Abstract
Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the oldest and most ubiquitous navigation strategies in the animal kingdom. Despite a plethora of computational models, from equational to neural network form, there is currently no consensus, even in principle, of how this important phenomenon occurs neurally. Recently, all path integration models were examined according to a novel, unifying classification system. Here we combine this theoretical framework with recent insights from directed walk theory, and develop an intuitive yet mathematically rigorous proof that only one class of neural representation of space can tolerate noise during path integration. This result suggests many existing models of path integration are not biologically plausible due to their intolerance to noise. This surprising result imposes significant computational limitations on the neurobiological spatial representation of all successfully navigating animals, irrespective of species. Indeed, noise-tolerance may be an important functional constraint on the evolution of neuroarchitectural plans in the animal kingdom.
The ability to navigate allows animals to vastly increase the action space for finding resources, mates, and to avoid predators. The benefits are many and it is commonly believed that modern brain functions have emerged from ancestral forms evolved for effective navigation. Since the time of Charles Darwin, it has been recognized that path integration is a navigation strategy innate to many species. Path integration involves adding the stepwise displacements during a circuitous journey to compute a net homeward direction. Over the past century, this phenomenon has been described for birds to mammals to arthropods, and a long list of mathematical, algorithmic, and neural network models have been proposed to explain the necessary computations. This work shows how the different types of models behave in the presence of noise. It turns out that only one class of models can function properly in the presence of noise. Since noise appears to be present at all levels of brain physiology, we arrive at the surprising conclusion that the general computational principles for path integration must be the same across all species. Two subtypes of path integration models share the same critical computational principles, and are compared to known neuroanatomy and physiology.
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