Collective behavior and self-organization are very common in living systems and exhibited across many different scales including cells, colonies of insects, schools of fish, and crowds of people. These systems, while familiar, are not well understood. Collective systems contain a large number of interacting components that exhibit complex dynamics. In nature, individuals benefit from the advantages of group living. It is expected that group behavior in animals often arises from evolutionary necessity. However, not much is known about the mechanics of these systems in nature due to their complexity. How do groups of animals work together to navigate complex environments? How does information travel throughout a group? We use computers and schools of fish to gain a more in depth knowledge of how and why collective groups organize themselves in such interesting ways.
Collecting Quantitative Data (Julia Giannini ‘18, Aawaz Pokhrel ‘19, Nicole Linard ‘20)
To investigate how individual interactions give rise to collective states, we use the apparatus above to observe the response of experimental schools to visual stimuli. This summer, we worked with two different species of schooling fish: Rummy-nose Tetra (left) and Golden Shiners (right). Both of these fish exhibit negative phototaxia, that is, they avoid bright regions in their environment. Therefore, we can project light gradients onto the tank and examine how they respond to both social and environmental cues. Using infrared lighting and high speed cameras, we record videos and use lots of machine vision techniques to extract individual trajectories. This information gives us insight into the state of the group over time and how it relates to individual movement. By using both Tetras and Shiners, we compare the behaviors of different species under the same stimuli.
Here is a video of Golden Shiners tracking a noisy dark blob – we compare experimental results such as these with those in simulations to test theoretical models for collective behavior.
Simulation of Collective Behavior (Aawaz Pokhrel ‘19)
So, how do fish find the darkest (safest) spot in their environment? Can they see the gradient (slope) of light and follow it to the safest place? Or do they use emergent sensing (group level sense)? We explore the answer to this with both simulations and experiments.
In the simulation, we use the Couzin model which has three different zones which dictates the movement of the fish on basis of the positions of neighbour fish in these zones. These three zones are zones of repulsion, orientation and attraction. One of the assumption of that we have in this model simulation is that fish are not able to sense the gradient or the change of light field in any direction.
Here is a short video of our simulation fish trying to follow the dark spot.
We amend this model by adding in a gradient sensing term which competes with the social-only Couzin model. By turning the “knob” of this weight (how well the fish can sense the gradient), we investigate how it affects the performance of the fish in finding the darkest spot.
We see that the more amount of information they have about the gradient, the less they are able to track the dark spot. Following graph shows that for a given number of fish, their ability to track the dark spot decreases Ψ as the amount of information about the gradient increases.
Use of neural network in Collective Behavior (Nicole Wang ‘19)
Another difficulty with understanding and predicting collective behavior is that the interactions are not known. And of course, it’s not possible to ask the fish how they are interacting. So we must build models and compare with experimental data. However, each model we build has assumptions about how the fish are interacting. A widely used model the Couzin model uses zones (repulsion, alignment, attraction) to predict the behavior of individuals. We are using neural networks to train a computer to learn how the fish are interacting.
As shown in above figure, the neural network uses an input layer which in our case is the visual field of nearby fish. This input layer is connected with several hidden layers and finally a single output neuron telling the fish which direction to turn. In our neural network, we use both convolutional and fully connected layers, which of course means — lots of linear algebra. We test this approach on a simulation of a fish school (using the Couzin model) so that we can directly compare the output generated by the Neural Network with the known model. Finally, we apply the NN-approach to our experimental data. We’re still working out some of the details, but the NN seems to be working very well !!!