(C) PLOS One This story was originally published by PLOS One and is unaltered. . . . . . . . . . . Cumulative route improvements spontaneously emerge in artificial navigators even in the absence of sophisticated communication or thought [1] ['Edwin S. Dalmaijer', 'School Of Psychological Science', 'University Of Bristol', 'Bristol', 'United Kingdom'] Date: 2024-06 Artificial navigator model Artificial navigators were agents that embarked on journeys from a set starting point to a set goal, although they did not always reach this goal. They were bound by 4 rules, each implemented as an iterative sampling process from a Von Mises distribution. The centre of each distribution was determined by a bearing, and the spread by certainty of information. At each time point, an agent’s heading was updated by sampling each distribution and computing a weighted circular mean (Eq 1). Weights were set at agent initialisation and added up to 1. Precision parameters were based on empirical data (see under “Experimental design”). The first rule was goal direction. The centre of this distribution was the bearing towards the goal b goal , its precision parameter was κ goal , and its weight w goal . The bearing was computed from the coordinates of the goal (x goal ,y goal ) and agent at time t (x t ,y t ) (Eq 2). The purpose of this rule was to orient agents towards the goal, just like pigeons can orient homewards upon being released from unfamiliar sites. This ability likely depends on the sun, as starlings and pigeons can learn to use light and time-of-day to orient towards rewards [21], and pigeons orient homeward when the sun is visible [23]. They can even do so when it is overcast, but their initial orientation becomes more random when magnets are glued to the back of their heads [23], suggesting that pigeons also use an internal compass. For more comprehensive overviews, see [22] and [29]. (2) The second rule was social proximity. This distribution is a weighted composite of a Von Mises distribution for social convergence that is centred on the bearing towards another agent’s estimated future position and another Von Mises distribution for social alignment that is centred on another agent’s current relative heading. The alignment of headings between agents at close proximity is a crucial part of flocking behaviour [42], but at larger distances agents need to converge rather than align to achieve social proximity. Samples drawn from the convergence distribution were weighted with proportion p and those drawn from the alignment distribution with (1-p). Proportion p was drawn from a cumulative normal distribution with mean 0.5 and standard deviation 0.1, which is equivalent to a distance of 30 metres, at which pigeons are estimated to be able to recognise individuals [43]. Both composite distributions have precision parameter κ social , and the combined distribution has weight w social . Bearings towards other agents were computed from an agent’s position at time t, (x t ,y t ) and other agent j’s expected position at time t+1 (Eq 3). The expected position of agent j at time t+1 was estimated on the basis of their velocity v (which was kept constant) and their heading h j,t at time t (Eq 4). (3) (4) The third rule was route memory. This was established during an agent’s first journey, in which passed landmarks were committed to memory. Across the map of 200 by 130 units, 6,500 landmarks were spread. This aligns with landmark detection using pigeon flight routes [26] and edge detection in aerial photography [25]. During consecutive journeys, an agent attempted to fly from one memorised landmark to the next by sampling from a Von Mises distribution centred on the bearing towards the next landmark b landmark , with spread κ memory,i for journey i, and weight w memory (Eq 5; see Fig C in S1 File). There were no memorised landmarks in the first journey, so the spread for κ memory,1 was set to 0, resulting in a completely uniform distribution. For all following journeys, κ memory,i was set to 1.82, 2.29, 2.98, 4.19, and then plateaued at 6.78. This was analogous to a linear decrease in standard deviation from 0.9 to 0.4 and was based on model fits to pigeon homing data (see under “Data reduction and statistics: Pigeons”). Agents proceeded to navigate towards the next landmark l+1 if they came within a threshold distance of landmark l. This threshold was set as 10 times the distance agents could travel between time t and time t+1. The gradual improvement in memory precision over several journeys and the anchoring to landmarks were based on Gaussian process models of pigeon navigation [26]. While the current implementation was less elegant than its inspiration, it was computationally inexpensive, and parsimonious with sampling from distributions of other bearings. (5) The fourth and final rule was continuity. This assured that during journey i, an agent’s next heading at time t+1 would be similar to their heading at time t. The continuity component was sampled from a Von Mises distribution centred on current heading h(t), with precision parameter κ continuity , and weight w continuity . Finally, agents set their next heading by drawing random samples a from each of the Von Mises distributions described above and computing their weighted circular mean (Eqs 6–8). (6) Where: (7) (8) Software was implemented in Python (version 3.10.12) [44] (for tutorials, see [45,46]), using external libraries Matplotlib (version 3.8.2) [47], NumPy (version 1.26.3) [48], SciPy (version 1.12.0) [49], and utm (version 0.7.0) [50]. [END] --- [1] Url: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3002644 Published and (C) by PLOS One Content appears here under this condition or license: Creative Commons - Attribution BY 4.0. via Magical.Fish Gopher News Feeds: gopher://magical.fish/1/feeds/news/plosone/