The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity

A qualitative analysis of the Hodgkin-Huxley model (Hodgkin and Huxley 1952), which closely mimics the ionic processes at a real nerve membrane, is performed by means of a singular perturbation theory. This was achieved by introducing a perturbation parameter that, if decreased, speeds up the fast variables of the Hodgkin-Huxley equations (membrane potential and sodium activation), whereas it does not affect the slow variables (sodium inactivation and potassium activation). In the most extreme case, if the perturbation parameter is set to zero, the original four-dimensional system degenerates to a system with only two differential equations. This degenerate system is easier to analyze and much more intuitive than the original Hodgkin-Huxley equations. It shows, like the original model, an infinite train of action potentials if stimulated by an input current in a suitable range. Additionally, explanations for the increased sensitivity to depolarizing current steps that precedes an action potential can be found by analysis of the degenerate system. Using the theory of Mishchenko and Rozov (1980) it is shown that the degenerate system does not only represent a simplification of the original Hodgkin-Huxley equations but also gives a valid approximation of the original model at least for stimulating currents that are constant within a suitable range.     

On the classification of regular systems of inbreeding

Regular systems of inbreeding are defined as those with discrete, nonoverlapping generations and with the same number of individuals and mating pattern in every generation. Given the number of individuals in a generation, there are many possible regular mating systems. A notion of when two such mating systems are equivalent is introduced, and several necessary conditions are given for such an equivalence. The use of these conditions is illustrated for N = 2, 3, 4 and 5 individuals, and a complete enumeration has been found for these cases: the numbers of inequivalent mating systems are 1, 5, 57 and 858, respectively. The maximal eigenvalue of the matrix q that specifies the recursion relations satisfied by the probabilities of identity have also been found for these cases. For N = 3 and 4 (and 2 trivially), circular mating gives the slowest rate of approach to genetic uniformity of those systems that do evolve to uniformity, but for N = 5 there are two other mating systems that have a slower rate of convergence, and for N = 6 partial results show that there are many such examples.Deceased     

Information transmission during intra- and interspecific courtship inEphestia elutella andCadra figulilella

Using information theory, courtship posturing in the moths Ephestia elutella(Hübner) and Cadra figulilella(Gregson) was analyzed for information transmission, which was partitioned into autocovariability (intraindividual transmission) and cross-covariability (interindividual transmission). This two-factor analysis was sufficient to account for more than 60% of the behavioral variance in males of E. elutellaand in both sexes of C. figulilelladuring intraspecific courtships; however, there were large residual variances in the behavior of male and female C. figulilelladuring interspecific courtships and in E. elutellafemales during both inter- and intraspecific courtships. In E. elutella,significant levels of transmission were attributable to both inter- and intraindividual effects, whereas in C. figulilella,only autocovariability was high and no interindividual communication could be assigned to courtship postures. Although courtship in these two species was qualitatively very similar and males readily courted nonconspecific females, high levels of reproductive isolation resulted from courtship. Male C. figulilellahad 94% fewer copulations with E. elutellafemales than with conspecific females and E. elutellamales had 78% fewer copulations with C. figulilellafemales than with conspecifics. These reductions were due to a differential response in both females and males, causing inter-specific courtships to be terminated much earlier than intraspecific courtships. This discrimination indicates that interindividual communication was indeed occurring during courtship and was only partially measured by analysis of postures. Thus, communication took place largely in some other modality, most likely the chemical modality, where species specificity is suggested for both male and female pheromones.     

Measurement of exchange of trace metals between the body and its surroundings with the use of trace methodology

Application of general tracer theory to the problem of estimating fluxes of tracee between the gastrointestinal tract and the body proper, from observations of the movement of tracer, shows that a number of assumptions must be fulfilled. Two specific sets of assumptions are discussed and, in both cases, measurement of tracer fluxes yields information on the integrated absorption of the tracee.     

The Why and How of Species

The biological species concept deals both with the meaning of the sexual species as a harmonious gene pool and with its protection against deleterious outbreeding (effected by isolating mechanisms). According to the Darwin-Muller-Mayr theory isolating mechanisms are acquired by incipient species during alloparty. Isolating mechanisms are not the result of ad hoc selection, but of a change of function of properties acquired during the preceding isolation of the incipient species. The role of behavioral properties (recognition) among the isolating mechanisms has long been recognized and described by naturalists but was rejected as basis of a species definition for a number of valid reasons.     

Annual plant life histories and the paradigm of resource allocation

Summary Much of life history theory follows from the idea that natural selection acts on the allocation of resources to competing and independent demographic functions. This paradigm has stimulated much research on the life histories of annual plants. Models of whole-plant resource budgets that use optimal control theory predict periods of 100% vegetative and 100% reproductive growth, sometimes with periods of mixed growth. I show here that this prediction follows from the assumption of independence of the competing vegetative and reproductive compartments. The prediction is qualitatively unchanged even after relaxing important simplifying assumptions used in most models. Although it follows naturally from the assumptions of the models, this kind of allocation pattern is unlikely to occur in many plants, because it requires that (1) leaf and flower buds can never simultaneously be carbon sinks; and (2) organs that accompany flowers, such as internodes and bracts, can never be net sources of photosynthate. Thus while resources are doubtless important for annual plants, an exclusively resource-based perspective may be inadequate to understand the evolution of their life histories. Progress in research may require models that incorporate, or are at least phenomenologically consistent with, the basic developmental reles of angiosperms.     

The effect of time-varying mortality and carbon assimilation on models of carbon allocation in annual plants

Summary Models of optimal carbon allocation schedules have influenced the way plant ecologists think about life history evolution, particularly for annual plants. The present study asks (1) how, within the framework of these models, are their predictions affected by within-season variation in mortality and carbon assimilation rates?; and (2) what are the consequences of these prediction changes for empirical tests of the models? A companion paper examines the basic assumptions of the models themselves. I conducted a series of numerical experiments with a simple carbon allocation model. Results suggest that both qualitative and quantitative predictions can sometimes be sensitive to parameter values for net assimilation rate and mortality: for some parameter values, both the time and size at onset of reproduction, as well as the number of reproductive intervals, vary considerably as a result of small variations in these parameters. For other parameter values, small variations in the parameters result in only small changes in predicted phenotype, but these have very large fitness consequences. Satisfactory empirical tests are thus likely to require much accuracy in parameter estimates. The effort required for parameter estimation imposes a practical constraint on empirical tests, making large multipopulation comparisons impractical. It may be most practical to compare the predicted and observed fitness consequences of variation in the timing of onset of reproduction.     

The use of optimal foraging theory in the understanding of fishing strategies: A case from Sepetiba Bay (Rio de Janeiro State,Brazil)

The community of Gamboa is located on Itacuruçá Island, Sepetiba Bay (State of Rio de Janeiro, Brazil) and includes 26 families, mostly of artisanal fishermen who use paddled or motor canoes, and encircling nets for fishing. In this study, predictions from optimal foraging theory (patch model), in particular of patch residence time, are compared to the observed behavior of fishermen on fishing trips. Fishermen's strategies differ depending on their intended prey. They spend more time in patches and use fewer patches for shrimp than for fish. Gamboa's fishermen tend to leave a patch later than predicted by the model. The difficulty in evaluating stock availability, the comparatively few patches available for shrimp, and the competitive aspects of fishing contribute to the explanation of this behavior.     

Effect of Zeitgeber Intensity Reduction on a Simulated Dual-Oscillator Human Circadian System: Classical and Dynamic Analysis

The two-oscillator model of human circadian rhythmicity was analyzed when a zeitgeber relative intensity of 1, 0.5, or 0.1 was introduced into the equations. Fourier analysis was compared with dynamic analysis such as attractor reconstruction or Liapunov exponent calculation. After a 50 or 90% reduction in zeitgeber intensity, the dynamics of the system became equivalent and differed significantly from those of a system with maximal zeitgeber intensity. When 10% aleatory noise was added to the data, the analysis was still applicable, and the results obtained were essentially the same as in the absence of noise. Dynamic analysis could thus provide a distinct classification for periodic data, based on the type of analysis.