Non-Linear Neuronal Responses as an Emergent Property of Afferent Networks: A Case Study of the Locust Lobula Giant Movement Detector

In principle it appears advantageous for single neurons to perform non-linear operations. Indeed it has been reported that some neurons show signatures of such operations in their electrophysiological response. A particular case in point is the Lobula Giant Movement Detector (LGMD) neuron of the locust, which is reported to locally perform a functional multiplication. Given the wide ramifications of this suggestion with respect to our understanding of neuronal computations, it is essential that this interpretation of the LGMD as a local multiplication unit is thoroughly tested. Here we evaluate an alternative model that tests the hypothesis that the non-linear responses of the LGMD neuron emerge from the interactions of many neurons in the opto-motor processing structure of the locust. We show, by exposing our model to standard LGMD stimulation protocols, that the properties of the LGMD that were seen as a hallmark of local non-linear operations can be explained as emerging from the dynamics of the pre-synaptic network. Moreover, we demonstrate that these properties strongly depend on the details of the synaptic projections from the medulla to the LGMD. From these observations we deduce a number of testable predictions. To assess the real-time properties of our model we applied it to a high-speed robot. These robot results show that our model of the locust opto-motor system is able to reliably stabilize the movement trajectory of the robot and can robustly support collision avoidance. In addition, these behavioural experiments suggest that the emergent non-linear responses of the LGMD neuron enhance the system''s collision detection acuity. We show how all reported properties of this neuron are consistently reproduced by this alternative model, and how they emerge from the overall opto-motor processing structure of the locust. Hence, our results propose an alternative view on neuronal computation that emphasizes the network properties as opposed to the local transformations that can be performed by single neurons.     

Neural networks as mechanisms to regulate division of labor

In social insects, workers perform a multitude of tasks, such as foraging, nest construction, and brood rearing, without central control of how work is allocated among individuals. It has been suggested that workers choose a task by responding to stimuli gathered from the environment. Response-threshold models assume that individuals in a colony vary in the stimulus intensity (response threshold) at which they begin to perform the corresponding task. Here we highlight the limitations of these models with respect to colony performance in task allocation. First, we show with analysis and quantitative simulations that the deterministic response-threshold model constrains the workers' behavioral flexibility under some stimulus conditions. Next, we show that the probabilistic response-threshold model fails to explain precise colony responses to varying stimuli. Both of these limitations would be detrimental to colony performance when dynamic and precise task allocation is needed. To address these problems, we propose extensions of the response-threshold model by adding variables that weigh stimuli. We test the extended response-threshold model in a foraging scenario and show in simulations that it results in an efficient task allocation. Finally, we show that response-threshold models can be formulated as artificial neural networks, which consequently provide a comprehensive framework for modeling task allocation in social insects.     

A Bio-inspired Collision Avoidance Model Based on Spatial Information Derived from Motion Detectors Leads to Common Routes

Avoiding collisions is one of the most basic needs of any mobile agent, both biological and technical, when searching around or aiming toward a goal. We propose a model of collision avoidance inspired by behavioral experiments on insects and by properties of optic flow on a spherical eye experienced during translation, and test the interaction of this model with goal-driven behavior. Insects, such as flies and bees, actively separate the rotational and translational optic flow components via behavior, i.e. by employing a saccadic strategy of flight and gaze control. Optic flow experienced during translation, i.e. during intersaccadic phases, contains information on the depth-structure of the environment, but this information is entangled with that on self-motion. Here, we propose a simple model to extract the depth structure from translational optic flow by using local properties of a spherical eye. On this basis, a motion direction of the agent is computed that ensures collision avoidance. Flying insects are thought to measure optic flow by correlation-type elementary motion detectors. Their responses depend, in addition to velocity, on the texture and contrast of objects and, thus, do not measure the velocity of objects veridically. Therefore, we initially used geometrically determined optic flow as input to a collision avoidance algorithm to show that depth information inferred from optic flow is sufficient to account for collision avoidance under closed-loop conditions. Then, the collision avoidance algorithm was tested with bio-inspired correlation-type elementary motion detectors in its input. Even then, the algorithm led successfully to collision avoidance and, in addition, replicated the characteristics of collision avoidance behavior of insects. Finally, the collision avoidance algorithm was combined with a goal direction and tested in cluttered environments. The simulated agent then showed goal-directed behavior reminiscent of components of the navigation behavior of insects.     

Learning cellular sorting pathways using protein interactions and sequence motifs

Proper subcellular localization is critical for proteins to perform their roles in cellular functions. Proteins are transported by different cellular sorting pathways, some of which take a protein through several intermediate locations until reaching its final destination. The pathway a protein is transported through is determined by carrier proteins that bind to specific sequence motifs. In this article, we present a new method that integrates protein interaction and sequence motif data to model how proteins are sorted through these sorting pathways. We use a hidden Markov model (HMM) to represent protein sorting pathways. The model is able to determine intermediate sorting states and to assign carrier proteins and motifs to the sorting pathways. In simulation studies, we show that the method can accurately recover an underlying sorting model. Using data for yeast, we show that our model leads to accurate prediction of subcellular localization. We also show that the pathways learned by our model recover many known sorting pathways and correctly assign proteins to the path they utilize. The learned model identified new pathways and their putative carriers and motifs and these may represent novel protein sorting mechanisms. Supplementary results and software implementation are available from http://murphylab.web.cmu.edu/software/2010_RECOMB_pathways/.     

Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects

 Motivated by experimental studies of insects, we propose a model for legged locomotion in the horizontal plane. A three-degree-of freedom, energetically conservative, rigid-body model with a pair of compliant virtual legs in intermittent contact with the ground allows us to study how dynamics depends on parameters such as mass, moment of inertia, leg stiffness, and length. We find periodic gaits, and show that mechanics alone can confer asymptotic stability of relative heading and body angular velocity. We discuss the relevance of our idealized models to experiments and simulations on insect running, showing that their gait and force characteristics match observations reasonably well. We perform parameter studies and suggest that our model is relevant to the understanding of locomotion dynamics across species. Received: 17 April 2001 / Accepted in revised form: 20 November 2001     

Photoperiodic time measurement in insects: a review of clock models

Based on analyses of responses of insects and mites to a wide range of diel and nondiel experimental light-dark schedules, a variety of models have been developed for the photoperiodic clocks in these species by nearly as many investigators. According to some of these models, the photoperiodic clock is based on a mechanism separate from the circadian system, that is, a so-called "hourglass." According to other models, the clock is based on one or more circadian oscillators that may be coupled to each other and that may or may not show a certain degree of damping. In this context, a rapidly damping oscillator could be regarded as an hourglass. The present article gives an overview of the many different clock models and their philosophies, and it makes comparisons among them to provide a better understanding about how these models are related, if at all, and why the double circadian oscillator model is the most favored model at present.     

Validity of thermal ramping assays used to assess thermal tolerance in arthropods

Proper assessment of environmental resistance of animals is critical for the ability of researchers to understand how variation in environmental conditions influence population and species abundance. This is also the case for studies of upper thermal limits in insects, where researchers studying animals under laboratory conditions must select appropriate methodology on which conclusions can be drawn. Ideally these methods should precisely estimate the trait of interest and also be biological meaningful. In an attempt to develop such tests it has been proposed that thermal ramping assays are useful assays for small insects because they incorporate an ecologically relevant gradual temperature change. However, recent model-based papers have suggested that estimates of thermal resistance may be strongly confounded by simultaneous starvation and dehydration stress. In the present study we empirically test these model predictions using two sets of independent experiments. We clearly demonstrate that results from ramping assays of small insects (Drosophila melanogaster) are not compromised by starvation- or dehydration-stress. Firstly we show that the mild disturbance of water and energy balance of D. melanogaster experienced during the ramping tests does not confound heat tolerance estimates. Secondly we show that flies pre-exposed to starvation and dehydration have "normal" heat tolerance and that resistance to heat stress is independent of the energetic and water status of the flies. On the basis of our results we discuss the assumptions used in recent model papers and present arguments as to why the ramping assay is both a valid and ecologically relevant way to measure thermal resistance in insects.     

Multiple Ecological Factors Influence the Location of Proboscis Monkey (<Emphasis Type="Italic">Nasalis larvatus</Emphasis>) Sleeping Sites in West Kalimantan,Indonesia

Multiple ecological factors have been hypothesized to influence primate sleeping site selection. Testing multiple hypotheses about sleeping site selection permits examination of the relative strength of distinct ecological factors and expands our ability to understand how selection pressures influence primate sleeping behavior. Here we examine how avoidance of biting insects, thermoregulation, foraging efficiency, tree stability, and interspecific competition influence selection of sleeping sites by proboscis monkeys (Nasalis larvatus) in Indonesian Borneo. We collected data on relative insect abundance, temperature, rainfall, food availability, group size, sleeping site location, and presence of other primates for 12 mo. Using formal model comparison and information criteria, we analyzed the relative importance of these ecological factors in determining one aspect of sleeping site location: distance from the river. Our models supported the avoidance of biting insects and the foraging efficiency hypotheses. Proboscis monkeys slept further inland on nights when the abundance of sandflies was high along the river, and when less food was available along the river. Many studies suggest that primates select sleeping trees and locations to reduce predation risk; our study indicates that additional factors may also be important in determining sleeping site selection.     

The erroneous courtship hypothesis: do insects really engage in aerial wars of attrition?

Males of various flying insects perform conspicuous aerial interactions around their mating stations. The broadly accepted interpretation of their aerial interaction is a war of attrition, where two contestants perform costly displays, and the one that reaches its cost threshold earlier gives up. The implicit but important requirement in this model is that some forces that match the intensity of display of the two contestants are necessary, and failure to enforce matching allows foul contestants that delay or stop their display to avoid paying contest costs. In addition, wars of attrition require flying insects to distinguish the sex of flying conspecifics because their aerial interactions begin when intruders fly into the territory. We investigated past research on the behaviour of odonates and butterflies aiming to clarify whether the two prerequisites of wars of attrition are fulfilled: (1) contestants can inflict substantial costs on nondisplaying opponents and (2) contestants can discriminate the sex of flying conspecifics. In odonates, we found an abundance of evidence suggesting that contests involve physical attack and that the ability of sexual discrimination is sufficient. Therefore, wars of attrition may occur in territorial odonates. In butterflies, however, we could not find any evidence that the two prerequisites are filled. The aerial interactions of butterflies are better interpreted as courtship between sexually active males (the erroneous courtship hypothesis). Based on these results, we discuss future directions of research on the aerial contests of flying insects.     

Better to be bimodal: the interaction of color and odor on learning and memory

Defended prey frequently advertise to potential predators usingmultimodal warning displays. Signaling through more than onesensory pathway may enhance the rate of avoidance learning andthe memorability of these learned avoidances. If this is so,then mimetic insects would gain more protection from mimickinga multimodal rather than a monomodal model. Day-old domesticchicks (Gallus gallus domesticus) were used to examine whethera common insect warning odor (pyrazine) enhanced learning andmemorability of yellow prey, a common warning color. Pyrazineincreased the rate at which the chicks learned to avoid unpalatableyellow prey, and how well this learned avoidance was rememberedafter a 96-h interval. After 96 h, mimics of the multimodalprey were avoided, whereas mimics of the monomodal prey werenot. In the absence of pyrazine, chicks generalized their learnedavoidance of the unpalatable yellow prey to palatable greenprey; however, the presence of pyrazine reduced this color generalization.These results suggest that much is to be gained from signalingmultimodally, for both models and mimetic prey species. Thepresence of multimodal prey in the habitat may also advantagethe predators as it allows it them to distinguish more easilybetween palatable and unpalatable prey.     

Division of labour and social insect colony performance in relation to task and mating number under two alternative response threshold models

Some social insects exhibit an exceptionally high degree of polyandry. Alternative hypotheses exist to explain the benefits of multiple mating through enhanced colony performance. This study critically extends theoretical analyses of the hypothesis that enhanced division of labour confers fitness benefits to the queen that are sufficient to explain the observed mating frequencies of social insects. The effects of widely varying numbers of tasks and matings were systematically investigated in two alternative computer simulation models. One model was based on tasks that have to be performed to maintain an optimal trait value, while the other model was based on tasks that only have to be sufficiently performed to exceed a minimum trait value to confer full fitness returns. Both model versions were evaluated assuming a broad and a narrow response threshold distribution. The results consistently suggest a beneficial effect of multiple mating on colony performance, albeit with quickly diminishing returns. An increasing number of tasks decreased performance of colonies with few patrilines but not of more genetically diverse colonies. Instead, a performance maximum was found for intermediate task numbers. The results from the two model versions and two response threshold distributions did not fundamentally differ, suggesting that the type of tasks and the breadth of response thresholds do not affect the benefit of multiple mating. In general, our results corroborate previous models that have evaluated simpler task/patriline scenarios. Furthermore, selection for an intermediate number of tasks is indicated that could constrain the degree of division of labour. We conclude that enhanced division of labour may have favoured the evolution of multiple mating but is insufficient to explain the extreme mating numbers observed in some social insects, even in complex task scenarios.     

Ecological validity of social interaction tests in rats and mice

Different rat and mouse models are used in studies of social interactions. Simple behavioral measures, which are commonly used in the laboratory, allow to perform relatively short experiments and to use multiple brain manipulation techniques. However, too much focus on the simplest behavioral models generates a serious risk of reducing ecological validity or even studying phenomena which would never happen outside of the laboratory. In this review, we discuss the suitability of mice and rats as model organisms for studying social behaviors, with focus on social transmission of fear paradigms. First, we briefly introduce the concept of domestication and what impact it had on laboratory rodents. Then, we present two aspects of social behaviors, sociability and dominance, which are crucial for social organization in these species. Finally, we present experimental models used for studying how animals transmit information about danger between each other, and how these models may reflect what happens in the natural environment. We discuss the difficulties that arise from our limited knowledge of rat and mouse ecology, especially their social life. We also explore the subject of balancing ecological validity and controllability in rodent models of social behaviors, the latter being particularly important for studying brain activity. Although it is very challenging, an efficient program for social neuroscience research should, in our opinion, aim at bridging the gap between laboratory and field studies.     

Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.     

Are footprint tracking tunnels suitable for monitoring giant weta (Orthoptera: Anostostomatidae)? Abundance,distribution and movement in relation to tracking rates

Appropriate monitoring tools are essential for assessing the effectiveness of management for all threatened insect taxa. In New Zealand the large-bodied flightless orthopterans in the genus Deinacrida have mostly been monitored by searching through habitat during the day or spotlighting at night but this is time consuming and the results depend on the skill of the searcher. Recently, footprint tracking tunnels, similar to those used for monitoring small mammals in New Zealand, were found to be effective for detecting adults of various giant weta species. In this study, we compared the abundance of Cook Strait giant weta (CSGW) in the vicinity of the tunnels, estimated by mark-recapture, with the number of tracking tunnels tracked by weta. We found strong indications that both baited and unbaited tracking tunnels can be used to estimate the number of adult weta present but that this probably depends on their responses to meteorological conditions which are not yet understood. Our results also show that footprint tracking tunnels are more effective for detecting adult CSGW than searching for these insects at night and that baiting tracking tunnels with peanut butter increases their effectiveness for detecting adult CSGW. We confirmed how far Cook Strait giant weta moved each night on Matiu-Somes Island by attaching transmitters to them and found that day roosts of three adult males were on average 8.6 m apart each day and those of adult females were on average 21.3 m apart. Both the low recapture rates of marked adult CSGW and the nightly displacements of those with transmitters suggest that adult CSGW show no site fidelity and are clearly capable of moving large distances each night. However, an individual weta is unlikely to track more than one tunnel per night if tunnels are 30 m apart. Tracking tunnels have the potential to be used with some other insects, provided their footprints are diagnostic. An advantage of using tracking tunnels is that they are non-lethal and would therefore be particularly suitable for monitoring other large threatened insect taxa.     

Age and size at maturity: A quantitative review of diet‐induced reaction norms in insects

Optimality models predict that diet‐induced bivariate reaction norms for age and size at maturity can have diverse shapes, with the slope varying from negative to positive. To evaluate these predictions, we perform a quantitative review of relevant data, using a literature‐derived database of body sizes and development times for over 200 insect species. We show that bivariate reaction norms with a negative slope prevail in nearly all taxonomic and ecological categories of insects as well as in some other ectotherm taxa with comparable life histories (arachnids and amphibians). In insects, positive slopes are largely limited to species, which feed on discrete resource items, parasitoids in particular. By contrast, with virtually no meaningful exceptions, herbivorous and predatory insects display reaction norms with a negative slope. This is consistent with the idea that predictable resource depletion, a scenario selecting for positively sloped reaction norms, is not frequent for these insects. Another source of such selection—a positive correlation between resource levels and juvenile mortality rates—should similarly be rare among insects. Positive slopes can also be predicted by models which integrate life‐history evolution and population dynamics. As bottom‐up regulation is not common in most insect groups, such models may not be most appropriate for insects.     

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

Summary We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.     

Use, misuse and extensions of "ideal gas" models of animal encounter

Biologists have repeatedly rediscovered classical models from physics predicting collision rates in an ideal gas. These models, and their two-dimensional analogues, have been used to predict rates and durations of encounters among animals or social groups that move randomly and independently, given population density, velocity, and distance at which an encounter occurs. They have helped to separate cases of mixed-species association based on behavioural attraction from those that simply reflect high population densities, and to detect cases of attraction or avoidance among conspecifics. They have been used to estimate the impact of population density, speeds of movement and size on rates of encounter between members of the opposite sex, between gametes, between predators and prey, and between observers and the individuals that they are counting. One limitation of published models has been that they predict rates of encounter, but give no means of determining whether observations differ significantly from predictions. Another uncertainty is the robustness of the predictions when animal movements deviate from the model's assumptions in specific, biologically relevant ways. Here, we review applications of the ideal gas model, derive extensions of the model to cover some more realistic movement patterns, correct several errors that have arisen in the literature, and show how to generate confidence limits for expected rates of encounter among independently moving individuals. We illustrate these results using data from mangabey monkeys originally used along with the ideal gas model to argue that groups avoid each other. Although agent-based simulations provide a more flexible alternative approach, the ideal gas model remains both a valuable null model and a useful, less onerous, approximation to biological reality.     

Spatial patterns and coexistence mechanisms in systems with unidirectional flow

River ecosystems are the prime example of environments where unidirectional flow influences the dispersal of individuals. Spatial patterns of community composition and species replacement emerge from complex interplays of hydrological, geochemical, biological, and ecological factors. Local processes affecting algal dynamics are well understood, but a mechanistic basis for large scale emerging patterns is lacking. To understand how these patterns could emerge in rivers, we analyze a reaction-advection-diffusion model for two competitors in heterogeneous environments. The model supports waves that invade upstream up to a well-defined "upstream invasion limit". We discuss how these waves are produced and present their key properties. We suggest that patterns of species replacement and coexistence along spatial axes reflect stalled waves, produced from diffusion, advection, and species interactions. Emergent spatial scales are plausible given parameter estimates for periphyton. Our results apply to other systems with unidirectional flow such as prevailing winds or climate-change scenarios.     

The East Indian Diaspora in Costa Rica: Inbreeding Avoidance, Marriage Patterns, and Cultural Survival

Anthropologists have long been interested in the survival of Indian cultural traits in the New World. In this article, we present results of an ongoing project with a Costa Rican community that descends from East Indian indentured servants. We focus on the group's marriage patterns and how these patterns might have helped keep the community as a cohesive ethnic group. We investigate the group's level of inbreeding by computing the inbreeding coefficient using two different methods. We show that the community has been successful at keeping its inbreeding low, despite its small size, by allowing marriage with nonmembers of the community. We propose that unless consanguineous marriages are allowed virtually all of the community's marriages will be with noncommunity members. Absorption into tourism, as well as the community's staunch avoidance of consanguineous marriages and virtually universal marriage with noncommunity members, will likely contribute to their disappearance as a viable ethnic group.