Billiards with Spatial Memory

Many classes of active matter develop spatial memory by encoding information in space. We present a framework based on mathematical billiards, wherein particles remember their past trajectories. Despite its deterministic rules, such a system is strongly nonergodic and exhibits intermittent statistics and complex pattern formation. We show how these features emerge from the dynamic change of topology. Our work illustrates how the dynamics of a single-body system can dramatically change with spatial memory, laying the groundwork to further explore systems with complex memory kernels.

Modularity and connectivity of nest structure scale with colony size

Large body sizes have evolved structures to facilitate resource transport. Like unitary organisms, social insect colonies must transport information and resources. Colonies with more individuals may experience transport challenges similar to large-bodied organisms. In ant colonies, transport occurs in the nest, which may consist of structures that facilitate movement. We examine three attributes of nests that might have evolved to mitigate transport challenges related to colony size: (1) subdivision-nests of species with large colonies are more subdivided to reduce crowd viscosity; (2) branching-nest tunnels increase branching in species with large colonies to reduce travel distances; and (3) shortcuts-nests of species with large colonies have cross-linking tunnels to connect distant parts of the nest and create alternative routes. We test these hypotheses by comparing nest structures of species with different colony sizes in phylogenetically controlled meta-analyses. Our findings support the hypothesis that nest subdivision and branching evolved to mitigate transport challenges related to colony size. Nests of species with large colonies contain more chambers and branching tunnels. The similarity in how ant nests and bodies of unitary organisms have evolved in response to increasing size suggests common solutions across taxa and levels of biological organization.

Better tired than lost: Turtle ant trail networks favor coherence over short edges

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.

We investigated the trail networks of arboreal turtle ants in the canopy of the tropical forest, to ask what characterizes the colony’s choice of foraging paths within the vegetation. We monitored day to day changes in the junctions and edges of trail networks of colonies in the dry forest of western Mexico. We compared the paths used by the ants to simulated random paths in the surrounding vegetation. We found that the paths of turtle ants prioritize coherence, keeping ants together on the trail, over minimizing the average edge length. The choice of paths reduces the number of junctions in the trail where ants could get lost, and favors junctions with a physical configuration that makes it likely that successive ants will reinforce the same path. Our work suggests that design principles that emphasize keeping information flow constrained to streamlined, coherent trails may be useful in human-designed distributed routing and transport networks or robot swarms.

From foraging trails to transport networks: how the quality-distance trade-off shapes network structure

Biological systems are typically dependent on transportation networks for the efficient distribution of resources and information. Revealing the decentralized mechanisms underlying the generative process of these networks is key in our global understanding of their functions and is of interest to design, manage and improve human transport systems. Ants are a particularly interesting taxon to address these issues because some species build multi-sink multi-source transport networks analogous to human ones. Here, by combining empirical field data and modelling at several scales of description, we show that pre-existing mechanisms of recruitment with positive feedback involved in foraging can account for the structure of complex ant transport networks. Specifically, we find that emergent group-level properties of these empirical networks, such as robustness, efficiency and cost, can arise from models built on simple individual-level behaviour addressing a quality-distance trade-off by the means of pheromone trails. Our work represents a first step in developing a theory for the generation of effective multi-source multi-sink transport networks based on combining exploration and positive reinforcement of best sources.

Nest choice in arboreal ants is an emergent consequence of network creation under spatial constraints

Biological transportation networks must balance competing functional priorities. The self-organizing mechanisms used to generate such networks have inspired scalable algorithms to construct and maintain low-cost and efficient human-designed transport networks. The pheromone-based trail networks of ants have been especially valuable in this regard. Here, we use turtle ants as our focal system: In contrast to the ant species usually used as models for self-organized networks, these ants live in a spatially constrained arboreal environment where both nesting options and connecting pathways are limited. Thus, they must solve a distinct set of challenges which resemble those faced by human transport engineers constrained by existing infrastructure. Here, we ask how a turtle ant colony’s choice of which nests to include in a network may be influenced by their potential to create connections to other nests. In laboratory experiments with Cephalotes varians and Cephalotes texanus, we show that nest choice is influenced by spatial constraints, but in unexpected ways. Under one spatial configuration, colonies preferentially occupied more connected nest sites; however, under another spatial configuration, this preference disappeared. Comparing the results of these experiments to an agent-based model, we demonstrate that this apparently idiosyncratic relationship between nest connectivity and nest choice can emerge without nest preferences via a combination of self-reinforcing random movement along constrained pathways and density-dependent aggregation at nests. While this mechanism does not consistently lead to the de-novo construction of low-cost, efficient transport networks, it may be an effective way to expand a network, when coupled with processes of pruning and restructuring.

Longitudinal Study of Foraging Networks in the Grass-Cutting Ant Atta capiguara Gonçalves, 1944

Colonies of leaf-cutting ants of the genus Atta need to collect large quantities of vegetal substrate in their environment to ensure their growth. They do so by building and extending over time a foraging network that consists of several underground tunnels extending above ground by physical trails. This paper presents a longitudinal study of the foraging network of two mature colonies of the grass-cutting ant Atta capiguara (Gonçalves) located in a pasture in central Brazil. Specifically, we investigated whether the extension of the foraging area of the colonies required to reach new resources occurs by building new and longer underground tunnels or by building new and longer physical trails. Each nest was surveyed at intervals of approximately 15 days during 1 year. At each survey we mapped the position of the tunnel entrances and foraging trails at which activity was observed. In addition, we assessed the excavation effort of the colonies since the last survey by the number and distance to the nest of new tunnel entrances, and the physical trail construction effort by the number and length of newly built physical trails. Our study reveals that in A. capiguara the collection of new resources around the nest required to ensure the continuous growth of the colonies is achieved mainly through the excavation of new underground tunnels, opening at greater distance from the nest, not through the building of longer aboveground physical trails.

Consequences of Climate Change-Induced Habitat Conversions on Red Wood Ants in a Central European Mountain: A Case Study

Simple Summary

The red wood ants are considered to be one of the main ecosystem engineers and keystone species of the habitats in which they exist. Most of the species from this species group inhabit coniferous forests, which, due to the consequences of anthropogenic climate change, are continuously cut down. Therefore, the main habitat of these important species is rapidly disappearing. We investigated the consequences of the absence of conifers (clear-cut area and deciduous forest) on one of the members of this species group, namely Formica polyctena. We have found that compared with the mixed-coniferous forest stand, the absence of coniferous species resulted in significant changes in the colony and nest structure of F. polyctena. In addition, the colony size was also smaller in these sites. These changes suggest that although F. polyctena is able to survive in suboptimal habitats, still their population decline is expected and urges conservation managers to apply necessary action plans for their protection.

Abstract

The consequences of anthropogenic climate change are one of the major concerns of conservation biology. A cascade of negative effects is expected to affect various ecosystems, one of which is Central European coniferous forests and their unique biota. These coniferous forests are the primary habitat of many forest specialist species such as red wood ants. Climate change-induced rising of temperature allows trees to skip winter hibernation, making them more vulnerable to storms that cause wind felling, and in turn, promotes bark beetle infestations that results in unscheduled clear-cuttings. Red wood ants can also be exposed to such habitat changes. We investigated the effects of bark beetle-induced clear-cutting and the absence of coniferous trees on colonies of Formica polyctena, including a mixed-coniferous forest as a reference. Our aim was to investigate how these habitat features affect the nest characteristics and nesting habits of F. polyctena. Our results indicate that, in the absence of conifers, F. polyctena tend to use different alternatives for nest material, colony structure, and food sources. However, the vitality of F. polyctena colonies significantly decreased (smaller nest mound volumes). Our study highlights the ecological flexibility of this forest specialist and its potential to survive under extreme conditions.

Transportation networks inspired by leaf venation algorithms

Biological systems have adapted to environmental constraints and limited resource availability. In the present study, we evaluate the algorithm underlying leaf venation (LV) deployment using graph theory. We compare the traffic balance, travel and cost efficiency of simply-connected LV networks to those of the fan tree and of the spanning tree. We use a Pareto front to show that the total length of leaf venations (LVs) is close to optimal. Then we apply the LV algorithm to design transportation networks in the city of Atlanta. Results show that leaf-inspired models can perform similarly or better than computer-intensive optimization algorithms in terms of network cost and service performance, which could facilitate the design of engineering transportation networks.

Meat ants cut more trail shortcuts when facing long detours

Engineered paths increase efficiency and safety but also incur construction and maintenance costs, leading to a trade-off between investment and gain. Such a trade-off is faced by Australian meat ants, which create and maintain vegetation-free trails between nests and food sources, and thus their trails are expected to be constructed selectively. To test this, we placed an artificial obstacle consisting of 300 paper grass blades between a sucrose feeder and the colony, flanked by walls either 10 cm or 80 cm long. To exploit the feeder, ants could detour around the walls or take a direct route by traversing through the obstacle. We found that, when confronted with a long alternative detour, 76% of colonies removed more grass blades and ants were also 60% more likely to traverse the obstacle instead of detouring, with clearing activity favouring higher ant flow or vice versa. An analysis of cut patterns revealed that ants did not cut randomly, but instead concentrated on creating a trail to the food source. Meat ants were thus able to collectively deploy their trail-clearing efforts in a directed manner when detour costs were high, and rapidly established cleared trails to the food source by focusing on completing a central, vertically aligned trail which was then followed by the ants.

An outer approximation method for the road network design problem

Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.

Balancing building and maintenance costs in growing transport networks

The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost. By varying the coefficient of the combination, the model interpolates between global and local length minimization, i.e., between minimum spanning trees and a local version known as dynamical minimum spanning trees. We show that cost balance within this ensemble of dynamical networks is a sufficient ingredient for the emergence of tradeoffs between the network's total length and transport efficiency, and of optimal strategies of construction. At the transition between two qualitatively different regimes, the dynamics builds up power-law distributed waiting times between global rearrangements, indicating a point of nonoptimality. Finally, we use our model as a framework to analyze empirical ant trail networks, showing its relevance as a null model for cost-constrained network formation.

Robust transport over networks

We consider transportation over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with initial and final marginal constraints on mass transport. We address the situation where initially the mass is concentrated on certain nodes and needs to be transported in a certain time period to another set of nodes, possibly disjoint from the first. The random evolution is selected to be closest to a prior measure on paths in the relative entropy sense-such a construction is known as a Schrödinger bridge between the two given marginals. It may be viewed as an atypical stochastic control problem where the control consists in suitably modifying the prior transition mechanism. The prior can be chosen to incorporate constraints and costs for traversing specific edges of the graph, but it can also be selected to allocate equal probability to all paths of equal length connecting any two nodes (i.e., a uniform distribution on paths). This latter choice for prior transitions relies on the so-called Ruelle-Bowen random walker and gives rise to scheduling that tends to utilize all paths as uniformly as the topology allows. Thus, this Ruelle-Bowen law (𝔐RB) taken as prior, leads to a transportation plan that tends to lessen congestion and ensures a level of robustness. We also show that the distribution 𝔐RB on paths, which attains the maximum entropy rate for the random walker given by the topological entropy, can itself be obtained as the time-homogeneous solution of a maximum entropy problem for measures on paths (also a Schrödinger bridge problem, albeit with prior that is not a probability measure). Finally we show that the paradigm of Schrödinger bridges as a mechanism for scheduling transport on networks can be adapted to graphs that are not strongly connected, as well as to weighted graphs. In the latter case, our approach may be used to design a transportation plan which effectively compromises between robustness and other criteria such as cost. Indeed, we explicitly provide a robust transportation plan which assigns maximum probability to minimum cost paths and therefore compares favourably with Optimal Mass Transportation strategies.

High-Resolution Laser Scanning Reveals Plant Architectures that Reflect Universal Network Design Principles

Transport networks serve critical functions in biological and engineered systems, and yet their design requires trade-offs between competing objectives. Due to their sessile lifestyle, plants need to optimize their architecture to efficiently acquire and distribute resources while also minimizing costs in building infrastructure. To understand how plants resolve this design trade-off, we used high-precision three-dimensional laser scanning to map the architectures of tomato, tobacco, or sorghum plants grown in several environmental conditions and through multiple developmental time points, scanning in total 505 architectures from 37 plants. Using a graph-theoretic algorithm that we developed to evaluate design strategies, we find that plant architectures lie along the Pareto front between two simple length-based objectives-minimizing total branch length and minimizing nutrient transport distance-thereby conferring a selective fitness advantage for plant transport processes. The location along the Pareto front can distinguish among species and conditions, suggesting that during evolution, natural selection may employ common network design principles despite different optimization trade-offs.

Resilience in social insect infrastructure systems

Both human and insect societies depend on complex and highly coordinated infrastructure systems, such as communication networks, supply chains and transportation networks. Like human-designed infrastructure systems, those of social insects are regularly subject to disruptions such as natural disasters, blockages or breaks in the transportation network, fluctuations in supply and/or demand, outbreaks of disease and loss of individuals. Unlike human-designed systems, there is no deliberate planning or centralized control system; rather, individual insects make simple decisions based on local information. How do these highly decentralized, leaderless systems deal with disruption? What factors make a social insect system resilient, and which factors lead to its collapse? In this review, we bring together literature on resilience in three key social insect infrastructure systems: transportation networks, supply chains and communication networks. We describe how systems differentially invest in three pathways to resilience: resistance, redirection or reconstruction. We suggest that investment in particular resistance pathways is related to the severity and frequency of disturbance. In the final section, we lay out a prospectus for future research. Human infrastructure networks are rapidly becoming decentralized and interconnected; indeed, more like social insect infrastructures. Human infrastructure management might therefore learn from social insect researchers, who can in turn make use of the mature analytical and simulation tools developed for the study of human infrastructure resilience.

Local cost minimization in ant transport networks: from small-scale data to large-scale trade-offs

Transport networks distribute resources and information in many human and biological systems. Their construction requires optimization and balance of conflicting criteria such as robustness against disruptions, transport efficiency and building cost. The colonies of the polydomous Australian meat ant Iridomyrmex purpureus are a striking example of such a decentralized network, consisting of trails that connect spatially separated nests. Here we study the rules that underlie network construction in these ants. We find that a simple model of network growth, which we call the minimum linking model (MLM), is sufficient to explain the growth of real ant colonies. For larger networks, the MLM shows a qualitative similarity with a Euclidean minimum spanning tree, prioritizing cost and efficiency over robustness. We introduce a variant of our model to show that a balance between cost, efficiency and robustness can be also reproduced at larger scales than ant colonies. Remarkably, such a balance is influenced by a parameter reflecting the specific features of the modelled transport system. The extended MLM could thus be a suitable source of inspiration for the construction of cheap and efficient transport networks with non-zero robustness, suggesting possible applications in the design of human-made networks.