Self-organized aggregation in cockroaches

Jean-louis Deneubourg

2005, Animal Behaviour

Abstract

Aggregation is widespread in invertebrate societies and can appear in response to environmental heterogeneities or by attraction between individuals. We performed experiments with cockroach, Blattella germanica, larvae in a homogeneous environment to investigate the influence of interactions between individuals on aggregations. Different densities were tested. A first phase led to radial dispersion of larvae in relation to wall-following behaviours; the consequence of this process was a homogeneous distribution of larvae around the periphery of the arena. A second phase corresponded to angular reorganization of larvae leading to the formation of aggregates. The phenomenon was analysed both at the individual and collective levels. Individual cockroaches modulated their behaviour depending on the presence of other larvae in their vicinity: probabilities of stopping and resting times were both higher when the numbers of larvae were greater. We then developed an agent-based model implementing individual behavioural rules, all derived from experiments, to explain the aggregation dynamics at the collective level. This study supports evidence that aggregation relies on mechanisms of amplification, supported by interactions between individuals that follow simple rules based on local information and without knowledge of the global structure.

Figures (8)

Figure 1. (a) Circles represent the detection radius for each cockroach. Two cockroaches detect each other when their interindividual distance (with reference to the head) is equal to or less than 6mm. (b) A moving cockroach A encounters a stopped cockroach B. Based on the assumption of the detection radius, A perceives B (and reciprocally) at a maximum of 12mm. The whole area of mutual perception is represented by the ellipse.

Table 1. Path characteristics of single cockroaches as a function of their spatial position in the arena

Figure 2. (a) Natural logarithm of the fraction of isolated larvae (N,) that are still stopped, and of aggregates (Nz, N3, Na; respectively, aggregates of 2, 3 and 4 larvae) not dissolved, as a function of time. (b) Curves for times below 400 s. For isolated larvae and for each aggregate size, the survival curve plotted on a log-normal scale showed a bilinear pattern. This suggested that stop durations belonged to two subpopulations (Fig. 2). For each aggre- gate size, the experimental survival curves were fitted with equation (1) by minimizing the residual sum of squares to estimate Pshort, Tshorty TLong (Table 3). For each type of stop duration (short or long), the inverse of the mean lifetime (Tshort ANd Tong) gave the individual probability per unit time to end spontaneously the motionless state. As the when encountering a stopped larva (or an aggregate). The probability for a cockroach to stop increased as the number of larvae in its neighbourhood increased (Table 2).

Table 2. Fraction of moving cockroaches that stopped wher encountering N larvae within their perception radius (Fstop,n) anc relative individual probabilities of stopping (1/tstop,n from equatior A8), fraction of stopped cockroaches that left the motionless state after collision with a moving larva (Fcollision,n) and relative individua probabilities of starting to move after a collision (1/tcotlision,n from equation A10) Sample sizes are given in parentheses.

Table 3. Individual probabilities for stopped cockroaches to display short stops and mean lifetime of stop durations as a function of the number of neighbours (N = 1: isolated larva; N = 2: aggregate of two cockroaches, etc.) Sample sizes are given in parentheses.

Table 4. Proportions of larvae that stopped and induced collisions (departure of a stopped larva) when encountering isolated cockroaches or aggregates in experiments and social simulations Experimental proportions are given with lower and upper 95% confidence limits in brackets; sample sizes are in parentheses. *Chi-square test.

Figure 3. Temporal evolution of the mean size of the largest aggregate for (a) 10 larvae and (b) 20 larvae for experiments (10 cockroaches: N = 20; 20 cockroaches: N = 22), social simulations (10 cockroaches: N = 200; 20 cockroaches: N = 200) and nonsocial simulations (10 cockroaches: N = 200; 20 cockroaches: N = 200). Error bars show 95% confidence intervals.

Figure 4. Spatiotemporal aggregation dynamics for experiments, social simulations and nonsocial simulations with (a) 10 and (b) 20 larvae. Black dots: positions of cockroaches as a function of time and angular position.