Information cascade ruling the fleeing behaviour of a gregarious insect

Animal Behaviour 85 (2013) 1271e1285

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Information cascade ruling the fleeing behaviour of a gregarious insect Michel-Olivier Laurent Salazar*, Jean-Louis Deneubourg, Gregory Sempo Unit of Social Ecology, Université Libre de Bruxelles, Brussels, Belgium

a r t i c l e i n f o Article history: Received 5 October 2012 Initial acceptance 8 November 2012 Final acceptance 20 February 2013 Available online 12 April 2013 MS. number: 12-00772R Keywords: cockroach collective fleeing modelling Periplaneta americana signal amplification

Collective fleeing is a complex process resulting from a network of environmental stimuli and interindividual interactions. Studies on fleeing behaviour have focused on the information spread initiated by a few stimulated individuals. Our goal was to link individuals’ responses to the collective fleeing dynamics for gregarious insects simultaneously exposed to a stimulus. We found that an information cascade process occurs in groups of cockroaches, Periplaneta americana, simultaneously exposed to a light stimulus. Moreover, the global fleeing pattern depended on group size. The steps of the response (reacting to the stimulus, finding an opening and leaving the shelter) differed in their sensitivity to group size. First, immobile individuals inhibited the fleeing response, while moving individuals amplified it. Second, once individuals had reacted, they reached an opening and stopped. Their low probability per unit time of finding this opening was constant regardless of group size or the mobility level of group members. Finally, the individual probability of leaving the shelter increased with the number of moving individuals still inside. We integrated the different behavioural steps, analysed independently, into a stochastic model. The results based on this model are in agreement with our experimental observations. This model constitutes a template that enables the exploration of the influence of environmental and social factors at work in other species and situations. Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

A fleeing behaviour is a reaction to a threatening stimulus that moves an individual away from the perceived threat (Driver & Humphries 1988; Eilam 2005). These behaviours are sufficiently unsystematic to prevent a predator from predicting the position or actions of the prey. Although individual fleeing behaviour has been studied extensively (e.g. Domenici et al. 2008, 2011a, b; Dupuy et al. 2011; Card 2012), the dynamics of group fleeing behaviour and the mechanisms of information transfer among group members are still poorly understood (Humphries & Driver 1970; Driver & Humphries 1988; Marras et al. 2011; King et al. 2012). The effect of group living on an individual’s probability of surviving predator attacks has been studied in many animal species (Davis 1975; Treherne & Foster 1981; Vulinec & Miller 1989; Vulinec 1990; Uetz et al. 2002; Caro 2005; Crane et al. 2012; Sorato et al. 2012). For instance, individuals within a group could reduce their domain of danger by occupying a central location (Hamilton 1971), decrease their probability of being attacked through a dilution effect (Foster & Treherne 1981) and/or benefit from the cognitive confusion of predators caused by a large number of possible targets (Landeau & Terborgh 1986; Ruxton et al. 2007; Ioannou et al. 2012). During an attack, the probability of being the targeted prey is lower within a * Correspondence: M.-O. Laurent Salazar, Unit of Social Ecology, CP. 231, Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe 1050, Brussels, Belgium. E-mail address: [email protected] (M.-O. Laurent Salazar).

group, whereas individual risk increases when separated from the group. This decreased survivorship of separated individuals has been demonstrated in several studies of various species, for example seaskaters, Halobates robustus (Treherne & Foster 1982), whirligig beetles, Gyrinus sp. (Watt & Chapman 1998), desert locusts, Schistocerca gregaria (Bazazi et al. 2008), Mormon crickets, Anabrus simplex (Sword et al. 2005; Bazazi et al. 2010), and redshanks, Tringa totanus (Quinn & Cresswell 2006). The probability of detecting a predator and, consequently, of alerting other group members can also increase with group size, either because more individuals are engaged in vigilance or simply because the presence of ‘many eyes’ increases the probability of detection (Short 1961; Pulliam 1973). This increased probability of detecting a predator is obtained even if individual vigilance declines (Roberts 1996; Childress 2003; Beauchamp 2008; Michelena & Deneubourg 2011; Gosselin-ildari & Koenig 2012). In groups in which earlier predator detection is not observed, a predator attack can induce a response from the victim that is then amplified through an information cascade within the group, mediated, for example, by contact (e.g. Kidd 1982). Once fleeing begins, the number of fleeing individuals can confuse the predator (Davis 1975; Treherne & Foster 1981; Vulinec & Miller 1989; Uetz et al. 2002; Caro 2005; Jeschke & Tollrian 2007). These benefits are not mutually exclusive, and each can play a role depending on the predator (Vulinec & Miller 1989; Watt & Chapman 1998; Sorato et al. 2012). Among the numerous factors that influence fleeing behaviour and its efficiency are the characteristics of the stimulus, group size

0003-3472/$38.00 Ó 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anbehav.2013.03.014

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

and the familiarity of the environment. The general scheme utilized in previous fleeing dynamics studies is based on an asymmetrical attack of the group by predators, in which case the threatening stimulus is likely to be closer to some individuals, whereas for other individuals the perception of it will be delayed or not even occur directly. The individual response and the collective pattern exist in a complex relationship between individual perception of the stimulus and the spreading of alarm signals between group members. Owing to the use of asymmetrical stimulation, these previous studies do not make it possible to uncouple the stimulation from the spread of information. Although signal amplification among individuals exposed to an asymmetrical threat is important for the survival of individuals within a group, it is less clear whether such amplification occurs in homogeneously exposed groups. In this study, we investigated whether amplification does take place. We simultaneously exposed all members of a group to a stimulus to isolate the effects of any amplification of the signal on the collective pattern. Experiments symmetrically exposing a group to a threatening stimulus have rarely been conducted. Examples include the sudden appearance of a large predator above a group (e.g. insects: Gish et al. 2010; copepods: Buskey et al. 1986; Buskey & Hartline 2003; crustaceans: Forward 1976; fish: Malavasi et al. 2008) or a sudden noise (cattle or flock of birds: Mott 1980; Manci et al. 1988). In these cases, the threatening stimulus was fast/large enough to prevent any delay between group members’ perceptions, ensuring simultaneous exposure of all individuals. Aside from the study of the natural occurrence of these stimuli, such research is valuable because the exposure of animal groups to stressful stimuli is a challenge for wildlife conservation and animal rearing, as stressed animals can injure themselves (Manci et al. 1988; Bowles 1995; Malavasi et al. 2008). In this study, we investigated the influence of group size on the collective fleeing behaviour of the American cockroach, Periplaneta americana, which has a cosmopolitan distribution and is closely associated with human dwellings (Bell & Adiyodi 1982). This species is negatively phototactic and forms aggregations in dark, warm and damp places during daylight hours (Canonge et al. 2011). When confronted with a sudden illumination of their resting place, they initiate a fleeing response (Bell & Adiyodi 1982; Okada & Toh 1998; Domenici et al. 2008). Periplaneta americana has many predators and some specific parasitoid species (Bell & Adiyodi 1982); however, its close association with human dwellings makes humans one of their primary threats. Some characteristics of P. americana (nocturnal, gregarious, shelters in confined spaces and flees by running) are shared with all domestic cockroach species (Grandcolas 1998). In patchy environments such as human-made ones, it may be advantageous to form groups in confined shelters and be able to flee collectively when disturbed, thus enabling better escape from humans (Grandcolas 1998). Based on the ecology of P. americana, a small shelter with a few openings is an appropriate reproduction of the environment described above. Moreover, light disturbance is a good indication of imminent predation risk because it signals the possible destruction of their shelter. Consequently, we used the light avoidance behaviour of this species to investigate the influence of conspecifics’ activity and group size on fleeing behaviour. With this global stimulus, we observed and analysed how the alarm signal is amplified even though all individuals were exposed to the stimulus simultaneously. METHODS Biological Model Periplaneta americana is a reddish-brown nocturnal cockroach of the Blattidae family that mostly uses tactile, vibratory and olfactory

cues (Bell & Adiyodi 1982). In the presence of light, cockroaches will hide in any dark place they find. Fleeing behaviour is initiated by the perception of light with their compound eyes and the two ocelli situated near the base of the antennae (Bell & Adiyodi 1982). During the fleeing response, other stimuli are detected principally by the antennae, legs and cerci. The antennae allow the detection and recognition of approaching objects (e.g. predators or conspecifics) and also intervene in guiding the cockroach in its fleeing route (Camhi & Johnson 1999). The legs detect soil vibrations, which could indicate the presence of an approaching predator or a conspecific (Schwartzkopff 1974; Schaefer et al. 1994). Finally, the cerci detect changes in air speed and tactile stimuli and are the principal organs used in detecting the direction of wind disturbances (Dagan & Volman 1982; Kanou et al. 2006). Experimental Set-up The experiments were conducted in a circular arena (Fig. 1a) that had an electric fence (19 V, 0.2 A) composed of three aluminium bands with alternate charges to prevent the cockroaches from escaping. The floor of the arena was covered with white paper (120 g/m2), which was changed after each experiment to prevent any chemical marking. A plastic ring 25 cm in diameter and 4.5 cm in height, centred in the arena, constituted the shelter. To test whether there was a collective choice while fleeing, two openings of 3
1.5 cm placed symmetrically opposite each other were the only ways out of the shelter. A glass cover was placed on top of the ring to prevent the cockroaches from leaving. A light bulb (Philips A55 FR, 100 W) centred on the arena at a height of 50 cm above the glass was switched on at the start of each experiment. An opaque tube enclosing the light bulb and reducing the light beam to the diameter of the shelter ensured that only the inside of the shelter was illuminated, with the rest of the arena staying dark. When the light was turned on, the inside of the shelter received approximately 1700 lx. These measurements were performed with

(a) Webcam Electric fen

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Figure 1. (a) Experimental set-up. Cockroaches were placed inside a plastic ring (shelter), which was illuminated with a lamp. The beam of light was shaded by an opaque tube so as to illuminate only the interior of the shelter. (b) Timeline of an experiment. Taking the illumination of the shelter as t0, we measured the reaction time (RT), arrival time (AT) and exit time (ET) of each individual. The waiting time (WT) is the time elapsed between AT and ET.

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

a luxmeter (Testo 545, Testo NV/SA, resolution: 1 lx). A webcam was used to record the cockroaches’ behaviour inside the shelter (20 frames/s). The experiments were conducted in a dark room illuminated by red light. This arrangement allowed us both to see and to keep the room ‘dark’ for the cockroaches (Mote & Goldsmith 1970). Experimental Procedure From the rearing room, we isolated into plastic containers (36
24 cm and 14 cm high) adult male cohorts of the same age that had undergone their imaginal moulting during the same month (see Appendix 1 for more details on P. americana rearing conditions). Only male adults were tested to exclude any behavioural variations related to the ovarian cycle (Paterson & Weaver 1997). Damaged individuals with missing leg segments or without antennae were rejected. According to the tested condition, isolated individuals (93 replicates) and groups of 2, 5, 10 or 20 cockroaches (40 replicates for each group size) were placed in plastic containers the day before the trial and were kept in the dark until the start of their respective trials. Our group sizes are consistent with group sizes used in the literature (e.g. Wharton et al. 1968; Leoncini & Rivault 2005). Although studies on aggregations in natural environments have not been conducted, empirical observations show that the number of individuals in an aggregation can vary greatly. The cockroaches had access to a piece of cotton soaked in water and dog pellets (Tom & Co., Delhaize Group, Brussels, Belgium). Before the start of each trial, the arena was cleaned with denatured ethanol, and a new sheet of paper was placed on the floor. After 10 min, the group was introduced under light CO2 narcosis into the shelter (the openings were closed), as is standard procedure (Jeanson et al. 2003, 2005; Halloy et al. 2007), and remained there for 30 min before the start of the trial. After this waiting period, the openings were opened and the light was turned on. The webcam recorded the group’s response for 5 min or until all of the cockroaches had left the shelter (Fig. 1b). As noted above, P. americana is a nocturnal animal that forms aggregations during daylight hours. During the night, they are active and leave their shelter to forage (Bell & Adiyodi 1982). For this reason, all trials were performed during daylight hours corresponding to the resting phase of P. americana. We recorded the following parameters. (1) Reaction time (RT) for each individual was the time interval between the turning on of the light (t0) and the initiation of its fleeing behaviour. We considered an individual to be reacting when it rotated its body or moved forward/backwards. (2) Arrival time (AT) for each individual was the time interval between the turning on of the light (t0) and the arrival at an opening. A cockroach was considered to have arrived when its head reached an opening. Individuals always stopped when arriving at an opening. (3) Waiting time (WT) was the time interval between the arrival at an opening and leaving the shelter (ET), defined as the moment at which the cockroach’s body was completely outside the shelter. The exit time (ET) is equal to ATþWT. We did not observe any crowding effect at the openings; an opening was always occupied by only one individual at a time. Measurements As the aim of our study was to investigate the fleeing behaviour, including individual RTs, we excluded trials in which at least one individual was walking prior to t0 (0.46, 0.19, 0.07, 0.04 and 0.04 of all individuals tested were moving at the beginning of trials with group sizes of 1, 2, 5, 10 and 20, respectively), leaving us with

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50, 26, 30, 29 and 27 replicates for group sizes of 1, 2, 5, 10 and 20 individuals, respectively (see Appendix 2). From the groups of 20 individuals in which all were immobile, seven trials were discarded owing to the death of an individual (see Appendix 3). From the isolated individuals, eight outliers were detected in the RT data using the ROUT method for outlier detection (Q ¼ 0.01; Motulsky & Brown 2006); these individuals showed strong atypical behaviour possibly because of poor condition (i.e. injuries or other health issues not visible prior to the experiment), and these trials were omitted from the analysis. Therefore, the number of retained replicates were as follows: one individual: N ¼ 42; two individuals: N ¼ 26; five individuals: N ¼ 30; 10 individuals: N ¼ 29; and 20 individuals: N ¼ 20. All of our time measurements are in seconds; however, for clarity, we express probability per unit time as probability per decisecond (per ds). RESULTS Qualitative Behavioural Description Prior to the illumination of the shelter, the individuals were motionless (with only their antennae moving or cleaning themselves). The trials began with the turning on of the light (t0). Once they perceived the stimulus, the cockroaches reacted by rotating their bodies or moving forwards/backwards. Their position within the shelter did not influence their reaction probability (see Appendix 4 for more information). After their initial reaction, they began to run, often maintaining contact with the wall of the shelter, which is consistent with their wall-following behaviour (Camhi & Johnson 1999). After running inside the shelter for a few seconds, individuals found one of the openings (AT), which they always waited in front of for a few seconds (WT) before leaving the shelter (ET). Qualitatively, reactions and exits appeared to occur in a spontaneous manner or after a collision with a moving individual (for more information on the fleeing behaviour of isolated individuals see Appendix 1). Global Behavioural Description The global profile of the average fraction of moving individuals (M) inside the shelter as a function of time was qualitatively the same for the four group sizes: a rapid increase in moving individuals followed by a slower decrease resulting from the individuals leaving the shelter (Fig. 2). Qualitatively, this first analysis shows that the maximum number of moving individuals was reached faster by the larger groups. In each trial, all individuals reacted to the light stimulus before any individual reached an opening. Reaction Times We used the methods developed by Pillot et al. (2011) and the latency time to characterize the probability of changing behavioural states. The latencies were recorded as a function of the numbers of moving (M) and immobile (U) individuals. The video recording consisted of a video frame each 0.05 s. Reactions were well-defined and discrete events with this frame rate; however, when we observed two individuals reacting within the same 0.05 s interval, we assigned half this value to DRTi (0.025 s), and they were ascribed to different reaction ranks. The latency of the first reaction (i ¼ 1) is the time interval between the moment we turned on the light (t0) and the first reaction. The latency DRTi of individual i corresponds to the time elapsed (s) between the reaction of individual i1 and individual i (the first individual to react is ranked 1; the second ranked 2 and so forth).

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The distributions of experimental latencies for all ranks i could be fitted by an exponential distribution (R2 > 0.80; Kolmogorove Smirnov test: P > 0.25 for all ranks of all group sizes; Fig. 3; more examples are shown in Appendix 5, Figs A4, A5, A6, A7). This finding indicates that, for the same configuration (numbers of moving and immobile individuals), the reaction probability (li) per unit time is constant. DRTi is the inverse of the reaction probability and of the number of immobile individuals (U; U ¼ G þ 1  i; G is the group size).

DRTi ¼ RTi  RTi1 ¼

1 U li

(1)

Our results indicate that the average reaction time of the first individual to react for each trial ð < DRT1 >Þ decreased with group size (G; two-tailed KruskaleWallis test: H4 ¼ 69.095, P < 0.0001). This decrease follows the fitted equation < DRT1 > ¼ 3:6G0:89 (R2 ¼ 0.34; KolmogoroveSmirnov test on the mean values: P > 0.99; Fig. 4). In this case, the number of still immobile individuals (U) is the same as the group size (G) because there are no moving individuals. Based on this fitting and on equation 1 1
, we calculate that the reaction probability for < DRT1 > ¼ Gl1 a the first individual to react is l1 ¼ d per ds where a ¼ 0.028 and G d ¼ 0.11.

We tested the relationship between the reaction probability and the numbers of moving and immobile individuals. Equation 2 takes into account the accelerating and inhibitory effects of the moving and immobile individuals, respectively (Michelena & Deneubourg 2011; Pillot et al. 2011).

li ¼

1 a þ bM c ¼ DRTi ðG þ 1  iÞ Ud

(2)

Parameter a corresponds to the reaction probability when G ¼ 1. In groups, this reaction probability increases with the number of moving individuals (M ¼ i1) and decreases with the number of immobile (U) individuals. The parameters b, c and d take into account the influence of conspecifics. The larger the value of b and/or c, the greater the influence of the moving individuals will be. The larger the value of d, the greater the influence of the immobile individuals will be. 0:028 Using l1 ¼ 0:11 per ds in equation 2, we obtain U a þ bM c 0:028 þ bM c li ¼ ¼ per ds, which is the reaction probaU 0:11 Ud bility of all individuals. We analysed this reaction probability by assuming that the inhibition caused by the immobile individuals behaves the same way for the RT (i > 1) of all individuals as for the first individual to react (i ¼ 1). Because the number of immobile individuals (U) depends on group size and on the number of moving individuals (M), we fitted

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

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the reaction probability multiplied by the number of immobile individuals as a function of the number of mobile individuals (li
U 0:11 ¼ 0:028 þ 0:0081M 0:96 , R2 ¼ 0.70; KolmogoroveSmirnov test: P > 0.95; Fig. 5a). This result indicates that for the tested group size, the individual probability to react li increases with the 0:028 þ 0:0081M 0:96 moving/immobile ratio: li ¼ per ds. U 0:11 Arrival Times The next stage in the fleeing behaviour begins with the finding of one of the two available openings (AT) and the subsequent leaving of the shelter (ET). The use of the two openings themselves followed a symmetric binomial distribution (two-tailed binomial test: P > 0.5 for all group sizes). This result indicates that, unlike ants (Altshuler et al. 2005), P. americana disperses and does not collectively select one of the two openings. Few individuals stayed

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Figure 3. Examples of reaction time latency (DRTi ) survival curves: (a) rank 1 for the groups of two individuals and (b) rank 3 for the groups of 10 individuals. The curves can be fitted by an exponential function (R2 ¼ 0.98 and 0.96, respectively).

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Figure 5. (a) The reaction probability multiplied by the number of immobile individuals as a function of the number of mobile individuals: li
U 0:11 ¼ 0:028 þ 0:0081M0:96 . (b) Probability of leaving the shelter after a waiting 1:74 . M is the number of moving inperiod (εi) for all groups: εi ¼ 0:0082 þ 0:0019M dividuals; the axis has been reversed to convey that as the experimental time progresses from left to right, the number of moving individuals decreases.

in the shelter and did not reach an opening by the end of the 5 min trial: 0.048, 0.02, 0.034 and 0.068 of individuals for groups of 1, 5, 10 and 20 individuals, respectively. These individuals were taken into account in the survival curve analysis with an AT and an ET of 300 s and no WT. During their movement within the shelter, individuals reached one of the openings (AT). The latency of the first arrival (i ¼ 1) is the time interval between when the light is turned on (t0) and the first arrival. The latency DATi corresponds to the time (s) between the arrival of individual i1 and individual i to an opening. The distributions of experimental latencies (DATi) for each rank i fitted exponential distributions, indicating a constant probability per unit time of arriving at an opening (ai) given the same number of moving individuals (M; KolmogoroveSmirnov test: P > 0.5 for all ranks of all group sizes). The first AT (i ¼ 1) occurred when all of the individuals were already moving, and the number of moving individuals diminished as individuals left the shelter (i > 1). We did not observe any correlation between the reaction and arrival times for isolated individuals, and we assume that this is also valid for groups. We did not find any relationship between arrival probability (ai) and group size; the average AT was constant regardless of group size. Moreover, we observed that the individual arrival probability a is constant, independently of M, U and group 1 size: a ¼ ¼ 0:0024 per ds. AT Waiting Times

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Figure 4. Average reaction time of the first individuals to react ð< DRT1 > þ SDÞ as a function of group size (G) ð< DRT1 > ¼ 3:6G0:89 ; R2 ¼ 0:34Þ.

Once an individual arrived at an opening (AT), it first stopped (WT) after perceiving the darkness outside the shelter (Okada & Toh 1998), then exited the shelter at a time here called the exit time (ET). An opening was never occupied by more than one

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individual. All individuals left the shelter by the first opening encountered:

WTi ¼ ATi  ETi ¼

1 ; εi

Stimulus

(3)

where εi is the exit probability once an individual has arrived at an opening. Similar to the individual arrival probability ai (see above), the
1 corresponding exit probability per unit time εi ¼ per ds is WTi constant over time for the same configuration (number of moving insects). Indeed, the DWTi for each rank i within each group size can also be fitted with an exponential function (Kolmogorove Smirnov test: P > 0.5 for all ranks of all group sizes).

Immobile individuals

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Exit Time The relationship between exit probability εi and the number of moving individuals M within the shelter was characterized with equation 4. Because there was always only one individual waiting at an opening, its probability of leaving the shelter was only influenced by the number of moving individuals (M).

εi ¼ a0 þ b0 Mc

0

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As we can see from Fig. 5b, the probability of leaving the shelter increases with the number of individuals moving inside the shelter. As noted earlier, all of the individuals begin moving before the first AT occurs. In other words, the number of moving individuals decreases by 1 each time an individual leaves the shelter. (εi ¼ 0:0082 þ 0:0019M 1:74 per ds, R2 ¼ 0.90; KolmogoroveSmirnov test: P > 0.7). In this case, we have a strong influence of the moving individuals on the probability of leaving (c0 ¼ 1.74). This value is greater than 1, indicating the need for strong interactions to overcome the tendency of cockroaches to stop once they find darkness. Simulations We constructed a simple model describing the global scenario of the fleeing behaviour (Fig. 6). This model combines the different steps of the fleeing behaviour listed previously: reacting, reaching an opening and leaving the shelter, these steps having been independently quantified. At t0 (starting time), all individuals are in an immobile state (U ¼ G). At each time step, their probability of switching to a moving state (M) is given by l as a function of M and U (equation 2). Once an individual is moving, it has a constant probability of finding an opening (a). Once an opening has been found, the individual leaves the shelter with probability ε as a function of M (equation 4). In the model, the different steps influence each other via the moving individuals, the number of which varies over time. In this model, no correlation between the reaction and exit time of an individual was taken into account. For the different group sizes, we performed 100 simulations of each experimental set (e.g. for the groups of two individuals, we did 26 ‘experiments’
100 simulations) using our model. These stochastic simulations validate our global scenario’s quantitative description of the fleeing behaviour of cockroaches: a fast initiation of movement of the individuals followed by a slower decrease in the number of moving individuals as individuals leave the shelter (Fig. 2). For the first RT, the results of the simulation are not surprising because they are the direct result of the equation. On the other hand, owing to the information cascade between the different steps

Figure 6. Schematic representation of the model. The fleeing process begins when a group of individuals is stimulated (double arrows). The connecting (thin) arrows represent the pathway leading individuals from the immobile state to the moving state and eventually outside the shelter. The inhibitory effect of the immobile individuals on the individuals that have yet to react is represented by the stop line. Moving individuals have an amplifying effect on immobile individuals and waiting individuals (indicated by the dark arrows).

of the fleeing process, the global RT, last RT, global ET, first ET and last ET that result from the model are less evident. Nevertheless, we have a good agreement between the simulated and experimental results (Fig. 7). For instance, the simulated and observed global profiles of the average fraction of moving individuals as a function of time (Fig. 2) are comparable in their general pattern, although our simulations show a slower decrease in the fraction of moving individuals for large groups (G ¼ 10, 20). Our simulations also confirm the absence of crowding at the openings. Indeed, our simulations indicate that, at most, 5% of individuals arrive at an opening at the same time. DISCUSSION Many studies have been conducted to understand how individual behaviour, social interactions and environmental heterogeneities influence the formation and cohesion of groups and their collective decision making (Krause & Ruxton 2002; Krause et al. 2010; Sumpter 2010; Pillot et al. 2011). Moreover, a wide range of research disciplines (including applied ethology and social psychology) are concerned with fleeing behaviours (Bowles 1995; Helbing et al. 2000, 2007; Forkman et al. 2007; Uitdehaag et al. 2009; Moussaïd et al. 2012). The present study of collective fleeing is included in the general framework of these studies of group dynamics. The main focus when studying the influence of how group living reduces predation risk has generally been on how vigilance varies with group size (Roberts 1996; Michelena et al. 2008; Michelena & Deneubourg 2011; Pays et al. 2012; Beauchamp & Ruxton 2012). However, as the fleeing dynamics of a group have been little studied, our aim was to quantify these fleeing dynamics and their different stages. In this respect, our results show that the individual probability of reacting to a perturbation decreases with the number of surrounding immobile individuals. Similarly to previous observations showing a decrease in individual vigilance with group size (Roberts

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

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Figure 7. Comparison between the observed (black rhombus) and simulated (white squares) averages of the RTs and ETs (þ0.95 confidence interval for the simulated results). Global RT and ET are the average reaction and exit times, respectively, of all the individuals in a group size. The first RT and last RT are the average reaction times of the first and last individuals to react, respectively. The first ET and last ET are the average exit times of the first and last individual to leave the shelter, respectively.

1996; Caro 2005; Beauchamp 2008), we show that the time to the initiation of fleeing (first fleeing reaction) decreases more slowly than the increase in group size. This influence of immobile individuals is similar to the modulation of the fraction of moving individuals prior to illuminating the shelter. Indeed, we observed that the fraction of moving individuals decreased as group size increased (0.46 of all isolated individuals compared to 0.04 of all individuals in groups of 20 individuals were moving). The gregarious behaviour of these cockroaches is also strongly influenced by the number of individuals: the probability of leaving a group decreases as the number of individuals already aggregated increases (Jeanson et al. 2005; Amé et al. 2006; Sempo et al. 2006, 2009; Halloy et al. 2007). Possibly, immobile individuals are in a sleep-like state, which is essential for their long-term viability (Stephenson et al. 2007); therefore, cockroaches within a group have to balance the needs to be in a sleep-like state and to be vigilant. In our case, in larger groups, either the fraction of individuals in a sleep-like state is greater or all individuals are in a ‘deeper’ sleep-like state. In contrast to the inhibitory role of the immobile individuals is the amplifying effect of moving individuals. This amplifying effect plays a role in the reactions of individuals as well as in their exit from the shelter. In the former case, not only is reaction inhibition countered by the amplifying effect, but also amplification actually allows larger groups to react globally faster than smaller groups. This indicates that the moving/immobile ratio is an indicator of risk and influences the decision to flee or to stay immobile at each time step. For group fleeing to be advantageous for all the group’s individuals, there must be mechanisms that spread the alarm signal to all members of the group. The propagation mechanism can be extremely different depending on the studied species. Some are based on amplification of the fleeing behavioural process; for example, unaware individuals imitate the fleeing behaviour of an already fleeing individual, which has been observed in vertebrates

(e.g. Davis 1975; Hilton et al. 1999; Beauchamp 2012). In arthropods, the most common way to propagate an alarm is through the release of alarm pheromones (e.g. insects: Tillman et al. 1999; mites: Kuwahara et al. 1980; harvestmen: Machado et al. 2002), which, to our knowledge, is not an amplifying phenomenon (Hatano et al. 2008; Verheggen et al. 2008). However, fleeing processes based on mechanical stimuli that act as positive feedback loops exist. For instance, in H. robustus, a gregarious marine insect, when a predator approaches the group, the movement speed and random encounters of individuals increase, which in turn are responsible for alarm signal propagation within the group in a nonlinear way (Treherne & Foster 1981, 1982). Vibrations of the substrate on which the group is gathered can also be used as a vector for alarm amplification. This can be observed, for example, in the colonial spider Metepeira incrassata (Uetz et al. 2002), in the fungus-growing termites Pseudacanthotermes spiniger and P. militaris (Connetable et al. 1999), and in whirligig beetles (Vulinec & Miller 1989; Watt & Chapman 1998). In these species, the alarm signal produced by the evasive behaviour of group members is amplified through vibrations on the silk, ground and water surface, respectively. Mechanical amplifying mechanisms can also play a role alongside alarm pheromones. The gregarious harvestman Goniosoma aff. proximum (Opiliones) uses secretions from its cephalothoracic scent glands for defence as well as for alarm signalling. Collisions with fleeing individuals amplify the response to the pheromone within the group, with the result that larger groups react faster (Machado et al. 2002). In the fleeing examples mentioned above, only a small fraction of individuals were aware of the predator and the alarm signal propagated through the group (Davis 1975; Vulinec & Miller 1989; Hilton et al. 1999). However, sometimes all individuals are exposed to a threat simultaneously, such as arthropods being abruptly exposed if their shelter is overturned by large predators (e.g. Mattson et al. 1991). In our experimental case mimicking such

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events, amplification occurred even though all the individuals were exposed to the threatening stimulus simultaneously. While an amplification of the alarm signal is advantageous in groups in which only a small fraction of individuals is aware of the threat, it was not clear whether this was also the case for a simultaneous exposure. If all individuals are able to perceive the threat simultaneously, then amplification could be thought to be unnecessary. Additionally, if all individuals react to the stimulus too fast, amplification might not have time to manifest itself. For these reasons, we could expect simultaneous fleeing behaviour of all individuals resulting from fast individual reactions, whereas other individuals’ behaviour would have a minimal effect. This strongly suggests that amplifying mechanisms also play a role in group synchronization during fleeing events. We have shown that the individual probability of reacting to the light stimulus increases with the number of moving individuals. On the other hand, immobile individuals have an inhibitor role. These positive and negative feedbacks are compatible with the hypotheses of dilution and confusion effects. If we consider only the dilution effect, it is more advantageous to stay within the group and not flee prematurely. In fact, any individual moving alone can be considered to be the target of a predator. On the other hand, once an individual starts to flee, it is advantageous for the rest of the individuals to flee synchronously and benefit from the confusion created before the complete scattering of the aggregation (Landeau & Terborgh 1986; Jeschke & Tollrian 2007; Ruxton et al. 2007). The amplification stimuli during cockroach fleeing are without a doubt the contacts between individuals, air flow and vibrations caused by movements. Cockroaches, like other insects, are very sensitive to wind, vibrational and mechanical stimuli (Bell & Adiyodi 1982; Schaefer et al. 1994; Stierle et al. 1994; Domenici et al. 2008; Dupuy et al. 2011), which could not be measured in our experiments. Surprisingly, amplification is not at work for all stages of the fleeing dynamics. Once all the cockroaches had reacted, we found that the number of moving individuals had no influence on an individual’s probability of finding an opening. Seemingly a disadvantage for a fleeing group, it is possible that a confusion effect caused by the large number of running individuals compensates for this lack of fleeing goal (Okada & Toh 1998; Jeschke & Tollrian 2007). Aside from the lack of amplification involved in finding an opening, we noted earlier that there was no collective choice regarding the openings. This finding is probably the result of the fleeing behaviour of this species, which is characterized by fast reaction times and running speed, which favour the dispersion of the group. After a cockroach found an opening, the time interval before leaving decreased with an increasing number of individuals still running inside the shelter (quadratic law). Similar to the reaction times, the moving individuals are a source of stimuli that will decrease the time spent waiting. Cockroaches do not leave the shelter as soon as they find an opening because their behaviour is to stop their fleeing behaviour once they locate a dark place (Okada & Toh 1998). Even though this study highlights the effect of group size on the fleeing behaviour of a group, the understanding of all the mechanisms that modulate fleeing behaviour is still incomplete. It would be interesting to determine how the availability of escape routes influences fleeing dynamics. We would expect that an increase in escape exits would reduce the time that elapses before leaving the shelter and thus accelerate dispersion. However, this acceleration could reduce the amplification process caused by the lower number of moving individuals and therefore increase the reaction time. Throughout our study, we used a constant shelter size, which led to an increase in the population density as the group size increased. Thus, a study of the influence of density on collective

fleeing would be interesting. It can be argued that an increase in density leads to an increase in contact rate and thus an increase in the amplification processes. However, if density was kept constant by increasing the diameter of the shelter in proportion to group size, we might observe similar results for the reaction times but different exit times. A bigger shelter would mean that openings are further apart, possibly reducing the probability of finding an opening and reducing the amplifying effect of running individuals. Because cockroach aggregation patterns are stable through time with individuals returning to the same resting place after foraging bouts (van Baaren & Deleporte 2001) and because marking of the substrate by cuticular hydrocarbons plays an important role in cockroach aggregation processes (Rivault et al. 1998), it is possible that this marking plays simultaneous inhibitory and guiding roles during fleeing (Jeanson & Deneubourg 2006). Similarly, familiarization and memory effects could have an impact on fleeing dynamics. In our study, aggregations were formed for only 30 min before the stimulus was triggered, which might not have been enough time for marking and familiarization processes to take place. While our model is not applicable to all species, our methodology is generic. The model is a template with which to study more complex situations for domestic cockroaches or species with similar life histories. The stages of fleeing behaviour that we described are general steps that can be attributed to the fleeing behaviour of species whose threatening stimulus perception and propagation are short ranged and that live in sheltered environments. As a perspective, a microscopic multiagent model is a necessary complement to this study to understand the qualitative and quantitative roles of the different interactions in the fleeing process. Indeed, the development of such a model would allow us to pinpoint the exact vectors of information transfer (e.g. collisions, soil/air vibrations) and their respective influence in the different behavioural steps. Acknowledgments We thank Guy Beauchamp for his insightful comments on the manuscript. We are also grateful to the three anonymous referees for their comments for improving the manuscript. This study was funded by a Ph.D. grant from FRIA (Fonds pour la Recherche dans l’Industrie et dans l’Agriculture). J.L.D. is a senior research associate from the Belgian National Fund for Scientific Research (F.N.R.S). G.S. is supported by a European grant (Symbrion) and the project ARC: Individual and collective issues in dispersal and aggregation: from proximal causes to ultimate consequences at contrasting scales. References Amé, J., Millor, J., Halloy, J., Sempo, G. & Deneubourg, J.-L. 2006. Collective decision-making based on individual discrimination capability in pre-social insects. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4095 LNAI, 713e724. Altshuler, E., Ramos, O., Núñez, Y., Fernández, J., Batista-Leyva, A. J. & Noda, C. 2005. Symmetry breaking in escaping ants. The American Naturalist, 166, 643e649. van Baaren, J. & Deleporte, P. 2001. Comparison of gregariousness in larvae and adults of four species of zetoborine cockroaches. Entomologia Experimentalis et Applicata, 99, 113e119. Ball, H. J. 1977. Spectral transmission through the cuticle of the American cockroach, Periplaneta americana. Journal of Insect Physiology, 23, 1e4. Bazazi, S., Buhl, J., Hale, J. J., Anstey, M. L., Sword, G., Simpson, S. J. & Couzin, I. D. 2008. Collective motion and cannibalism in locust migratory bands. Current Biology, 18, 735e739. Bazazi, S., Ioannou, C. C., Simpson, S. J., Sword, G., Torney, C. J., Lorch, P. D. & Couzin, I. D. 2010. The social context of cannibalism in migratory bands of the Mormon cricket. PLoS One, 5, e15118. Beauchamp, G. 2008. What is the magnitude of the group-size effect on vigilance? Behavioral Ecology, 19, 1361e1368.

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APPENDIX 1. THE BIOLOGICAL MODEL Periplaneta americana is a reddish brown cockroach of the Blattidae family. The adults measure 35e50 mm in length, with a maximum breadth of 10 mm. They have a cosmopolitan distribution but are originally from the tropical regions of the African continent. They are nocturnal, negatively phototactic and form aggregations in dark, warm and damp places (resting phase) during the daylight hours. These aggregations include both males and females of all stages (Bell & Adiyodi 1982). Rearing Conditions The cockroaches were taken from the rearing room of the Université Libre de Bruxelles (ULB). Periplaneta americana has been

reared in the ULB since 2002 in five Plexiglas vivaria (80
40 cm and 100 cm high) in which cardboard tubes are hung from the walls to serve as shelters. Each vivarium has individuals of each sex and from all developmental stages. They were provided with dog pellets and water ad libitum. The rearing room was kept at 26  1  C with a photoperiod of 12:12 h. Stimuli detection Periplaneta americana individuals initiate a fleeing response when confronted with a sudden illumination of their resting place (Bell & Adiyodi 1982) and stop their fleeing course when they pass under a shady area, even in very low light conditions (0.01 lx). Based on this behaviour, cockroaches would be expected to look actively for these shady places in their environment; however P. americana does not have an intended visual goal in their fleeing behaviour (Okada & Toh 1998). This behaviour is initiated by the perception of light with their compound eyes, which cover both sides of the head, and the two ocelli situated near the base of the antennae (Bell & Adiyodi 1982). The compound eyes are essential for the interruption of the fleeing response once the cockroach has reached a shady place, while the ocelli detect light and modulate the function of the compound eyes (Okada & Toh 1998). Moreover, cockroaches have dermal light sense. This means that they can perceive light that diffuses through the cuticle. This way of perceiving light is seen mainly in the pronotum, the vertex and in the sixth abdominal segment, which is close to the light-sensitive terminal ganglion (used during reactions to lighting; Ball 1977). Periplaneta americana mostly use tactile, vibratory and olfactory cues. They can use virtually any part of their body to perceive tactile stimuli (e.g. collision with another cockroach). Tactile stimulation of different parts of a cockroach’s body leads to a rotation of varying amplitude. The rotation amplitude increases the nearer the head the stimulation is (Schaefer et al. 1994). Three body parts are prominent in stimuli detection: the antennae, legs and cerci. The antennae are responsible for perceiving chemical substances, such as cuticular hydrocarbons, and thus play a role in conspecific recognition. Cockroaches use sexual pheromones for reproduction (Tillman et al. 1999); they also use chemical cues to aggregate, such as cuticular hydrocarbons (Saïd et al. 2005) or the odour of other cockroaches’ faeces which act as a locomotion inhibitor (Deleporte 1988). In addition, the antennae also play a role in detecting tactile stimuli. When a cockroach stands on the ground its antennae are constantly moving which allows a threat to be detected. They also intervene in guiding the cockroach in its fleeing route (Camhi & Johnson 1999). The legs are responsible for detecting soil vibrations, which could indicate the presence of an approaching predator or a conspecific. However, the reaction of a cockroach after perceiving a vibration depends on what it was previously doing: if a cockroach is moving it will stop and if an individual is immobile it will start running (Schwartzkopff 1974). The cerci detect changes in air speed and tactile stimuli. These are located at the end of the ninth abdominal sternite and are the principal organs used in wind detection. Each cercus bears 220 wind-receptive filiform hairs, essential for triggering wind-induced fleeing behaviour (Dagan & Volman 1982; Kanou et al. 2006). The mechanosensory sensilla of these different body parts have a preferential plane of bending. Bending in one direction induces action potentials, while bending in the opposite direction reduces the frequency of action potentials (Dagan & Volman 1982). This property allows the cockroach to know from which direction the wind puff is coming. Fleeing behaviour for isolated individuals The fleeing behaviour of individuals when stimulated with a mechanical stimulus (wind puff or contact) can be summarized as follows: (1) the cockroach perceives the external threatening

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

stimulus, (2) it orients its body following one of a set of preferred trajectories (approximately 90 , 120 , 150 and 180 from the direction of the stimulus; Domenici et al. 2008), (3) starts running, and (4) it finally stops running, usually when encountering a shady place (Okada & Toh 1998). In our study we induced fleeing behaviour of a whole group of individuals and unlike wind puffs or direct contact, the lighting stimulation came from above and could be perceived by all the individuals. This lack of threat direction and the fact that individuals were within a group led to a somewhat different behaviour: (1) the cockroaches perceive the stimulus, (2) they turn, back up before turning, or keep their current orientation, (3) they start to run, (4) finally stop running when reaching an opening, and (5) they leave the shelter. Their tendency to stop momentarily once an opening has been reached can be explained by the fact that outside the shelter it is dark, which elicits their shade response (Okada & Toh 1998). APPENDIX 2. GROUPS WITH MOBILE INDIVIDUALS In our study we discarded the trials in which at least one individual was moving; however, analysis suggests that the collective behaviour was not different from the retained trials. We compared the groups in which all the individuals were immobile and those in which at least one was moving. We considered the time it took for all individuals to react (reaction time of the last individual to react minus that for the first individual to react), as well as the time it took each group to leave the shelter (exit time of last individual to leave minus that for the first individual to leave). We found that there was no significant difference (two-tailed ManneWhitney test: P > 0.05 for 2, 5, 10 and 20 individuals for both conditions; e.g. five individuals’ reaction time: ManneWhitney test: U ¼ 153.50, Nall immobile ¼ 30, Nmoving ¼ 10, P ¼ 0.93; exit time: two-tailed

Fraction of individuals

0.5

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to see whether the lack of dead individuals in the other groups pointed to such an effect. Using the probability of having a dead individual from the groups of 20 individuals (Pm ¼ 0.013) we calculated the probability of obtaining 0 dead individuals in the trials of 1, 2, 5 and 10 individuals. Our results showed that the probability was indeed high (Pm ¼ 0.99, 0.97, 0.94 and 0.88, for 1, 2, 5 and 10 individuals, respectively). We also compared the distributions of these probabilities and found that the multinomial distributions of the observed and theoretical probabilities were not significantly different (Fisher’s exact test: P > 0.1 for all group sizes). These results indicate that the death observed among the groups of 20 individuals was not due to crowding, and that all individuals in all group sizes had the same probability of dying. As for the exact cause, we suspect some individuals suffered injuries during manipulation; however, such injuries were not visible and prevented us from excluding those individuals prior to the experiments. APPENDIX 4. POSITION WITHIN THE SHELTER To analyse the positions of the individuals we divided the arena into five circular areas 2.5 cm wide. We compared the position of all the tested individuals to the theoretical homogeneous distribution. The individuals that were tested isolated and in groups of two showed a homogeneous distribution (chi-square: isolated: P ¼ 0.07; two individuals: P ¼ 0.35). The individuals of the groups of 5, 10 and 20 individuals showed a distribution significantly different from the theoretical one. There were more individuals in the ring consisting of the 7.5 and 10 cm radius than theoretically predicted (Fig. A1; chi-square: five individuals: P < 0.0001; 10 individuals: P ¼ 0.0004; 20 individuals: P ¼ 0.01).

5 individuals 10 individuals 20 individuals Theoretical

0.4 0.3 0.2 0.1 0

2.5

5

7.5 Radius (cm)

10

12.5

Figure A1. Fraction of individuals within the radius of each ring for group sizes of 5, 10, and 20 individuals.

ManneWhitney test: U ¼ 166, Nall immobile ¼ 30, Nmoving ¼ 10, P ¼ 0.63). We did find a significant difference for the exit time for the isolated individuals (two-tailed ManneWhitney test: U ¼ 1352.5, Nall immobile ¼ 42, Nmoving ¼ 43, P < 0.0001). This was certainly the result of having just one individual within the shelter that was already moving and thus capable of finding and leaving the shelter as soon as the openings were opened. APPENDIX 3. MORTALITY During our experiments, seven individuals died in the groups of 20 individuals (total population: 540). To test whether this mortality was due to a crowding effect we conducted multinomial tests

Regarding the angular position of cockroaches, we observed that for all group sizes, the individuals were distributed uniformly without showing a preferred angle (Rayleigh test: z < 2 for all group sizes, P > 0.1). In our experiments, individuals were exposed simultaneously to a light stimulus; however, their position in the shelter might have had an influence on their reactions. We compared the distribution of the first individuals that reacted with the position of the rest of the individuals. We found that their distributions were not significantly different (chi-square: P > 0.5 for all group sizes; e.g. Figs A2, A3). This result shows that the reaction to the light stimulus was not influenced by the position of the individuals within the shelter.

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90 15 120

60

10 150

30 5

180

0

330

210

300

240 270

Figure A2. Position of the first individuals to react in the groups of 20 individuals (one individual per trial).

90 15 60

120

10 30

150 5

180

0

210

330

240

300 270

Figure A3. Distribution of the individuals that were not the first to react in the groups of 20 individuals (19 individuals per trial).

M.-O. Laurent Salazar et al. / Animal Behaviour 85 (2013) 1271e1285

tributions of experimental latencies for all ranks i is fitted by an exponential distribution as seen in Fig. A4 (isolated individual and two individuals), Fig. A5 (five individuals), Fig. A6 (10 individuals) and Fig. A7 (20 individuals).

APPENDIX 5. REACTION LATENCIES

Fraction of immobiles within rank

Reaction latencies (DRTi ) correspond to the time elapsed (s) between the reaction of individual i1 and individual i. The dis-

1

1

1 individual

1 2 individuals

2 individuals

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

5

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10

0

1st Rank

2

0.8

4 RT (s)

6

2nd Rank

0

10

20

Figure A4. Distributions of experimental latencies for all ranks of the isolated individuals and groups of two individuals.

1

1

1

Fraction of immobiles within rank

1st Rank

2nd Rank

3rd Rank

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0.5

1

1.5

2

1

0

1

0

1

1 4th Rank

5th Rank

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

2

1

2

3

4

0

2

4

6

RT (s) Figure A5. Distributions of experimental latencies for all ranks of the groups of five individuals.

2

3

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1

1

1

Fraction of immobiles within rank

1st Rank

3rd Rank

5th Rank

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0.5

1

1.5

0

1

0.5

1

1.5

0

0.5

1

1.5

1 8th Rank

10th Rank

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

5

10

0

2

4 RT (s)

Figure A6. Distributions of experimental latencies for ranks 1, 3, 5, 8 and 10 of the groups of 10 individuals.

1

1

1

Fraction of immobiles within rank

1st Rank

5th Rank

10th Rank

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

0.5

1

0

1

1

0

0.5

1 15th Rank

20th Rank

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0.5

0.5

1

1.5

2

0

1

2

3

RT (s) Figure A7. Distributions of experimental latencies for ranks 1, 5, 10, 15 and 20 of the groups of 20 individuals.

1

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APPENDIX 6. SUMMARY OF THE PARAMETER VALUES Table A1 gives the values of the different parameters of our study. For each value we show their confidence intervals (95%).

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< DRT1 > is the average reaction time of the first individual to react in each trial. li and εi are the individual probability to react and to leave the shelter, respectively.

Table A1. Parameter values and their confidence interval Equation

Values

< DRT1 > ¼ kGg a l1 ¼ d per ds G li
U 0:11 ¼ 0:028 þ bMc

< DRT1 > ¼ 3:6 0:028 l1 ¼ 0:11 per ds G li
U 0:11 ¼ 0:028 þ 0:0081M0:96

0

εi ¼ a0 þ b0 M c per ds

Confidence interval (95%) G0:89 s

εi ¼ 0:0082 þ 0:0019M 1:74 per ds

k: 3.062 to 4.13

g: 1.21 to 0.57

a: 0.022 to 0.036

d: 0.025 to 0.35

b: 0.001653 to 0.01460 a0 : 0.0 to 0.025

c: 0.6533 to 1.273 b0 : 0.0 to 0.0042

Equations used to describe the fleeing behaviour of Periplaneta americana. G ¼ group size, M ¼ moving individuals and U ¼ immobile individuals.

c0 : 1.30 to 2.18