  Movement is a fundamental behaviour of organisms that brings about beneficial
encounters with resources and mates, but at the same time exposes the organism
to dangerous encounters with predators. The movement patterns adopted by
organisms should reflect a balance between these contrasting processes. This
trade-off can be hypothesized as being evident in the behaviour of plankton,
which inhabit a dilute 3D environment with few refuges or orienting landmarks.
We present an analysis of the swimming path geometries based on a volumetric
Monte Carlo sampling approach, which is particularly adept at revealing such
trade-offs by measuring the self-overlap of the trajectories. Application of
this method to experimentally measured trajectories reveals that swimming
patterns in copepods are shaped to efficiently explore volumes at small scales,
while achieving a large overlap at larger scales. Regularities in the observed
trajectories make the transition between these two regimes always sharper than
in randomized trajectories or as predicted by random walk theory. Thus real
trajectories present a stronger separation between exploration for food and
exposure to predators. The specific scale and features of this transition
depend on species, gender, and local environmental conditions, pointing at
adaptation to state and stage dependent evolutionary trade-offs.
