We study how the arboreal turtle ant (Cephalotes goniodontus) solves a fundamental computing problem: maintaining a trail network and finding alternative paths to route around broken links in the network. Turtle ants form a routing backbone of foraging trails linking several nests and temporary food sources. This species travels only in the trees, so their foraging trails are constrained to lie on a natural graph formed by overlapping branches and vines in the tangled canopy. Links between branches, however, can be ephemeral, easily destroyed by wind, rain, or animal movements. Here we report a biologically feasible distributed algorithm, parameterized using field data, that can plausibly describe how turtle ants maintain the routing backbone and find alternative paths to circumvent broken links in the backbone. We validate the ability of this probabilistic algorithm to circumvent simulated breaks in synthetic and real-world networks, and we derive an analytic explanation for why certain features are crucial to improve the algorithm’s success. Our proposed algorithm uses fewer computational resources than common distributed graph search algorithms, and thus may be useful in other domains, such as for swarm computing or for coordinating molecular robots.

Neural arbors (dendrites and axons) can be viewed as graphs connecting the cell body of a neuron to various pre-and post-synaptic partners. Several constraints have been proposed on the topology of these graphs, such as minimizing the amount of wire needed to construct the arbor (wiring cost), and minimizing the graph distances between the cell body and synaptic partners (conduction delay). These two objectives compete with each other-optimizing one results in poorer performance on the other. Here, we describe how well neural arbors resolve this network design trade-off using the theory of Pareto optimality. We develop an algorithm to generate arbors that near-optimally balance between these two objectives, and demonstrate that this algorithm improves over previous algorithms. We then use this algorithm to study how close neural arbors are to being Pareto optimal. Analysing 14 145 arbors across numerous brain regions, species and cell types, we find that neural arbors are much closer to being Pareto optimal than would be expected by chance and other reasonable baselines. We also investigate how the location of the arbor on the Pareto front, and the distance from the arbor to the Pareto front, can be used to classify between some arbor types (e.g. axons versus dendrites, or different cell types), highlighting a new potential connection between arbor structure and function. Finally, using this framework, we find that another biological branching structure-plant shoot architectures used to collect and distribute nutrients-are also Pareto optimal, suggesting shared principles of network design between two systems separated by millions of years of evolution.

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.

1To create and maintain a backbone routing network is a basic challenge in many engineered and 2 biological systems [1][2][3], from wireless sensor networks and robot swarms to neural circuits 3 and blood circulation. Optimal routing in such networks often seeks to minimize transport 4 delay [4][5][6][7][8], but routing decisions may be influenced by variability in the terrain [9][10][11][12]. Here 5 we find that turtle ants build trail networks that emphasize coherence, keeping the ants together 6 on the trail in a heterogeneous environment, rather than minimizing the distance travelled. The 7 routing backbone of turtle ants (Cephalotes goniodontus), an arboreal species that forages in the 8 1 tree canopy of tropical forests, connects many nests [13][14][15], using trail pheromone that the ants 9 put down continuously, not just on the way back from a food source. Unlike species that forage 10 on the ground, arboreal ants are constrained to travel within the vegetation network of branches 11 and vines. We compared observed turtle ant trails with random, hypothetical trails in the same 12 surrounding vegetation. Strikingly, the trails do not minimize distance travelled, but instead 13 minimize the total number of nodes in the backbone, and favor nodes with 3d configurations 14 that are easily reinforced with pheromone. Thus, rather than forming the shortest paths, turtle 15 ants take advantage of natural variation in the environment to build coherent trails. This ensures 16 that the nests and food sources stay connected, at the expense of longer travel time. This design 17 principle may be beneficial in applications where distributed agents, such as swarms of robots, 18 must coordinate using a communication backbone in complex environments to collectively 19 solve a task, such as building a structure, searching for resources, or surveying terrain [16]. 20 Introduction 21The goal of a backbone routing network is to ensure that there is a path for any two 22 devices on the network to communicate. In real-world systems, however, physical variation in the 23 environment can affect the accuracy and rate of communication [9][10][11][12][17][18][19]. Understanding the 24 physical structure of the environment may improve the design of routing algorithms [16,[20][21][22][23][24], for 25 example, by reducing the search space of possible routing paths and steering network construction 26 away from parts of the terrain that are difficult to reach. 27The 14,000 species of ants have evolved diverse distributed routing and search algorithms to 28 search for, obtain, and distribute resources [25] in the diverse environments that they inhabit [26-29 29]. For example, species such as Formica and Argentine ants, which forage and build trails in 30 a 2d-plane, have minimal constraints on trail geometry [30][31][32], and can minimize the distance 31 travelled by forming trails with branch points that approximate Steiner trees [27, 33, 34], an NP-32 complete generalization of the minimal spanning tree concept. By contrast, many specie...

Understanding the optimization objectives that shape shoot architectures remains a critical problem in plant biology. Here, we performed 3D scanning of 152 Arabidopsis shoot architectures, including wildtype and 10 mutant strains, and we uncovered a design principle that describes how architectures make trade-offs between competing objectives. First, we used graph-theoretic analysis to show that Arabidopsis shoot architectures strike a Pareto optimal that can be captured as maximizing performance in transporting nutrients and minimizing costs in building the architecture. Second, we identify small sets of genes that can be mutated to shift the weight prioritizing one objective over the other. Third, we show that this prioritization weight feature is significantly less variable across replicates of the same genotype compared to other common plant traits (e.g., number of rosette leaves, total volume occupied). This suggests that this feature is a robust descriptor of a genotype, and that local variability in structure may be compensated for globally in a homeostatic manner. Overall, our work provides a framework to understand optimization trade-offs made by shoot architectures and provides evidence that these trade-offs can be modified genetically, which may aid plant breeding and selection efforts.