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Dynamics of aggregation and emergence of cooperation.

Introduction

In animal societies, collective decisions and patterns emerge from a variety of interactions among individuals. Self-organization is the theory of how minimal complexity at the individual level can generate much greater complexity at the collective one. The rules specifying the interactions among the system's components are executed using only local information, that is, without reference to the global pattern. Thus collective decisions that can be made using rules of thumb that require only a limited cognitive ability and a limited knowledge of the environment might be characterized in terms of the multiplicity of parameters as well as by heterogeneity and unpredictability (Camazine et al., 2001).

Most self-organized decisions and patterns arise as a result of a competition between different sources of information that are then amplified through different forms of positive feedback. In contrast, negative feedback often arises "automatically" as a result of the system's constraints (e.g., limits on the supply of food, the space for settlement, and the number of available workers). An example of such processes is the competition between trail recruitments to multiple food sources in social insects or gregarious arthropods (social caterpillars or spiders) where the modulation of communication is essential (Deneubourg and Goss, 1989; Camazine et al., 1990, 2001; Camazine and Sneyd, 1991; Seeley et al., 1991; Seeley, 1995; Fitzgerald, 1995; Detrain et al., 1999; Saffre et al., 1999). For instance, the ability of a bee or an ant to modulate its dancing or trail-laying behaviors, in relation to its perception of the profitability of a particular source, is sufficient for a collective and adapted decision to b e made.

We generally observe a high diversity of collective patterns at both intraspecific and interspecific levels. But how is this diversity produced in self-organized systems? Do individuals need specific behavioral algorithms and a modulation of their communication for each situation? Or do they just modulate some generic rules without changing their individual interactions? Can we find a convergence of similar and simple mechanisms for different species and for different collective tasks? These are fundamental questions, not only for better understanding mechanisms of organization, but also for making the link between the proximal and ultimate view of social evolution (Krebs and Davies, 1997).

To discuss these questions, we choose to focus on a very widespread phenomenon, that of aggregation. It is of particular interest because it is a prerequisite for the development of other forms of cooperation and is involved in many tasks performed by an insect society. In addition, the gathering of individuals at the same place is significant because it is often the consequence of a collective choice.

Through two empirical studies--on the gregarious behavior of cockroaches (Blattela germanica) and on self-assembly in weaver ants (Oecophylla)--we show (1) how collective decisions are a by-product of the mechanisms involved in aggregation; and (2) how different collective patterns, with different functions, arise from the same generic rules, based on the individual response (mainly the resting time) to local signals including the presence of conspecifics (positive feedback). Though we do not deny the possible modulation of a signal depending on the environment, we demonstrate here that such modulation is neither observed nor necessary for the emergence of aggregation patterns.

Self-Assembly in Oecophylla

Ants of the genus Oecophylla (Ledoux, 1950; Holldoler and Wilson, 1978, 1990; Lioni et al., 2001; Lioni and Deneubourg, unpubl. data) are characterized by their capacity to hang on to each other to form chains. This allows the bridging of an empty space, for example between two branches (see Holldobler and Wilson, 1990, pp. 618-629). These self-assembled structures are a particular type of aggregation. In nature the challenge of such an activity is to avoid the formation of multiple small and inefficient chains. What are the mechanisms that allow the colony to focus its activity at a particular and useful site?

To address this question, we set up an experimental apparatus using a binary choice (Fig. la), and we observed how the probability of an ant entering ([P.sub.ci]) or leaving ([P.sub.li]) a chain depends on the size of the chain (Fig. lb). We found that

[P.sub.ci] = a + b[X.sub.i]/1 + c[X.sub.i] (1)

[P.sub.li] = d[X.sub.i]/1 + e[X.sup.h.sub.i] (2)

where [X.sub.i] is the number of ants in the chain i.

The fitting of the experimental values gives the following parameter values: a = 0.55; b = 0.11; c = 0.28 (r = 0.89; P < 0.001); d = 0.33; e = 0.48; h = 1.3 (r = 0.92; P < 0.001).

The function [P.sub.ci] expresses the idea that the probability for an ant to join the chain grows with the number of nestmates already present (X) and reaches a plateau value equal to a + b[X.sub.i]; a is the value of spontaneous hanging when [X.sub.i] = 0. The probability for an ant to leave the chain ([P.sub.li]) decreases with [X.sub.i]. Considering [T.sub.p] as the total population in the nest, we also observed a linear dependence between the arrival flow [[phi].sub.p] and the population remaining in the nest ([T.sub.p] - ([X.sub.1] + ([X.sub.2])).

At the beginning of the experiment, we observe a similar increase in the number of ants in both chains. A slight asymmetry between the populations appears, after 10 mm, and is amplified during the rest of the experiments. After 20 mm there is a strong asymmetry, which results in the survival of one chain with a high number of ants (Fig. 2). The asymmetry is not due to a higher flow of arrivals from the nest to the strongest chain (this flow remains equal on both branches); it is due only to the process of the ants entering and leaving the chains.

Positive feedback mechanisms expressed by equations (1) and (2) generate a nonlinear growth that focuses activity on a single and functional chain instead of on several small and inefficient ones.

Furthermore, these probabilities ([P.sub.ei]) and ([P.sub.li]) can be triggered by the presence of a visual stimulus or by the geometry of the environment (e.g., a dead-end). The symmetry of the set-up can be broken by placing a visual stimulus under one branch (black bar, 1 cm width, placed 6 cm below one branch). In this situation the growth and the persistence of the chain above the stimulus are favored (Fig. 3). There is still an equal flow of arrivals on both branches, and the same logic applies as in the symmetrical setup. The visual stimulus quantitatively changes the individual response by slightly increasing [P.sub.c] and decreasing [P.sub.1], thereby increasing the resting time in the chain. As a result, the visual stimulus can be reached by the ants, and the chain is used as a bridge.

To summarize, this example shows that a slight modulation of the resting time, which corresponds to 1/[P.sub.1], can generate different patterns and allow the colony to focus its activity. The individual response is based on the local density of nestmates and can be triggered by any favorable configuration, such as the presence of leaves in a tree. It is important to note that this decision is reached without any need for an active modulation of the communication.

Cockroach Aggregation and Strain Odor Recognition

Cockroaches in the species Blattella germanica exhibit gregarious behavior in shelters during their resting period. The shelters are an important resource for these insects, and the gregarious behavior facilitates cooperation (Dambach and Goehlen, 1999). Binary choice tests were carried out between two large and identical shelters each with a carrying capacity (S) large enough to contain the whole population. Tested groups of larvae show a strong tendency to aggregate on a unique, randomly selected, resting site (Fig. 4; Rivault and Cloarec, 1998). This collective choice results from a random walk and hence random discovery of the shelter by larvae and a probability [P.sub.i] to leave the shelter i ([P.sub.i] = 1/resting time). Due to inter-attraction between individuals, this probability decreases with the number of conspecifics ([X.sub.i]) in the shelter i and is ruled by an empirical equation very similar to that proposed for Oecophylla (Rivault et al., 1999; Ame et al., Universite Libre de Bruxelles, unpu bl. data):

[P.sub.i] = a/1 + b[X.sup.2.sub.i] (3)

with a = 0.01, b = 0.16. The characteristics of the shelter affect the resting time of the individuals, which for an isolated animal is [congruent to] 1/a. The expression (1 + b[X.sup.2.sub.i]) describes how the presence of other conspecifics increase the resting time. A theoretical model suggests that these basic mechanisms account for the clustering of insects (Rivault et al., 1999; Ame et al., unpubl. data). This model also predicts that other collective patterns can emerge, keeping the same individual rules.

For instance, a group of cockroaches is able to select a single shelter only if the number of shelters is small or its population is large. This result shows that different patterns of aggregation may be spontaneously adopted based only on changes in the environment.

In natural situations, the shelters are not identical, and they are characterized by different parameters, which are more or less easily detected and integrated by an individual. Any parameter of the shelter that increases the individual resting time favors the formation of the cluster in this shelter. Because of the competition between shelters, most of the larvae will aggregate in the site that has the highest resting time. Furthermore, the interactions between individuals increase the probability of an individual staying on the site that produces the largest resting time and benefit per capita.

Individual tests show that the larvae prefer the odor of their own strain to that of another (Rivault et al., 1999). However, in mixed groups with individuals from two strains, experiments show that the final aggregation is not different for mixed or pure groups (Rivault and Cloarec, 1998). In simulations, it is rather easy to take these interactions between strains into account:

[P.sub.1i] = a/1 + b[([X.sub.1i] + [beta][X.sub.2i]).sup.2] (4)

[P.sub.2i] = a/1 + b[([X.sub.2i] + [beta][X.sub.1i]).sup.2] (5)

where [P.sub.1] ([P.sub.2]) are the probabilities for an individual of strain 1 (2) to leave the shelter i, [X.sub.1i] and [X.sub.2i] are respectively the number of individuals of strain 1 and 2 in this shelter i. [beta] is the inter-attraction between both strains: if [beta] = 1, there is no difference between the strains; and if [beta] = 0, there is no inter-attraction between the strains. Simulations show that even with a very low attractivity between strains ([beta] is low), there is no difference between the gregarious patterns of mixed and pure groups.

However, the model also predicts that the two strains are able to segregate when the resting sites are overcrowded (S [congruent to] total population). Each cluster is characterized by a majority of larvae from the same strain. In this case, group closure is an emergent component of the dynamics, in that the segregation is obtained without aggressive parameters or any other form of repulsion between strains. The smaller the shelter and the greater the difference between the two strains ([beta] small), the more easily the segregation emerges. If the two strains are similar enough ([beta] > 0.5), the segregation is never observed. To summarize, the crowding in the shelter and the degree to which individuals recognize each other (proximity between strains given by [beta]) affect the dynamics of aggregation and lead to opposite patterns.

Conclusion and Perspectives

Both examples given in this paper illustrate how one parameter (here the resting time) can produce different patterns of aggregation independent of any active signaling by animals. In cockroaches, the amplification is modulated only by the time spent in a shelter, which is enough to produce the patterns. The resting time is increased by the presence of conspecifics and is used as a key for assessing the quality of the site. In Oecophylla, the same mechanisms act to focus the colonial activity in a particular area.

Our conviction is that these self-organized processes are numerous despite the fact that the individual or group benefits will differ and will occur in different situations. The mechanisms involved in the aggregation and segregation of the cockroaches--amplification of the resting time and chemical recognition--could have their equivalent in different spatial organization of items by insect societies (Camazine, 1991; Deneubourg et al., 1991; Franks and Sendova-Franks, 1992) and of workers from different castes or from different matrilines or patrilines. For gregarious and eusocial insects, communication relies essentially on chemical signals and amplification mechanisms (Camazine et al., 2001). Phenotypic recognition that is mainly chemically based (Vander Meer and Morel, 1998; Rivault et al., 1998, 1999; Lenoir et al., 1999) can be modulated by genetic background and environment and can be associated with division of labor (Bonavita-Cougourdan and Clement, 1994; Wagner et al., 1998).

In cockroaches, the unique modulated parameter contrasts with the different patterns. The shift between aggregation and segregation is obtained without any behavioral modification, such as the introduction of aggressive behavior. In Oecophylla, these mechanisms regulate the location of the chain and prevent the formation of numerous and inefficient ones. Moreover, experimental and theoretical results show that, through such mechanisms, the colony can adjust the number of chains: a small colony will not form more than one chain, but a large colony will be able to produce several functional chains (Lioni and Deneubourg, unpubl. data).

In the context of self-organization and transition between different social organizations, aggregation, and its resulting increase in density, is a prerequisite for the emergence of higher forms of cooperation. The density could be involved in, or even lead, the process of the social differentiation. The interplay between amplification mechanisms (e.g., growth or learning) and the competition in a cluster could be enough to produce the social differentiation that has been described for very different species, such as social spiders (Rypstra, 1993), sea urchins (Grosjean et al., 1996), and ant queens (Fewell and Page, 1999); for a model, see Bonabeau et al. (1998).

Considering specifically the eusocial species, one of the key questions is the emergence of division of labor. Though there is no doubt that some genetic or physiological aspects must be taken into account (Page and Erber, 2002), we can assume that division of labor is also the result of self-organized mechanisms where amplification is essential (Beshers and Fewell, 2001). Eusocieties express a strong correlation between the colony size and the level of individual specialization (Anderson and McShea, 2001): the bigger the colony, the higher the specialization. As we have shown in the weaver ant (the number of chains depends on the colony size) and the cockroach (aggregation and segregation depend on the available place on a site), aggregation can lead to segregation into a few clusters, depending on the total population of the group. Thus, depending on their location, the individuals constituting a cluster will have different probabilities of being involved in one or another task. For example, a cluster locat ed close to the nest entrance will have a higher probability of interacting with the foragers and being involved in collective recruitment. In contrast, a cluster located close to the food reserves will be stimulated to perform the tasks of sorting and management. To summarize, task allocation and individual specialization will be shaped by the dynamics of aggregation and segregation, and in return these specialized activities will shape the spatial organization within the nest.

The consequence of such a generic logic could then be one of the keys to understanding the transition between different forms of cooperativity, and therefore different degrees of sociality. For instance, it could help to explain how animal species have shifted, through evolution, from solitary to some simple forms of social life. Furthermore, it also brings new ideas on how a solitary species might be manipulated to become gregarious, or how a gregarious species might be manipulated to exhibit more complex forms of cooperation and social specialization (see, e.g., the experimental shift from solitary to social organization in the spider Coelotes terrestris, Gunderman et al., 1993). In this context, it is important to notice that even solitary species use amplification mechanisms based on the chemical marking of resting sites or on trail orientation (see, e.g., for spiders, Saffre et al., 1997; B. Krafft, Universite de Nancy, pers. comm.).

Our theoretical results on cockroaches show that a slight inter-attraction between the marking of different individuals may induce the formation of a cluster (see also Saffre et al., 1999). We could hypothesize that, for some species, this marking gives the opportunity to shift from solitary to gregarious behavior: the greater this phenotypic recognition, the easier the shift towards gregariousness. Because genetic proximity is one way to increase phenotypic recognition, the clustering of individuals having a similar genotype should be easier, and the synergy between amplification and genetic proximity should facilitate the emergence of cooperation. Therefore, we consider haplodiploidy to be one element that favors the evolution of cooperativity and sociality, but not the keystone of the process.

Finally, positive feedbacks and their synergy with genetic proximity and phenotypic recognition are essential to resolving cooperation problems and conflict situations. This could explain why these aggregative mechanisms are so widespread in group living systems.

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Acknowledgments

Many thanks to J. M. Ame, Ph. Rasse, and C. Rivault (University of Rennes) for their interest and work on this topics. Jean-Louis Deneubourg and Claire Detrain are research associates of the Belgian National Foundation for Scientific Research. This work was financially supported by grant number 2.4510.01 for Joint Basic Research. Jean-Louis Deneubourg thanks Les Instituts Solvay and the Santa Fe Institute, and the members of the working group "Social Insects."

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JEAN-LOUIS DENEUBOURG *

* To whom correspondence should be addressed. E-mail: j]deneub@ ulb.ac.be

This paper was originally presented at a workshop titled The Limits to Self-Organization in Biological Systems. The workshop, which was held at the J. Erik Jonsson Center of the National Academy of Sciences, Woods Hole, Massachusetts, from 11-13 May 2001, was sponsored by the Center for Advanced Studies in the Space Life Sciences at the Marine Biological Laboratory, and funded by the National Aeronautics and Space Administration under Cooperative Agreement NCC 2-896.
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Author:Deneubourg, Jean-Louis; Lioni, A.; Detrain, Claire
Publication:The Biological Bulletin
Geographic Code:1USA
Date:Jun 1, 2002
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