A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

Stick insects walking along inclined surfaces

In the experiments stick insects walk on an inclined substratesuch that the legs of one side of the body point uphill andthe legs of the other side point downhill. In this situationthe vertical axis of the body is rotated against the inclinationof the substrate as if to compensate for the effect of substrateinclination. A very small effect has been found when the experimentwas performed with animals standing on a tilted platform whichshows that the effect depends on the behavioral context. When,however, animals first walked along the inclined surface andthen, before measurement, stopped walking spontaneously, a rotationof the body has been observed similar to that in walking animals.In a second experiment it was tested whether the observed bodyrotation is caused by the change of direction of gravity vectoror by the fact that on an inclined surface gravity necessarilyhas a component pulling the body sideways. Experiments withanimals standing on horizontal ground and additional weightsapplied pulling the body to the side showed similar body rotationssupporting the latter idea. In a simulation study it could beshown that the combined activity of proportional feedback controllersin the leg joints is sufficient to explain the observed behavior.This is however only possible if the gain factors of coxa-trochanterjoint controller and of femur-tibia joint controller show aratio in the order of 1 : 0.05 to 1 : 1.8. In order to describethe behavior of animals standing on a tilted platform, a ratioof 1 : 1.7 is necessary. In walking animals, this body rotationrequires to change the trajectories of stance and swing movements.The latter have been studied in more detail. During swing, thefemur-tibia joint is more extended in the uphill legs. Conversely,the coxa-trochanter joint appears to be more elevated in thedownhill legs which compensates the smaller lift in the femur-tibiajoint. The results are discussed in the context of differenthypotheses.     

Simulation of a model for the coordination of leg movement in free walking insects

A computer has been used to simulate the behaviour of a model proposed to explain certain asymmetries in the free walking step patterns of adult stick insects. Complete sequences of behaviour including turns, changes in velocity, and transitions between different step patterns have been simulated and are compared with the real sequences produced by 1st instar and adult animals. The procedure for simulating the complete walking behaviour suggests that there are subtle differences in the walking system at these two stages of growth in addition to those outlined in an earlier paper. The model also provides a formal structure for expressing quantitative differences between the walking behaviour of the cockroach, locust, grasshopper, and stick insect.     

A two-dimensional aerodynamic model of freely flying insects

Possible free flights of insects by a single flapping motion were studied. It is well-known that insects utilize vortices generated by flapping, by which they generate larger lift than that evaluated by the ordinary aerodynamic theory. However, the effect of the motion of the center of mass (CM) of the insect on its flight has not been clarified. To clarify the effect, numerical simulation was performed for a simple model considering the coupling between the vertical CM motion and the separation vortices generated by flapping wing. As a result, it is shown that the flapping flight has the following interesting features. First, despite a single flapping motion, the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights are selected by the initial conditions even when all the parameters are the same. Second, at a certain critical parameter value, the steady flight loses its stability and undergoes an abrupt transition to the wandering flight. Interestingly, at this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple assumption. These results suggest the significance of the effect of CM motion.     

农田景观格局变化对昆虫的生态学效应

景观格局变化是全球变化的一个重要内容。农田是由人类赖以生存所种植的人工栽培作物组成的生态系统。在该景观系统中,多种植物-害虫-天敌相互作用、相互制约,形成有机整体。研究农田景观格局对害虫和天敌种群动态影响,不仅在害虫生物防治的实践中有重要意义,而且对于揭示人类活动对生物多样性结构与功能的影响,阐明农田景观中生物多样性整合、维持机理有重大的理论意义。本文从农田景观格局的"质、量、形、度"4个方面,系统地论述了农田景观格局变化对害虫和天敌的作用,分析了农田景观的生物控制服务功能,指出了未来研究发展的方向。     

A self-organizing neural network model for the development of complex cells

On the basis of recent neurophysiological findings on the mammalian visual cortex, a selforganizing neural network model is proposed for the understanding of the development of complex cells. The model is composed of two kinds of connections from LGN cells to a complex cell. One is direct excitatory connections and the other is indirect inhibitory connections via simple cells. Inhibitory synapses between simple cells and complex cells are assumed to be modifiable. The model was simulated on a computer to confirm its behavior.     

A model of pattern generation of cockroach walking reconsidered

Cockroaches that have been decapitated or that have cut thoracic connectives can show rhythmic bursting in motoneurons to intrinsic leg muscles. These preparations have been studied as models for walking and to evaluate the functions of leg proprioceptors. The present study demonstrates that headless cockroaches walk extremely poorly and slowly with considerable discoordination of motoneuronal activity, these preparations show rhythmic motoneuron bursting that is similar to righting responses (attempts to turn upright) of intact animals when placed on their backs, and bursting is inhibited when a headless animal is turned or turns itself upright. Thus, rhythmic motoneuron activity of these preparations is most probably attempted righting rather than walking. It is concluded that the headless cockroach is useful for understanding the motor mechanisms underlying righting and walking but is not of value in assessing the functions of proprioceptive feedback.     

A stochastic model for evolution of sociality in insects

We study population biology of eusocial insects such as Ropalidia marginata through a stochastic model based on random (matrix) difference equations. This facilitates a study of dynamics of such populations when the survival and other rates vary randomly over time. The worker-brood relatedness, which is a function of the underlying population structure, can be used to explain theories on the evolution of altruism. The effect of demographic parameters and the queen takeover probabilities on the worker-brood relatedness has been studied. Based on the proposed model, we simulate insect colonies where queens are replaced. Simulation results help us to study the effect of various factors on the worker-brood relatedness. Further, we study two estimators of the worker-brood relatedness and suggest procedures for estimating their standard errors. Approximate confidence intervals for the same can be constructed with the help of these results.     

A computer simulation of a neuron net model as a self-organizing system

A neural net model is simulated on an IBM-1130 digital computer. The model includes rules for learning of the presented patterns. The learning algorithm uses an iteration procedure, in order to compute the ultimate cross coupling-coefficients between the neurons for a specific pattern. The network has a set of latent cyclic modes or reverberations. If the net is stimulated briefly, by presenting a pattern, it will subsequently either return to quiescence or settle into periodic activity in one of its cyclic modes.     

Mathematical model of self-organizing hierarchies in animal societies

We propose a mathematical approach to the modelling of self-organizing hierarchies in animal societies. This approach relies on a basic positive feedback mechanism that reinforces the ability of a given individual to win or to lose in a hierarchical interaction, depending on how many times it won or lost in previous interactions. Motivated by experiments carried out on primitively eusocial waspsPolistes, the model, is based on coupled differential equations supplemented with a small stochastic term. Numerical integrations allow many different hierarchical profiles to be obtained depending on the model parameters: (1) the particular form of the probability for an individual to win or lose a fight given its history, (2) the probability of interaction between two individuals, (3) the forgetting strength, which determines the rate at which events in the past are forgotten and no longer influence the force of an individual and (4) two individual recognition parameters, which set the contribution of individual recognition in the process of hierarchical genesis. We compare the results, expressed in terms of a hierarchical index or of the Landau number that describes the degree of linearity of the hierarchy, with various experimental results.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

A model of human walking energetics with an elastically-suspended load

Elastically-suspended loads have been shown to reduce the peak forces acting on the body while walking with a load when the suspension stiffness and damping are minimized. However, it is not well understood how elastically-suspended loads can affect the energetic cost of walking. Prior work shows that elastically suspending a load can yield either an increase or decrease in the energetic cost of human walking, depending primarily on the suspension stiffness, load, and walking speed. It would be useful to have a simple explanation that reconciles apparent differences in existing data. The objective of this paper is to help explain different energetic outcomes found with experimental load suspension backpacks and to systematically investigate the effect of load suspension parameters on the energetic cost of human walking. A simple two-degree-of-freedom model is used to approximate the energetic cost of human walking with a suspended load. The energetic predictions of the model are consistent with existing experimental data and show how the suspension parameters, load mass, and walking speed can affect the energetic cost of walking. In general, the energetic cost of walking with a load is decreased compared to that of a stiffly-attached load when the natural frequency of a load suspension is tuned significantly below the resonant walking frequency. The model also shows that a compliant load suspension is more effective in reducing the energetic cost of walking with low suspension damping, high load mass, and fast walking speed. This simple model could improve our understanding of how elastic load-carrying devices affect the energetic cost of walking with a load.     

Thermal constraints on activity patterns in nectar-feeding insects

ABSTRACT.

• 1 All the insects visiting Tilia and Heracleum flowers showed diel patterns of activity, which could best be explained in terms of weather. Of the recorded parameters, solar radiation gave the best correlations with activity.
• 2 Correlations between activity and radiation depended on the size and colour of particular groups of insects; small bright species visited fully insolated flowers, (r high), while large dark forms visited early and late in the day (r low or negative).
• 3 Consequently mean reflectance and mean weight of foragers showed consistent trends through a day and predictable relations with radiation for both flowers, suggesting that thermal costs are a critical determinant of feeding times.
• 4 By contrast, the nectar reward (as sugar amounts) in flowers was poorly correlated with timing of insect visits, indicating that caloric reward is not limiting; although nectar concentration (only measurable for Tilia) did correlate reasonably well with total visitation.
• 5 The exception to this pattern was Bombus. This endothermic species visited early in the day when nectar was abundant. Thus visits correlated well with reward and negatively with radiation, showing a dependence on high rewards to offset thermoregulatory metabolic costs.
• 6 For most insects foraging appeared to be largely determined by the visitors thermal requirements and the restrictions imposed by avoidance of overheating. Nectar rewards were not critical, and nectar concentration, itself dependent upon climatic parameters, was probably only incidentally correlated with diel patterning for all but the largest (endothermic) insects.

     

Altitudinal patterns in host suitability for forest insects

Conspecific trees growing at high and low-elevations encounter different growing conditions and may vary in their suitability as hosts for herbivorous insects. Mountain tree populations may be more resistant to herbivory if low temperatures constrain growth more than they constrain photosynthesis, resulting in increased secondary metabolism (temperature hypothesis). Alternatively, mountain trees may be fertilized by atmospheric nitrogen deposition and become more palatable to insects (atmospheric deposition hypothesis). We evaluated these two hypotheses by comparing high- and low-elevation trees with insect bioassays and analyses of foliar nitrogen and condensed tannin. Contrary to the temperature hypothesis, high-elevation foliage had higher leaf nitrogen (six of six tree species) and allowed higher growth rates of Lymantria dispar larvae (five of six tree species). The nitrogen deposition hypothesis was broadly supported by measurements from two mountains showing that high-elevation trees tended to have higher leaf nitrogen, lower leaf tannins, and support higher insect growth performance than conspecific trees from lower elevations. The deposition hypothesis was further supported by fertilization studies showing that simulated atmospheric nitrogen deposition changed the foliar chemistry of valley trees to resemble that of high-elevation trees. Predictions that the altitudinal gradient in foliar chemistry and host suitability should be steepest on mountains receiving more deposition were largely not supported, but interpretations are complicated by lack of replication among mountains. In the northeastern United States, increased host suitability of high-elevation trees seems sufficient to influence the population dynamics and community composition of herbivores. Atmospheric nitrogen deposition offers a promising hypothesis to explain and predict some important spatial patterns in herbivory. Received: 21 September 1997 / Accepted: 12 June 1998     

A general model for host plant selection in phytophagous insects

We develop a general theoretical framework for exploring the host plant selection behaviour of herbivorous insects. This model can be used to address a number of questions, including the evolution of specialists, generalists, preference hierarchies, and learning. We use our model to: (i) demonstrate the consequences of the extent to which the reproductive success of a foraging female is limited by the rate at which they find host plants (host limitation) or the number of eggs they carry (egg limitation); (ii) emphasize the different consequences of variation in behaviour before and after landing on (locating) a host (termed pre- and post-alighting, respectively); (iii) show that, in contrast to previous predictions, learning can be favoured in post-alighting behaviour--in particular, individuals can be selected to concentrate oviposition on an abundant low-quality host, whilst ignoring a rare higher-quality host; (iv) emphasize the importance of interactions between mechanisms in favouring specialization or learning.     

A population and energetic model of an outbreak of forest insects

A model of the population dynamics of insects has been developed, which takes into account the food consumption by insects and the reaction of food plants to the damage. Equations have been derived that describe the relationship between the coefficient of insect reproduction, the weight of females, the energetic effectiveness of the food consumption by insects, and the reaction of food plants. The scenarios of population outbreaks have been analyzed as a function of the weight of females in the stable state. The results of modeling have been compared with the data of natural observations.     

Synthesis of human walking: A planar model for single support

A mathematical model for the single support phase of normal, level, human walking is formulated. The motion of the lower extremity is synthesized using a preprogrammed set of inputs, recognized by the model as a simple collection of applied joint moments.

Two mechanisms are forwarded as candidates for producing the observed peaks in the vertical ground reaction. The first, stance knee flexion-extension, generates the necessary level of whole-body vertical acceleration during the initial region of single support (opposite toe-off to heel-off). A model accounting for the determinants of foot and knee interaction then predicts the second peak to be the result of an increasing ankle moment in the region from heel-off to opposite heel-strike.