Allee Effect and Control of Lake System Invasion

We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal invasion stopping. We consider possible values of model parameters for zebra mussels. The general N-lake control problem has to be solved numerically, and we show a number of typical features of solutions: distribution of control efforts in space and optimal stopping configurations related with the clusters in lake connection structure.     

Studies in the mathematical theory of excitation

The general linear two-factor nerve-excitation theory of the type of Rashevsky and Hill is discussed and normal forms are derived. It is shown that in some cases these equations are not reducible to the Rashevsky form. Most notable is the case in which the solutions are damped periodic functions. It is shown that in this case one or more—in some cases infinitely many—discharges are predictable, following the application of a constant stimulusS. The number of discharges increases withS, but the frequency is a constant, characteristic of the fiber and independent ofS.     

A physico-chemical theory of sweet and bitter taste excitation based on the properties of the plasma membrane

Summary This paper is concerned with physical and chemical changes occurring in the taste buds due to the presence of sapid substances, and not with the nervous mechanism transmitting impulses to the brain. From this standpoint taste phenomena are closely allied with general cell physiology or pharmacology. It has been shown that the great majority of anesthetic or toxic substances have a bitter taste and it is considered that the same structural changes occur in the cell membranes in taste buds as in other cells of the body when such substances are present. From consideration of a large amount of experimental data on the taste of organic compounds it is shown that thesweet and bitter substances are chemically very closely related and there is no line of demarcation between them. In many homologous series there is a continuous (rather than discontinuous) transition from sweet to bitter. Sweet substances having a bitter after-taste are also common.It has been pointed out that it is a general property of anesthetics to be stimulants (i. e. to accelerate cell activities)when in low concentrations. The continuous transition from stimulant to narcotic action is correlated with the sweet-bitter transition. FollowingClowes, Lillie and others the cell membrane is looked upon as a balanced emulsion partly of the water in oil type and partly of the reverse type.The phenomena cited above have been explained in terms of adsorption and surface tension action of substances on this emulsion system and the consequent changes in cell membrane permeability due to changes in the phase ratio of the emulsion types.     

A relational theory of biological systems II

The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism. A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed. In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence is obtained. Some further implications of the above assumptions are then discussed.     

Properties of solution of the diffusion-reaction equation

An arbitrary set of chemical reactions is considered to occur among chemical speciesX _i . In a closed uniform reaction system certain linear combinations of the concentrations of theX _i are constants. The general construction of all such linear combinations with non-negative coefficients is given in terms of the molecular formulae for theX _i . It is shown that to each such linear combination there corresponds another which is a harmonic function when the reactions take place in an open spatially distributed stationary reaction system of arbitrary shape. Under the usual boundary conditions these harmonic functions are constants. With some restrictions upon the diffusion and permeability coefficients these constants are evaluated. This evaluation is the basis for relations between the total concentration of a given chemical group (e.g., the sum of the concentrations of a free molecule, or ion, and its various bound forms) in the reaction system, and in the surrounding medium. The bearing of these relations on apparent active transport is noted and illustrated.     

A mathematical model for the population dynamics of army ants

A stochastic cellular automata model for the population dynamics of the army antEciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusion-like, although it is random. This has implications for the kind of model that is chosen.     

An ecological classification of European Drosophila species

Summary The associations shown between species of Drosophila collected in three European countries are analysed using a clustering method. The resulting dendrograms are combined to give a plan of associations shown by all three surveys. These general groupings are interpreted in the light of what is known about Drosophila breeding sites.One ecological group, the fungal breeding species are examined in detail and their pattern of geographical associations investigated. The three most abundant species in collections, D. transversa, D. phalerata and D. cameraria appear to replace one another in a north-south direction in western Europe. It is suggested that ecologically marginal areas may be defined using the frequency of a species within its ecological group.     

Does K-selection imply prudent predation?

Competition models are derived from predator-prey models. The population parameters r and K are thus expressed as composites of quantities measuring properties of the individual. This enables us to show that the idea that K-selection maximizes K is not valid as a general principle and is equivalent to asserting that selection on predators leads to prudent predation. Models of density-dependent selection, which predict maximization of K, implicitly assume no evolution of hunting efficiency. A valid general principle instead states that K-selection minimizes the equilibrium density of prey or food resource. It is then shown that the phenotypic profiles of r- and K-selected organisms are often identical. They diverge only if there are genetic constraints of a particular kind between the various evolving traits. Furthermore, divergence is in opposite direction to that which is commonly expected.     

Recent Progress in First Principles O(N) Methods

Abstract

We describe recent progress in developing practical first principles methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then outline some of the main technical problems which must be solved in order to develop a practical O(N) method based on density functional theory and the pseudopotential method. Recent progress in solving these problems is presented, and we show that the spatial cut-off distances needed to achieve good accuracy are small enough to make the calculations feasible. Parallel implementation of the O(N) methods in the CONQUEST code is outlined, and it is shown that the code exhibits excellent linear-scaling behaviour on test systems of several thousand atoms. It is pointed out that the most important remaining problem concerns the optimal strategy for seeking the ground state. It is argued that there are three different mechanisms of ill-conditioning which cause present search methods to be inefficient, and some partial solutions are suggested.     

Turing's theory in morphogenesis

Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions. This, together with the presence of concentration-independent sink terms is responsible for the solutions becoming negative ast→∞. It is pointed out that this deficiency is an accident related to the choice of the model, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.     

Proposal for a standard system for drawing structural diagrams of N‐ and O‐linked carbohydrates and related compounds

Symbolic diagrams are commonly used to depict N‐ and O‐linked glycans but there is no general consensus as to how individual constituent monosaccharides or linkages are shown. This article proposes a system that avoids ambiguities inherent in most other systems and is appropriate for both hand drawing and computer applications. Constituent monosaccharides are depicted by shapes modified to show OAc, deoxy, etc. Linkage is indicated by the bond angle and anomericity by solid (β) or dashed (α) lines.     

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.     

A note on sporadic nonperiodic oscillations in the activity of the endocrine system and on the endocrine—Nervous system feedback

By generalizing a previous paper on periodicities in the endocrine system (Bull. Math. Biophysics,30, 735–749, 1968), it is shown that nonperiodic, sporadic oscillations in the system are also possible. A procedure of describing the feedback mechanism between the endocrine system and the central nervous system is suggested. It is shown that the combined system: endocrine—CNS, also may show sporadic fluctuations.     

Natural organic matter (NOM) has the potential to modify the multixenobiotic resistance (MXR) activity in freshwater amphipods Eulimnogammarus cyaneus and E. verrucosus

Based on the chemical features of natural organic matter (NOM) with its variety of functional groups, we hypothesized that NOM will modify the multixenobiotic-resistance (MXR) of an organism as xenobiotic chemicals do. The MXR system is a general first rather non-specific line of defense against environmental contaminants. The aim of this study was to compare the impacts on MXR activity in amphipod species (Eulimnogammarus cyaneus and E. verrucosus, from Lake Baikal) stressed by cadmium chloride or dissolved NOM for 24 h. NOM exposure concentrations were environmentally realistic. MXR activity was assessed based on rhodamine B efflux; its specificity was proven by a verapamil inhibition assay. It was shown that both NOM and CdCl₂ lead to substantial reduction of the rhodamine B efflux. This suggests that NOM may be regarded as a chemosensor which is able to reduce the efficiency of the MXR system. Possible mechanisms of direct NOM impact on MXR processes are discussed, such as peroxidation of the membranes (including P-glycoproteins) or internal blockage of the MXR pump by bioconcentrated NOM. In general, our results show that well-developed depuration pathways of freshwater organisms in contaminated environments may be impaired by strong chemical stressors and, more important, by natural biogeochemical matrices such as humic substances — humic substances are present in all freshwater systems.     

A storage role for albumins in pea cotyledons

Abstract It is widely held that the albumins of pea seeds are mainly enzyme proteins. In the present study of Pisum sativum cv. Greenfeast, certain major polypeptides confined to the albumin fraction from the cotyledons were shown to be degraded in vivo following germination, thus functioning as a reserve of amino nitrogen and carbon skeletons. A general definition of seed storage proteins is proposed, to encompass any protein present in major quantity in the seed which is degraded following imbibition, and for which no other function may be demonstrated.     

Abstract biological systems as sequential machines: Behavioral reversibility

Rosen’s identification of abstract biological systems, called (M,R)-systems, with sequential machines is formally characterized. It is then shown that the determination of environmental alterations of (M,R)-systems from a knowledge of the response sequence and the structure of the system, which we call behavioral reversibility, can be interpreted as information-losslessness of sequential machines. Applying this relationship, necessary conditions for behavioral reversibility are derived. It is further shown that, similar to Rosen’s work on structural reversibility, (M,R)-systems are behaviorally reversible only if the number of physically realizable mappings are restricted.     

Leptodon Smith (Hedw.) Mohr in Ireland

Abstract

A new Irish locality is recorded for L. smithii, and the general features of the station are described. An account of the bryophyte succession on tree trunks in the area is given and the part played by L. smithii indicated. It is shown that gatherings from both Irish localities consisted entirely of male plants and the distribution and age of the antheridia on both specimens are recorded. It is suggested that rarity of sporophyte production in the British Isles is probably due to too great a spatial separation of male and female plants and not to the absence, or low production, of sex organs. It is also suggested that rarity of spores and impermanence of the habitat are the chief factors contributing to its rareness in climatically suitable areas of the British Isles. The known distribution of the plant in the British Isles is related to its European and world distribution, and it is shown that L. smithii may be expected in further Irish vice counties.

I have pleasure in acknowledging my thanks to Mr Wallace for the gift of a specimen of L. smithii from Knocklofty and for details of its habitat; to Mrs C. E. M. Shelswell-White for permission to enter and collect in the grounds of Bantry House, and to my colleague Dr J. G. Hawkes for confirming the identification of the two shrubs.     

Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks

Summary For a general multiple loop feedback inhibition system in which the end product can inhibit any or all of the intermediate reactions it is shown that biologically significant behaviour is always confined to a bounded region of reaction space containing a unique equilibrium. By explicit construction of a Liapunov function for the general n dimensional differential equation it is shown that some values of reaction parameters cause the concentration vector to approach the equilibrium asymptotically for all physically realizable initial conditions. As the parameter values change, periodic solutions can appear within the bounded region. Some information about these periodic solutions can be obtained from the Hopf bifurcation theorem. Alternatively, if specific parameter values are known a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map. The single loop Goodwin oscillator is analysed in detail. The methods are then used to treat an oscillator with two feedback loops and it is found that oscillations are possible even if both Hill coefficients are equal to one.     

A note on Rashevsky's theorem about point-bases in topological biology

A graphG may have more than one point-baseB _G. In a primordial graphP of Rashevsky's (1954) TransformationT, some of the pointbases may consist of nonspecialized points only, and some other pointbases may contains specialized points. In this case, Rashevsky's Theorem (1955a) on point-bases may not hold. The Theorem is certainly true ifall point-bases ofP consists of nonspecialized points. A rigorous proof is given. Some results are derived for the more general case, when point-bases include both kinds of points. A general expression for the point-base ratio of the transformed graphP(T) is obtained. It is shown that with some biologically plausible assumptions Rashevsky's interpretation of the point-base ratio and his conclusions are still true. A few simple Theorems on point-bases of graphs are included in this work.     

Contribution to the theory of organismic sets,III

In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern>1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.