# The random elements in the systematic search behavior of the desert isopod *Hemilepistus reaumuri*

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## Summary

Most of the year the isopod crustacean *Hemilepistus reaumuri* depends for survival on the protection of a permanent shelter (i.e., the burrow occupied by its family), despite its remarkable physiological adaptations to its desert habitat. If an isopod gets lost after an excursion from the burrow, it has to find it as quickly as possible.

Displacement experiments show that *H. reaumuri* is indeed successful in homing. Even if a desert isopod is displaced in an arbitrary direction over a distance (starting distance *r*_{0}) from the burrow that exceeds 15 times the distance from which it can detect the entrance, it returns on average in less than 400 s.

The homing behavior of *H. reaumuri* is successful not because of the isopod's ability to navigate to its burrow by using external orientation stimuli but because of the intrinsic structure of its search pattern. An isopod that is displaced from its burrow first searches approximately in the form of a spiral, then it moves through increasing loops on which meanders are superimposed. It concentrates these subunits of its search around the starting point by occasionally returning there. The time course of the azimuthal direction component of its position is not clearly regular. The surroundings of the starting point are searched evenly in every direction.

The search behavior of *H. reaumuri* is composed of systematic subunits together with many random elements. The form of discrete brownian (random) search without directional correlations between its steps that best describes the observed behavior of *H. reaumuri* for search-path segments with a length between 1 and 7 m has an average step length of 33 cm. For segments with a searchpath length below 1 m the agreement between theory and observations is better if one starts from a discrete brownian search with a much smaller step length (one body length), but in which the direction of the steps is strongly correlated.

Despite these geometrical similarities to a brownian search the search behavior of *H. reaumuri* is distinctly more successful because of the combination of two characteristics. *H. reaumuri* avoids the disadvantage of the most successful form of a brownian search (i.e., the frequent passage through a region in which it has searched just before) by moving in straighter lines. A brownian search with the same directional constancy shown by *H. reaumuri* would be inefficient because the thoroughness with which a given region is searched would be too low. *H. reaumuri* avoids this problem and concentrates its search around the starting point by sometimes returning to that place.

## Keywords

Step Length Random Element Search Behavior Orientation Stimulus Direction Component## Preview

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