Behav Ecol Sociobiol (2011) 65:265–273 DOI 10.1007/s00265-010-1041-x
ORIGINAL PAPER
Group structure in locust migratory bands Jerome Buhl & Gregory A. Sword & Fiona J. Clissold & Stephen J. Simpson
Received: 19 April 2010 / Revised: 29 July 2010 / Accepted: 2 August 2010 / Published online: 19 August 2010 # Springer-Verlag 2010
Abstract Locust swarms are spectacular and damaging manifestations of animal collective movement. Here, we capture fundamental features of locust mass movement in the field, including a strongly non-linear relationship between collective alignment and density known only from earlier theoretical models and laboratory experiments. Migratory bands had a distinct structure, with a single high-density peak at the front, where collective alignment was high, followed by an exponential decay in density. As predicted by theory, alignment decreased with decreasing density, and fluctuations of movement direction became large until order amongst group members at the back of the band was totally lost. Remarkably, we found that the coordinated movement of migratory bands, which can be several kilometres wide and contain many millions of individuals, results from interactions occurring at a scale of 13.5 cm or less. Our results indicate that locust band structure and dynamics differ markedly from what is known (or assumed) about other large moving groups such as fish schools or bird flocks, yet they still conform to key general predictions made by collective movement models that explain how billions of individuals can align using local interactions. Keywords Collective behaviour . Collective movement . Locusts . Migration
Communicated by J. Krause J. Buhl (*) : G. A. Sword : F. J. Clissold : S. J. Simpson School of Biological Sciences and Centre for Mathematical Biology, Heydon-Laurence Building, A08, The University of Sydney, NSW 2006 Sydney, Australia e-mail:
[email protected]
Introduction How do massive groups of animals organise their movement? Minimal models arising from statistical physics have identified features that should be shared by most moving groups, such as the emergence of cohesion resulting from individuals responding to moving neighbours (Vicsek et al. 1995; Gregoire et al. 2003). One of the most fundamental signatures of such self-organised mass movement is a phase transition from disorder to order with increasing local density. Empirical studies in simple, standardised environments have confirmed this transition in several biological entities such as migrating cells (Szabo et al. 2006), fish (Becco et al. 2006) and locusts (Buhl et al. 2006). However, most of our understanding of animal collective movement has been limited to either simulation studies (Couzin and Krause 2003) or quantifying basic features of group movement in small-scale experiments where fundamental features of moving groups such as spatial structure and the trajectory of the whole group cannot be studied (but see Ballerini et al. 2008a). Placing individual interactions in the context of such group characteristics is likely to be central to answering key questions about the formation, maintenance, and movement of groups of animals or other entities (Giardina 2008). Answers to questions about group movement assume an extra significance when applied to one of its most devastating manifestations: swarming in locusts. Locusts are defined by their capacity to shift between two phenotypic forms in response to crowding: the shy, cryptic “solitarious” and the actively aggregating “gregarious” forms (Pener and Simpson 2009). Gregarious juveniles aggregate into migratory bands that can contain billions of individuals that walk and hop through the habitat during the day and roost at night (Clark 1949; Ellis and Ashall 1957;
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Uvarov 1977; Lecoq et al. 1999; Hunter et al. 2008). These hopper bands can cover from a few hundred square metres up to kilometres and take a variety of shapes, ranging from columnar to frontal structures (Uvarov 1977). The latter, with the highest concentration of hoppers at the front of the group, seems to be the most frequent shape in the Australian plague locust, Chortoicetes terminifera (Clark 1949; Hunter et al. 2008), the desert locust, Schistocerca gregaria (Ellis and Ashall 1957) and Rhammatocerus schistocercoides (Lecoq et al. 1999). Unlike some other massive animal groups, such as many fish schools and bird flocks, locust bands can arise from isolated individuals and may either remain cohesive or disband entirely depending upon the conditions they encounter. The transition between the solitarious and gregarious behavioural forms has been extensively studied at several biological levels [reviewed by Pener and Simpson (2009)], from the physiology of these changes [e.g. (Anstey et al. 2009)] to the spatial patterns of vegetation favouring the emergence of gregarization (Collett et al. 1998). Yet, the formation, dynamics and trajectories of locust bands, which presage full-blown outbreaks and offer obvious targets for early control (Hunter 2004; Holt and Cooper 2006), have rarely been quantified, especially in terms of individual movements [but see (Lorch et al. 2005; Sword 2005; Sword et al. 2005; Sword et al. 2008) for studies of Mormon cricket band formation and movement]. We studied seven migratory bands of the Australian plague locust (APL), C. terminifera, during outbreaks from 2006 to 2009. Using cameras mounted on tripods, locust bands were filmed, and the position and orientation of over 64,000 different locusts were extracted. This allowed us to characterise the structure of these groups and quantify how density relates to collective alignment and the direction of locust movement.
Material and methods Recording of band movement and data acquisition APL bands were studied during February 2006 near Topar (S31.8897 E142.006), New South Wales (two bands filmed), November 2006 near Katanning (S33.58321 E118.44487 and S33.66786 E117.60031), Western Australia (two bands filmed), November 2007 near Ravensthorpe (S33.3626 E120.186), Western Australia (one band filmed) and January 2009 near Parkes (S33.1377 E148.059 and S33.0624 E 148.269), New South Wales (two bands filmed). The locust bands comprised late instar juveniles (3rd to 5th) and were reported to us by the control organisations in charge of the study areas: the
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Australian Plague Locust Commission in Topar, the Department of Agriculture and Food in Western Australia, and the Department of Primary Industries of News South Wales for Parkes. Data were collected by setting up a camera mounted on a tripod, the camera objective pointing vertically toward the ground. The central column of the tripod was extended horizontally so that the recorded area was not obstructed by the tripod legs. This yielded a recorded area of a maximal surface of approximately 0.6 m2 using Standard Definition cameras (Canon XM 2) in the Topar site, and 1 m2 using HDV 1080i cameras (Sony HDR-HDC3/9) for all the other study sites. If the position of the band front was known and accessible, the tripod was placed ahead of the band front so that the direction of the band movement resulted in the recorded area sampling the centre of the front and then the rest of the band, from front to back, as it passed through the recorded area. At the Topar site, the nature of the landscape (Mitchell Grassland) and the relatively small size of the bands (approximately 50 to 200 m long) allowed us to follow the position of the front and attempt to record ahead of it, moving the camera as necessary. This yielded eight recordings out of 19 at this site. For the rest of the Topar recordings and at the other sites, the tripod was set in the middle of the flow of marching locusts, or in the wake of the marching band (50–100 m away from the active flow of marching and in an area that the band had left 3 days ago). In these cases, the recording was only started 2 to 5 min after the experimenter set up the tripod and left the area to let the flow recover from disturbances. Even in the smallest bands, the end of the recordings did not represent a clearly defined end of the band, as very low densities (typically less than 10 m−2) can remain in the wake of a band for some time and make it difficult to define a finite boundary. The recorded area was selected to be flat, smooth and without any vegetation. Whenever the soil was of sandy composition, the area was raked to improve its homogeneity. The recorded area was always located away (at least several metres, and 50 m in the case of trees and creeks) from any major obstacles or landmarks such as trees, creeks, dense vegetation patches or any feature that could prevent, constrain or deflect the flow of marching locusts. To record the scale, a ruler was briefly placed in the recorded area during the set-up. We obtained 37 recordings of band movement, representing a total duration of 27 h and 24 min. Videos were captured onto computer, and we analysed one frame every 30 s in the marching bands, and one frame per second in the wake of marching. The frame sizes were either 720×576 pixels for the Topar study or 1,440×
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1,080 pixels for the rest of the study. These frames were loaded in a custom graphical interface developed with Matlab that allowed pointing and clicking to acquire the coordinates of the front and the back of each locust to be observed on the frame. The analysis was conducted on a total of 3,168 frames allowing us to acquire the position and orientation of 64,715 different locusts within marching bands, and a total of 3,598 frames and 9,440 locusts’ positions and orientations in the wake of marching (these latter frames were only used in the analysis referring to the wake of marching band). Characterization of locust density, alignment and entropy For each frame, the density was calculated by dividing the total number of locusts N by the area of the frame. We calculated the direction of the locust as the angle θ(t) of the vector starting from the coordinates of the abdomen (xt,yt) and ending at the tip of the head (xh,yh) for each of the N locusts. Each locust was then characterised by its position vector ci using coordinates x þ x y þ y h t h t ; 2 2 and its unit direction vector Vi using the angle θ(t). To measure alignment and order of locusts, we computed the polarisation for all locusts present in the frame: 1 ΦðtÞ ¼ N
X N Vi ðtÞ i¼1
Vi(t) being unit vectors, polarisation has a theoretical maximal value of 1 when all locusts have the exact same direction and a minimal value of 0 (for a large N) when locust directions are spread at random, or in groups of opposing directions. Polarisation is probably the most widely used measure to quantify the level of alignment in a moving group, but it has some limitations. First, it is dependent on the number of individuals and tends to yield larger values for very small N (Motsch 2009). Second, it is also an ambiguous measurement for ordering, as equivalent low values of polarisation could result either from evenly distributed directions or, for example, from sets of narrowly distributed but opposing directions, the former situation having less order than the latter. Although less frequently used in studies of animal collective movement, entropy as a measure of alignment does not suffer from these limitations and provides a complementary measure to polarisation. Therefore, the order of the locusts’ movement was also measured using an adaptation of Boltzmann entropy Em described by
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Baldassarre (Baldassare 2008) as follows: N! Em ¼ k ln N1 !N2 ! . . . Nc ! ! C C X X ln½Ni ! ; Ni ¼ N ¼ k ln½N ! i¼1
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Locusts are classified according to their direction, with C corresponding to a division of the directions in an arbitrary number of C=72 classes of width of 5°. Ni is the number of locusts in the directional class i and k is a scaling factor (defined below). For N>170, we used Stirling’s approximation hpffiffiffiffiffii 1 ln½n! n þ ln½n n þ ln 2p 2 to overcome limitations due to factorial computation. The classes were set with the angle 0 chosen as 2.5° clockwise with respect to the angle of a randomly chosen locust excluded from the computation. The entropy for M locusts was thus calculated with respect to the N=M−1 remaining locusts. The scaling factor k was set to normalise Em in [0,1], which can be achieved by setting it to max k ¼ 1= ln½wmax m where wm ¼
N! Nh1 !Nh2 ! . . . NhC !
being the value obtained for the most uniform with wmax m distribution of N among the C classes, Nhi being the number of elements in each class i and given this uniform distribution. In other words, when locusts directions are spread the most uniformly, the entropy is maximal, that is, Em =1. The more the locusts’ directions are grouped in a limited number of directions, the lower the entropy and the higher the order in the locust flow. The direction of the flow was given by the angle denoting the average direction of locusts, hqðtÞi ¼ arctan½hsinðqðtÞi=hcosðqðtÞi, where θ(t) corresponds to the angle representing the locust directions. The directional change was calculated as the absolute value of the difference between the direction of the flow at the time of the frame and its direction 5 min before.
Results Density profiles Out of the eight recordings that were successfully started ahead of the band, six were used to study how density varied from the front to the back of the band (the two other profiles were excluded due to locusts perching in the vegetation, which interrupted band movement and induced
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Fig. 1 Three examples of density profiles of a small locust band from front to back (studied in Broken Hill, NSW, February 2006). The recording started before the front of the band reached the camera and continued for approximately 1 h. The x-axis origin has been made relative to the occurrence of the density peak. The density profiles show a very sharp increase in density at the band front, maximal almost immediately in the two recordings where marching was well established (27/2 and 28/2), whereas, the increase was more progressive, although still very steep, for the recording where the band was only just starting to march at a slower speed (26/2)
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strong fluctuations of density throughout the period recorded). The density profiles showed an extremely inhomogeneous structure, with a single peak at the front (Fig. 1; average time of occurrence of peak density after the first locust observed, 4.58 min±3.26 SD; n=6), followed by a sharp, exponential decay, as shown by the linear trend on a semi-logarithmic representation (Fig. 2; all R2 >0.77 for a linear regression of Ln (density) with time). The density profiles of the front of the larger bands were not recorded because they either could not be found or were inaccessible. The persistence of the flow of locusts in the same location for several days indicated that these larger bands were potentially several kilometres long, but their overall structure was likely to be similar to those of the small bands observed in Topar: qualitative descriptions and aerial photographs of large bands indicate a very similar marked concentration of locusts at the front (the larger the bands, the higher the peak densities and the deeper the fronts) that vanishes rapidly behind it (Clark 1949; Hunter et al. 2008). We found the density profiles behind the front to be most often less than 50 m−2 (95% of observations below 46 m−2, median=11.01, n=1,653), but persisted up to several days at fixed locations of recording. Most of the
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Fig. 2 Density profiles of the small band followed on the 26th [a at 9:35, b at 10:56], 27th [c at 10:58] and 28th of February 2006 [d at 9:06, e at 10:29, f at 13:59] in Broken Hill on a semi-logarithmic scale, showing the exponential decay of density with time past the peak density (which is evidenced by a linear regression in such a representation of the data). The results of a linear regression are shown (black line) for each profile. Note that the slope of the linear
regression for the semi-logarithmic representation corresponds to the value of the exponent in the standard representation. The densities occurring before the peak have been omitted in these figures. In f, the band stopped perching and resumed marching after clouds obscured the sun, but the reappearance of sun after 12 min triggered perching again and rapidly stopped the whole band
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Densities above roughly 50 m−2 showed consistently high levels of polarisation, whereas those below showed large variation in polarisation, suggesting a weaker alignment of locusts. Polarisation tended to decrease slightly at the highest densities from values centred on 0.9 (median for 100< densities 400 m−2). Given that polarisation was highly variable and that even randomly distributed orientations can generate high polarisation values for small N (Motsch 2009), polarisation did not allow us to assess how order varies at low densities. To gain a clearer insight into this, we also measured the degree of ordering in locust directions by computing an adaptation of the Boltzmann entropy, normalised so that a value of 1 corresponded to a homogeneous distribution of locust directions, and a decrease of entropy corresponds to an increase in the ordering of locust directions. The relation between entropy and density was clearer than when using polarisation, showing a sharp transition at lower densities (at similar values to that of polarisation, < approx. 50 m−2), which could be approximated as a power law (Fig. 4; exponent of the power law, 0.035, estimated from a linear
variations in the density observed at one location as the band flowed through could be associated with the daily rhythm of alternating between marching and perching in the vegetation, as previously described both in S. gregaria and C. terminifera (Clark 1949; Ellis and Ashall 1957; Hunter et al. 2008): marching developed in the morning, but densities dropped around midday as a result of an increasing proportion of locusts perching in the vegetation (generally associated with the increasing temperatures). Later in the afternoon, locusts resumed marching, and densities increased progressively again (Fig. 3) until nightfall stopped the activity. Ordering and alignment within bands Theory predicts that the extreme variation in density within bands will be coupled with large fluctuations in locust alignment and therefore the trajectories of flow (Buhl et al. 2006; Yates et al. 2009). To investigate these relationships, we measured alignment by computing the polarisation of locusts in each frame, which ranges from 0 for complete dispersion to 1 when all locust directions are identical.
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Time (h:min) Fig. 3 Example of densities of locusts (black circles) observed at a fixed recording location (at an unknown distance behind the front) as a large band moved through the area and ground temperature (grey circles) during the 22nd (a) and 23rd (b, c) of November 2007 near Ravensthorpe (Western Australia). On the 22nd, temperature increased and reached around 50°C at the end of the morning, while density progressively decreased due to locusts perching. At midday, almost no
locusts were seen marching until perching decreased again later in the afternoon. Note that on the morning of the 23rd (b), broken clouds yielded large fluctuations in temperatures, and locusts alternated between bouts of perching and marching, easily seen in the large variations of density in the figure. At the middle of the day though, marching finally stopped and only resumed later in the afternoon (c; no temperature was recorded due to a thermocouple failure)
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To analyse how the alignment of pairs of locusts might depend on distance between the two insects, we selected frames from the wake of bands where only two locusts were present. We then applied the technique introduced by Hanisch (Hanisch 1984; Diggle 2003) to account for a potential border bias by only considering locusts when the distance between them was less than the distance to any of the borders of the frame. By testing the distribution of polarisation of pairs separated by increasing distance, we determined that this distribution ceased to be significantly different from uniform beyond 13.45 cm apart (n=56,
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Fig. 4 Relationship between collective alignment (measured by polarisation and entropy), fluctuations in direction of movement and density across 37 recordings from seven bands. a Polarisation was consistently high at high locust densities, but showed a large variability with decreasing locust density. b The relationship between the average Boltzmann entropy (for locust directions) and density. The plain curve shows a power law fit for the initial decrease of entropy which corresponds to a rapid increase in the ordering of locust directions with increasing density. c Fluctuations in the direction of movement quantified by the absolute value of the difference between the group direction in each frame and its direction in the frame 5 min before. The inset d shows average values in a log-log representation
regression on log (entropy) versus log (density), n=64, R2 = 0.825, F=292.6, P400 m−2), decreases in entropy ceased and reached a plateau. At very low densities (below 10 m−2), locust directions were almost completely disordered; entropy was higher than 0.9, meaning that the distributions of locust directions were approaching homogeneity. Similarly, there was a highly non-linear relationship between fluctuations of the average direction of locust flow and density (Fig. 4). The direction of flow was relatively constant at densities above 100 m−2. However, fluctuations increased dramatically at lower densities, particularly below 10 m-2 with a potential loss of group cohesion at the back
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Z=1.19, P=0.119), while pairs separated by less than this distance had a polarisation distributed significantly differently from a uniform distribution (n=142, Z=5.01, P= 13.5 cm
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Fig. 6 Alignment in pairs of locusts. Highly aligned pairs were only observed when the two locusts were close together, as seen on the distribution of polarisation for individuals less than 13.5 cm apart (a), which showed a peak in polarity values close to 1. In contrast, individuals separated by 13.5 cm or more showed a widespread distribution of polarisation indicative of an absence of alignment (b)
2008), we have quantified and characterised the structure of locust bands and their dynamics under natural conditions. Our analysis reproduced the predicted transition from order to disorder with decreasing density (Buhl et al. 2006), but additionally revealed two distinctive features of natural locust bands. First, the alignment between individuals that determines band cohesion and movement occurs within a distance of only 13.5 cm. Hence, the collective behaviour of migratory bands that can be several kilometres wide contain billions of locusts and travel hundreds of metres per day results from events occurring at the scale of a hand span. Second, bands comprise an extremely dense front followed by an exponential decay of density, with a consequent loss of cohesion towards the back. Polarisation tended to decrease at higher densities, while entropy seemed to reach a plateau. The former would suggest a decrease in the degree of locust alignment, perhaps due to congestion effects, but the reason why there was no increase in the entropy values at similar densities is not known. It is possible that the entropy had not reached a plateau, but was increasing slowly with density—a feature which the availability of more data might have resolved. Moreover, the apparent decrease in polarisation at high densities might be enhanced or explained by the tendency for the polarisation value to decrease with increasing N independently of actual alignment among the measured agents (Motsch 2009). Alignment between pairs of locusts occurred at a very short range. We know that local visual and tactile interactions related to the threat of cannibalism are keys for the onset of locust collective motion (Bazazi et al. 2008), and behavioural entrainment among locusts within non-marching groups also occurs at a very short range (Despland and Simpson 2006). However, further work will be needed to determine how locusts interact with multiple individuals within this distance, in particular, whether it defines a metric range where all locusts’ orientations influence an individual, or whether this influence is limited to a defined number of nearest neighbours as evidenced in starlings (Ballerini et al. 2008a). Having a single sharp frontal density peak also seems to differ markedly from other large moving groups. The concentration of locusts at the front of the bands is such that large bands can often be spotted from the sky and recognised by their typical pattern: the front forms a thin crescent shape where densities can reach several thousand individuals per square meter, while the rest of the group behind this line rapidly (exponentially in the bands studied here) fall below 50/m2 and can only be spotted from the ground (Hunter et al. 2008). Fish groups also have higher densities at the front (Partridge et al. 1980; Bumann et al. 1997; Hemelrijk and Kunz 2005; Hemelrijk and Hildenbrandt 2008); however, the density gradients in
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fish groups appear to be less pronounced, and the groups themselves are smaller than locust bands, making a direct comparison difficult. Some marine species form massive shoals, but exhibit complex structures with multiple nuclei of higher density within the group (Freon et al. 1992; Gerlotto and Paramo 2003). Recent studies of starling flocks showed yet another form of group structure with higher densities distributed all along the well-defined edges of the group (Ballerini et al. 2008b). Large density gradients do appear in theoretical models of collective motion (Chate et al. 2008), but probably arise due to the periodic boundary conditions used in these simulations (Nagy et al. 2007) and take the form of successive density waves instead of a single front as in locusts. The origin of such large-scale features of animal groups that are not accounted for by current theoretical models will need to be sought in the specific aspects of movement rules (Gautrais et al. 2009; Hildenbrandt et al. 2009), interactions (Ballerini et al. 2008a) or other unconsidered behaviours. For example, although our recordings were made on bare ground, the high-density fronts might result from previous bouts of feeding where density builds up on suitable vegetation (Clark 1949). Alternatively, locusts at the front might slow down in the absence of other individuals ahead of them, or simply turn more often, making their net displacement decrease in comparison to those behind [(Uvarov 1977); as also proposed in models of fish schools (Hemelrijk and Kunz 2005; Hemelrijk and Hildenbrandt 2008)]. Locust bands exhibit a lack of cohesion and marked disorder in their rear. The implication is that locusts separated from the group seem unlikely to relocate the band, consequently with an increased risk of predation (Sword et al. 2005), but the death of stragglers and slow attrition of bands over time is not the only possible outcome. Stragglers may be recruited by other bands sweeping through the area, or they may form new groups as locusts in the vicinity converge on available patchy resources and once again reach threshold densities conducive to collective movement (Collett et al. 1998). Alternatively, locusts that remain isolated may revert from the expression of gregariousness to the solitarious phenotypic form (Gray et al. 2009), spread even more, and potentially experience the fitness benefits of a solitary lifestyle given the appropriate environmental conditions (Simpson and Sword 2009). Although band movement has typically been described as unpredictable (Clark 1949; Ellis and Ashall 1957; Uvarov 1977), we quantified changes of direction within bands and showed that they decrease in a highly non-linear way with increasing locust density. Previous studies reported that bands spread as they move, and their density typically decreases with time spent marching (Clark 1949; Ellis and Ashall 1957; Uvarov 1977; Lecoq et al. 1999),
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therefore, their direction should be less variable early after marching commences. With more data on band movement in the field, anticipated travel distances and fluctuations of direction could be computed, building a parameterised predictive model such as in Yates et al. (2009). Better models of band movement can be used to optimise and reduce the environmental impacts of existing management strategies such as the placement of pesticide barriers (Holt and Cooper 2006), the success of which depends upon the very mass movement of locusts that they aim to control. Acknowledgements We thank Mark Logue and Alex Stewart from the WA Department of Agriculture and Food, Brad Hazell from the NSW Department of Primary Industries, Ted Deveson, Rob Graham, and Peter Spurgin from the Australian Plague Locust Commission, and the landowners of the surveyed properties. We thank Julie-Anne Popple, Marie-Pierre Chapuis, Karine Berthier, Gabriel Miller, and Matthew Collett for their assistance in the field. We also thank two anonymous referees for their invaluable comments and suggestions. This work was funded by the Australian Research Council (ARC) Linkage and Discovery programmes, and SJS was supported by ARC Federation and Laureate Fellowships.
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