New research from a Florida State University professor and colleagues explains the mathematics behind how initial predispositions and additional information affect decision making.

The research team’s findings show that when decision makers quickly come to a conclusion, the decision is more influenced by their initial bias, or a tendency to err on the side of one of the choices presented. If decision makers wait to gather more information, the slower decision will be less biased. The work was published today in Physical Review E.

“The basic result might seem sort of intuitive, but the mathematics we had to employ to prove this was really non-trivial,” said co-author Bhargav Karamched, an assistant professor in the FSU Department of Mathematics and the Institute of Molecular Biophysics. “We saw that for the first decider in a group, the trajectory of their belief is almost a straight line. The last decider hovers around, going back and forth for a while before making a decision. Even though the underlying equation for each agent’s belief is the same except for their initial bias, the statistics and behavior of each individual is very different.”

The researchers built a mathematical model that represented a group of agents required to decide between two conclusions, one which was correct and one which was incorrect. The model assumed each actor within a group was acting rationally, that is, deciding based off their initial bias and the information they are presented, rather than being swayed by the decisions of individuals around them.

Even with evidence and assuming perfect rationality, bias toward a particular decision caused the earliest deciders in the model to make the wrong conclusion 50% of the time. The more information actors gathered, the more likely they were to behave as if they weren’t biased and to arrive at a correct conclusion.

Of course, in the real world, people are swayed by all sorts of inputs, such as their emotions, the decisions their friends made and other variables. This research offers a metric showing how individuals within a group should make decisions if they are acting rationally. Future research could compare real-world data against this metric to see where people are diverting from optimally rational choices and consider what might have caused their divergence.

The researchers’ model is known as a drift diffusion model, so called because it combines two concepts: individual actor’s tendency to “drift,” or move toward an outcome based on evidence, and the random “diffusion,” or variability of the information presented.

The work could be used, for example, to understand when people are being unduly swayed by early decisions or falling victim to groupthink. It even helps describe other complex scenarios with many individual actors, such as the immune system or the behavior of neurons.

“There is still a lot of work to do to understand decision making in more complicated situations, such as cases where more than two alternatives are presented as choices, but this is a good starting point,” Karamched said.

This research was a multi-institution collaboration involving doctoral candidate Samantha Linn and Associate Professor Sean D. Lawley of the University of Utah, Associate Professor Zachary P. Kilpatrick of the University of Colorado, and Professor Krešimir Josic of the University of Houston.

This research was supported by the National Science Foundation and the National Institutes of Health.

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When bacteria interact, they give off cellular signals that can trigger a response in their neighbors, causing them to behave in different ways or produce different substances. For example, they can communicate to coordinate movement away from danger or to emit light to ward off predators.

In new research published by Biophysical Reports, researchers from Florida State University and Cleveland State University lay out a mathematical model that explains how bacteria communicate within a larger ecosystem. By understanding how this process works, researchers can predict what actions might elicit certain environmental responses from a bacterial community.

“Typically, models of bacteria in synthetic environments have involved many, many equations describing many, many things, but they weren’t really flexible for different applications,” said co-author Bhargav Karamched, an assistant professor in FSU’s Department of Mathematics and the Institute of Molecular Biophysics. “What my collaborators and I have done is to create a flexible mathematical model that can be applied to a variety of experimental settings.”

Models like the one developed by Karamched’s team help to predict how those bacterial communities coordinate activity, allowing designers to adjust the parameters of a community, such as the population sizes of different types of bacteria or feedback loops, and tailor them for different purposes. For example, in a population of two kinds of bacteria, having more of one kind of bacteria can be dangerous for a host organism while having more of the other can be beneficial. Getting the right mix is crucial, and models help researchers design and analyze the bacterial communities they create.

“What’s lacking in synthetic biology right now are these general, flexible models that are ready off-the-shelf,” Karamched said. “This may not capture all the details in a bacteria community, but it still captures the general framework of what’s going on. Scientists and engineers can use that to compare against their experimental work and move forward.”

The researchers also tested their model against previously published research that examined how bacteria communicate across large spatial gaps. The previous research found that the bacteria only needed a positive feedback loop in order to signal to each other. But Karamched and his collaborators’ model predicts that the rate of production of signaling molecules must also be within a specific range for coordination to occur.

“This model lays the groundwork for a wide range of future experiments testing different strain interactions and geometries,” said co-author Shawn Ryan, an associate professor in the Department of Mathematics and Statistics and the co-director of the Center for Applied Data Analysis and Modeling at Cleveland State University.

Ryan Godin, a former Cleveland State University student and current Iowa State University doctoral student in chemical engineering, was the lead author on this paper.

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