Observations on the locomotion of two British terrestrial planarians (Platyhelminthes, Tricladida)

The locomotion of Microplana terrestris and of M. britannicus is described. Forward locomotion is normally by means of cilia which are confined to the ventral surface of the animals. M. terrestris may however involve stationary peristaltic waves in locomotion. In this case neither muscular nor ciliary forces can alone account for the locomotion and it is necessary that the two mechanisms are combined. Such stationary waves should be distinguished from retrograde and direct locomotory waves. Reversal in both species is by retrograde muscular waves.     

The role of the individual in social dynamics

The mathematical theories of social dynamics developed previously are deterministic and leave no room for the effects of single “exceptional” individuals. They all, however, lead to the existence of instability points and threshold phenomena. It is shown that in the neighborhood of such instability points, exceptional individuals, who appear rarely, can appreciablyadvance orretard the moment at which the instability is reached and at which a sudden change in the society occurs. Such individuals, however, do not eitherprevent orcause the instability, or the change, to occur. The indeterminacy introduced by “rare” individuals into the time course of social change is inversely proportional to the rate of social change.     

Retinal and optical adaptations for nocturnal vision in the halictid bee<Emphasis Type="Italic"> Megalopta genalis</Emphasis>

The apposition compound eye of a nocturnal bee, the halictid Megalopta genalis, is described for the first time. Compared to the compound eye of the worker honeybee Apis mellifera and the diurnal halictid bee Lasioglossum leucozonium, the eye of M. genalis shows specific retinal and optical adaptations for vision in dim light. The major anatomical adaptations within the eye of the nocturnal bee are (1) nearly twofold larger ommatidial facets and (2) a 4–5 times wider rhabdom diameter than found in the diurnal bees studied. Optically, the apposition eye of M. genalis is 27 times more sensitive to light than the eyes of the diurnal bees. This increased optical sensitivity represents a clear optical adaptation to low light intensities. Although this unique nocturnal apposition eye has a greatly improved ability to catch light, a 27-fold increase in sensitivity alone cannot account for nocturnal vision at light intensities that are 8 log units dimmer than during daytime. New evidence suggests that additional neuronal spatial summation within the first optic ganglion, the lamina, is involved.B.G. is thankful for travel awards from the Royal Physiographic Society, the Per Westlings Fond, the Foundation of Dagny and Eilert Ekvall and the Royal Swedish Academy of Sciences. E.J.W. is grateful for the support of a Smithsonian Short-Term Research Fellowship, the Swedish Research Council, the Crafoord Foundation, the Wenner-Gren Foundation and the Royal Physiographic Society of Lund for their ongoing support     

Instability in a generalized Keller-Segel model

We present a generalized Keller-Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although this mechanism was already known to exist in the original Keller-Segel model, here we show that it is more generally applicable by significantly enlarging the class of models exhibiting this instability phenomenon which may lead to pattern formation.     

Pattern formation and morphogenesis: A reaction-diffusion model

The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.     

The geometry and motion of reaction-diffusion waves on closed two-dimensional manifolds

Chemical or biological systems modelled by reaction diffusion (R.D.) equations which support simple one-dimensional travelling waves (oscillatory or otherwise) may be expected to produce intricate two or three-dimensional spatial patterns, either stationary or subject to certain motion. Such structures have been observed experimentally. Asymptotic considerations applied to a general class of such systems lead to fundamental restrictions on the existence and geometrical form of possible structures. As a consequence of the geometrical setting, it is a straightforward matter to consider the propagation of waves on closed two-dimensional manifolds. We derive a fundamental equation for R.D. wave propagation on surfaces and discuss its significance. We consider the existence and propagation of rotationally symmetric and double spiral waves on the sphere and on the torus. On leave of absence from: Department of Mathematics, Glasgow College of Technology, Cowcaddens Road, Glasgow G4 0BA, Scotland, UK     

Instability in a generalized Keller–Segel model

We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although this mechanism was already known to exist in the original Keller–Segel model, here we show that it is more generally applicable by significantly enlarging the class of models exhibiting this instability phenomenon which may lead to pattern formation.     

Delimitation of Trypanosoma cruzi zymodemes by numerical taxonomy

Summary Based on the absence or presence of 24 isoenzyme characters, Brazilian Trypanosoma cruzi stocks can be separated by methods of numerical taxonomy into three principal, distinct groups; these groups correspond to the three T. cruzi zymodemes previously reported from north Brazil. A distinction is drawn between taxonomy, which may be of zoological interest only, and identification of medically important groups according to one or a few distinguishing characters.This paper is reprinted from Transactions of the Royal Society of Tropical Medicine and Hygiene, 74, 238–242.This paper is reprinted from Transactions of the Royal Society of Tropical Medicine and Hygiene, 74, 238–242.     

An improved algorithm for the detection of dynamical interdependence in bivariate time-series

 We describe a new algorithm for the detection of dynamical interdependence in bivariate time-series data sets. By using geometrical and dynamical arguments, we produce a method that can detect dynamical interdependence in weakly coupled systems where previous techniques have failed. We illustrate this by comparison of our algorithm with another commonly used technique when applied to a system of coupled Hénon maps. In addition, an improvement of ∼20% in the detection rate is observed when the technique is applied to human scalp EEG data, as compared with existing techniques. Such an improvement may assist an understanding of the role of large-scale nonlinear processes in normal brain function. Received: 28 December 2001 / Accepted in revised form: 2 October 2002 Correspondence to: J.R. Terry (e-mail: J.R.Terry@lboro.ac.uk) Acknowledgements. JRT acknowledges the support of the Royal Society and the London Mathematical Society for jointly funding a trip to the School of Physics at the University of Sydney and The Brain Dynamics Centre at Westmead Hospital, Sydney. The authors thank Professor Peter Robinson for useful conversations and the provision of local facilities within the School of Physics during the visit of JRT. The support of the EPSRC via Grant GR/N00340 is also acknowledged. MJB is a recipient of a University Postgraduate Award from the University of Sydney.     

Dissipative pattern formation in ternary non-linear reaction-electrodiffusion systems with concentration-dependent diffusivities

Conditions for the emergence of ionic dissipative structures after Turing instability of a spatially and temporaly homogeneous stationary concentration distribution are derived for electroneutral ternary ionic reaction systems with concentration-dependent diffusivities. The inhomogeneous solution branch first bifurcating while crossing a critical ratio of diffusivities is given as a series of eigenfunctions of the Laplace operator. The results are specified for a model reaction system and polynomial concentration dependence of diffusion. It is shown that the inclusion of concentration dependence controls the amplitudes of the spatial distribution.     

Propagation of Turing patterns in a plankton model

The paper is devoted to a reaction-diffusion system of equations describing phytoplankton and zooplankton distributions. Linear stability analysis of the model is carried out. Turing and Hopf stability boundaries are found. Emergence of two-dimensional spatial structures is illustrated by numerical simulations. Travelling waves between various stationary solutions are investigated. Transitions between homogeneous in space stationary solutions and Turing structures are studied.     

The publication dates of the Transactions of the Linnean Society of London,Series I,1791–1875*

Evidence for the dates of publication of the parts of the Transactions of the Linnean Society of London, Series 1,1791–1875, has been collected from the Minute Books of the Linnean Society, the Journal Books of the Royal Society, The Times, Bent's Monthly Literary Advertiser, the Bookseller, the Gardener's Chronicle, and the Athenaeum. Dates have been traced for all parts except five, and two of those may have been issued with other parts that have been dated.     

Propagation of Turing patterns in a plankton model

The paper is devoted to a reaction–diffusion system of equations describing phytoplankton and zooplankton distributions. Linear stability analysis of the model is carried out. Turing and Hopf stability boundaries are found. Emergence of two-dimensional spatial structures is illustrated by numerical simulations. Travelling waves between various stationary solutions are investigated. Transitions between homogeneous in space stationary solutions and Turing structures are studied.     

Lepidopteran wing patterns and the evolution of satyric mimicry

The hypothesis of satyric mimicry postulates that the colour patterns of an animal may make its identity ambiguous, and this ambiguity interferes with the process of perception in vertebrate predators for a sufficient time to allow the potential prey to take evasive action. It has now been found that eyespots and other designs on the wings of many insect species are often coupled with other wing patterns and designs. These composite images often closely resemble heads and bodies of vertebrates (including birds and reptiles) and of various invertebrates. Such images can be perceived in living insects, although only rarely in set specimens because of displacement of the components. Visual processing by non‐mammalian vertebrates generally involves attention to detail, suggesting that, at least initially, and unlike humans, they perceive embedded images on insect wings and bodies and ignore the whole or Gestalt. They are therefore likely to be confused by the ambiguity of the potential prey. It can be calculated that a delay of the order of only tenths of a second in the attack on a stationary insect by a predator could result in failure of capture. It is proposed in the present review that the concept of satyric mimicry be extended to include complex imagery of other organisms. Such iconic images, which often represent toxic or dangerous animals, are particularly common amongst saturniid moths and nymphalid and danaid butterflies (including the Monarch butterfly, Danaus plexippus). © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 109 , 203–214.     

Jumping Gene gs of Lycopersicon lycopersicum (L.) Karsten ex Farw

Studies on tomato culture revealed for the first time two phenomena: (1) instability of gene gs (green stripes on fruits) and (2) spontaneous expression of the character determined by the gs gene without involvement of sexual reproduction in some cultivars. The instability of the gs gene was detected by the phenotypic expression of character in different plants from the same strain, racemes of the same plant, fruits of the same raceme, and parts of the same fruit. The instability of the gsgene may be determined by endogenous regulatory genetic elements causing specific changes of the character, with the degree of these changes varying for different parts of the fruit and places of its formation on the plant. The instability of the gs gene was expressed for four generations. There were no other phenotypic changes in the offsprings studied. In addition, migration of the recessive gs gene to other cultivars followed by its complete expression in a whole plant or some parts of the plant was observed. Exogenous transfer of thegsgene is suggested.     

Classical versus stochastic kinetics modeling of biochemical reaction systems

We study fundamental relationships between classical and stochastic chemical kinetics for general biochemical systems with elementary reactions. Analytical and numerical investigations show that intrinsic fluctuations may qualitatively and quantitatively affect both transient and stationary system behavior. Thus, we provide a theoretical understanding of the role that intrinsic fluctuations may play in inducing biochemical function. The mean concentration dynamics are governed by differential equations that are similar to the ones of classical chemical kinetics, expressed in terms of the stoichiometry matrix and time-dependent fluxes. However, each flux is decomposed into a macroscopic term, which accounts for the effect of mean reactant concentrations on the rate of product synthesis, and a mesoscopic term, which accounts for the effect of statistical correlations among interacting reactions. We demonstrate that the ability of a model to account for phenomena induced by intrinsic fluctuations may be seriously compromised if we do not include the mesoscopic fluxes. Unfortunately, computation of fluxes and mean concentration dynamics requires intensive Monte Carlo simulation. To circumvent the computational expense, we employ a moment closure scheme, which leads to differential equations that can be solved by standard numerical techniques to obtain more accurate approximations of fluxes and mean concentration dynamics than the ones obtained with the classical approach.     

Immunocompetence increases with larval body size in a phytophagous moth

Despite the obvious benefit of an immune system, its efficacy against pathogens and parasites may show great variation among individuals, populations and species. Understanding the causes of this variation is becoming a central theme in ecology. Many biotic and abiotic factors are known to influence immunocompetence (temperature, age, etc.). However, for a given age, size among individuals varies, probably as a result of accumulated resources. Thus, these variable resources could be allocated to immune defence and, consequently, body size may explain part of the variation in immune responsiveness. However, the influence of body size on immune defence is often overlooked. The present study investigates variations in haemocyte count and phenoloxidase activity in larvae of the phytophagous vine moth Eupoecilia ambiguella Hübner of the same age, although differing in body size. The measurements of immune function are made both when the insects are immunologically naïve and 24 h after a bacterial immune challenge. The base levels of these immune parameters do not covary with body size in naïve larvae. After the bacterial immune challenge, more haemocytes and phenoloxidase enzyme are mobilized, and the mobilization of these immune effectors is correlated positively with individual body size. Thus, larger larvae exhibit higher immunocompetence than smaller ones, suggesting that smaller larvae might be more vulnerable to infection. These results suggest that body size is probably an underestimated variable, which nevertheless modulates the insect immune system and should thus be considered as a covariate in insect immune system measurement. It is recommended therefore, that body size should be taken into account in ecological immunity studies with insects. © 2013 The Royal Entomological Society     

Traveling waves in a chemotactic model

A model for chemotaxis in a bacteria-substrate mixture introduced by Keller and Segel, which is described by nonlinear partial differential equations, is studied analytically. The existence of traveling waves is shown for the system in which the substrate diffusion is taken into account and the chemotactic coefficient is greater than the motility one, and the instability of traveling waves is discussed.     

Kelvin-Helmholtz instability on the magnetopause, magnetohydrodynamic waveguide in the outer magnetosphere, and Alfvén resonance deep in the magnetosphere

Oscillations of the “magnetosphere-solar wind” system are studied analytically in the framework of a plane-stratified model of the medium. The properties of oscillations are determined by three phenomena: Kelvin-Helmholtz instability on the tangential discontinuity (magnetopause) separating the magnetosphere and the solar wind, the presence of a waveguide for fast magnetosonic waves in the magnetosphere, and the Alfvén resonance—a sharp increase in the amplitude of oscillations having the properties of Alfvén waves—in the inner magnetosphere. The oscillations of the system form a discrete spectrum of eigenmodes. Analytical expressions are obtained for the frequency and growth rate of instability of each mode, as well as for the functions describing the spatial structure of these modes. All these characteristics of the eigenmodes are shown to depend on the velocity of the solar wind as a parameter. The dependences of the main mode characteristics (such as the instability thresholds, the points of the maximum and minimum growth rate, and the spatial distributions of the oscillation energy) on this parameter are determined for each eigenmode.