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OPTIMAL INTERMITTENT NAVIGATION

The dung beetle dance

 

Motivation

Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation. These processes are accompanied by uncertainty in sensory acquisition of information, planning and execution. We were inspired by observations of dung beetle navigational strategies that show switching between geocentric and egocentric strategies. 

Foraging beetles look for nutrient-rich dung, and then attempt to roll a dung ball along a straight path radially away from the pile [1] with the aim of providing food for their brood. Beetles acquire navigation information using a variety of long-range cues before initiating a roll, and then push the dung ball while walking backwards with their hind legs. Still, they are able to maintain a consistent bearing. They do by performing the the dung beetle 'dance':

Reorientation behavior

Dung beetles stop intermittently and get atop the ball and walk on it to reorient themselves before continuing to roll the dung bal. Video: Dacke Lab

Rough surface

When the surface is rough, the beetles stop to reorient frequently. Video: Dacke Lab

Flat surface

When the surface is flat, the beetles don't stop to reorient very often. Video: Dacke Lab

To learn more about these experiments, visit the Dacke/Baird Lab website at Lund University

 

Model

If the beetles stops to reorient often, it would have a straight trajectory but would loose a lot of time; vice verse, if the beetle don't stop to reorient, it might deviate significantly from its intended trajectory.

How often should the beetle stop to reorient, on a specific surface roughness?

To answer this question, we consider an agent moving along a preferred direction in the presence of multiple sources of noise. We address this using a model  of a correlated random walk at short time scales that is punctuated by reorientation events leading to a biased random walks at long time scales. This allows us to identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition as well as performance errors linked with variations in environmental conditions and agent–environment interactions.

 
 

This allows us to identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition as well as performance errors linked with variations in environmental conditions and agent–environment interactions.

 
 

Optimal reorientation intervals

 In the simplest setting, we find that the optimal reorientation interval is inversely proportional to the environmental noise and is invariant to sensory acquisition noise. In more complex settings, our study highlights the variations in the optimal navigation strategy that balances accuracy, speed and effort.

 
 

What triggers reorientation?

Having understood this simple scenario, we now go back to address the complexities associated with noise in acquisition, planning and execution, in addition to the noise in the turning angle distribution θ*. To address this, we use numerical simulations with the acquisition error ϵd≠0, the error amplification associated with attention A>1, and ask how the agent must optimize the attention span τ≠1 and the threshold activation angle for reorientation θa to minimize the cost

 
 

We use the covariance matrix adaptation algorithm (CMA–ES) to determine the optimal strategy, where given a set (θ*,A,ϵd), we determine the optimal set (θa,τ). The CMA-ES is a stochastic derivative-free optimization method for nonlinear or non-convex continuous optimization problems.

 
 

We have posed and solved an optimization problem of geocentric navigation interspersed by egocentric cue integration. In the simplest setting, we find that the optimal reorientation interval is inversely proportional to the environmental noise and is invariant to sensory acquisition noise. In more complex settings, our study highlights the variations in the optimal navigation strategy that balances accuracy, speed and effort. Our study might well be generalizable more broadly to animal navigation, and perhaps even artificial vehicular navigational situations, all of which use egocentric and geocentric cues with varying attention to create optimal strategies that balance accuracy and efficiency in the presence of noise, and additional constraints such as finite cognitive bandwidth.

To learn more about this work, read our paper:

O.Peleg, L. Mahadevan

Optimal switching between geocentric and egocentric strategies in navigation

R. Soc. Open Sci., 3, 160128 (2016)

Future directions include linking our model predictions to experimental observations, in collaboration with Prof. M. Dacke (Lund University). We do so by systematically modifying the ground roughness on which the beetles are navigating (using hurdles at different spacing, the reliability of the navigational cues, and memory degradation of the beetles.