Modeling Optimal Strategies for Finding a Resource-Linked, Windborne Odor Plume: Theories, Robotics, and Biomimetic Lessons from Flying Insects

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Abstract

Male moths locate females by navigating along her pheromone plume, often flying hundreds of meters en route. As the first male to find a calling female is most apt to be her mate, this can be termed "a race to find the female" and it is assumed to be under strong selective pressure for efficiency and rapidity. Locating a distant, odor-linked resource involves two strategies. The first is to contact the outer envelope of the odor plume. When wind direction is relatively invariant, the plume stretches and then crosswind flights may be favored, although when wind direction shifts over 60°, upwind and downwind paths may be optimal. Alternatively, the path may be random with respect to the direction of wind flow, with periodic changes in direction, as in either Lévy or Random Walks. After first detecting the pheromone, a second strategy follows: moths navigate along the plume by heading upwind when the pheromone is detected, with crosswind casting to re-establish contact if the plume is lost. This orientation path is not straightforward in nature, however, because atmospheric turbulence fragments the plume, thereby creating large odor gaps. Furthermore, a shifting wind direction can lead the responder out of the plume. One way to explore which strategies are optimal for enabling initial contact with the plume and subsequent navigation is through modeling of plumes' dispersal and of insects' flight strategies. Our simulations using the flight characteristics of the male gypsy moth (Lymantria dispar) suggest that search strategies similar to Lévy Walks are most apt to result in a high probability of contact with plumes. Although a searching trajectory aimed predominately crosswind performed almost as well as those with a random orientation when wind direction was relatively stable, downwind biased trajectories were least successful. A random orientation with respect to immediate wind flow, as used in our simulations of Lévy and Random Walks, seems optimal both for initial discovery of the plume and likelihood of locating an odor source. In the two available direct field observations, moths adopted a random orientation with respect to concurrent wind direction.

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Random walk models in biology.

Edward A. Codling, Michael J. Plank, Simon Benhamou (2008)

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

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'Infotaxis' as a strategy for searching without gradients.

Massimo Vergassola, Emmanuel Villermaux, Boris Shraiman (2007)

Chemotactic bacteria rely on local concentration gradients to guide them towards the source of a nutrient. Such local cues pointing towards the location of the source are not always available at macroscopic scales because mixing in a flowing medium breaks up regions of high concentration into random and disconnected patches. Thus, animals sensing odours in air or water detect them only intermittently as patches sweep by on the wind or currents. A macroscopic searcher must devise a strategy of movement based on sporadic cues and partial information. Here we propose a search algorithm, which we call 'infotaxis', designed to work under such conditions. Any search process can be thought of as acquisition of information on source location; for infotaxis, information plays a role similar to concentration in chemotaxis. The infotaxis strategy locally maximizes the expected rate of information gain. We demonstrate its efficiency using a computational model of odour plume propagation and experimental data on mixing flows. Infotactic trajectories feature 'zigzagging' and 'casting' paths similar to those observed in the flight of moths. The proposed search algorithm is relevant to the design of olfactory robots, but the general idea of infotaxis can be applied more broadly in the context of searching with sparse information.