on a fringing reef in the Red Sea near Aqaba (Mergner & Schuhmacher, 1974; Mergner & Svoboda, 1977) this paper presents a quantitative analysis of the faunal and floral stock in one of the selected test areas (5×5 m) located in the reef lagoon studied. During the observation period 237 macrobenthic species of 192 genera were found. Species numbers were 22 (algae), 18 (cnidarians), 22 (crustaceans), 113 (molluscs), 27 (echinoderms), 14 (fishes) and 21 (smaller animal taxa including foraminiferans, sponges, turbellarians, polychetes and ascidians). These numbers, though derived from a small and relatively monotonous reef area, exceed by far all data known from comparable reef zones. The ecological conditions as well as habitat preferences, times of occurrence, seasonal abundances, species diversities and dominances of the inhabitants observed in the test area are discussed. Comparisons of the population data of October, 1975 and March, 1976 indicate the influence of the succession, abundance and disappearance of the phytal on the environmental conditions of the mobile fauna, for example molluscs, echinoderms and fishes. The increase of some of its species, especially of juvenile individuals, is remarkable. Within the same period juvenile colonies of some xeniids and the stony coralStylophora pistillata undergo similar seasonal fluctuations; colonies eliminated by grazers or other, unknown circumstances, are replaced by new settlers. Altogether, the faunal and algal stock of this lagoon area can be interpreted as a climax community; its impressive density is apparently the result of a high number of various microhabitats. Each of these ecological niches provides manyfold living spaces for specific communities with different adaptive strategies. The highest number of species plus the highest diversity indices rank mostly among the mobile groups.

Notes: Abstract Jassa falcata (Leach), an unselective suspension feeder, was cultivated in standing, unaerated finger bowls, feeding on a mixture ofBrachionus plicatilis, Scrippsiella faeroense, Ulva spec., and natural detritus. This amphipod can also be maintained with diets composed of dead or live material of both plant and animal origin, but an addition of living zooplankton is necessary for longterm cultivation. Starvation resistance is higher in females than in males, and it is increased by lower temperatures. The life span ofJ. falcata increases with decreasing temperature, and it is generally higher in females (maximum: 252 days at 10°C) than in males. In laboratory culture, a bimodal mortality pattern is typical with high juvenile death rates, low mortality during the reproductive phase, and again increasingly high death rates toward the end of the life cycle. Growth rate depends on temperature, sex, and individual age. The temperature dependence of growth is particularly high in males, and it is higher in adults than in juveniles. The total number of moults is lower in males (5 to 6) than in females (7 to 9). Sexual maturity is attained at moult IV to V. The average incubation time of eggs is about 9 to 16 days (highest value at 10°C). Three to 4 broods were observed, with largest numbers of offspring at 10°C.

Notes: Zusammenfassung In einer Baumpieperpopulation N Antwerpen, die von 1961–1970 kontrolliert wurde, setzte der Legebeginn frühestens Ende April ein. Im August brüteten nur noch wenige ♀. Das 1. Ei der Population wurde gelegt, wenn die Summe der April-Temperaturen 227° C erreichte oder überschritt bzw. die mittlere Tagestemperatur 2 bis 5 Tage über 10° C blieb. Im Mittel wurde das 1. Ei von Erstbruten am 12. Mai, das 1. Ei von Zweitbruten am 14. Juni gelegt. Verschachtelung von Bruten wurde nicht festgestellt. Das Nest einer Zweitbrut kann jedoch schon im Bau sein, bevor die Jungen der Erstbrut das Nest verlassen haben. Für die Ablage des 1. Eies einzelner ♀ scheinen die Temperaturen vom 4. und 6. Tag vorher maßgebend zu sein. Benachbarte ♀ zeigen oft auffallend ähnlichen Legebeginn. Zweimal konnte eine Drittbrut nachgewiesen werden. Erstbruten hatten mehr 5er- und 6er-Gelege, Zweitbruten vor allem 4er-Gelege. Zweitoder Nachbruten individueller ♀ enthielten nicht immer weniger Eier als die betreffenden Erstbruten. Die mittlere Gelegegröße einzelner Jahre variierte kaum. Innerhalb einer Brutzeit bleibt sie bis Ende Mai konstant, nimmt dann aber stark ab. Im Mittel ergaben 53% der abgelegten Eier flügge Junge; die mittlere Anzahl flügger Junge pro Vollgelege war 2,4, pro Paar und Jahr 3,6. In Erstbruten waren 4er-Gelege signifikant erfolgreicher als andere (obwohl 5er-Gelege überwogen); in Zweitbruten ergaben 6er-Gelege mehr Junge als andere (obwohl 4er-Gelege überwogen). Von 861 abgelegten Eiern ergaben 7% keine Nestlinge; von 627 geschlüpften Jungen flogen 4,5% nicht aus. Bei unterdurchschnittlichem Bruterfolg waren ♂ (!) im kommenden Jahr nicht auf der Probefläche nachzuweisen. Zwischen Brutorttreue der ♀ und Totalverlusten konnte keine Korrelation gefunden werden, wohl aber flogen bei reviertreuen ♀ bedeutend mehr Nestlinge aus. Gleiches konnte bei reviertreuen ♂ der Zweit-, Dritt- und Ersatzbruten festgestellt werden.

Notes: Zusammenfassung 1971–1976 wurden 147 Rohrweihenbruten in Schleswig-Holstein regelmäßig kontrolliert. 86% der Nester waren in Schilfbeständen zu finden. Der Rest verteilte sich auf Rohrkolbenrasen, Steifseggenbestände und Getreideanbauflächen. Im vierjährigen Mittel lag die Erstankunft der Rohrweihen im Brutrevier um den 30.3. Rund 75% der zwischen 1971 und 1975 ermittelten Gelege wurden zwischen dem 16.4. und dem 5.5. (im Mittel am 1.5.) begonnen. Die mittlere Eizahl aus 123 Vollgelegen beträgt 4,4 Eier. Pro begonnener Brut flogen 1,9 und pro erfolgreicher Brut 2,75 Junge aus. Verlustursachen, getrennt nach Einzelund Totalverlusten, werden beschrieben. Hauptgründe der Verluste waren in vielen Fällen direkte oder indirekte menschliche Einwirkungen. Die Bedeutung der verschiedenen Biotope und wichtige Ergebnisse des Fortpflanzungsgeschehens werden diskutiert. Abschließend wird versucht, die Dynamik der schleswig-holsteinischen Rohrweihenpopulation für den Untersuchungszeitraum darzustellen und den Trend für die nächsten Jahre aufzuzeigen. Seit Einstellung der Bejagung im Jahre 1970 begann eine Wiederbesiedlung freier Biotope, die nun in einigen traditionellen Gebieten ihren Höhepunkt erreicht zu haben scheint. Neben einer unbegrenzten Unterschutzstellung — eine endgültige Jagdruhe eingeschlossen — bleibt die Sicherung von Brutbiotopen und wo nötig, deren Neuschaffung, die derzeitig wirksamste und erfolgversprechendste Art des Rohrweihenschutzes.

Notes: Abstract The influence of domestic sewage on intertidal sand and mud flat benthic communities has been studied at three minor outfalls around the North Sea island of Sylt (F. R. Germany) and at the main outfall of Vancouver, B. C. (Canada). During high tide, domestic waste water was found at the water surface due to its lower specific gravity. Consequently, O2 depletion and salinity decrease occured mainly in surface waters. Oxygen deficiency prevailed in the sediment-water layer, when settled sewage particles were re-suspended by strong tidal currents. This resulted in anaerobic conditions at the sediment surface for up to 40% of the day. Substantial pH decrease and increase in seston load of the water were observed only along the sewage channels and around the outlets when large quantities of sewage were discharged. The amount of particulate organic material increased up to 10% and more in muddy sediments due to sedimentation of sewage sludge. Considerable eutrophication of the mud flats resulted from nutrient load of the sewage and from decomposition of faecal material deposited on the sediments. The vertical distribution of microalgae in the sediment was not influenced by sewage. Primary productivity of microalgae on the sediment surface was positively correlated with the degree of pollution. In heavily and mediumly polluted zones, heterotrophic bacterial production exceeded primary production rates at the sediment surface. Compared with unpolluted intertidal flats the number of macrobenthic species was not reduced in polluted mud flats. In regard to overall species abundance, the macrofauna associations of the disposal area showed three distinct zones: (1) Heavy pollution around the outfall resulted in a degradation zone either without benthic invertebrates or with a very low density of individuals; (2) medium polluted areas were characterized by a zone of maximum density; (3) with decreasing or diminishing pollution the number of individuals returned to normal values (“background values”). The distribution of species within these zones indicated a significant difference between the response of the “channel fauna” and the “flat fauna” to pollution: while the number of species increased continously inside the channels with decreasing pollution, the species variety of the tidal flats was positively correlated with the number of individuals. The diversity of the benthos inside the channels was negatively correlated with the degree of pollution, whereas the diversity indices for the fauna on the tidal flats increased quickly from the centre of pollution, remained at a high level in the medium polluted zone, and decreased again to the area of diminishing pollution. The number of dominating species in the sewage channel increased from the outlet towards the low-tide level, with ratios of 0.9 to 0.33; on the flats the number remained constant throughout the three zones, with maximum ratios of 0.5, demonstrating that no qualitative changes for the macrobenthos of intertidal flats result from domestic sewage disposals. In polluted intertidal flats the macrobenthos is dominated by muddy-sand species whose adaptability to varying sedimentary factors, such as grain size distribution and content of organic material (coefficients of variability: 50.7 and 45.7%, respectively), is relatively high compared with mud and sand species. A special indicator community for polluted intertidal areas does not exist. Intensified waste-water treatment prior to discharge reduced the size of the degradation zone around the outfalls while it simultaneously caused a lower density of the macrobenthos in the medium polluted zone.

Notes: Abstract Eggs of Pacific herring (Clupea pallasi) were incubated at 5°C in salinities of 5, 20, and 35‰, and in cadmium concentrations of 0.05, 0.1, 1, 5, and 10 ppm (20‰ S). Bursting pressures of eggs in the eight groups were measured throughout incubation. In general, bursting pressures rose to a primary maximum after fertilization, declined, rose to a secondary maximum, then declined again toward hatching. Rate of attainment of the primary maximum was related to salinity of the incubation medium. Bursting pressures at the primary and secondary maxima reached final values of about 1300 and 700 g, respectively, in incubation salinities at and above 20‰. Corresponding egg volumes were greatest in low salinities (5‰) and near minimum values in salinities of 20‰ or greater (35‰). Cadmium in the incubation medium delayed attainment of primary maximum bursting pressures and primary and secondary maxima were reduced to 200–350 g at Cd concentrations near 1 ppm. Egg volumes also decreased with increased Cd concentration. It appears that Ca++/Cd++ ratios, depending on salinity and Cd levels in the incubation medium, influence the properties of both the jelly coat and the capsule of herring eggs. Changes in the properties of these layers could make the eggs more susceptible to mechanical damage, particularly at combinations of higher (⋝1 ppm) Cd concentration and lower (⋜20 ‰) salinities.

Notes: Abstract Developmental patterns in four species of Ceramiaceae were determined using excised thallus apices grown under a range of light periods. Models of thallus development and organization based on these patterns are presented. Increased rates of apical cell division, greater growth of apical fragments and increased average cell size were found with increasing number of hours light per day between 8–16 and 16–8 h. No aspect of growth investigated was associated with photoperiodic phenomena, and growth occuring during the light break (8-7.5-1-7.5 h) was intermediate between that in 8–16 and 12–12 h. Three patterns of cell elongation were found in the four species in which (1) cell age, (2) cell age and position and (3) cell age, cell position and light period determined cell length at different axial cell positions. Elongation was followed within cells, along axes ofAntithamnion spirographidis for plants grown under different day lengths. Three regions of development were found along main axes: (1) an apical region in which basipetal expansion was greater than acropetal expansion. (2) a zone of stability with equal elongation in apical and basal growth region of cells, and (3) a basal region with greater acropetal expansion. With increasing daylength, the zone of stability was extended to greater ranges of cell length.

Notes: Abstract Eggs of Baltic herring were incubated (10°C; 16‰S) in sea water containing mixtures of Cd, Cu and Pb at concentrations of 0.56–5.0, 0.0167–0.15, 0.56–5.0 mg metal/l; embryonic survival until hatching, viable hatch and uptake of metals by embryos and early larvae were measured. Negative effects of metals on embryonic survival and viable hatch were additive in the case of Cu and Cd. Pb did not exer detrimental effects. Uptake of metals with exposure time was non-linear in eggs and linear in larvae. Total uptake of Cu and Cd by eggs was subjected to antagonistic or synergistic action of the other two metals present. Accumulation of Pb by eggs was enhanced when Cu was also present.

Notes: Abstract Balgetia pacifica nov. spec. from coarse sand beaches along the west coast of San Juan Island (Washington) is described and its taxonomy discussed. The species is characterized by its large bursal apparatus with a strengthened copulatory bursa.B. pacifica is the first free-living species of the Turbellaria Dalyellioida recorded from the Pacific Ocean.

Notes: Abstract The ultrastructure of the flagellar apparatus in the quadriflagellate zoospores ofUlva lactuca was examined. The two L-shaped pairs of basal bodies are arranged in mirror image relation. Two apical capping plates connect adjacent basal bodies of different pairs with each other. The flagellar root system is cruciate and exhibits a microtubular part (4-2-4-2 system) and a complex and elaborate fibrillar part. The latter consists of two striated fibres (striation pattern 32 nm) closely associated with the two-stranded roots and four differently patterned fibres (striation pattern 150–160 nm) which are more internally located and run parallel to all four microtubular roots. The presence of four microtubular roots and six striated fibres is at present not known for any other green alga and taxonomic implications are discussed.