Workshop 7: Systems Biology of Decision Making

(June 16,2008 - June 20,2008 )

Organizers


Nigel Franks
School of Biological Sciences, University of Bristol
Naomi Leonard
Mechanical and Aerospace Engineering, Princeton University
Kevin Passino
MBI - Long Term Visitor, The Ohio State University
Roger Ratcliff
Psychology, The Ohio State University
Thomas Seeley
Department of Neurobiology and Behavior, Cornell University
Thomas Waite
EEOB, The Ohio State University

Experimental biology is uncovering the mechanisms supporting decision-making in individual animals (e.g., in monkeys) and social animal groups (e.g., bees and ants). Multiscale mathematical models are being developed and validated for several species, including those for the (i) neuron-to-behavioral levels in cognitive neuroscience (e.g., diffusion or decision field theory models), (ii) organism-to-group levels for social insects (e.g., differential equations and individual-oriented models), and (iii) individual/group-to-ecological levels in behavioral ecology (e.g., optimization or evolutionary game-theoretic models). Several of these models and species share common features; hence there exists significant opportunities for cross-fertilization and progress toward an understanding mechanisms and whole-system emergent properties. Mathematical, statistical, and computational analyses are being to used to study (i) properties of the dynamics of decision making (e.g., feedback mechanisms, coupling, stability, and speed-accuracy trade-offs), (ii) cross-scale effects (e.g., impact of massively parallel mechanisms at one level on emergence of choice discrimination or distractor elimination abilities at a higher level), (iii) effects of context (e.g., similarity and attractivity effects), and (iv) Darwinian evolution of robustness or reliability in the presence of uncertainty (e.g., isolated failures at one level and environmental variations). The goal of this workshop is to facilitate the development of an integrated "systems biology" of decision-making processes that spans multiple spatio-temporal scales and levels of biological organization, and accounts for the perspectives of biologists, psychologists, economists, mathematicians, and engineers.

Accepted Speakers

Melissa Bateson
Centre for Behaviour and Evolution, University of Newcastle
Nick Britton
Department of Mathematical Sciences, University of Bath
Iain Couzin
Department of Ecology & Evolutionary Biology, Princeton University
Sophie Deneve
Group for Neural Theory, Collège de France
Jochen Ditterich
Center for Neuroscience, University of California, Davis
Nigel Franks
School of Biological Sciences, University of Bristol
Luc-Alain Giraldeau
Département of Biological Sciences, UQAM
Hauke Heekeren
Neurocognition of Decision Making Group, Berlin Neuroimaging Center & Max-Planck-Institute for Human Development
Philip Holmes
Mechanical & Aerospace Engineering and Program in Applied & Computational Mathematics, Princeton University
Naomi Leonard
Mechanical and Aerospace Engineering, Princeton University
James Marshall
Computer Science, University of Bristol
William Newsome
Department of Neurobiology, Stanford University
Stephen Pratt
School of Life Sciences, Arizona State University
Roger Ratcliff
Psychology, The Ohio State University
Jeffrey Schall
Department of Psychology, Vanderbilt University
Thomas Seeley
Department of Neurobiology and Behavior, Cornell University
David Stephens
Ecology, Evolution & Behavior, University of Minnesota
Marius Usher
School of Psychology, University of London
Thomas Waite
EEOB, The Ohio State University
Monday, June 16, 2008
Time Session
09:00 AM
10:00 AM
Roger Ratcliff - Modeling Simple Decision Processes with Applications to EEG, Aging, and Sleep Deprivation

I will talk about 2-3 topics in simple decision making. I will first briefly introduce the diffusion model for simple decision making and note that it can account for correct and error RT distributions as well as accuracy. Then I will show that an EEG measure indexes trial by trial variability in drift rate in the model. I will then show interpretations of the effects of age and sleep deprivation on performance in terms of an analysis based on the model. If time permits I will show how the model can uncover the main individual differences on speed of processing in simple two choice tasks such as recognition memory and word identification.



 
10:30 AM
11:30 AM
Philip Holmes - Stochastic models for individual decisions and social influence in groups

I will describe two modeling studies: of an individual stimulus identification task, and of a gambling task performed individually and with group feedback. In the first we model accuracy in a two-alternative forced-choice task with cued responses using an Onstein-Uhlenbeck reduction of a leaky competing accumulator model. This provides explicit predictions of psychometric functions, which we fit to data from monkeys performing a motion discrimination task. We then compute optimal (reward maximizing) strategies when reward magnitudes for the alternatives differ, and assess the abilities of individuals to achieve them. In the second study we extend a probabilistic model developed to account for individual choices on matching shoulders and rising optimum gambling tasks by Egelman, Montague, et al., to predict choice patterns in a group context. The model is equivalent to a drift diffusion (DD) process driven by the difference in predicted rewards for two alternatives, based on reward feedback and temporal difference learning. We couple multiple DD processes by incorporating influences from the choices and/or rewards earned by other players in the group. We fit this model to data from human subjects playing a two-armed bandit game, singly and in groups, and with various types of feedback on their own and other group members' rewards and choices.


The modeling work was done with Sam Feng (study 1) and Andrea Nedic, Jonathan Cohen and Deborah Prentice (study 2). Experimental data was collected and provided by Alan Rorie and Bill Newsome (study 1), and Damon Tomlin (study 2), who also advised on the modeling. Support was provided by AFOSR under the 2007 MURI Programs 15 and 16.

01:30 PM
02:30 PM
Hauke Heekeren - A Multi-level Perspective on the Neurocognition of Decision Making

There is a long history of decision-making research in psychology and economics that has resulted in the development of formal models of behavior, which are inspired by behavioral data or the computational demands of a task. However, cognitive functions such as decision making cannot be completely understood on the basis of mathematical models and behavioral data alone; we have to investigate how mental (cognitive) and neuronal processes map onto each other. We investigate decision making in different domains. First, at the basis of a number of different decisions we are facing in everyday-life stands perceptual decision making. I will discuss how we may use stochastic diffusion models in combination with brain imaging to investigate perceptual decision making. Second, many of our decisions are influenced by the potential outcomes associated with different options. Specifically, I will discuss how dopaminergic neuromodulation (COMT-genotype, aging) affects reward-based decision making.

03:00 PM
04:00 PM
Sophie Deneve - Bayesian decision with spiking neurons

N/A

Tuesday, June 17, 2008
Time Session
09:00 AM
10:00 AM
Jeffrey Schall - Actions, reasons, neurons, and causes

Movements of inanimate objects explained by external forces referred to as causes. In contrast, many movements of humans are described as actions directed toward a goal for a reason. A purposeful action (a wink) is distinguished from a mere event (a blink) by reference to some intelligible plan because actions are performed to achieve a goal. In other words, actions have reasons ("I did it for..."), but events just have causes ("It happened because..."). Reasons for actions are explanations in terms of purposes, goals and beliefs. But if all actions are really caused by just neurons firing and muscles contracting, then how can there be any reasons for actions? This presentation will seek to articulate how intentional reasons can be reconciled with neural causes. The answer will emphasize the many-to-one mapping of neural activity onto behavior and cognition so that if a given action can arise from different brain states, then the relationship of the behavior to an intention holds in virtue of the content of the representation of the intention and not its neural realization as such. Thus, a movement can be called an intentional action if and only if it originates from a cognitive state with meaningful content, and this content defines the cognitive state's causal influence. But this analysis depends on whether the brain knows what it means to do. In fact, recent cognitive neuroscience research has described particular brain circuits that register errors and success. Such signals can be used to adjust behavior and provide the basis for distinguishing "I did" from "it happened" which is just what is needed to feel like we are acting with freedom and responsible power.

10:30 AM
11:30 AM
Jochen Ditterich - The use of multidimensional stimuli in multi-alternative perceptual decision tasks: A tool for decoupling speed and accuracy and for exploring the effect of changes in the sensory noise level

While first theoretical attempts have been made to study possible decision making mechanisms underlying choices between multiple alternatives, most behavioral and neurophysiological studies have so far focused on choices between two alternatives. The available data sets from choice experiments between multiple alternatives are largely not quantitative enough to address the underlying computational mechanism. The 2AFC version of the random dot motion direction discrimination task has been very helpful in advancing our understanding of the neural and computational mechanisms underlying choices between two alternatives.


Here we present behavioral data from a new version of the random dot motion discrimination task. Subjects are presented with a random dot stimulus containing up to three coherent motion components with different directions. They are asked to pick the dominant direction of motion out of three alternatives. The viewing duration is controlled by the subjects (reaction time task). Response times (RTs) and the subject's choice are measured. The advantage of this task is that it provides the experimenter with full control over the sensory evidence provided for each of the alternatives.


In the 2AFC version of the task both the behavioral as well as neurophysiological data recorded from the parietal cortex of monkeys performing the task could be explained by a computational model based on the idea of a race to threshold between two integrators accumulating the net sensory evidence for a particular choice. Here we show that the behavioral data (probabilities of particular choices as well as RT distributions) from our new 3-choice task are quite well explained by a computational model assuming a race to threshold between three integrators, one for each alternative. Each integrator accumulates the net sensory evidence for a particular alternative. The net sensory evidences are calculated as linear combinations of the activities of three relevant pools of sensory neurons with a positive weight assigned to the pool providing evidence for a particular choice and negative weights assigned to the pools providing evidence against a particular choice.


Previous 2AFC tasks have usually manipulated one stimulus strength parameter, resulting in monotonic relationships between stimulus strength and accuracy and between stimulus strength and mean RT. In these tasks, mean RT is usually also a monotonic function of accuracy. I will demonstrate how the multidimensional stimuli allow us to eliminate this tight coupling between speed and accuracy. Furthermore, in previous diffusion models of binary decision making it has often been assumed that the overall noise level in the decision circuitry stays constant and only the drift rate is affected by changing stimulus strength. I will highlight some aspects of our data set, which suggest that taking changes in the noise level of the sensory representation into account is essential for being able to explain our experimental findings.

01:30 PM
02:30 PM
William Newsome - Considering the evidence: integration of sensory and reward information for informing behavioral decisions

A generally useful decision mechanism must include a stage at which information from very disparate sources (i.e. sensory, reward, priors, etc) can be cast into a common neural currency for establishing the likelihood of one choice vs. the other. In monkeys, the lateral intraparietal area is thought to play such a role in oculomotor decisions, and past studies have indeed produced evidence for neural decision variables in LIP originating from sensory input (e.g. stimulus motion) or from economic value (reward size or probability). But no study has determined whether disparate signals are actually integrated in LIP, what the weights of the disparate signals are at the single cell level, and whether the relative weights at the neural level matches the relative weights inferred from behavior. Alan Rorie, a graduate student in my lab, and I addressed these questions by training monkeys on a choice paradigm in which sensory information about visual motion must be combined with information about reward size to make optimal choices. We show for the first time that sensory and reward signals are combined in single neuron activity in LIP, and that the relative magnitude of their influence at the population level matches their influence at the behavioral level. The data provide quantitative support for the notion that LIP activity reflects a high level of processing in which information from disparate sources are cast into a common neural currency for guiding oculomotor choices.

03:00 PM
04:00 PM
Marius Usher - Contrasting neurocomputational models of perceptual choice

A number of neurocomputational models have been proposed to account for the algorithm used by the brain to make decisions when faced with ambiguous information. In this talk I examine shared and diverging assumptions that these models make in accounting for choice patterns. For example, I examine the need to assume an integration over noisy samples during stimulus presentation, the existence of competition (or lateral inhibition) between choice alternatives and the assumption that a response criterion is used even in non-speeded judgments (making the impact of early evidence more strongly weighted). Preliminary data on choice tasks that manipulate the time-course of the information flow will be presented examining the models' predictions. Finally, I discuss how these models can be used to account for judgments of confidence, and for the fact that observers have the metacognitive ability to judge incorrect responses as less confident.


Work done in collaboration with Eddy J. Davelaar.

05:30 PM
06:30 PM
Thomas Seeley - Real democracy: how honey bees choose a home

Real democracy - when citizens meet in a face-to-face assembly and bind themselves under decisions they make themselves - has been practiced for some 2500 years by humans, but for more than 20 million years by honey bees. We will examine the remarkable democratic decision-making process of a honey bee swarm as it chooses a new home. We will see that bees have evolved sophisticated ways of working together to identify a dozen or more potential dwelling places, to choose the highest quality one for their new home site, and to make a decision without undue delay. We will conclude with some take-home lessons from the bees ("swarm smarts") on how to foster good decision making by democratic groups of humans.

Wednesday, June 18, 2008
Time Session
10:30 AM
11:30 AM
David Stephens - Impulsivity, Discounting, and Ecological Rationality with comments on four basic problems in animal decision-making

Experimental studies show that animals have strong preferences for immediacy. Specifically, experimental data suggest that animals make systematic errors by over-valuing small but immediate benefits, and under-valuing larger later consequences. Why would natural selection favor a mechanism that makes such a glaring error? One hypothesis is that these are not errors at all, because delay reduces or discounts the fitness value of benefits. A second hypothesis is that the 'impulsive' rules revealed by these experiments seldom lead to errors in natural situations. I call this the 'ecological rationality' hypothesis. My laboratory has developed this idea via experiments that compare the standard 'self-control' preparation to a more naturalistic choice preparation that attempts to mimic patch exploitation decisions. I review several of these experiments. We consistently find that subjects achieve higher levels of performance (e.g. higher long term intake rates) in our more naturalistic 'patch' situation, but many simple hypotheses (including the short-term rate model) fail to explain this difference. Finally, I will discuss four general problems in decision-making and how they emerge my groups studies of impulsivity. These are: 1) can we specify the relationship between learned and evolved solutions to behavioral problems; 2) how can we meaningfully integrate mechanistic and functional approaches to decision-making; 3) can we build a predictive theory of bounded rationality or is this fundamentally a post hoc approach; and 4) are animal decision mechanisms special tools for specific tasks or general mechanisms that apply across the broad, and how would we know?

01:30 PM
02:30 PM
Luc-Alain Giraldeau - Social Foraging Decisions: Evolution and the Plasticity Gambit

Many animals seek resources socially, that is under conditions where the pay-off of foraging strategies depends on the frequency of strategies present in the population. Here I present a brief overview of a number of social foraging decisions, many of which have yet to be studied empirically, focussing more on producer-scrounger decisions which have been the subject of several studies in my laboratory. As is typically done in behavioural ecology, I rely heavily on evolutionary modelling to derive predictions about behaviour. However, I will raise questions concerning what I call the "plasticity gambit", an implicit and untested (unfounded?) assumption that cognitive decision processes must ultimately provide individual foragers with the ability to make decisions in their everyday lives that match behaviour expected to have evolved over evolutionary time.

03:00 PM
04:00 PM
Melissa Bateson - The cognitive ecology of mate choice: individual decision mechanisms and group behaviour

Mate choice is the behavioural mechanism underlying sexual selection, and as such is of huge importance in evolutionary biology. Over the past 30 years research in behavioural ecology has provided lots of data about what traits animals prefer in their mates and why these preferences have evolved. Importantly, it is common for animals to attend to multiple different cues when making mating decisions because different cues may reveal different kinds of information about a potential mate. However, there has been much less attention given to the mechanisms of mate choice. How do animals integrate multiple sources of information about potential mates and compare the options available? Luckily similar problems have been considered in other areas of behavioural science, particularly studies of human decision making. One of my research aims for the past few years has been to try to bring together these different fields and ask whether the choice phenomena identified in human decision making also occur in animals faced with complex decisions. One general finding that is likely to be particularly important is that the choices we make are often dependent on the range of options on offer: our evaluations of options appear to be relative as opposed to absolute. In this talk I will describe some of the cognitive mechanisms that could be responsible for this context-dependency, and argue that on functional grounds similar mechanisms are likely to exist in animals. I will describe experiments from my lab on both human and bird mate choice designed to explore the possibility of context dependency. Finally, I will argue that context-dependency in mating decisions could have implications for the behaviour of animal groups that have not thus far been explored.

Thursday, June 19, 2008
Time Session
09:00 AM
10:00 AM
Thomas Seeley - Real democracy: how honey bees choose a home

Real democracy - when citizens meet in a face-to-face assembly and bind themselves under decisions they make themselves - has been practiced for some 2500 years by humans, but for more than 20 million years by honey bees. We will examine the remarkable democratic decision-making process of a honey bee swarm as it chooses a new home. We will see that bees have evolved sophisticated ways of working together to identify a dozen or more potential dwelling places, to choose the highest quality one for their new home site, and to make a decision without undue delay. We will conclude with some take-home lessons from the bees ("swarm smarts") on how to foster good decision making by democratic groups of humans.

10:30 AM
11:30 AM
Kevin Passino - Swarm Cognition in Honey Bees

Systems biology of decision making focuses on understanding the structures, dynamics, and evolution of complex interconnected biological mechanisms that support decision making by individuals and social animal groups. In this talk, an experimentally validated model of the nest-site selection process of honey bee swarms is introduced. In this spatially distributed dynamical feedback process individual bee actions and bee-to-bee communications combine to produce an emergent "consensus" nest choice. The process has connections to neurobiological cognition systems, especially at the behavioral level: the swarm can effectively discriminate between different quality nest sites and eliminate from consideration relatively inferior distractor sites. Simulations indicate that individual-level bee decision-making mechanisms have been tuned by natural selection to provide a balance between the need for fast and accurate decisions at the group level. For more information see: http://www.ece.osu.edu/~passino/

01:30 PM
02:30 PM
Iain Couzin - N/A

N/A

03:00 PM
04:00 PM
Naomi Leonard - Spatial Dynamics, Information Flow and Consensus in Fish Schools

Decision-making dynamics and spatial dynamics in fish schools are naturally coupled when individuals only sense locally. As relative positions of fish change, neighbors come and go and the flow of information varies; changes in information flow affect the dynamics of consensus and this in turn influences collective motion. I will describe a study of consensus dynamics for a school using a model that extends coupled oscillator dynamics to include spatial dynamics and represents changing information flow with time-varying graphs. We examine the case of periodically time-varying information flow, motivated by fish schooling data of I. Couzin and A. Kao, in which killifish exhibit oscillatory speed profiles and nearest neighbors anti-synchronize the phases of their speed oscillations. We explore the possible advantages for speed and accuracy in consensus dynamics and for increased density of spatial sampling.

Friday, June 20, 2008
Time Session
09:00 AM
10:00 AM
Nigel Franks - Individual and Collective Decision-Making in House Hunting Rock Ants

Social insects exhibit both individual and collective intelligence. I will illustrate this distributed decision-making with house hunting in rock ants. Each worker, among the 100 or so in a colony, has less than 100,000 neurones (compared to 1011 neurones in humans) yet these ants employ the most sophisticated of all consumer strategies when choosing a new nest. Indeed, they can choose the best-of-N among alternative nests even though each has many different and important attributes. I will show how information can cascade through these social networks enabling colonies to benefit from both individual and collective intelligence. They use quorum sensing to conjure up collective intelligence and to fashion flexible speed accuracy trade-offs. When these ants have achieved a quorum in the new nest they switch from forward tandem running, from the old to the new nest, to social carrying. In addition, they often employ reverse tandem runs from the new nest back to the old one. During tandem runs one leader literally teaches one follower the route between the two nests. I will show how reverse tandem runs can expedite emigrations when these ants have used low quorums in emergencies. Tandem runs seem to be useful even when they do not progress all of the way to the target. I will describe the behaviour of both leaders and followers when tandems break up and show that followers without leaders use L?vy-like searches. I will also describe very recent work, using RFID tags on all workers, that shows how they can choose a better nest that is 9 times further away than a collinear poor one. Certain ants act as consensus breakers to re-route the whole colony. Such ants lead disproportionately more tandem runs first to the poor nest and then onto the more distant better one. Such switchers may have better access to the information needed to make well informed comparisons. Finally, I suspect that these tiny ants have larger behavioural repertoires than many if not most vertebrates. This begs the question; what are big brains for?



 
10:30 AM
11:30 AM
Stephen Pratt - The interaction of group and individual decision-making during nest-site selection by ants

Social insects have special interest in the study of decision-making, because they make choices both as individuals and as collectives. I will describe how these levels interact in nest-site selection by Temnothorax ants. Individual ants follow a complex behavioral algorithm that allows a group of poorly informed individuals to collectively choose the best site, without any central control. This algorithm is based on quality-dependent positive feedback and a threshold response, two features of general importance to collective decision-making systems. Quantitative tuning of this algorithm allows colonies to emphasize either the speed or accuracy of decision-making. The algorithm hinges on attainment of a nestmate quorum that triggers full commitment to a particular option. A simple model derived from the study of vertebrate decision-making may explain how the quorum can be detected by the integration of encounter rates between ants. Recent work suggests that the concept of rationality may reveal more about the interaction of group and individual levels. Decision-makers are irrational when they fail to attach consistent values to options. For individuals, irrationality can reliably be obtained through several experimental paradigms involving options with multiple, conflicting attributes. Faced with one of these paradigms, Temnothorax colonies nonetheless show consistent preferences, suggesting that collective decision-making algorithms may filter out the effects of irrationality at the level of individual workers.

01:30 PM
02:30 PM
Nick Britton - Pheromone Trails and Ant Foraging Decisions

Pheromone trails are an important component of ant foraging behaviour. It has been known for a long time that ants lay pheromone trails to attract nest-mates to productive foraging sources, but it has recently become clear that at least some species use more complex pheromone signalling behaviour. We define positive and negative pheromones to be those laid after successful and unsuccessful foraging respectively, and attractive and repulsive pheromones to be those that encourage ants to follow a trail and deter them from it respectively. We might expect positive pheromones to be attractive, and negative pheromones to be repulsive. We address the following questions. Under what circumstances is it advantageous to use more than one pheromone? When are repulsive pheromones advantageous? When are long-term as well as short-term pheromones advantageous?



 
03:00 PM
04:00 PM
James Marshall - Optimal decision-making in brains and social insect colonies

The problem of how to compromise between speed and accuracy in decision-making faces organisms at many levels of biological complexity. Recent models of decision-making in the vertebrate brain have shown how simple neural models can implement statistically optimal decision-making processes that are able to minimise decision time for any desired error rate. Such models consider mutually inhibitory populations of neurons. The activation threshold required of these populations can be varied to emphasise speed, or accuracy, of decision-making. There are some striking similarities between these models and models of the decision-making processes in social insect colonies when searching for a new nest site. In this talk I will present stochastic models of collective behaviour in social insects that can be directly compared with corresponding neural models, and show how they may also implement statistically optimal decision-making in a similar manner to neural circuits.

Name Email Affiliation
, jsv@stat.osu.edu MBI - Long Term Visitor, The Ohio State University
Aguda, Baltazar bdaguda@gmail.com MBI - Long Term Visitor, The Ohio State University
Ahn, Sungwoo ahn91@math.ohio-state.edu Mathematics, The Ohio State University
Baker, Greg baker.27@osu.edu MBI - Long Term Visitor, The Ohio State University
Bansal, Arjun Arjun_Bansal@brown.edu Department of Neuroscience, Brown University
Bateson, Melissa Melissa.Bateson@newcastle.ac.uk Centre for Behaviour and Evolution, University of Newcastle
Bazazi, Sepideh sepideh.bazazi@zoo.ox.ac.uk Zoology Department, University of Oxford
Best, Janet jbest@mbi.osu.edu
Britton, Nick nfb@maths.bath.ac.uk Department of Mathematical Sciences, University of Bath
Cao, Ming mingcao@princeton.edu Mechanical and Aerospace Engineering, Princeton University
Chen, Linda chen.151@osu.edu MBI - Long Term Visitor, The Ohio State University
Chen, Zhan chenzha1@msu.edu Mathematics, Michigan State University
Coskun, Huseyin hcusckun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Couzin , Iain icouzin@Princeton.EDU Department of Ecology & Evolutionary Biology, Princeton University
Day, Judy jday@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Deneve, Sophie sophie.deneve@ens.fr Group for Neural Theory, Collège de France
Deshmukh, Abhijit deshmukh@tamu.edu Industrial & Systems Engineering, Texas A & M University
Ditterich , Jochen jditterich@ucdavis.edu Center for Neuroscience, University of California, Davis
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Dornhaus, Anna dornhaus@email.arizona.edu Ecology and Evolutionary Biology, University of Arizona
Dyson, Rosemary rosemary.dyson@math.ox.ac.uk MBI - Long Term Visitor, University of Oxford
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Franks, Nigel Nigel.Franks@bristol.ac.uk School of Biological Sciences, University of Bristol
Giraldeau, Luc-Alain giraldeau.luc-alain@uqam.ca Département of Biological Sciences, UQAM
Goldfarb, Stephanie sgoldfar@princeton.edu Mechanical and Aerospace Engineering, Princeton University
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Green, Edward egreen@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Grotewold, Erich grotewold.1@osu.edu MBI - Long Term Visitor, The Ohio State University
Guttal, Vishwesha vguttal@princeton.edu Ecology and Evolution, Princeton University
Hamblin, Steven steven.hamblin@gmail.com Department of Biological Sciences, University of Quebec
Hamilton, Ian hamilton.598@osu.edu MBI - Long Term Visitor, The Ohio State University
Heekeren, Hauke heekeren@mpib-berlin.mpg.de Neurocognition of Decision Making Group, Berlin Neuroimaging Center & Max-Planck-Institute for Human Development
Heestand, Espirit heestand.3@osu.edu EEOB, The Ohio State University
Holmes, Phil pholmes@Math.Princeton.EDU Mechanical & Aerospace Engineering and Program in Applied & Computational Mathematics, Princeton University
Hovmoller, Rasmus rhovmoller@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Kane, Abdoul kane.abdoul@utoronto.ca Department of Physiology, University of Toronto
Kao, Chiu-Yen kao.71@osu.edu MBI - Long Term Visitor, The Ohio State University
Kassen, Rune r.kaasen@mat.dtu.dk MBI - Long Term Visitor, Technical University of Denmark
Keller, Ben keller.362@osu.edu ECE, The Ohio State University
Kim, Yangjin ykim@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
King , Andrew andrew.king@ioz.ac.uk Behavioural & Population Ecology, Institute of Zoology (IoZ) & University College London (UCL)
Leite, Fabio leite.11@osu.edu Psychology, Ohio State University
Leonard, Naomi naomi@princeton.edu Mechanical and Aerospace Engineering, Princeton University
Lin, Shili lin.328@osu.edu MBI - Long Term Visitor, The Ohio State University
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Luque, Gloria luque.3@osu.edu EEOB, The Ohio State University
Machiraju, Raghu machiraju@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Mahalingam, Muhilan mahalingam@ccs.fau.edu Center for Complex Systems and Brain Sciences, Florida Atlantic University
Marshall , James marshall@cs.bris.ac.uk Computer Science, University of Bristol
Martinez, Aliex martinez.158@osu.edu MBI - Long Term Visitor, The Ohio State University
Masoudieh, Amirali masoudieha@mail.nih.gov Biochemistry, The Ohio State University
Matzavinos, Tasos tasos@math.ohio-state.edu MBI - Long term visitor, The Ohio State University
Myerscough, Mary m.myerscough@maths.usyd.edu.au School of Mathematics and Statistics, University of Sydney
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Newsome, William bill@monkeybiz.stanford.edu Department of Neurobiology, Stanford University
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Park, Hyejin parkh@math.ohio-state.edu Mathematics, The Ohio State University
Passino, Kevin passino.1@osu.edu MBI - Long Term Visitor, The Ohio State University
Pavlic, Theodore pavlic.3@osu.edu Computer Science and Engineering, The Ohio State University
Potter, Dustin potter.153@osu.edu MBI - Long Term Visitor, The Ohio State University
Pratt, Stephen Stephen.Pratt@asu.edu School of Life Sciences, Arizona State University
Quijano, Nicanor nquijano@uniandes.edu.co Department of Electrical & Computer Engineering, Universidad de los Andes
Raczkowski, Joe raczkowski.2@osu.edu EEOB, The Ohio State University
Ratcliff, Roger roger@eccles.psy.ohio-state.edu Psychology, The Ohio State University
Rayala, Harika rayala.2@osu.edu Department of Neuroscience, The Ohio State University
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Rissing, Steve rissing.2@osu.edu Department of Evolution, Ecology & Organismal Biology, The Ohio State University
Santner, Tom santner.1@osu.edu Department of Statistics, The Ohio State University
Sasaki, Takao Applied Psychology, Arizona State University
Scardovi, Luca scardovi@Princeton.EDU Mechanical and Aerospace Engineering, Princeton University
Schall, Jeffrey jeffrey.d.schall@vanderbilt.edu Department of Psychology, Vanderbilt University
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Schultz, Kevin schultzk@ece.osu.edu Electrical and Computer Engineering, The Ohio State University
Seeley, Thomas tds5@cornell.edu Department of Neurobiology and Behavior, Cornell University
Shih, Chih-Wen shih@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Smith, Greg greg@as.wm.edu MBI - Long Term Visitor, The Ohio State University
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stephens , David dws@umn.edu Ecology, Evolution & Behavior, University of Minnesota
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Sun, Shuying ssun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Usher, Marius m.usher@psychology.bbk.ac.uk School of Psychology, University of London
Waite, Thomas waite.1@osu.edu EEOB, The Ohio State University
Wang, Xueying wang.816@osu.edu Mathematics, The Ohio State University
Wang, Zhongkui wang.1231@osu.edu ECE, The Ohio State University
Wenzel, John W. wenzel.12@osu.edu Director, Museum of Biological Diversity, The Ohio State University
White, Corey white.1198@osu.edu Psychology, The Ohio State University
Wong-Lin , KongFatt kfwong@math.princeton.edu Applied and Computational Mathematics, Princeton University
Young, George dpais@princeton.edu Mechanical and Aerospace Engineering, Princeton University
Zhao, Yi zhao.178@osu.edu MBI - Long Term Visitor, The Ohio State University
The cognitive ecology of mate choice: individual decision mechanisms and group behaviour

Mate choice is the behavioural mechanism underlying sexual selection, and as such is of huge importance in evolutionary biology. Over the past 30 years research in behavioural ecology has provided lots of data about what traits animals prefer in their mates and why these preferences have evolved. Importantly, it is common for animals to attend to multiple different cues when making mating decisions because different cues may reveal different kinds of information about a potential mate. However, there has been much less attention given to the mechanisms of mate choice. How do animals integrate multiple sources of information about potential mates and compare the options available? Luckily similar problems have been considered in other areas of behavioural science, particularly studies of human decision making. One of my research aims for the past few years has been to try to bring together these different fields and ask whether the choice phenomena identified in human decision making also occur in animals faced with complex decisions. One general finding that is likely to be particularly important is that the choices we make are often dependent on the range of options on offer: our evaluations of options appear to be relative as opposed to absolute. In this talk I will describe some of the cognitive mechanisms that could be responsible for this context-dependency, and argue that on functional grounds similar mechanisms are likely to exist in animals. I will describe experiments from my lab on both human and bird mate choice designed to explore the possibility of context dependency. Finally, I will argue that context-dependency in mating decisions could have implications for the behaviour of animal groups that have not thus far been explored.

Pheromone Trails and Ant Foraging Decisions

Pheromone trails are an important component of ant foraging behaviour. It has been known for a long time that ants lay pheromone trails to attract nest-mates to productive foraging sources, but it has recently become clear that at least some species use more complex pheromone signalling behaviour. We define positive and negative pheromones to be those laid after successful and unsuccessful foraging respectively, and attractive and repulsive pheromones to be those that encourage ants to follow a trail and deter them from it respectively. We might expect positive pheromones to be attractive, and negative pheromones to be repulsive. We address the following questions. Under what circumstances is it advantageous to use more than one pheromone? When are repulsive pheromones advantageous? When are long-term as well as short-term pheromones advantageous?



 
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Bayesian decision with spiking neurons

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The use of multidimensional stimuli in multi-alternative perceptual decision tasks: A tool for decoupling speed and accuracy and for exploring the effect of changes in the sensory noise level

While first theoretical attempts have been made to study possible decision making mechanisms underlying choices between multiple alternatives, most behavioral and neurophysiological studies have so far focused on choices between two alternatives. The available data sets from choice experiments between multiple alternatives are largely not quantitative enough to address the underlying computational mechanism. The 2AFC version of the random dot motion direction discrimination task has been very helpful in advancing our understanding of the neural and computational mechanisms underlying choices between two alternatives.


Here we present behavioral data from a new version of the random dot motion discrimination task. Subjects are presented with a random dot stimulus containing up to three coherent motion components with different directions. They are asked to pick the dominant direction of motion out of three alternatives. The viewing duration is controlled by the subjects (reaction time task). Response times (RTs) and the subject's choice are measured. The advantage of this task is that it provides the experimenter with full control over the sensory evidence provided for each of the alternatives.


In the 2AFC version of the task both the behavioral as well as neurophysiological data recorded from the parietal cortex of monkeys performing the task could be explained by a computational model based on the idea of a race to threshold between two integrators accumulating the net sensory evidence for a particular choice. Here we show that the behavioral data (probabilities of particular choices as well as RT distributions) from our new 3-choice task are quite well explained by a computational model assuming a race to threshold between three integrators, one for each alternative. Each integrator accumulates the net sensory evidence for a particular alternative. The net sensory evidences are calculated as linear combinations of the activities of three relevant pools of sensory neurons with a positive weight assigned to the pool providing evidence for a particular choice and negative weights assigned to the pools providing evidence against a particular choice.


Previous 2AFC tasks have usually manipulated one stimulus strength parameter, resulting in monotonic relationships between stimulus strength and accuracy and between stimulus strength and mean RT. In these tasks, mean RT is usually also a monotonic function of accuracy. I will demonstrate how the multidimensional stimuli allow us to eliminate this tight coupling between speed and accuracy. Furthermore, in previous diffusion models of binary decision making it has often been assumed that the overall noise level in the decision circuitry stays constant and only the drift rate is affected by changing stimulus strength. I will highlight some aspects of our data set, which suggest that taking changes in the noise level of the sensory representation into account is essential for being able to explain our experimental findings.

Individual and Collective Decision-Making in House Hunting Rock Ants

Social insects exhibit both individual and collective intelligence. I will illustrate this distributed decision-making with house hunting in rock ants. Each worker, among the 100 or so in a colony, has less than 100,000 neurones (compared to 1011 neurones in humans) yet these ants employ the most sophisticated of all consumer strategies when choosing a new nest. Indeed, they can choose the best-of-N among alternative nests even though each has many different and important attributes. I will show how information can cascade through these social networks enabling colonies to benefit from both individual and collective intelligence. They use quorum sensing to conjure up collective intelligence and to fashion flexible speed accuracy trade-offs. When these ants have achieved a quorum in the new nest they switch from forward tandem running, from the old to the new nest, to social carrying. In addition, they often employ reverse tandem runs from the new nest back to the old one. During tandem runs one leader literally teaches one follower the route between the two nests. I will show how reverse tandem runs can expedite emigrations when these ants have used low quorums in emergencies. Tandem runs seem to be useful even when they do not progress all of the way to the target. I will describe the behaviour of both leaders and followers when tandems break up and show that followers without leaders use L?vy-like searches. I will also describe very recent work, using RFID tags on all workers, that shows how they can choose a better nest that is 9 times further away than a collinear poor one. Certain ants act as consensus breakers to re-route the whole colony. Such ants lead disproportionately more tandem runs first to the poor nest and then onto the more distant better one. Such switchers may have better access to the information needed to make well informed comparisons. Finally, I suspect that these tiny ants have larger behavioural repertoires than many if not most vertebrates. This begs the question; what are big brains for?



 
Social Foraging Decisions: Evolution and the Plasticity Gambit

Many animals seek resources socially, that is under conditions where the pay-off of foraging strategies depends on the frequency of strategies present in the population. Here I present a brief overview of a number of social foraging decisions, many of which have yet to be studied empirically, focussing more on producer-scrounger decisions which have been the subject of several studies in my laboratory. As is typically done in behavioural ecology, I rely heavily on evolutionary modelling to derive predictions about behaviour. However, I will raise questions concerning what I call the "plasticity gambit", an implicit and untested (unfounded?) assumption that cognitive decision processes must ultimately provide individual foragers with the ability to make decisions in their everyday lives that match behaviour expected to have evolved over evolutionary time.

A Multi-level Perspective on the Neurocognition of Decision Making

There is a long history of decision-making research in psychology and economics that has resulted in the development of formal models of behavior, which are inspired by behavioral data or the computational demands of a task. However, cognitive functions such as decision making cannot be completely understood on the basis of mathematical models and behavioral data alone; we have to investigate how mental (cognitive) and neuronal processes map onto each other. We investigate decision making in different domains. First, at the basis of a number of different decisions we are facing in everyday-life stands perceptual decision making. I will discuss how we may use stochastic diffusion models in combination with brain imaging to investigate perceptual decision making. Second, many of our decisions are influenced by the potential outcomes associated with different options. Specifically, I will discuss how dopaminergic neuromodulation (COMT-genotype, aging) affects reward-based decision making.

Stochastic models for individual decisions and social influence in groups

I will describe two modeling studies: of an individual stimulus identification task, and of a gambling task performed individually and with group feedback. In the first we model accuracy in a two-alternative forced-choice task with cued responses using an Onstein-Uhlenbeck reduction of a leaky competing accumulator model. This provides explicit predictions of psychometric functions, which we fit to data from monkeys performing a motion discrimination task. We then compute optimal (reward maximizing) strategies when reward magnitudes for the alternatives differ, and assess the abilities of individuals to achieve them. In the second study we extend a probabilistic model developed to account for individual choices on matching shoulders and rising optimum gambling tasks by Egelman, Montague, et al., to predict choice patterns in a group context. The model is equivalent to a drift diffusion (DD) process driven by the difference in predicted rewards for two alternatives, based on reward feedback and temporal difference learning. We couple multiple DD processes by incorporating influences from the choices and/or rewards earned by other players in the group. We fit this model to data from human subjects playing a two-armed bandit game, singly and in groups, and with various types of feedback on their own and other group members' rewards and choices.


The modeling work was done with Sam Feng (study 1) and Andrea Nedic, Jonathan Cohen and Deborah Prentice (study 2). Experimental data was collected and provided by Alan Rorie and Bill Newsome (study 1), and Damon Tomlin (study 2), who also advised on the modeling. Support was provided by AFOSR under the 2007 MURI Programs 15 and 16.

Spatial Dynamics, Information Flow and Consensus in Fish Schools

Decision-making dynamics and spatial dynamics in fish schools are naturally coupled when individuals only sense locally. As relative positions of fish change, neighbors come and go and the flow of information varies; changes in information flow affect the dynamics of consensus and this in turn influences collective motion. I will describe a study of consensus dynamics for a school using a model that extends coupled oscillator dynamics to include spatial dynamics and represents changing information flow with time-varying graphs. We examine the case of periodically time-varying information flow, motivated by fish schooling data of I. Couzin and A. Kao, in which killifish exhibit oscillatory speed profiles and nearest neighbors anti-synchronize the phases of their speed oscillations. We explore the possible advantages for speed and accuracy in consensus dynamics and for increased density of spatial sampling.

Optimal decision-making in brains and social insect colonies

The problem of how to compromise between speed and accuracy in decision-making faces organisms at many levels of biological complexity. Recent models of decision-making in the vertebrate brain have shown how simple neural models can implement statistically optimal decision-making processes that are able to minimise decision time for any desired error rate. Such models consider mutually inhibitory populations of neurons. The activation threshold required of these populations can be varied to emphasise speed, or accuracy, of decision-making. There are some striking similarities between these models and models of the decision-making processes in social insect colonies when searching for a new nest site. In this talk I will present stochastic models of collective behaviour in social insects that can be directly compared with corresponding neural models, and show how they may also implement statistically optimal decision-making in a similar manner to neural circuits.

Considering the evidence: integration of sensory and reward information for informing behavioral decisions

A generally useful decision mechanism must include a stage at which information from very disparate sources (i.e. sensory, reward, priors, etc) can be cast into a common neural currency for establishing the likelihood of one choice vs. the other. In monkeys, the lateral intraparietal area is thought to play such a role in oculomotor decisions, and past studies have indeed produced evidence for neural decision variables in LIP originating from sensory input (e.g. stimulus motion) or from economic value (reward size or probability). But no study has determined whether disparate signals are actually integrated in LIP, what the weights of the disparate signals are at the single cell level, and whether the relative weights at the neural level matches the relative weights inferred from behavior. Alan Rorie, a graduate student in my lab, and I addressed these questions by training monkeys on a choice paradigm in which sensory information about visual motion must be combined with information about reward size to make optimal choices. We show for the first time that sensory and reward signals are combined in single neuron activity in LIP, and that the relative magnitude of their influence at the population level matches their influence at the behavioral level. The data provide quantitative support for the notion that LIP activity reflects a high level of processing in which information from disparate sources are cast into a common neural currency for guiding oculomotor choices.

Swarm Cognition in Honey Bees

Systems biology of decision making focuses on understanding the structures, dynamics, and evolution of complex interconnected biological mechanisms that support decision making by individuals and social animal groups. In this talk, an experimentally validated model of the nest-site selection process of honey bee swarms is introduced. In this spatially distributed dynamical feedback process individual bee actions and bee-to-bee communications combine to produce an emergent "consensus" nest choice. The process has connections to neurobiological cognition systems, especially at the behavioral level: the swarm can effectively discriminate between different quality nest sites and eliminate from consideration relatively inferior distractor sites. Simulations indicate that individual-level bee decision-making mechanisms have been tuned by natural selection to provide a balance between the need for fast and accurate decisions at the group level. For more information see: http://www.ece.osu.edu/~passino/

The interaction of group and individual decision-making during nest-site selection by ants

Social insects have special interest in the study of decision-making, because they make choices both as individuals and as collectives. I will describe how these levels interact in nest-site selection by Temnothorax ants. Individual ants follow a complex behavioral algorithm that allows a group of poorly informed individuals to collectively choose the best site, without any central control. This algorithm is based on quality-dependent positive feedback and a threshold response, two features of general importance to collective decision-making systems. Quantitative tuning of this algorithm allows colonies to emphasize either the speed or accuracy of decision-making. The algorithm hinges on attainment of a nestmate quorum that triggers full commitment to a particular option. A simple model derived from the study of vertebrate decision-making may explain how the quorum can be detected by the integration of encounter rates between ants. Recent work suggests that the concept of rationality may reveal more about the interaction of group and individual levels. Decision-makers are irrational when they fail to attach consistent values to options. For individuals, irrationality can reliably be obtained through several experimental paradigms involving options with multiple, conflicting attributes. Faced with one of these paradigms, Temnothorax colonies nonetheless show consistent preferences, suggesting that collective decision-making algorithms may filter out the effects of irrationality at the level of individual workers.

Modeling Simple Decision Processes with Applications to EEG, Aging, and Sleep Deprivation

I will talk about 2-3 topics in simple decision making. I will first briefly introduce the diffusion model for simple decision making and note that it can account for correct and error RT distributions as well as accuracy. Then I will show that an EEG measure indexes trial by trial variability in drift rate in the model. I will then show interpretations of the effects of age and sleep deprivation on performance in terms of an analysis based on the model. If time permits I will show how the model can uncover the main individual differences on speed of processing in simple two choice tasks such as recognition memory and word identification.



 
Actions, reasons, neurons, and causes

Movements of inanimate objects explained by external forces referred to as causes. In contrast, many movements of humans are described as actions directed toward a goal for a reason. A purposeful action (a wink) is distinguished from a mere event (a blink) by reference to some intelligible plan because actions are performed to achieve a goal. In other words, actions have reasons ("I did it for..."), but events just have causes ("It happened because..."). Reasons for actions are explanations in terms of purposes, goals and beliefs. But if all actions are really caused by just neurons firing and muscles contracting, then how can there be any reasons for actions? This presentation will seek to articulate how intentional reasons can be reconciled with neural causes. The answer will emphasize the many-to-one mapping of neural activity onto behavior and cognition so that if a given action can arise from different brain states, then the relationship of the behavior to an intention holds in virtue of the content of the representation of the intention and not its neural realization as such. Thus, a movement can be called an intentional action if and only if it originates from a cognitive state with meaningful content, and this content defines the cognitive state's causal influence. But this analysis depends on whether the brain knows what it means to do. In fact, recent cognitive neuroscience research has described particular brain circuits that register errors and success. Such signals can be used to adjust behavior and provide the basis for distinguishing "I did" from "it happened" which is just what is needed to feel like we are acting with freedom and responsible power.

Real democracy: how honey bees choose a home

Real democracy - when citizens meet in a face-to-face assembly and bind themselves under decisions they make themselves - has been practiced for some 2500 years by humans, but for more than 20 million years by honey bees. We will examine the remarkable democratic decision-making process of a honey bee swarm as it chooses a new home. We will see that bees have evolved sophisticated ways of working together to identify a dozen or more potential dwelling places, to choose the highest quality one for their new home site, and to make a decision without undue delay. We will conclude with some take-home lessons from the bees ("swarm smarts") on how to foster good decision making by democratic groups of humans.

The decision-making process of a honeybee swarm as it chooses a nest site

Over last two decades, significant progress has been made toward understanding the mechanistic basis of decision making, both in individual animals and in animal groups. I will review one of the systems where the strongest progress has been made toward understanding group decision making: nest-site choice in honeybees. We will see that the bees' decision-making process has many remarkable consistencies with the picture that has emerged from neurobiological studies of individual decision making. In both cases, the process of decision-making involve building a sensory representation of the external world, then transforming this sensory representation into a decision, and finally implementing the chose course of action. Furthermore, in both cases, the decision-making process is essentially a race between competing accumulations of evidence in support of the various alternatives, with the choice determined by which accumulation first reaches the threshold level of evidence needed for a response. These and other similarities between neuronal and social systems of decision making point to principles in the "design" of distributed decision-making systems, and these will be discussed.

Impulsivity, Discounting, and Ecological Rationality with comments on four basic problems in animal decision-making

Experimental studies show that animals have strong preferences for immediacy. Specifically, experimental data suggest that animals make systematic errors by over-valuing small but immediate benefits, and under-valuing larger later consequences. Why would natural selection favor a mechanism that makes such a glaring error? One hypothesis is that these are not errors at all, because delay reduces or discounts the fitness value of benefits. A second hypothesis is that the 'impulsive' rules revealed by these experiments seldom lead to errors in natural situations. I call this the 'ecological rationality' hypothesis. My laboratory has developed this idea via experiments that compare the standard 'self-control' preparation to a more naturalistic choice preparation that attempts to mimic patch exploitation decisions. I review several of these experiments. We consistently find that subjects achieve higher levels of performance (e.g. higher long term intake rates) in our more naturalistic 'patch' situation, but many simple hypotheses (including the short-term rate model) fail to explain this difference. Finally, I will discuss four general problems in decision-making and how they emerge my groups studies of impulsivity. These are: 1) can we specify the relationship between learned and evolved solutions to behavioral problems; 2) how can we meaningfully integrate mechanistic and functional approaches to decision-making; 3) can we build a predictive theory of bounded rationality or is this fundamentally a post hoc approach; and 4) are animal decision mechanisms special tools for specific tasks or general mechanisms that apply across the broad, and how would we know?

Contrasting neurocomputational models of perceptual choice

A number of neurocomputational models have been proposed to account for the algorithm used by the brain to make decisions when faced with ambiguous information. In this talk I examine shared and diverging assumptions that these models make in accounting for choice patterns. For example, I examine the need to assume an integration over noisy samples during stimulus presentation, the existence of competition (or lateral inhibition) between choice alternatives and the assumption that a response criterion is used even in non-speeded judgments (making the impact of early evidence more strongly weighted). Preliminary data on choice tasks that manipulate the time-course of the information flow will be presented examining the models' predictions. Finally, I discuss how these models can be used to account for judgments of confidence, and for the fact that observers have the metacognitive ability to judge incorrect responses as less confident.


Work done in collaboration with Eddy J. Davelaar.