Neural correlates of contrast detection at threshold

Human psychophysical studies have demonstrated that, for stimuli near the threshold of visibility, detection of motion in one direction is unaffected by the superimposition of motion in the opposite direction. To investigate the neural basis for this perceptual phenomenon, we recorded from directionally selective neurons in macaque visual area MT (middle temporal visual area). Contrast thresholds obtained for single gratings moving in a neuron's preferred direction were compared with those obtained for motion presented simultaneously in the neuron's preferred and antipreferred directions. A simple model based on probability summation between neurons tuned to opposite directions could sufficiently account for contrast thresholds revealed psychophysically, suggesting that area MT is likely to provide the neural basis for contrast detection of stimuli modulated in time.     

Reappraising Social Insect Behavior through Aversive Responsiveness and Learning

Background

The success of social insects can be in part attributed to their division of labor, which has been explained by a response threshold model. This model posits that individuals differ in their response thresholds to task-associated stimuli, so that individuals with lower thresholds specialize in this task. This model is at odds with findings on honeybee behavior as nectar and pollen foragers exhibit different responsiveness to sucrose, with nectar foragers having higher response thresholds to sucrose concentration. Moreover, it has been suggested that sucrose responsiveness correlates with responsiveness to most if not all other stimuli. If this is the case, explaining task specialization and the origins of division of labor on the basis of differences in response thresholds is difficult.

Methodology

To compare responsiveness to stimuli presenting clear-cut differences in hedonic value and behavioral contexts, we measured appetitive and aversive responsiveness in the same bees in the laboratory. We quantified proboscis extension responses to increasing sucrose concentrations and sting extension responses to electric shocks of increasing voltage. We analyzed the relationship between aversive responsiveness and aversive olfactory conditioning of the sting extension reflex, and determined how this relationship relates to division of labor.

Principal Findings

Sucrose and shock responsiveness measured in the same bees did not correlate, thus suggesting that they correspond to independent behavioral syndromes, a foraging and a defensive one. Bees which were more responsive to shock learned and memorized better aversive associations. Finally, guards were less responsive than nectar foragers to electric shocks, exhibiting higher tolerance to low voltage shocks. Consequently, foragers, which are more sensitive, were the ones learning and memorizing better in aversive conditioning.

Conclusions

Our results constitute the first integrative study on how aversive responsiveness affects learning, memory and social organization in honeybees. We suggest that parallel behavioral modules (e.g. appetitive, aversive) coexist within each individual bee and determine its tendency to adopt a given task. This conclusion, which is at odds with a simple threshold model, should open new opportunities for exploring the division of labor in social insects.     

Quantitative predictions for patch occupancy of capercaillie in fragmented habitats

A major conclusion of studying metapopulation biology is that species conservation should favor regional rather than local population persistence. Regional persistence is tightly linked to size, spatial configuration and quality of habitat patches. Hence it is important for the management of endangered species that priority patches can be identified. We developed a predictive model of patch occupancy by capercaillie, a threatened grouse species, based on a single snapshot of data. We used logistic regression to predict patch occupancy as a function of patch size, isolation, connectivity, relative altitude, and biogeographical area. The probability of a patch being occupied increased with patch size and increasing altitude, and decreased with increasing distance to the next occupied patch. Patch size was the most important predictor although occupied patches varied considerably in size. Our model only uses data on the number, size and spatial configuration of habitat patches. It is a useful tool to designate priority areas for conservation, i.e. large core patches with high resilience in habitat quality, smaller island‐patches that still have high probability of being inhabited or becoming recolonised, and patches functioning as “stepping stones”. If capercaillie is to be preserved, habitat suitability needs to be maintained in a functional network of patches that account for size and inter‐patch distance thresholds as found in this study. We suggest that similar area‐isolation relationships are valid for almost any region within the distribution range of capercaillie. The thresholds for occupancy are however likely to depend on characteristics of the respective landscape. The outcome of our study emphasises the need for future investigations that explore the relationship between patch occupancy, matrix quality and its resistance to dispersing individuals.     

A feature-based neurocomputational model of semantic memory

According with a featural organization of semantic memory, this work is aimed at investigating, through an attractor network, the role of different kinds of features in the representation of concepts, both in normal and neurodegenerative conditions. We implemented new synaptic learning rules in order to take into account the role of partially shared features and of distinctive features with different saliency. The model includes semantic and lexical layers, coding, respectively for object features and word-forms. Connections among nodes are strongly asymmetrical. To account for the feature saliency, asymmetrical synapses were created using Hebbian rules of potentiation and depotentiation, setting different pre-synaptic and post-synaptic thresholds. A variable post-synaptic threshold, which automatically changed to reflect the feature frequency in different concepts (i.e., how many concepts share a feature), was used to account for partially shared features. The trained network solved naming tasks and word recognition tasks very well, exploiting the different role of salient versus marginal features in concept identification. In the case of damage, superordinate concepts were preserved better than the subordinate ones. Interestingly, the degradation of salient features, but not of marginal ones, prevented object identification. The model suggests that Hebbian rules, with adjustable post-synaptic thresholds, can provide a reliable semantic representation of objects exploiting the statistics of input features.     

Ants in a labyrinth: a statistical mechanics approach to the division of labour

Division of labour (DoL) is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic) interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.     

The differential infectivity and staged progression models for the transmission of HIV

Recent studies of HIV RNA in infected individuals show that viral levels vary widely between individuals and within the same individual over time. Individuals with higher viral loads during the chronic phase tend to develop AIDS more rapidly. If RNA levels are correlated with infectiousness, these variations explain puzzling results from HIV transmission studies and suggest that a small subset of infected people may be responsible for a disproportionate number of infections. We use two simple models to study the impact of variations in infectiousness. In the first model, we account for different levels of virus between individuals during the chronic phase of infection, and the increase in the average time from infection to AIDS that goes along with a decreased viral load. The second model follows the more standard hypothesis that infected individuals progress through a series of infection stages, with the infectiousness of a person depending upon his current disease stage. We derive and compare threshold conditions for the two models and find explicit formulas of their endemic equilibria. We show that formulas for both models can be put into a standard form, which allows for a clear interpretation. We define the relative impact of each group as the fraction of infections being caused by that group. We use these formulas and numerical simulations to examine the relative importance of different stages of infection and different chronic levels of virus to the spreading of the disease. The acute stage and the most infectious group both appear to have a disproportionate effect, especially on the early epidemic. Contact tracing to identify super-spreaders and alertness to the symptoms of acute HIV infection may both be needed to contain this epidemic.     

The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes’ thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. We demonstrate that for a given size of the initiator set, there is a specific variance of the threshold distribution for which an opinion spreads optimally. Furthermore, in the case of synthetic graphs we show that the spread asymptotically becomes independent of the system size, and that global cascades can arise just by the addition of a single node to the initiator set.     

Evolution of equal division among unequal partners

One of the hallmarks of human fairness is its insensitivity to power: although strong individuals are often in a position to coerce weak individuals, fairness requires them to share the benefits of cooperation equally. The existence of such egalitarianism is poorly explained by current evolutionary models. We present a model based on cooperation and partner choice that can account for the emergence of a psychological disposition toward fairness, whatever the balance of power between the cooperative partners. We model the evolution of the division of a benefit in an interaction similar to an ultimatum game, in a population made up of individuals of variable strength. The model shows that strong individuals will not receive any advantage from their strength, instead having to share the benefits of cooperation equally with weak individuals at the evolutionary equilibrium, a result that is robust to variations in population size and the proportion of weak individuals. We discuss how this model suggests an explanation for why egalitarian behaviors toward everyone, including the weak, should be more likely to evolve in humans than in any other species.     

A theoretical model of shoaling behavior based on a consideration of patterns of overlap among the visual fields of individual members

We propose a hypothetical visual field overlap (VFO) model for shoaling behavior. While solitary individuals have the disadvantage of a substantial blind zone to their rear, the overlapping visual fields among shoal members allows the shoal to collectively view nearly 360°. A highly polarized shoal (i.e., a school) would be less advantageous than randomly oriented shoals because a substantial area blind to all school members (common blind zone) would occur at some distance behind the school. However, in situations where fishes must orient in one direction, the visual fields of individuals in the school overlap such that the common blind zone is considerably farther behind than the blind zone of any particular fish. A simple geometric relationship between school width, the blind angle, and the distance to the common blind zone predicts that larger schools can detect predators at a greater distance than smaller schools. Additionally, the model provides a novel explanation for the nearly universally observed tendency for fish to school together with like-sized individuals. Finally, the effect of school shape on the visual field overlap pattern would have a strong impact on predator–prey interactions. However, our model does not directly take into account the range of visibility or social interaction affects and applies only to small groups. The VFO model suggests that schooling may have arisen as an adaptation to enhance feeding efficiency by reducing the need for individual vigilant behavior while oriented into the current for feeding. We believe the VFO model promises to provide insight into the behavioral ecology of shoaling fishes and that it is highly amenable to both field and laboratory testing.     

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

Self-amplification as a source of interindividual variability: Shelter selection in cockroaches

Although group effect and collective decisions have been described in many insect species, the behavioral mechanisms involved in the process remain poorly documented at the individual level. We examined how individual behavior depends on the environmental context and we precisely characterized the behavioral rules leading to settlement of individual cockroaches in resting site. We focused on the spatial and temporal distribution of individuals in absence of conspecifics. Using isolated adult males of the cockroach Periplaneta americana, we showed that the quality of resting sites and the duration of the settlement exerted an influence on the individual decision-making: the probability of leaving a resting site decreased with the time spent under a shelter. A numerical model derived from experimental data suggested that this simple rule of self-amplification can also account for the interindividual variability.     

A Systems Model Approach to Determining Resilience Surrogates for Case Studies

Resilience theory offers a framework for understanding the dynamics of complex systems. However, operationalizing resilience theory to develop and test empirical hypotheses can be difficult. We present a method in which simple systems models are used as a framework to identify resilience surrogates for case studies. The process of constructing a systems model for a particular case offers a path for identifying important variables related to system resilience, including the slowly-changing variables and thresholds that often are keys to understanding the resilience of a system. We develop a four-step process for identifying resilience surrogates through development of systems models. Because systems model development is often a difficult step, we summarize four basic existing systems models and give examples of how each may be used to identify resilience surrogates. The construction and analysis of simple systems models provides a useful basis for guiding and directing the selection of surrogate variables that will offer appropriate empirical measures of resilience.     

Evidence of a novel reproductive tactic in female kokanee Oncorhynchus nerka

Body composition analysis confirmed that egg development and reproductive senescence were delayed in silver female kokanee Oncorhynchus nerka (a small proportion of female kokanee exhibit extreme prespawning waiting and are called 'silvers' because of their colouration) relative to that of red female kokanee (most female kokanee exhibit this 'normal' phenology and are called 'reds'). Silver females were also smaller and younger than red females. A simple life-history model with two size thresholds is proposed to account for the observed body size and age differences. Adoption of the silver tactic by small females is proposed as a means to minimize intrasexual competition.     

Museum collections, species distributions, and rarefaction

Biological specimens in museums and herbaria are sometimes used to compare the geographical distribution of different species. In doing so, it is necessary to account for differences in the numbers of specimens. We show how rarefaction can be used for this purpose. Rarefaction is a simple mathematical method originally designed to compare species richness in communities that differed in the number of sampled individuals. We present an example involving two Phragmipedium orchid species. In this case, rarefaction suggests that the apparent difference in range can be explained by the difference in the numbers of specimens.     

Developmental thresholds and the evolution of reaction norms for age and size at life-history transitions

It is quite common in studies of life-history plasticity to find a negative relationship between the age at which various life-history transitions occur and the growth conditions under which individuals develop. In particular, high growth typically results in earlier transitions, often at a larger size. Here, we use a relatively general optimization model for age and size at life-history transitions to argue that current life-history theory cannot adequately explain these results. Specifically, most such theory requires key assumptions that are unlikely to be generally met. This suggests that some important component of the biology of many organisms must be missing from many of the models in life-history theory. We suggest that this missing component might be the phenomenon of developmental thresholds. There are at least two different types of developmental thresholds possible, and we incorporate these into our general optimality model to demonstrate how they can cause a negative relationship between growth conditions and age at a transition. If developmental thresholds are common throughout taxa, then this might explain the empirical results. Our model formulation and analysis also formalizes the popular Wilbur-Collins hypothesis for age and size at metamorphosis in amphibians. The results demonstrate that optimal combinations of age and size, and the slope of the reaction norm connecting them, depend on the existence and type of threshold assumed. Our results also provide an evolutionary framework that can be used to view the data and many of the proximate submodels derived from the Wilbur-Collins hypothesis.     

Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Extracellular local field potentials are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of extracellular local field potentials, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is nonhomogeneous, there is induction of nonhomogeneous charge densities that may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na(+)-mediated action potentials) attenuate very steeply with distance, whereas slower (K(+)-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.     

A simple and efficient algorithm for genome‐wide homozygosity analysis in disease

Here we propose a simple statistical algorithm for rapidly scoring loci associated with disease or traits due to recessive mutations or deletions using genome‐wide single nucleotide polymorphism genotyping case–control data in unrelated individuals. This algorithm identifies loci by defining homozygous segments of the genome present at significantly different frequencies between cases and controls. We found that false positive loci could be effectively removed from the output of this procedure by applying different physical size thresholds for the homozygous segments. This procedure is then conducted iteratively using random sub‐datasets until the number of selected loci converges. We demonstrate this method in a publicly available data set for Alzheimer's disease and identify 26 candidate risk loci in the 22 autosomes. In this data set, these loci can explain 75% of the genetic risk variability of the disease.     

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e. all individuals behave in the same way. In this work, we shall take into account different tactics that predators can use for exploiting a common self-reproducing resource, the prey population. Predators fight together in order to keep or to have access to captured prey individuals. Individual predators can use two behavioural tactics when they encounter to dispute a prey, the classical hawk and dove tactics. We assume two different time scales. The fast time scale corresponds to the inter-specific searching and handling for the prey by the predators and the intra-specific fighting between the predators. The slow time scale corresponds to the (logistic) growth of the prey population and mortality of the predator. We take advantage of the two time scales to reduce the dimension of the model and to obtain an aggregated model that describes the dynamics of the total predator and prey densities at the slow time scale. We present the bifurcation analysis of the model and the effects of the different predator tactics on persistence and stability of the prey-predator community are discussed.     

Epidemiological models with prevalence dependent endogenous self-protection measure

A simple mathematical model for human disease epidemics that takes the human learning behaviour and self-protective measures into account is proposed and investigated. We have analysed the effect of endogenous self-protective measures with respect to the prevalence level of the disease and conversely. In the model it is assumed that people start reacting against contracting a disease with self-protective measures whenever they are informed about the disease and when the burden of the disease is in a recognizable stage. It is shown that increasing the average effectiveness of self-protective measures is more important in decreasing the prevalence of a disease than increasing the proportion of individuals in a population into which awareness is created.     

Active linking in evolutionary games

In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favour cooperation over defection.