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Use of radio-tagging to map spatial organization and social interactions in insects

Use of radio-tagging to map spatial organization and social interactions in insects The Journal of Experimental Biology 214, 17-21 © 2011. Published by The Company of Biologists Ltd doi:10.1242/jeb.050526 METHODS & TECHNIQUES Mathieu Moreau, Patrick Arrufat, Gérard Latil and Raphaël Jeanson* Centre de Recherches sur la Cognition Animale, CNRS, 31062 Toulouse Cedex 9, France and Centre de Recherches sur la Cognition Animale, Université de Toulouse, 31062 Toulouse Cedex 9, France *Author for correspondence ([email protected]) Accepted 20 October 2010 SUMMARY Understanding of the organization of animal societies often requires knowledge of the identity of group members and their spatial location. We propose an original experimental design to track automatically the position of individuals using radio frequency identification technology (RFID). Ants equipped with passive transponders were detected by a reader mounted on a mobile arm moving across the nest surface. We developed an algorithm to accurately extract the positions of individuals moving in two dimensions. Our method was validated on synthetic test cases and then used for characterization of the spatial distribution of ants within nests. This approach provides an amenable system for monitoring large populations of individuals over long periods of time. Supplementary material available online at http://jeb.biologists.org/cgi/content/full/214/1/17/DC1 Key words: ant, passive transponder, social network. INTRODUCTION of interest but this method can quickly become expensive due to In a wide variety of contexts and across several taxa, knowledge of the cost of a reader. the identity and spatial location of individuals is crucial for We propose an alternative solution that consists of mounting an understanding the organization of animal groups. In arthropods, RFID reader on a mobile arm moving along two orthogonal axes external marking techniques – such as the use of numbered tags to scan the domain of interest. We developed an algorithm to extract (Monnin and Peeters, 1999), dots of paints (Sendova-Franks and the position of the ant and to discriminate multiple detections of a Franks, 1993) or wire loops tied around body parts (Mirenda and motionless individual from a true displacement. As a case study, Vinson, 1979) – are routinely used to individually tag animals within we studied the spatial distribution and mapped the network of social groups. Alternatively, the position of individuals within groups can interactions in the ant Odontomachus hastatus. be automatically extracted from digitalized pictures, but at the cost of losing identity (Cole and Cheshire, 1996). The knowledge of both MATERIALS AND METHODS identity and position usually requires photographing nests of marked Animals animals and analyzing pictures afterwards. These processes are We used one colony of the ant Odontomachus hastatus Fabricius, fastidious and slow down the survey of large groups of individuals containing one queen, 55 workers and brood (eggs, larvae and pupae) over long periods of time. Commercial software can automatically collected in French Guiana in February 2009. These ants form track the positions of several individuals. However, this method colonies comprising up to a few hundred monomorphic workers usually requires light, which prevents monitoring animal activity in (worker length, 1.5mm). During the experiment, ants were total darkness and is inefficient when individuals enter dark places introduced into an experimental set-up (see below) placed in a (e.g. nests). Radio frequency identification (RFID) technology climate room (25°C; 40% RH) under a 12h:12h light:dark cycle. represents a powerful alternative. Animals can be equipped with The colony was surveyed for seven consecutive days and fed twice passive tags consisting of an antenna and a semi-conductor chip. a week with live house flies (Lucilia sericata) and vitamin-enriched The power required for reading the unique identification number food (Dussutour and Simpson, 2008). of each tag is provided by an external device. Passive tags are of particular interest because of their miniaturized size and their Experimental set-up virtually infinite operational life (Want, 2006). This technology has RFID tags and reader were purchased from Lutronic been successfully employed in different taxa (Molet et al., 2008; (http://www.nonatec.net). The tags were encapsulated in resin, were Robinson et al., 2009; Sumner et al., 2007). In these studies, 6mm long and weighed ~6mg (about one-third of the mass of an however, the reader was immobile and the identity of an individual ant). The frequency of RFID is 13.56MHz. Tags were glued onto was read whenever it passed underneath the reader or through a the thorax of each ant, including the queen, with Superglue . Tagged circular antenna. Although this methodology can provide valuable ants were gently introduced into the foraging area of an artificial information on activity levels or foraging rate, it does not accurately nest (height1cm, width18cm, length24cm), which was divided inform on the spatial location of individuals. To overcome this with a plastic strip into two compartments (Fig.1). Each limitation, an option is to use as many readers as spatial domains compartment was covered with a transparent plastic plate to prevent THE JOURNAL OF EXPERIMENTAL BIOLOGY 18 M. Moreau and others Fig.1. Experimental set-up to scan 18 cm nests of ants equipped with RFID tags. The reader was piloted by a microcontroller and moved along two orthogonal axes above the nest Hall ne st Inner nest surface. The inset shows the course chamber chamber of the reader. Circles: detection field of the reader (not to scale). The RFID 24 cm forward (dotted line) and backward reader (solid line) paths followed by the reader are slightly shifted for illustrative purposes. Foraging area Microcontroller Motor driver Stepper motor Timer Motor driver Stepper motor Interface Computer ants from escaping. One compartment (18cm12cm) formed the the number of positions, we solved EqnA10 for values of N ranging foraging area. This area was connected to the second compartment from 1 to N . Put simply, the algorithm aims to maximize the max (18cm12cm), which was further partitioned into two number of detections within a circle of radius L. One position is interconnecting chambers (inner nest chamber and hall nest randomly drawn from M (X R , with m[1,M]), and S (X ) 1 m R n chamber) covered with a red film filter (Fire #19; Rosco, London, (EqnA10) was maximized. If S (X )≥M, the extraction of a position R n UK). The floor of all compartments was covered with plaster, and was successful. If not, a supplementary position was randomly drawn a layer of moistened dirt was added. from M (X R , with m[1,M]), and S (X ) was maximized. This N m R n algorithm was applied successively for each tag and across scans. RFID scanner All the computations were done using R statistical software The detection field of the RFID reader was 35mm, and the reading (http://www.R-project.org). distance was approximately 1cm. An apparatus, hereafter referred to as RFID scanner, was specifically designed to move the reader across the surface of the nest. The reader is cylindrical in shape Ai Aii (18cm3.5cm) and was mounted on a device moving on a rail along the x-axis. This rail can move independently on a second rail along the y-axis. Movements along each rail were driven by stepper L L motors (TECO Electric & Machinery Co. Ltd, Taipei, Taiwan) X X piloted by a microcontroller (Microchip Technology Inc., Chandler, AZ, USA) via motor drivers (STMicroelectronics, Geneva, Switzerland). The step displacement along the x-axis was chosen to allow an overlap of the detection field of the reader (Fig.1). For each detection of a tag, the mobile arm stopped for a duration of 35ms, which corresponds to the time required for sending information to the computer. Each scan (i.e. forward and backward path of the reader) lasted ~500s (~1200scans/week). Detection algorithm and extraction of each ant’s positions –1 When the reader detected a tag, the microcontroller sent its number, the spatial coordinates of the reader and the time to a computer. Tags were rarely associated with a unique location but were detected several times during each scan. Multiple detections resulted either from the displacement of the reader above a motionless ant –2 and the overlap of the reader detection field or from the true displacement of an individual between distinct locations (supplementary material Fig.S1). We developed an algorithm to discriminate both situations and to extract the spatial coordinates –3 of each individual. 1 10 100 1000 Number of directions, M We aimed to extract each ant’s position (X ) from a series of M discrete reader positions (R ) obtained at time t . This corresponds m R Fig.2. Validation of the algorithm of position reconstruction for theoretical test to a multidimensional optimization problem, i.e. the maximization cases. (A)Asterisks show detections drawn randomly within a radius L of a of the non-linear function S (X ) (EqnA10 in Appendix) in a 2N R n position X (black circle) either uniformly (i) or along the paths followed by the dimension space, where N is the number of positions of the ant reader (indicated by broken lines) (ii). (B)Mean distance error as a function of during a scan (i.e. forward and backward path). S (X ) is the number R n the number of detections, M, drawn randomly, either uniformly (circles, of detections associated with at least one ant’s position. To determine n5000) or along the paths followed by the reader (squares, n5000). THE JOURNAL OF EXPERIMENTAL BIOLOGY Electronic board Error/L Radio tagging in social insects 19 RESULTS algorithm can satisfactorily distinguish discrete positions of a Validation of the algorithm for position reconstruction mobile individual. We considered two theoretical test cases to assess the performance of the algorithm to reconstruct positions. A position, X , was Application of the algorithm for position reconstruction in randomly sampled in the domain, and M positions (R ) were ants randomly drawn within a radius L of X either uniformly or along We assessed the efficiency of detection as the number of detections the paths followed by the reader (Fig.2A). The mean distance for each tag divided by the total number of scans (1200scans). between the exact and reconstructed positions of X was used to Across tags, the median efficiency equalled 0.97 (1st quartile0.95; estimate the performance of the algorithm. We determined the mean 3rd quartile0.99). This indicates that tags were detected at almost Euclidean distance error (n5000) as a function of M (Fig.2B). For every scan. We then determined the number of distinct positions the first case, the error converges uniformly to zero with increasing extracted for each tag during each scan and calculated the distance M. This demonstrates that the algorithm can precisely reconstruct between the two furthest locations when multiple positions occurred the position. For the second case, the error reached a plateau value (i.e. true displacement). The median number of detections for each of 0.3L. This asymptotic behaviour results from the constraints tag was six (1st quartile3, 3rd quartile9). This indicates that, on imposed by the path followed by the reader, which reduces the spatial average, each position was reconstructed from six detections. On resolution. In our experiments (see below), the length 0.3L4.5mm average, a unique ant’s position was extracted in 50% of cases. Two was smaller than the size of an ant; the algorithm was thus positions (i.e. true displacement) were obtained for 35% of ants, sufficiently accurate to locate ants within the domain. and 14% had three or more positions (supplementary material We assessed the performance of the algorithm for discriminating Fig.S2). When two positions were obtained, the average distance positions of moving ants. Two positions, X and X , separated by equalled 4.3cm (supplementary material Fig.S2). 1 2 a constant distance, were randomly drawn within the domain. A number of detections, M and M , were sampled randomly either Spatial distribution in ant colonies and social network 1 2 uniformly or along the paths followed by the reader within a radius We used the coordinates of each ant to examine how colony L of X andX , respectively (Fig.3A,B). Theoretically, the algorithm members were spatially distributed in the experimental set-up. Fig.4 1 2 should discriminate both positions if there exists at least two shows representative patterns obtained for three workers. detections that satisfy the condition ||R –R ||>2L. We calculated a Qualitatively, some individuals displayed a fidelity to spatial zones i j discrimination rate as the proportion of cases where the algorithm and remained mostly in the foraging area or in the nest. By contrast, discriminates both positions accurately (Fig.3C,D). As expected, some ants were mobile and shared their time more evenly between the discrimination rate increased with the number of detections, M, both zones. From the positions of individuals, we mapped the for each position and with the distance between positions. In network of social interactions among ants. We considered that two addition, the algorithm discrimination rate closely matches the individuals were interacting if their inter-individual distance was theoretical prediction (broken lines, Fig.3C,D). This means that the ≤14mm. We considered all possible pairs of ants and determined Fig.3. (A,B)Theoretical examples where 1.0 the distance between the detections associated with positions X and X was 1 2 A R –R <2L 1 2 0.8 smaller (A) and greater (B) than 2 (detection field of the reader). Asterisks show detections associated with the 0.6 positions X and X ; broken lines show 1 2 the path of the reader; circles show the detection field of the reader. (C,D)Mean 0.4 discrimination rate as a function of the distance between two positions, X and 0.2 . The number of detections, M, was set to 1 and/or 10 for each position, X 2L and X (n5000). The broken lines 01 2 3 45 represent the theoretical optimal detection rate (i.e. the probability of having ||R –R ||>2L). 1 2 1.0 B R –R >2L 1 2 0.8 0.6 X X 0.4 M =M =1 1 2 2 M =M =10 1 2 M =1; M =10 0.2 1 2 Theory 2L 12 3 45 X –X /L 1 2 THE JOURNAL OF EXPERIMENTAL BIOLOGY Discrimination rate 20 M. Moreau and others 0.24 Fig.4. Individual density plots of three workers within the experimental set-up. The dotted line represents the limit between the nest and the foraging area. The surface of the experimental set-up was discretized in 900 bins of 0.06m0.08m. The color scale gives the number of times an ant was detected in each bin. 0.12 0 0.09 0.18 0 0.09 0.18 0 0.09 0.18 Width (m) whether they met the distance criterion to build an adjacency matrix moving across the nest surface. We developed an algorithm for of interactions. The network obtained is highly connected, with an extracting the positions of each ant, which was first validated on average degree of 26, indicating that ants were directly interacting theoretical test cases and then used for characterizing the spatial with half of the colony (Fig.5). distribution of individuals within nests. In our system, the temporal and spatial resolution allowed the characterization of spatial patterns DISCUSSION in ant colonies and the ability to build a network of social interactions In this study, we proposed an original design to track the position among ants. This system provides a valuable tool for addressing of ants within groups. Individuals equipped with RFID passive several questions including the influence of colony size on the rate transponders were detected by a reader mounted on a mobile arm of social interactions or the impact of variations in environmental conditions on task allocation. These issues are currently under investigation. Our methodology can easily be adapted to any system where individuals evolve in two dimensions. Depending on biological models, there is no restriction in enlarging the size of the domains to monitor and changing the frequency of scanning. The number of readers can also be augmented and/or the overlap of their detection field increased to improve spatial resolution. Finally, the speed of the mobile arm can be boosted to enhance temporal resolution. Our system, which is suitable for organisms of reduced size, offers a promising method for collecting automatically large amounts of data relative to the identity and spatial positions of individuals. APPENDIX Problem statement In a continuum point of view, the form of the distribution function of measurements r(x, t) during one scan is: r (x ,t ) = δ || x − R || δ t − t , (A1) ∑() m () R m=1 where R is the position vector of the reader, t is the time at m R which the tag is detected, M is the number of detections of an ant during one scan and  stands for the Dirac function. Multiple Fig.5. Network of social interactions in a colony of 55 workers and the detections can occur for two reasons. First, the reader can detect a queen of the ant Odontomachus hastatus. The nodes are distributed along motionless tag at a distance L. Second, an ant can move within the the x-axis as a function of the proportion spent by ants in the foraging area and randomly distributed along the y-axis. The queen is indicated by the domain and can be detected in distinct locations (supplementary red circle. material Fig.S1). The algorithm should discriminate both origins. THE JOURNAL OF EXPERIMENTAL BIOLOGY Length (m) Foraging area Nest Radio tagging in social insects 21 The distribution function of ant positions f(x, t) is defined such The dimension number of the problem is then reduced from 3N to that f(x, t)1 if the ant is present at position x at time t and null 2N. elsewhere. We define the detection field f(x, t) (i.e. the area where Second, we replace the discontinuous Heaviside functions H(x) an ant can be detected) by a space filtering of f(x, t): by the hyperbolic tangents function, introducing a numerical smoothing parameter, s. According to numerical tests (not presented f(x, t)   G (x – x) f(x, t) dx, (A2) here), the smoothing parameter s is set to sL/15: where G (x) is a top hat filter in physical space: ⎛ ⎞ 1 ⎛ x − L+ s ⎞ G (x)  1 if  x ≤ L H x − L ≈ 1+ tanh . (A9) L () ⎜ ⎜ ⎟ ⎟ 2 ⎝ s ⎠ ⎝ ⎠  0 elsewhere. (A3) 2N Finally, the continuous IR rIR function to maximize for We introduce the scalar function: determining the positions (X ) of an ant is given by: S (f)   f(x, t) r(x, t) dx dt. (A4) ⎛ ⎞ 1 ⎛ || R − X || − L+ s ⎞ m n S X = max 1+ tanh . (A10) R() n ∑ ⎜ ⎟ ⎜ ⎟ The value of S (f) varies, by construction, between 0 and M. For R n=1,...,N 2 ⎝ s ⎠ ⎝ ⎠ m=1 S (f)M, all detections are associated with ant position. The process of detection consists of finding the function f(x, t) This optimization problem, EqnA10, is solved in two steps: a that maximizes S (f). To achieve this, some assumptions on the form stochastic global optimization method (Belisle, 1992) coupled with of f(x, t) are needed. Assuming that during one scan an ant occupies an ad hoc resampling process followed by a simplex algorithm successively N discrete positions, X , and instantaneously changes method (Nelder and Mead, 1965). Eqn A10 is used to test the position at time t , the distribution function of ant positions is: convergence of the algorithm for position reconstruction. f  (x, t) (x – X ) H(t – t ) H(t – t), (A5) N n n n+1 LIST OF ABBREVIATIONS L radius of the detection field of the reader where H(t) is the Heaviside step function. Using this model, m integer varying from 1 to M equation A4 reduces to: M the number of detections of an ant during one scan M N n integer varying from 1 to N S X ,t = H(|| R − X || − L)H(t − t )H(t − t ) . R() n n ∑ ∑ m n R n n+1 R () N number of positions of the ant during a scan m m n=1,N m=1 n=1 R position vector (X- and Y-coordinates) of the reader for the (A6) detection m S (X ) number of detections associated with ant position X With (R , t ) given, the process of position extraction consists of R n n m R t time at which the tag was detected Rm finding the minimum number N of points, (X , t ) , that maximize n n n1,N X position vector of the ant S . The problem then reduces to an optimization problem in 3N dimensions, the number of ant discrete positions N being unknown. REFERENCES Belisle, C. J. P. (1992). Convergence theorems for a class of simulated annealing Numerical implementation algorithms on Rd. J. Appl. Prob. 29, 885-895. Cole, B. J. and Cheshire, D. (1996). Mobile cellular automata models of ant behavior: Due to the large number of dimensions and the discontinuous nature movement activity of Leptothorax allardycei. Am. Nat. 148, 1-15. of EqnA6, resolving the optimization problem needs specific tools Dussutour, A. and Simpson, S. J. (2008). Description of a simple synthetic diet for studying nutritional responses in ants. Insect Soc. 55, 329-333. and can be numerically expensive. For simplicity, we used two Mirenda, J. T. and Vinson, S. B. (1979). Marking technique for adults of the red approximations. imported fire ant (Hymenoptera, Formicidae). Fla. Entomol, 62, 279-281. Molet, M., Chittka, L., Stelzer, R. J., Streit, S. and Raine, N. E. (2008). Colony First, we reduce the dimension number. By construction, each nutritional status modulates worker responses to foraging recruitment pheromone in measure (R , t ) can only be associated with a single ant position m R m Bombus terrestris. Behav. Ecol. Sociobiol, 62, 1919-1926. the bumblebee Monnin, T. and Peeters, C. (1999). Dominance hierarchy and reproductive conflicts (X , t ). We use this property to discard time dimension from n n Behav. Ecol. 10, 323-332. among subordinates in a monogynous queenless ant. Eqn A6: Nelder, J. C. and Mead, R. (1965). A simplex algorithm for function minimization. Comput. J. 7, 308-313. M N Robinson, E. J. H., Richardson, T. O., Sendova-Franks, A. B., Feinerman, O. S X = H(|| R − X || − L)T ( m, n) , (A7) () R n=1,N ∑ ∑ m n R ,X and Franks, N. R. (2009). Radio tagging reveals the roles of corpulence, m=1 n=1 experience and social information in ant decision making. Behav. Ecol. Sociobiol, 63, 627-636. where the function T (m, n) ensures that each detection contributs R,X Sendova-Franks, A. and Franks, N. R. (1993). Task allocation in ant colonies within once to S (X ) and is defined by: Bull. Math. R n variable environments (a study of temporal polyethism: experimental). Biol. 55, 75-96. (A8) Sumner, S., Lucas, E., Barker, J. and Isaac, N. (2007). Radio-tagging technology T ( m, n)= 1 if || R − X || = min (|| R − X ||) R ,X m n m n n=1,N reveals extreme nest-drifting behavior in a eusocial insect. Curr. Biol. 17, 140-145. IEEE. Pervasive. Comput. 5, 25- Want, R. (2006). An introduction to RFID technology. = 0 elsewhere . THE JOURNAL OF EXPERIMENTAL BIOLOGY http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Experimental Biology The Company of Biologists

Use of radio-tagging to map spatial organization and social interactions in insects

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The Journal of Experimental Biology 214, 17-21 © 2011. Published by The Company of Biologists Ltd doi:10.1242/jeb.050526 METHODS & TECHNIQUES Mathieu Moreau, Patrick Arrufat, Gérard Latil and Raphaël Jeanson* Centre de Recherches sur la Cognition Animale, CNRS, 31062 Toulouse Cedex 9, France and Centre de Recherches sur la Cognition Animale, Université de Toulouse, 31062 Toulouse Cedex 9, France *Author for correspondence ([email protected]) Accepted 20 October 2010 SUMMARY Understanding of the organization of animal societies often requires knowledge of the identity of group members and their spatial location. We propose an original experimental design to track automatically the position of individuals using radio frequency identification technology (RFID). Ants equipped with passive transponders were detected by a reader mounted on a mobile arm moving across the nest surface. We developed an algorithm to accurately extract the positions of individuals moving in two dimensions. Our method was validated on synthetic test cases and then used for characterization of the spatial distribution of ants within nests. This approach provides an amenable system for monitoring large populations of individuals over long periods of time. Supplementary material available online at http://jeb.biologists.org/cgi/content/full/214/1/17/DC1 Key words: ant, passive transponder, social network. INTRODUCTION of interest but this method can quickly become expensive due to In a wide variety of contexts and across several taxa, knowledge of the cost of a reader. the identity and spatial location of individuals is crucial for We propose an alternative solution that consists of mounting an understanding the organization of animal groups. In arthropods, RFID reader on a mobile arm moving along two orthogonal axes external marking techniques – such as the use of numbered tags to scan the domain of interest. We developed an algorithm to extract (Monnin and Peeters, 1999), dots of paints (Sendova-Franks and the position of the ant and to discriminate multiple detections of a Franks, 1993) or wire loops tied around body parts (Mirenda and motionless individual from a true displacement. As a case study, Vinson, 1979) – are routinely used to individually tag animals within we studied the spatial distribution and mapped the network of social groups. Alternatively, the position of individuals within groups can interactions in the ant Odontomachus hastatus. be automatically extracted from digitalized pictures, but at the cost of losing identity (Cole and Cheshire, 1996). The knowledge of both MATERIALS AND METHODS identity and position usually requires photographing nests of marked Animals animals and analyzing pictures afterwards. These processes are We used one colony of the ant Odontomachus hastatus Fabricius, fastidious and slow down the survey of large groups of individuals containing one queen, 55 workers and brood (eggs, larvae and pupae) over long periods of time. Commercial software can automatically collected in French Guiana in February 2009. These ants form track the positions of several individuals. However, this method colonies comprising up to a few hundred monomorphic workers usually requires light, which prevents monitoring animal activity in (worker length, 1.5mm). During the experiment, ants were total darkness and is inefficient when individuals enter dark places introduced into an experimental set-up (see below) placed in a (e.g. nests). Radio frequency identification (RFID) technology climate room (25°C; 40% RH) under a 12h:12h light:dark cycle. represents a powerful alternative. Animals can be equipped with The colony was surveyed for seven consecutive days and fed twice passive tags consisting of an antenna and a semi-conductor chip. a week with live house flies (Lucilia sericata) and vitamin-enriched The power required for reading the unique identification number food (Dussutour and Simpson, 2008). of each tag is provided by an external device. Passive tags are of particular interest because of their miniaturized size and their Experimental set-up virtually infinite operational life (Want, 2006). This technology has RFID tags and reader were purchased from Lutronic been successfully employed in different taxa (Molet et al., 2008; (http://www.nonatec.net). The tags were encapsulated in resin, were Robinson et al., 2009; Sumner et al., 2007). In these studies, 6mm long and weighed ~6mg (about one-third of the mass of an however, the reader was immobile and the identity of an individual ant). The frequency of RFID is 13.56MHz. Tags were glued onto was read whenever it passed underneath the reader or through a the thorax of each ant, including the queen, with Superglue . Tagged circular antenna. Although this methodology can provide valuable ants were gently introduced into the foraging area of an artificial information on activity levels or foraging rate, it does not accurately nest (height1cm, width18cm, length24cm), which was divided inform on the spatial location of individuals. To overcome this with a plastic strip into two compartments (Fig.1). Each limitation, an option is to use as many readers as spatial domains compartment was covered with a transparent plastic plate to prevent THE JOURNAL OF EXPERIMENTAL BIOLOGY 18 M. Moreau and others Fig.1. Experimental set-up to scan 18 cm nests of ants equipped with RFID tags. The reader was piloted by a microcontroller and moved along two orthogonal axes above the nest Hall ne st Inner nest surface. The inset shows the course chamber chamber of the reader. Circles: detection field of the reader (not to scale). The RFID 24 cm forward (dotted line) and backward reader (solid line) paths followed by the reader are slightly shifted for illustrative purposes. Foraging area Microcontroller Motor driver Stepper motor Timer Motor driver Stepper motor Interface Computer ants from escaping. One compartment (18cm12cm) formed the the number of positions, we solved EqnA10 for values of N ranging foraging area. This area was connected to the second compartment from 1 to N . Put simply, the algorithm aims to maximize the max (18cm12cm), which was further partitioned into two number of detections within a circle of radius L. One position is interconnecting chambers (inner nest chamber and hall nest randomly drawn from M (X R , with m[1,M]), and S (X ) 1 m R n chamber) covered with a red film filter (Fire #19; Rosco, London, (EqnA10) was maximized. If S (X )≥M, the extraction of a position R n UK). The floor of all compartments was covered with plaster, and was successful. If not, a supplementary position was randomly drawn a layer of moistened dirt was added. from M (X R , with m[1,M]), and S (X ) was maximized. This N m R n algorithm was applied successively for each tag and across scans. RFID scanner All the computations were done using R statistical software The detection field of the RFID reader was 35mm, and the reading (http://www.R-project.org). distance was approximately 1cm. An apparatus, hereafter referred to as RFID scanner, was specifically designed to move the reader across the surface of the nest. The reader is cylindrical in shape Ai Aii (18cm3.5cm) and was mounted on a device moving on a rail along the x-axis. This rail can move independently on a second rail along the y-axis. Movements along each rail were driven by stepper L L motors (TECO Electric & Machinery Co. Ltd, Taipei, Taiwan) X X piloted by a microcontroller (Microchip Technology Inc., Chandler, AZ, USA) via motor drivers (STMicroelectronics, Geneva, Switzerland). The step displacement along the x-axis was chosen to allow an overlap of the detection field of the reader (Fig.1). For each detection of a tag, the mobile arm stopped for a duration of 35ms, which corresponds to the time required for sending information to the computer. Each scan (i.e. forward and backward path of the reader) lasted ~500s (~1200scans/week). Detection algorithm and extraction of each ant’s positions –1 When the reader detected a tag, the microcontroller sent its number, the spatial coordinates of the reader and the time to a computer. Tags were rarely associated with a unique location but were detected several times during each scan. Multiple detections resulted either from the displacement of the reader above a motionless ant –2 and the overlap of the reader detection field or from the true displacement of an individual between distinct locations (supplementary material Fig.S1). We developed an algorithm to discriminate both situations and to extract the spatial coordinates –3 of each individual. 1 10 100 1000 Number of directions, M We aimed to extract each ant’s position (X ) from a series of M discrete reader positions (R ) obtained at time t . This corresponds m R Fig.2. Validation of the algorithm of position reconstruction for theoretical test to a multidimensional optimization problem, i.e. the maximization cases. (A)Asterisks show detections drawn randomly within a radius L of a of the non-linear function S (X ) (EqnA10 in Appendix) in a 2N R n position X (black circle) either uniformly (i) or along the paths followed by the dimension space, where N is the number of positions of the ant reader (indicated by broken lines) (ii). (B)Mean distance error as a function of during a scan (i.e. forward and backward path). S (X ) is the number R n the number of detections, M, drawn randomly, either uniformly (circles, of detections associated with at least one ant’s position. To determine n5000) or along the paths followed by the reader (squares, n5000). THE JOURNAL OF EXPERIMENTAL BIOLOGY Electronic board Error/L Radio tagging in social insects 19 RESULTS algorithm can satisfactorily distinguish discrete positions of a Validation of the algorithm for position reconstruction mobile individual. We considered two theoretical test cases to assess the performance of the algorithm to reconstruct positions. A position, X , was Application of the algorithm for position reconstruction in randomly sampled in the domain, and M positions (R ) were ants randomly drawn within a radius L of X either uniformly or along We assessed the efficiency of detection as the number of detections the paths followed by the reader (Fig.2A). The mean distance for each tag divided by the total number of scans (1200scans). between the exact and reconstructed positions of X was used to Across tags, the median efficiency equalled 0.97 (1st quartile0.95; estimate the performance of the algorithm. We determined the mean 3rd quartile0.99). This indicates that tags were detected at almost Euclidean distance error (n5000) as a function of M (Fig.2B). For every scan. We then determined the number of distinct positions the first case, the error converges uniformly to zero with increasing extracted for each tag during each scan and calculated the distance M. This demonstrates that the algorithm can precisely reconstruct between the two furthest locations when multiple positions occurred the position. For the second case, the error reached a plateau value (i.e. true displacement). The median number of detections for each of 0.3L. This asymptotic behaviour results from the constraints tag was six (1st quartile3, 3rd quartile9). This indicates that, on imposed by the path followed by the reader, which reduces the spatial average, each position was reconstructed from six detections. On resolution. In our experiments (see below), the length 0.3L4.5mm average, a unique ant’s position was extracted in 50% of cases. Two was smaller than the size of an ant; the algorithm was thus positions (i.e. true displacement) were obtained for 35% of ants, sufficiently accurate to locate ants within the domain. and 14% had three or more positions (supplementary material We assessed the performance of the algorithm for discriminating Fig.S2). When two positions were obtained, the average distance positions of moving ants. Two positions, X and X , separated by equalled 4.3cm (supplementary material Fig.S2). 1 2 a constant distance, were randomly drawn within the domain. A number of detections, M and M , were sampled randomly either Spatial distribution in ant colonies and social network 1 2 uniformly or along the paths followed by the reader within a radius We used the coordinates of each ant to examine how colony L of X andX , respectively (Fig.3A,B). Theoretically, the algorithm members were spatially distributed in the experimental set-up. Fig.4 1 2 should discriminate both positions if there exists at least two shows representative patterns obtained for three workers. detections that satisfy the condition ||R –R ||>2L. We calculated a Qualitatively, some individuals displayed a fidelity to spatial zones i j discrimination rate as the proportion of cases where the algorithm and remained mostly in the foraging area or in the nest. By contrast, discriminates both positions accurately (Fig.3C,D). As expected, some ants were mobile and shared their time more evenly between the discrimination rate increased with the number of detections, M, both zones. From the positions of individuals, we mapped the for each position and with the distance between positions. In network of social interactions among ants. We considered that two addition, the algorithm discrimination rate closely matches the individuals were interacting if their inter-individual distance was theoretical prediction (broken lines, Fig.3C,D). This means that the ≤14mm. We considered all possible pairs of ants and determined Fig.3. (A,B)Theoretical examples where 1.0 the distance between the detections associated with positions X and X was 1 2 A R –R <2L 1 2 0.8 smaller (A) and greater (B) than 2 (detection field of the reader). Asterisks show detections associated with the 0.6 positions X and X ; broken lines show 1 2 the path of the reader; circles show the detection field of the reader. (C,D)Mean 0.4 discrimination rate as a function of the distance between two positions, X and 0.2 . The number of detections, M, was set to 1 and/or 10 for each position, X 2L and X (n5000). The broken lines 01 2 3 45 represent the theoretical optimal detection rate (i.e. the probability of having ||R –R ||>2L). 1 2 1.0 B R –R >2L 1 2 0.8 0.6 X X 0.4 M =M =1 1 2 2 M =M =10 1 2 M =1; M =10 0.2 1 2 Theory 2L 12 3 45 X –X /L 1 2 THE JOURNAL OF EXPERIMENTAL BIOLOGY Discrimination rate 20 M. Moreau and others 0.24 Fig.4. Individual density plots of three workers within the experimental set-up. The dotted line represents the limit between the nest and the foraging area. The surface of the experimental set-up was discretized in 900 bins of 0.06m0.08m. The color scale gives the number of times an ant was detected in each bin. 0.12 0 0.09 0.18 0 0.09 0.18 0 0.09 0.18 Width (m) whether they met the distance criterion to build an adjacency matrix moving across the nest surface. We developed an algorithm for of interactions. The network obtained is highly connected, with an extracting the positions of each ant, which was first validated on average degree of 26, indicating that ants were directly interacting theoretical test cases and then used for characterizing the spatial with half of the colony (Fig.5). distribution of individuals within nests. In our system, the temporal and spatial resolution allowed the characterization of spatial patterns DISCUSSION in ant colonies and the ability to build a network of social interactions In this study, we proposed an original design to track the position among ants. This system provides a valuable tool for addressing of ants within groups. Individuals equipped with RFID passive several questions including the influence of colony size on the rate transponders were detected by a reader mounted on a mobile arm of social interactions or the impact of variations in environmental conditions on task allocation. These issues are currently under investigation. Our methodology can easily be adapted to any system where individuals evolve in two dimensions. Depending on biological models, there is no restriction in enlarging the size of the domains to monitor and changing the frequency of scanning. The number of readers can also be augmented and/or the overlap of their detection field increased to improve spatial resolution. Finally, the speed of the mobile arm can be boosted to enhance temporal resolution. Our system, which is suitable for organisms of reduced size, offers a promising method for collecting automatically large amounts of data relative to the identity and spatial positions of individuals. APPENDIX Problem statement In a continuum point of view, the form of the distribution function of measurements r(x, t) during one scan is: r (x ,t ) = δ || x − R || δ t − t , (A1) ∑() m () R m=1 where R is the position vector of the reader, t is the time at m R which the tag is detected, M is the number of detections of an ant during one scan and  stands for the Dirac function. Multiple Fig.5. Network of social interactions in a colony of 55 workers and the detections can occur for two reasons. First, the reader can detect a queen of the ant Odontomachus hastatus. The nodes are distributed along motionless tag at a distance L. Second, an ant can move within the the x-axis as a function of the proportion spent by ants in the foraging area and randomly distributed along the y-axis. The queen is indicated by the domain and can be detected in distinct locations (supplementary red circle. material Fig.S1). The algorithm should discriminate both origins. THE JOURNAL OF EXPERIMENTAL BIOLOGY Length (m) Foraging area Nest Radio tagging in social insects 21 The distribution function of ant positions f(x, t) is defined such The dimension number of the problem is then reduced from 3N to that f(x, t)1 if the ant is present at position x at time t and null 2N. elsewhere. We define the detection field f(x, t) (i.e. the area where Second, we replace the discontinuous Heaviside functions H(x) an ant can be detected) by a space filtering of f(x, t): by the hyperbolic tangents function, introducing a numerical smoothing parameter, s. According to numerical tests (not presented f(x, t)   G (x – x) f(x, t) dx, (A2) here), the smoothing parameter s is set to sL/15: where G (x) is a top hat filter in physical space: ⎛ ⎞ 1 ⎛ x − L+ s ⎞ G (x)  1 if  x ≤ L H x − L ≈ 1+ tanh . (A9) L () ⎜ ⎜ ⎟ ⎟ 2 ⎝ s ⎠ ⎝ ⎠  0 elsewhere. (A3) 2N Finally, the continuous IR rIR function to maximize for We introduce the scalar function: determining the positions (X ) of an ant is given by: S (f)   f(x, t) r(x, t) dx dt. (A4) ⎛ ⎞ 1 ⎛ || R − X || − L+ s ⎞ m n S X = max 1+ tanh . (A10) R() n ∑ ⎜ ⎟ ⎜ ⎟ The value of S (f) varies, by construction, between 0 and M. For R n=1,...,N 2 ⎝ s ⎠ ⎝ ⎠ m=1 S (f)M, all detections are associated with ant position. The process of detection consists of finding the function f(x, t) This optimization problem, EqnA10, is solved in two steps: a that maximizes S (f). To achieve this, some assumptions on the form stochastic global optimization method (Belisle, 1992) coupled with of f(x, t) are needed. Assuming that during one scan an ant occupies an ad hoc resampling process followed by a simplex algorithm successively N discrete positions, X , and instantaneously changes method (Nelder and Mead, 1965). Eqn A10 is used to test the position at time t , the distribution function of ant positions is: convergence of the algorithm for position reconstruction. f  (x, t) (x – X ) H(t – t ) H(t – t), (A5) N n n n+1 LIST OF ABBREVIATIONS L radius of the detection field of the reader where H(t) is the Heaviside step function. Using this model, m integer varying from 1 to M equation A4 reduces to: M the number of detections of an ant during one scan M N n integer varying from 1 to N S X ,t = H(|| R − X || − L)H(t − t )H(t − t ) . R() n n ∑ ∑ m n R n n+1 R () N number of positions of the ant during a scan m m n=1,N m=1 n=1 R position vector (X- and Y-coordinates) of the reader for the (A6) detection m S (X ) number of detections associated with ant position X With (R , t ) given, the process of position extraction consists of R n n m R t time at which the tag was detected Rm finding the minimum number N of points, (X , t ) , that maximize n n n1,N X position vector of the ant S . The problem then reduces to an optimization problem in 3N dimensions, the number of ant discrete positions N being unknown. REFERENCES Belisle, C. J. P. (1992). Convergence theorems for a class of simulated annealing Numerical implementation algorithms on Rd. J. Appl. Prob. 29, 885-895. Cole, B. J. and Cheshire, D. (1996). Mobile cellular automata models of ant behavior: Due to the large number of dimensions and the discontinuous nature movement activity of Leptothorax allardycei. Am. 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Radio-tagging technology T ( m, n)= 1 if || R − X || = min (|| R − X ||) R ,X m n m n n=1,N reveals extreme nest-drifting behavior in a eusocial insect. Curr. Biol. 17, 140-145. IEEE. Pervasive. Comput. 5, 25- Want, R. (2006). An introduction to RFID technology. = 0 elsewhere . THE JOURNAL OF EXPERIMENTAL BIOLOGY

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Journal of Experimental Biology – The Company of Biologists

Published: Jan 1, 2011

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