Do Ants Need to Estimate the Geometrical Properties of Trail Bifurcations to Find an Efficient Route? A Swarm Robotics Test Bed

Interactions between individuals and the structure of their environment play a crucial role in shaping self-organized collective behaviors. Recent studies have shown that ants crossing asymmetrical bifurcations in a network of galleries tend to follow the branch that deviates the least from their incoming direction. At the collective level, the combination of this tendency and the pheromone-based recruitment results in a greater likelihood of selecting the shortest path between the colony''s nest and a food source in a network containing asymmetrical bifurcations. It was not clear however what the origin of this behavioral bias is. Here we propose that it results from a simple interaction between the behavior of the ants and the geometry of the network, and that it does not require the ability to measure the angle of the bifurcation. We tested this hypothesis using groups of ant-like robots whose perceptual and cognitive abilities can be fully specified. We programmed them only to lay down and follow light trails, avoid obstacles and move according to a correlated random walk, but not to use more sophisticated orientation methods. We recorded the behavior of the robots in networks of galleries presenting either only symmetrical bifurcations or a combination of symmetrical and asymmetrical bifurcations. Individual robots displayed the same pattern of branch choice as individual ants when crossing a bifurcation, suggesting that ants do not actually measure the geometry of the bifurcations when travelling along a pheromone trail. Finally at the collective level, the group of robots was more likely to select one of the possible shorter paths between two designated areas when moving in an asymmetrical network, as observed in ants. This study reveals the importance of the shape of trail networks for foraging in ants and emphasizes the underestimated role of the geometrical properties of transportation networks in general.     

Early social context does not influence behavioral variation at adulthood in ants

Early experience can prepare offspring to adapt their behaviors to the environment they are likely to encounter later in life. In several species of ants, colonies show ontogenic changes in the brood-to-worker ratio that are known to have an impact on worker morphology. However, little information is available on the influence of fluctuations in the early social context on the expression of behavior in adulthood. Using the ant Lasius niger, we tested whether the brood-to-worker ratio during larval stages influenced the level of behavioral variability at adult stages. We raised batches of 20 or 180 larvae in the presence of 60 workers until adulthood. We then quantified the activity level and wall-following tendency of callow workers on 10 successive trials to test the prediction that larvae reared under a high brood-to-worker ratio should show greater behavioral variations. We found that manipulation of the brood-to-worker ratio influenced the duration of development and the size of individuals at emergence. We detected no influence of early social context on the level of between- or within-individual variation measured for individual activity level or on wall-following behavior. Our study suggests that behavioral traits may be more canalized than morphological traits.     

Individual complexity and self-organization in foraging by leaf-cutting ants

Leaf-cutting ants cut vegetation into small fragments that they transport to the nest, where a symbiotic fungus cultivated by the ants processes the material. Since the harvested leaf fragments are incorporated into the fungus garden and not directly consumed by the workers, it is expected that foraging workers select plants by responding to those physical or chemical traits that promote maximal fungal growth, irrespective of the potential direct effects of these leaf features on them. In this paper I summarize experimental work focusing on the decision-making processes that occur at the individual level, and discuss to what extent individual complexity contributes to the emergence of collective foraging patterns. Although some basic features of self-organizing systems, such as the existence of regulatory positive and negative feedback loops, are expected to be involved in the collective organization of leaf-cutting ant foraging, I contend that they are combined with complex individual responses that may result from the integration of local information during food collection with an assessment of colony conditions.     

Fallen Branches as Part of Leaf-Cutting Ant Trails: Their Role in Resource Discovery and Leaf Transport Rates in Atta cephalotes

Fallen branches, logs, and exposed roots (fallen branches hereafter) commonly form part of the trunk trail system of leaf-cutting ants that inhabit the tropical rain forest. We studied the role of fallen branches on resource discovering and on leaf transport rates in Atta cephalotes . Fallen branches were common components of the A. cephalotes trail system; they were present in all the nests, and in the majority of the trunk trails examined (13/16). A field experiment revealed that, at the beginning of their foraging activity, ants discovered food sources located at the end of fallen branches earlier than those located on the leaf litter. Additionally, laden ants walked faster along a fallen branch than along soil tracks of the trunk trails. This increment in speed was higher in slow-walking ants ( e.g. , with larger loads) than in fast-walking ants ( e.g. , with smaller loads). These results suggest that the presence of fallen branches may direct the searching effort of leaf-cutters and increase the foraging speed of laden ants when these structures are part of the trunk trail system. The advantages of using fallen branches as part of a trail system, and their potential consequences in the spatial foraging pattern of leaf-cutting ants, are discussed.     

Individual rules for trail pattern formation in Argentine ants (Linepithema humile)

We studied the formation of trail patterns by Argentine ants exploring an empty arena. Using a novel imaging and analysis technique we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times. Then we derived the response function of individual ants to pheromone concentrations by looking at correlations between concentrations and changes in speed or direction of the ants. Ants were found to turn in response to local pheromone concentrations, while their speed was largely unaffected by these concentrations. Ants did not integrate pheromone concentrations over time, with the concentration of pheromone in a 1 cm radius in front of the ant determining the turning angle. The response to pheromone was found to follow a Weber's Law, such that the difference between quantities of pheromone on the two sides of the ant divided by their sum determines the magnitude of the turning angle. This proportional response is in apparent contradiction with the well-established non-linear choice function used in the literature to model the results of binary bridge experiments in ant colonies (Deneubourg et al. 1990). However, agent based simulations implementing the Weber's Law response function led to the formation of trails and reproduced results reported in the literature. We show analytically that a sigmoidal response, analogous to that in the classical Deneubourg model for collective decision making, can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.     

Experimental studies of the capacity of ants for the addition and subtraction of small numbers]

In the laboratory experiments Formica polyctena ants had to transmit the information about the position of a "branch" situated on a long "trunk". Each branch ended in an empty trough, save one filled with syrup. The food was placed on different branches with different frequencies; on the preliminary chosen special branches the troughs were filled substantially more frequently than on the others. For example, in 1993 we chose two special branches, nos. 10 and 20, on which the food was placed with a probability of 1/3, while for any of the other 28 branches the probability was 1/84. When the ants had learnt this, they changed the way of information transmission about the coordinates of the branch containing food and spent less time to transmit the messages about branches nos. 10 or 20. Careful analysis of time required for transmitting messages about trough coordinates suggests that ants "present" the number of a branch in a way similar to that for the Roman figures, and the "special" numbers (10 and 20 in the case) have the same significance as the basic Roman figures V, X, L, etc. Thus, the ants seem to be able, first, to put the duration of a message into agreement with its frequency and, second, to add and subtract small numbers, as people do when use the Roman figures.     

The interaction of thorns and symbiotic ants as an effective defence mechanism of swollen-thorn acacias

Evidence is provided for the interaction of ants (Crematogaster spp.) and thorns as a means of defence against browsing mammals for one species of African myrmecophyte, Acacia drepanolobium. Two experiments were conducted using goats as representative mammalian browsers. In the first experiment, the defences of individual branches were manipulated in order to assess the effectiveness of ants and thorns both on their own and together as anti-herbivore defences. It was shown that ants on their own are more effective defences for a single branch than having neither ants nor thorns, but ants from a single branch do not add significantly to the effectiveness of thorns as an anti-herbivore defence. The second experiment looked at the effect of a whole tree of ants and how they interacted with thorns in the defence of the tree. It was shown that ants from a whole tree do significantly add to the effectiveness of thorns as an anti-herbivore defence. In all cases, the goat refused to go back to and feed from a tree whose ants had just attacked it. Thorns on their own, however, do not act as total browsing deterrents. They slow down the rate of feeding but animals may compensate for this by feeding for longer periods of time. The interaction of a whole tree of ants and thorns is a very effective browsing deterrent which causes the animal to stop feeding almost immediately, therefore keeping the amount of foliage lost to a minimum. These results provide support for the hypothesis that the ant-acacia relationship (in the case of A. drepanolobium) evolved at least partly because of pressure from browsing mammals. Received: 20 October 1997 / Accepted: 28 February 1998     

Ants show a leftward turning bias when exploring unknown nest sites

Behavioural lateralization in invertebrates is an important field of study because it may provide insights into the early origins of lateralization seen in a diversity of organisms. Here, we present evidence for a leftward turning bias in Temnothorax albipennis ants exploring nest cavities and in branching mazes, where the bias is initially obscured by thigmotaxis (wall-following) behaviour. Forward travel with a consistent turning bias in either direction is an effective nest exploration method, and a simple decision-making heuristic to employ when faced with multiple directional choices. Replication of the same bias at the colony level would also reduce individual predation risk through aggregation effects, and may lead to a faster attainment of a quorum threshold for nest migration. We suggest the turning bias may be the result of an evolutionary interplay between vision, exploration and migration factors, promoted by the ants'' eusociality.     

Modeling collective animal behavior with a cognitive perspective: a methodological framework

The last decades have seen an increasing interest in modeling collective animal behavior. Some studies try to reproduce as accurately as possible the collective dynamics and patterns observed in several animal groups with biologically plausible, individual behavioral rules. The objective is then essentially to demonstrate that the observed collective features may be the result of self-organizing processes involving quite simple individual behaviors. Other studies concentrate on the objective of establishing or enriching links between collective behavior researches and cognitive or physiological ones, which then requires that each individual rule be carefully validated. Here we discuss the methodological consequences of this additional requirement. Using the example of corpse clustering in ants, we first illustrate that it may be impossible to discriminate among alternative individual rules by considering only observational data collected at the group level. Six individual behavioral models are described: They are clearly distinct in terms of individual behaviors, they all reproduce satisfactorily the collective dynamics and distribution patterns observed in experiments, and we show theoretically that it is strictly impossible to discriminate two of these models even in the limit of an infinite amount of data whatever the accuracy level. A set of methodological steps are then listed and discussed as practical ways to partially overcome this problem. They involve complementary experimental protocols specifically designed to address the behavioral rules successively, conserving group-level data for the overall model validation. In this context, we highlight the importance of maintaining a sharp distinction between model enunciation, with explicit references to validated biological concepts, and formal translation of these concepts in terms of quantitative state variables and fittable functional dependences. Illustrative examples are provided of the benefits expected during the often long and difficult process of refining a behavioral model, designing adapted experimental protocols and inversing model parameters.     

Composite collective decision-making

Individual animals are adept at making decisions and have cognitive abilities, such as memory, which allow them to hone their decisions. Social animals can also share information. This allows social animals to make adaptive group-level decisions. Both individual and collective decision-making systems also have drawbacks and limitations, and while both are well studied, the interaction between them is still poorly understood. Here, we study how individual and collective decision-making interact during ant foraging. We first gathered empirical data on memory-based foraging persistence in the ant Lasius niger. We used these data to create an agent-based model where ants may use social information (trail pheromones), private information (memories) or both to make foraging decisions. The combined use of social and private information by individuals results in greater efficiency at the group level than when either information source was used alone. The modelled ants couple consensus decision-making, allowing them to quickly exploit high-quality food sources, and combined decision-making, allowing different individuals to specialize in exploiting different resource patches. Such a composite collective decision-making system reaps the benefits of both its constituent parts. Exploiting such insights into composite collective decision-making may lead to improved decision-making algorithms.     

Sink strength manipulation in branches of a Mediterranean woody plant suggests sink-driven allocation of biomass in fruits but not of nutrients in seeds

The relative autonomy of branches within an individual plant may favor different resource allocation responses after reproductive losses. The assessment of these reproductive strategies at the branch level before their integration at the plant level would provide more insight into how plants deal with reproductive losses. Here, we present a field experiment to assess changes in the allocation strategies at the branch level after sink strength manipulation in a Mediterranean woody plant (Cistus ladanifer). We applied three levels of removal of developing fruits (75, 25 and 0 %) on branches of the same plants, and measured their effects on resource allocation (biomass, nitrogen and phosphorus) and seed production after controlling for the effects of branch diameter and leaf weight per branch. Our results suggest that after experimental fruit thinning, C. ladanifer branches presented a sink-driven allocation of biomass to fruits but this was not the case for the allocation of nutrients to seeds, which could be driven by competition with leaf biomass. Reductions in biomass per fruit resulted in a reduction in seed output since the average weight per seed remained constant. From these results, it could be suggested that an heterogeneous distribution of fruit losses among the branches within a crown would produce a higher impact on reproductive output than a more equitable distribution.     

Pheromone trail decay rates on different substrates in the Pharaoh's ant, Monomorium pharaonis

Abstract. Many ants use pheromone trails to organize collective foraging. This study investigated the rate at which a well‐established Pharaoh's ant, Monomorium pharaonis (L.), trail breaks down on two substrates (polycarbonate plastic, newspaper). Workers were allowed to feed on sucrose solution from a feeder 30 cm from the nest. Between the nest and the feeder, the trail had a Y‐shaped bifurcation. Initially, while recruiting to and exploiting the feeder, workers could only deposit pheromone on the branch leading to the feeder. Once the trail was established (by approximately 60 ants per min for 20 min), the ants were not allowed to reinforce the trail and were given a choice between the marked and unmarked branches. The numbers of ants choosing each branch were counted for 30 min. Initially, most went to the side on which pheromone had been deposited (80% and 70% on the plastic and paper substrates, respectively). However, this decayed to 50% within 25 min for plastic and 8 min for paper. From these data, the half‐life times of the pheromone are estimated as approximately 9 min and 3 min on plastic and paper, respectively. The results show that, for M. pharaonis, trail decay is rapid and is affected strongly by trail substrate.     

A simple threshold rule is sufficient to explain sophisticated collective decision-making

Decision-making animals can use slow-but-accurate strategies, such as making multiple comparisons, or opt for simpler, faster strategies to find a 'good enough' option. Social animals make collective decisions about many group behaviours including foraging and migration. The key to the collective choice lies with individual behaviour. We present a case study of a collective decision-making process (house-hunting ants, Temnothorax albipennis), in which a previously proposed decision strategy involved both quality-dependent hesitancy and direct comparisons of nests by scouts. An alternative possible decision strategy is that scouting ants use a very simple quality-dependent threshold rule to decide whether to recruit nest-mates to a new site or search for alternatives. We use analytical and simulation modelling to demonstrate that this simple rule is sufficient to explain empirical patterns from three studies of collective decision-making in ants, and can account parsimoniously for apparent comparison by individuals and apparent hesitancy (recruitment latency) effects, when available nests differ strongly in quality. This highlights the need to carefully design experiments to detect individual comparison. We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out. However, by using a simple threshold rule, decision-making groups are able to effectively compare options, without relying on any form of direct comparison of alternatives by individuals. This parsimonious mechanism could promote collective rationality in group decision-making.     

Does substrate coarseness matter for foraging ants? An experiment with Lasius niger (Hymenoptera; Formicidae)

We investigated whether workers of the ant species Lasius niger are able to sense and discriminate the coarseness of the substrate on which they walk. First, we studied the way in which substrate coarseness affects the ants' locomotory behaviour. Second, we investigated the spontaneous preference of ants for substrates of different coarseness. And third, we tested with a differential conditioning procedure the ants' capacity to learn to associate a given coarseness with a food reward. The locomotory behaviour of ants differed according to substrate coarseness: ants moved significantly faster and had more sinuous trajectories on a fine than on a coarse substrate. No spontaneous preference for a substrate of a given coarseness was observed and, even after 20 successive conditioning trials, there was little evidence of the effect of experience on substrate coarseness discrimination. Overall however, ants trained on fine sand made significantly more correct choice than those trained on coarse sand. We discuss these results and argue that in L. niger substrate coarseness may be more important at the collective level, by interacting with the chemical properties of the pheromone trail used in mass recruitment to food source, than at the individual level.     

Angiogenic morphogenesis driven by dynamic and heterogeneous collective endothelial cell movement

Angiogenesis is a complex process, which is accomplished by reiteration of modules such as sprouting, elongation and bifurcation, that configures branching vascular networks. However, details of the individual and collective behaviors of vascular endothelial cells (ECs) during angiogenic morphogenesis remain largely unknown. Herein, we established a time-lapse imaging and computer-assisted analysis system that quantitatively characterizes behaviors in sprouting angiogenesis. Surprisingly, ECs moved backwards and forwards, overtaking each other even at the tip, showing an unknown mode of collective cell movement with dynamic 'cell-mixing'. Mosaic analysis, which enabled us to monitor the behavior of individual cells in a multicellular structure, confirmed the 'cell-mixing' phenomenon of ECs that occurs at the whole-cell level. Furthermore, an in vivo EC-tracking analysis revealed evidence of cell-mixing and overtaking at the tip in developing murine retinal vessels. In parametrical analysis, VEGF enhanced tip cell behavior and directed EC migration at the stalk during branch elongation. These movements were counter-regulated by EC-EC interplay via γ-secretase-dependent Dll4-Notch signaling, and might be promoted by EC-mural cell interplay. Finally, multiple regression analysis showed that these molecule-mediated tip cell behaviors and directed EC migration contributed to effective branch elongation. Taken together, our findings provide new insights into the individual and collective EC movements driving angiogenic morphogenesis. The methodology used for this analysis might serve to bridge the gap in our understanding between individual cell behavior and branching morphogenesis.     

An ambiguous function of an alarm pheromone in the collective displays of the Australian meat ant,Iridomyrmex purpureus

Alarm pheromones, which have been documented in many species of ants, are thought to elicit responses related to aggressive or defensive behaviour. The volatile odour 6-methyl-5-hepten-2-one is described as an alarm pheromone in several species of ants, including the Australian meat ant, Iridomyrmex purpureus. The alarm pheromone is released by displaying workers that aggregate in the characteristic collective display grounds, located mid-way between colonies or near contested food trees. Workers are typically more aggressive at the latter location, and the alarm pheromone may regulate the collective level of aggression. We investigated this possibility by exposing displaying workers to synthesised alarm pheromone 6-methyl-5-hepten-2-one in a field experiment, and measuring their aggressive behaviour. We found no evidence that exposure to synthesised alarm pheromone caused changes in the aggressive level of workers. Subsequent field experiments revealed that the pheromone functions as an attractant, thereby increasing the density of displaying workers. More densely populated workers also display more aggressively, indicating that the interaction rate of displaying workers may determine the level of aggression in collective displays. This underlying mechanism can explain why displaying ants are more aggressive at the more densely populated food-tree locations than those displaying at locations midway between two neighbouring colony nest sites.     

From individual to collective displacements in heterogeneous environments

Animal displacement plays a central role in many ecological questions. It can be interpreted as a combination of components that only depend on the animal (for example a random walk) and external influences given by the heterogeneity of the environment. Here we treat the case where animals switch between random walks in a homogeneous 2D environment and its 1D boundary, combined with a tendency for wall-following behaviour (thigmotactism) that is treated as a Markovian process. In the first part we use mesoscopic techniques to derive from these assumptions a set of partial differential equations (PDE) with specific boundary conditions and parameters that are directly given by the individual displacement parameters. All assumptions and approximations made during this derivation are rigorously validated for the case of exploratory behaviour of the ant Messor sanctus. These PDE predict that the stationary density ratio between the 2D (centre) and 1D (border) environment only depends on the thigmotactic component, not on the size of the centre or border areas. In the second part we test this prediction with the same exploratory behaviour of M. sanctus, in particular when many ants move around simultaneously and may interact directly or indirectly. The prediction holds when there is a low degree of heterogeneity (simple square arena with straight borders), the collective behaviour is “simply” the sum of the individual behaviours. But this prediction breaks down when heterogeneity increases (obstacles inside the arena) due to the emergence of pheromone trails. Our approach may be applied to study the effects of animal displacement in any environment where the animals are confronted with an alternation of 2D space and 1D borders as for example in fragmented landscapes.     

嵌套式回归建立树木生物量模型

 该文介绍了一种建立树木生物量模型的简单快速方法——嵌套式回归。基本原理是以枝轴为基本单位, 逐级拟合。过程是把枝条分解成枝轴, 从枝轴到枝条, 再到单株, 拟合不同层次或尺度的生物量模型。建立枝轴生物量方程, 估计各级枝轴生物量, 将枝轴生物量(实测值或模拟值)总和起来便得到枝条生物量。由于样本单元之间有包含关系, 实际测定的样本很小, 具有快速实用的特点。检验结果显示, 模型预测值和实测值具有较高的一致性。     

Foliar boron applications increase the final number of branches and pods on branches of field-grown soybeans

Our previous work demonstrated that boron (B) supplied to soybeans (Glycine max [L.] Merrill cv `Williams 82') by a stem infusion technique increased the number of pods on branches and led to a significant yield increase. Therefore, research was continued to determine whether soil or foliar applications of B could be used to achieve the same results. Field experiments were completed with both soil and foliar applications of B. Only the foliar applications of B resulted in a significant increase in the number of pods/branch. When split foliar treatments were applied twice during flowering, the total application of 0.56 kilograms of B per hectare was the optimal treatment for increasing pods/branch. In a second field experiment in 1987, soybeans were treated weekly from flowering through podfill with six split foliar applications of aqueous H₃BO₃ solutions so that total applications were either 0, 1.1, or 2.24 kilograms of B per hectare. Foliar applications increased the number of branches/plant at the end of the season and significantly stimulated the formation of pods on branches, with 1.12 kilograms of B per hectare being the optimal treatment for these variables. This rate also tended to increase the number of seeds/plant and seed yield/plant. A duplicate experiment with minor modifications was conducted during the summer of 1988, and again the 1.12 kilograms of B per hectare application rate resulted in significant increases in number of branches at harvest as well as number of pods on branches. The 2.24 kilograms of B per hectare application rate also significantly increased these parameters. Foliar B applications induced increases in leaf B concentration far above the 60 micrograms per gram level that was previously accepted as the upper level of tolerance for soybeans. Since optimal branching and per plant yield parameters were achieved by plants with B leaf concentrations greater than 160 micrograms per gram, the accepted range of soybean tolerance for B must be reconsidered when B is foliarly applied.