Insects rely predominantly on their olfactory system to sense their environment, locate resources, and move to areas with food.  In static environments (i.e. air and water) with zero flow, odour is dispersed by diffusion, showing smooth concentration gradients from the source. In environments with moving fluids, 

diffusion is trumped by turbulent mixing and odourants are advected in discontinuous filaments with decreased concentrations and filament sizes as they are carried away from the source (Murlis et al., 2000; Webster and Weissburg, 2001; Celani et al 2014). Hence, in either flow condition, overall concentration profile and odor landscape statistics change with distance.

Information about the spatial distribution of odorants can be acquired by comparison between bilateral olfactory organs (Takasaki et al., 2012; Gaudry et al 2013) and temporal signal integration of subsequent samplings (Vickers, 2000; Keene and Waddell, 2007). The American cockroach is equipped with extremely long antennae (40-50 mm) covered by roughly 200,000 olfactory receptor neurons (ORNs), giving a wide working range for odor detection. However, the question whether the ORNs also transmit spatial information of the odor landscapes along the antennae is still open. In principle, all ORNs  bearing the same olfactory receptor along the flagellum converge onto the same glomerulus within the antennal lobe (the first olfactory processing centre, analogous to the mammalian olfactory bulb)(Figure \ref{div-511309}a-a”’). Hence such information about stimulus’ location along an antenna may be lost.  Behavioral studies had shown that cockroaches can efficiently locate a source of the female sex pheromone also after the removal of one antenna, suggesting that bilateral comparison is not a prerequisite for pheromone localization (Bell and Tobin, 1981; Lockey and Willis, 2015). In addition,  it had recently been shown that  pheromone-responsive ORNs terminate in the macroglomerulus of the antennal lobe with an antennotopic organization. Instead of the typical arrangement of a single projection neuron' (PN) innervation by the ordinary glumeruli, twelve types of pheromone-responsive PNs were identified at the macroglomerulus, maintaining spatially distinct and partially overlapping receptive field along the antenna. 

Is this type of information indeed exclusive only for the female sex pheromone? Raising the question of

why a system would evolve an architecture that seems to discard environmentally relevant information as would have happen if no spatial information can be transmitted by the ordinary ORNs, we searched for alternative mechanisms for encoding odor landscapes along the antennae. 

By integrating information from time-dependent stimulus response of both the ORNs and their corresponding output neurons (the PNs), we suggest a model that can be tuned to enable local gradient detection using a single output neuron within ecologically relevant temporal and spatial scales.... In specific, recent observations from drosophila suggest that response latency of ORNs scale with odor concentration levels  (Martelli et al 2013; Egea-Weiss et al. 2018).  We suggest that these latencies could match the time scales of response propagations of ORNs in a way that facilitates responses of positive odor gradients along the antennae. For testing our hypothesis we developed a linear spiking model for mimicking ORN transmission and PN innervation. Response latencies and propagation time values were obtained by recording response times of ORNs and the corresponding PNs in the antennal lobe of the American cockroaches. Finally, we test applicability of the model for turbulent environment where smooth gradients are replaced by pockets of odor filaments with varying size and density. 

o determine the speed and temporal precision of odorant-evoked spikes in olfactory receptor neurons,