Modeling collective behavior

There are many challenges in developing models of collective behavior, in particular when relating mechanism of social interaction with processes of (natural) selection. Even over the ecological scale there exists a complex recursive feedback between individual and group behavior; individual decisions influence group dynamics, which influence individual decisions, and so on. The majority of existing modeling work on collective dynamics has focused on how group-level properties emerge from inter-individual interactions. An example of such a simulation is:

Couzin, I.D., Krause, J., James, R., Ruxton, G.D. & Franks, N.R., (2002) Collective memory and spatial sorting in animal groupsJournal of Theoretical Biology 218, 1-11.

Which demonstrated how discrete types of group structure emerge from relatively local social interactions.

Such general predictive power has resulted in such models being a useful tool in the study of animal groups, and many of these predictions have been found to hold for real animal groups (the three different group structures exhibited by golden shiner fish schools is shown below), despite their increased complexity.

For a detailed comparison please see:

Tunstrom, K., Katz, Y., Ioannou, C.C., Huepe, C., Lutz, M. & Couzin, I.D. (2013) Collective states, multistability and transitional behavior in schooling fishPLoS Computational Biology, 9(2), e1002915.

Such models have also been useful to understand collective response to external influence, such as attack by predators. I worked with the BBC for their ‘Predators’ series (broadcast in 2000), providing the computer simulation in the video below.

When considering the fitness consequences of social behavior, therefore, we must often represent accurately the fine-scale dynamics of individual motion and interactions. In addition for evolutionary models investigating such group dynamics we need to maintain individual identities within generations (to represent genetically and/or phenotypically distinct individuals) and to consider a sufficiently large population to prevent potential artifacts such as fixation of strategies by drift. Finally, these computations must be performed over ecological and evolutionary timescales where the statistical relationship between (sometimes changing) strategies and fitness (which itself is frequency-dependent) can be accurately determined.

Massively-parallel computation

To achieve our simulation goals we have developed next-generation massively parallel computational techniques using graphics processing units (GPUs) instead of traditional CPUs. GPUs have thousands of processing cores, allowing unprecedented access to supercomputing capabilities (even on desktop machines). We have been working with NVIDIA’s CUDA programming language and their GeForce and Tesla GPU hardware.

Here Iain is interviewed by NVIDIA about GPU-Accelerated Swarm Behavior.

This acceleration has allowed us to explore a wide range of topics, including:

Collective decision-making

Couzin, I.D., Ioannou, C.C., Demirel, G., Gross, T., Torney, C.J., Hartnett, A., Conradt, L., Levin, S.A. & Leonard, N.E. (2011) Uninformed individuals promote democratic consensus in animal groupsScience 334(6062) 1578-1580.

Emergent sensing of complex environments

Berdahl, A., Torney, C.J., Ioannou, C.C., Faria, J. & Couzin, I.D. (2013) Emergent sensing of complex environments by mobile animal groupsScience 339(6119) 574-576.

The evolution of virtual prey under selection by real predators

Ioannou, C.C., Guttal, V. & Couzin, I.D. (2012) Predatory fish select for coordinated collective motion in virtual preyScience 337(6099) 1212-1215.

The evolution of extreme phenotypic plasticity in locusts

Guttal, V., Romanczuk, P., Simpson, S.J., Sword, G.A. & Couzin, I.D. (2012) Cannibalism as a driver of the evolution of behavioral phase polyphenism in locusts. Ecology Letters 15, 1158-1166.

The evolution of collective migration in cells and organisms

Guttal, V. & Couzin, I. D. (2010) Social interactions, information use and the evolution of collective migration. PNAS 107(37), 16172-16177.

Signaling and the evolution of cooperation

Torney, C., Berdahl, A. and Couzin, I.D. (2011) Signaling and the evolution of cooperative foraging in dynamic environmentsPLoS Computational Biology 7(9), e1002194.

Multi-level selection and the evolution of collective behavior

Migration is a hallmark life history strategy of a diverse range of organisms. We found that, for a broad range of of ecological conditions and population densities, the evolutionarily stable strategy is for a small proportion of individuals in a population to exploit information from the environment (e.g. micro-organisms and cells typically use chemical or thermal cues, whereas many migratory birds use magnetic, visual and olfactory information) while the majority exploit social cues.

Our entire biosphere is under severe threat due to increasing anthropogenic influences, and as a consequence many migrations around the world are at risk. Our approach may provide useful insights into how human activities such as hunting (or otherwise causing populations to decline) or habitat fragmentation on animal migrations. As shown in (Guttal & Couzin, 2010), our model predicts a potentially bleak future for migrants, in that it suggests that it may be extremely difficult to recover lost migrations through habitat restoration.

In (Torney, Berdahl & Couzin, 2011) we explored the evolution of signaling among individuals in environments with complex and heterogeneous habitat (resource) quality. Understanding cooperation in animal social groups remains an ongoing challenge for evolutionary theory. Even if individuals are of low relatedness, we find evidence that individuals can evolve signaling behavior to allow more effective exploitation of resources. This seemingly altruistic behavior results from highly nonlinear benefits inherent in collective taxis; thus signaling can be an evolutionarily stable strategy under certain environmental conditions, even when signalers incur costs. In addition to numerical modeling, we also analyzed the evolutionary dynamic using a simplified, but analytically tractable model which demonstrated the importance of the timescale associated with acquiring information from the environment.

In many of our studies we integrate numerical and analytical approaches. Analysis of reduced (simplified) models allow us to isolate mechanisms, to understand more clearly how individual behaviors scale to population properties, and to generalize our results to other systems. For example in

Torney, C., Levin, S. A. & Couzin, I. D. (2010) Specialization and evolutionary branching within migratory populationsPNAS 107(47), 20394-20399.

we developed a novel mean-field approximation of (Guttal & Couzin, 2010) which allowed us not only to validate our numerical results (and to explore the nature of information as a public good using adaptive dynamics) but also to demonstrate clearly how consideration of the non-linear nature of collective dynamics can have a dramatic impact on the evolution of behavioral strategies.

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