Barn owls provide an experimentally well-specified example of a temporal map, a neuronal representation of the outside world in the brain by means of time. Their laminar nucleus exhibits a place code of interaural time differences, a cue which is used to determine the azimuthal location of a sound stimulus, e.g., prey. We analyze a model of synaptic plasticity that explains the formation of such a representation in the young bird and show how in a large parameter regime a combination of local and nonlocal synaptic plasticity yields the temporal map as found experimentally. Our analysis includes the effect of nonlinearities as well as the influence of neuronal noise. DOI: 10.1103/PhysRevLett.87.248101 PACS numbers: 87.18. -h, 43.64. +r, 87.19.La Many animals have in their brain neuronal representations of the outside world, which we call maps. These representations are due to sensory organs. Vision, for instance, provides a direct map through the lens of the eye onto the retina and, accordingly, is dominantly spatial. Audition, on the other hand, has far fewer cues but time is one of them, a very important one. Here we face the question of how a temporal map can arise and provide an answer by considering a specific example, the barn owl's sound localization.Barn owls are nocturnal predators that are able to catch mice in complete darkness. In so doing they reach an amazing azimuthal resolution of 2 ± . Interaural (inter-ear) time differences have been shown [1] to be their only cue. The spatial resolution implies a temporal precision at least as good as 40 ms [2,3].We focus on the laminar nucleus as the first station in the brain receiving input from both ears. Interaural time differences (ITDs) are represented there by means of a place code. That is to say, the azimuthal position is mapped one-to-one onto corresponding neuronal sites in the laminar nucleus, each neuron signaling its preferred azimuthal location through a maximal firing rate. As the stimulus location is varied, so is the maximal ITD response in the laminar nucleus [2]; cf. Fig. 1. Henceforth the resulting map is a neuronal representation of azimuthal stimulus locations. We can now ask two questions. How does it function, in particular, why is the precision that good (40 ms), and how does it arise? As we will see, the answers to both questions are interrelated in that the map as it evolves leads to firing precision.Here we analyze how a novel mechanism of synaptic plasticity [5] gives rise to a temporal map. As was indicated by a numerical study [5], local so-called Hebbian learning depending on spike timing of the pre-and postsynaptic neuron [6,7], which precede and follow the synapse under consideration (hence Hebbian), and small, axonally propagated, synaptic modifications [8] together induce a temporal map. One may call the underlying mechanism "axon-mediated spike-based learning" (AMSL). We now present an analytic solution to the proposed synaptic dynamics and explain the model's performance in dependence upon the learning procedure, biol...