brood sorting by ants: two phases and differential diffusion

ANIMAL BEHAVIOUR, 2004, 68, 1095–1106doi:10.1016/j.anbehav.2004.02.013

Brood sorting by ants: two phases and differential diffusion

ANA B. SENDOVA-FRANKS*†, SAMUEL R. SCHOLES†, NIGEL R. FRANKS‡ & CHRIS MELHUISH†

*School of Mathematical Sciences, University of the West of England

yIntelligent Autonomous Systems Laboratory, University of the West of England

zCentre for Behavioural Biology and School of Biological Sciences, University of Bristol

(Received 9 July 2003; initial acceptance 1 October 2003;

final acceptance 9 February 2004; published online 18 September 2004; MS. number: 7785R)

Leptothorax ant colonies sort their brood in concentric annuli with the smallest items in the middle and thelargest on the periphery. Such brood sorting is a prime example of collective structure formation by socialinsects. Its underlying mechanism, however, is still not understood. We tested the hypothesis that broodsorting has two phases: the phase of clustering, proposed earlier, is followed by a phase of spacing, whenants move brood items away in a random direction but in a type-specific way so that items of differentbrood types spread out to a different extent. We hypothesized that in phase 2, spacing, items of thesmallest brood type spread out the least and end up in the centre, whereas items of the largest brood typespread out the most and end up on the periphery. We found two distinct phases in the direction of broodmovement during brood sorting associated with nest emigration. In phase 1, ants moved brood items inthe direction away from the nest entrance. This was the clustering phase. In phase 2, ants moved brooditems in a random direction. This was the spacing phase. Ants moved smaller items for longer than largeritems. This is consistent with the hypothesis that ants put down brood items as a function of their weight.The diffusion coefficient and the frequency of movement were different for different brood types. Themeasure of the average spread (root-mean-square displacement) for each brood type was consistent withtheir order from the centre to the periphery of the sorted brood structure. The process underlying thisspread, however, could not be simple diffusion since the movements of different brood types areinterdependent. We discuss the mechanisms that could underlie the switch between the two phases.

� 2004 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Social insects are famous for their ability to solve problemsat the collective level, which by virtue of their scale arebeyond the scope of an individual’s overview (Camazineet al. 2001). For example, recent work has demonstratedthe extraordinary feats of collective decision makingduring house hunting in ants and bees (Franks et al.2002). Social insect colonies, however, are also amazing atbuilding structures. Many species construct fascinatingnests (Jeanne 1975; Grasse 1984; Franks et al. 1992; Franks& Deneubourg 1997). Honeybees order nectar, pollen andbrood in their combs (Camazine 1991). Ants structuretheir traffic flow (Couzin & Franks 2003), cluster items of

Correspondence: A. B. Sendova-Franks, School of MathematicalSciences, University of the West of England, Frenchay Campus,Coldharbour Lane, Bristol BS16 1QY, U.K. (email: [email protected]). N. R. Franks is at the Centre for BehaviouralBiology and School of Biological Sciences, University of Bristol,Woodland Road, Bristol BS8 1UG, U.K.

1090003–3472/04/$30.00/0 � 2004 The Association for the S

different kinds (Deneubourg et al. 1991; Bonabeau et al.1999), sort their brood (Franks & Sendova-Franks 1992)and even themselves (Sendova-Franks & Franks 1994;Backen et al. 2000; Sendova-Franks & Van lent 2002).Brood sorting in Leptothorax ant colonies (Franks &

Sendova-Franks 1992) is one of the prime examples ofsuch collective intelligence. Leptothorax ant colonies livein approximately flat nests in rock fissures and organizetheir brood in a single cluster. The brood cannot move ontheir own and any change in their position is dependenton the workers. The brood cluster is composed of concen-tric annuli each containing brood items of a differenttype. Eggs and small larvae are in the middle whereasmedium and large larvae are in concentric annuli in-creasingly further out towards the periphery. The posi-tions of prepupae and pupae vary but usually they areplaced between the annuli of the medium and largelarvae. The possibility that this spatial structure of thebrood has some adaptive significance is strongly suggestedby its rapid recreation following colony emigration to

5tudy of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

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ANIMAL BEHAVIOUR, 68, 51096

a new nest site. Its presence may promote efficient broodcare as well as an efficient division of labour for brood-caring tasks (Sendova-Franks & Franks 1995) and thusfacilitate brood survival and development. For example,the positions of the hungriest brood, the large larvae, areon the periphery of the cluster. This ensures that thebrood items in which ants have invested most are fed first.Prepupae and pupae do not feed (Franks & Sendova-Franks 1992).Brood sorting in Leptothorax ant colonies not only poses

a fascinating biological question about the link betweenindividual and collective animal behaviour but beyondthat it has also inspired much work by computer scientists(e.g. Lumer & Faieta 1994; Kuntz et al. 1999) and robot-icists (Melhuish et al. 2001; Wilson 2003; Wilson et al.2004) interested in the new fields of ant algorithms andcollective minimalist robotics.The mechanism underlying brood sorting, however,

remains elusive. There are several models that are relevantbut none addresses the issue explicitly. Deneubourg et al.(1991) proposed a clustering algorithm inspired by broodclustering in ants for application in computer science androbotics. The model comprises a simple algorithm ofindividual behaviour based on conditional probabilitiesof picking up and putting down items. An item is morelikely to be picked up if the number of items of the sametype in the immediate neighbourhood is small. Conversely,an item ismore likely to be put down if the number of itemsof the same type in the immediate neighbourhood is large.Inherent in this algorithm is the ability of the individual torecognize items of different types and to estimate theirdensity in the immediate neighbourhood. The modelproduces the segregation of items by type into differentclusters (Deneubourg et al. 1991). This is similar to thepiling of same-age brood items within a single chamber incolonies of the ponerine ant Odontomachus troglodytes(Dejean& Lachaud 1991) but different from the concentricbrood annuli in Leptothorax ant colonies (Bourke & Franks1995, page 435). Therefore, the clustering algorithm doesnot provide a satisfactory model for brood sorting inLeptothorax.A model that involves concentric spheres rather than

concentric annuli is the differential adhesion model(Steinberg 1963). It aims to explain the sorting out ofadhering cells of the same type during morphogenesis.Potentially, however, the basic idea could be applied to thebrood in ant colonies. Consider two types of item, A andB. The strength of adhesion between two items ofdifferent type is denoted by WAB and between two itemsof the same type by WAA and WBB for items of type A andB, respectively. A spherical structure of cells is formed withcells of type A in the middle and cells of type B on theperiphery when (WAA CWBB)/2O WAB R WBB. This ideacould be applied to brood sorting in Leptothorax where thestrength of adhesion is replaced by the probability ofputting down an item of type A or B next to another itemof type A or B. (A similar rule could be applied to theprobabilities of picking up an item next to another itembut then the above relationship should have its signsreversed.) Wilson (2003) found that applying this type ofalgorithm to the simulation of object sorting by groups of

minimalist robots leads to a good degree of annularsortedness. However, when there are more than two itemtypes, the quality of annular sortedness decreases withincreasing number of item types. This occurs because,with an increasing number of types, the differencesbetween probabilities of putting down an item next toanother item according to its type are reduced and hencethe separation of the concentric annuli decreases. Broodin Leptothorax ant colonies is classified not in two but infive types: eggs and small larvae, medium larvae, largelarvae, prepupae and pupae. Therefore, it is unlikely thata model based on the idea of differential adhesion wouldbe satisfactory.

The muesli effect (Barker & Grimson 1990) is anothermodel that could shed light on the mechanism underly-ing brood sorting in Leptothorax ant colonies. The mueslieffect is a phenomenon of self-sorting by size in whichparticles form strata with the largest on the top of the pileand the smallest at the bottom. It occurs under theinfluence of shaking and gravity as the smaller particlesare able to move down the crevices that lie between thelarger particles (Franks & Sendova-Franks 1992). McCoy(1991) explored several versions of a simulation modelbased on the muesli effect. It involved two types of item,larger and smaller discs. The sieving effect was representedby the movement of items and the gravity effect bya point of attraction. The outcome for all models was theexpected pattern with the smaller items in the middle andthe larger items on the periphery (McCoy 1991). It islikely that the tendency of the ants to cluster their broodprovides a centripetal force that could serve instead ofgravity in McCoy’s model (Franks & Sendova-Franks1992). However, the muesli-type effect model shares thesame problem as a model of brood sorting in Leptothoraxas the clustering and differential adhesion models de-scribed earlier. All three models lead to clustering. Whileants have a clear propensity to cluster brood items in theearly stages of the sorting process, clustering on its ownleaves the brood too close to one another for ants to beable to tend them. The brood need spacing out, that is,each item needs the allocation of a ‘domain of care’appropriate for its brood type (Franks & Sendova-Franks1992). Such crucial spacing out is absent in all threemodels.

We tested a hypothesis about brood sorting in Lepto-thorax that combines the tendency for brood clusteringwith the need for brood spacing. The clustering of all thebrood items together constitutes the first phase followedby a second phase of moving items outwards to spacethem and to allow room for brood tending. We hypoth-esized that it is in the second phase that the concentricannuli are formed and items of different type take theirrelative positions through a mechanism of differentialdiffusion.

We studied brood sorting in the context of emigrationto a new nest site when ants have to transport the broodto the new nest and have to sort them de novo. Franks &Sendova-Franks (1992) demonstrated that the brood aresorted within 48 h after the start of the emigration andthis is the time frame we used for our experiments. Ourresults are based on 936 movements of brood items picked

SENDOVA-FRANKS ET AL.: BROOD SORTING BY ANTS 1097

up and put down inside the new nest during this period infive experimental colonies.We asked the following specific questions. (1) Is there

a switch in the direction of brood movement by ants? (2)Are the diffusion coefficient, mean duration and meanlinear distance of movement different for different broodtypes? (3) Do ants move some brood types more frequentlythan others? (4) Is the spread for different brood typesconsistent with a differential diffusion mechanism forbrood sorting?

METHODS

Experimental Colonies

The study involved five colonies of the ant Leptothoraxalbipennis. All colonies were collected from rock crevices inDorset, U.K., in the spring of 1996 and 1997. In thelaboratory, colonies were housed in nests made from a pairof microscope slides separated by a thin cardboardperimeter to make a nest cavity of 35 ! 23 ! 1 mm withone missing short wall (Fig. 1). Water and the two sourcesof food (honey solution and Drosophila larvae) werereplenished weekly. The temperature was controlled andvaried between 20 and 23 �C. The ratio of light to darkhours followed the ratio for the season with a minimum of8 h darkness per 24 h. The details for culturing coloniesunder laboratory conditions followed Sendova-Franks &Franks (1995). The number of workers in the experimentalcolonies varied from 37 to 82 and the total number ofbrood items from 55 to 109 (Table 1). Table 1 also containsthe number of items from each brood type in each of thecolonies.

Experimental Procedure and Data Collection

We studied the brood sorting associated with colonyemigration to a new nest site (Franks & Sendova-Franks1992; Sendova-Franks et al. 2002). The emigration exper-

X

90°

0°

180°

270°

0YFar short wall

Nest chamber

Entrance

Figure 1. A schematic representation of the experimental nest withthe orientation and coordinate system used in the analyses of brood

movement during brood sorting.

iment for each colony was carried out in May–June in theyear it was collected. Each emigration took place in anarena with an area of 75 ! 43 cm. The distance betweenthe old and new nests was 6 cm. A pile of sand grains,serving as a source of building blocks for filling in themissing nest wall, was situated 2 cm away from the newnest. We provoked an emigration by removing the topslide of the current nest site (the old nest) in the presenceof the new intact nest site (new nest) nearby, which theants could colonize.We recorded on 3-h videotape in 48-h time-lapse mode

all events inside the new nest for 48 h starting from themoment the top slide of the old nest was removed (videocamera: Panasonic WV-E550E; lens: Schneider Optics,Century Division, Van Nuys, California, U.S.A. 25 mm,f2.8, C18848; video recorder: Panasonic AG-6370; intervalbetween frames in 48-h time-lapse mode: 0.68 s; this wasshort enough not to miss any brood movement). How-ever, in colony 5, which was very slow to find the newnest and make the decision to emigrate, the 48-h time-lapse mode recording began 3 h after the top slide of theold nest was removed.From the videotape for each of the five colonies, we

recorded the following measurements for each movementof a brood item by ants inside the new nest: (1) broodtype; (2) time when picked up; (3) time when put down;(4) X and Y coordinates of position (item centre) whenpicked up and (5) X and Y coordinates of position (itemcentre) when put down.For each brood movement we then calculated: (1)

duration (the difference between the time when pickedup and the time when put down); (2) linear distance (theEuclidean distance between the position when picked upand the position when put down); and (3) direction oflinear movement (angle of linear movement from posi-tion when picked up to position when put down).

Direction Switch in Brood Movement

We defined the end of phase 1 (clustering) and thebeginning of phase 2 (spacing) as the time when thedirection of brood movement reversed, that is, the time ofthe first occurrence of two consecutive angles of brood

Table 1. Number of workers and brood items of each type in each ofthe experimental colonies

Colony No. of workers

Brood type

4 6 8 9 10 Total

1 54 29 23 33 9 10 1042 37 22 10 13 4 6 553 59 15 18 18 15 10 764 82 17 14 16 27 29 1035 66 56 13 10 6 24 109

Total 298 139 78 90 61 79 447

4: Eggs and small larvae; 6: medium larvae; 8: large larvae; 9:prepupae; 10: pupae.


movement by ants that were outside the interval [80 �,280 �] (Fig. 1). An exception was made for colony 3 wherethe first such occurrence corresponded to only four broodmovements and therefore the time of the second occur-rence was taken (see Table 2 for the number of broodmovements in each phase and overall). This definition forseparating the two phases was a compromise betweenobtaining a good sample size for phase 1 (interval of 200 �

rather than 180 �) and avoiding one-off events (twoconsecutive angles rather than a single one). This wasthe definition we first chose.We used the package Oriana (1994 Warren L. Kovach,

Kovach Computing Services, Pentraeth, Wales, U.K.) tocalculate circular statistics (Batschelet 1981) for the di-rection of linear brood movement by ants. The meanvector direction with its standard error and 95% confi-dence interval summarizes the direction of brood move-ment.We tested whether direction distributions were different

from uniform with the Rayleigh test (RZ Nr, where N isthe sample size and r is the mean vector length, Zar 1999,page 617).We used the chi-square test to determine whether

direction of brood movement in phase 1 was differentfrom direction of brood movement in phase 2 by com-paring their frequencies for a given number of angleintervals. The number of angle intervals was determinedon the basis of sample size and varied from 4 (90 � each) to6 (60 � each) for the different colonies.

Diffusion Coefficient, Movement Durationand Distance

In a random walk process, the diffusion coefficient, D, isproportional to the square of the step length, d, divided bythe time per step, t (Berg 1993). Therefore, the diffusioncoefficient for each brood type is proportional to CdD

2

CtD,

where CdD is the mean linear distance of movement and CtDis the mean duration of movement for that brood type. Tofind the mean duration of brood movement, we fitteda linear regression model to the log-survivorship plot(Martin & Bateson 1993; Sendova-Franks et al. 2002) of

the duration data, pooled over all five colonies, for eachof the five brood types, for each of the two phases andover the whole period (Fig. 2a). The linear regressionmodel fitted well in all cases (Appendix, Table A1). Thismeans that individual ants were putting down brooditems of each type at a constant rate over time (probabil-ity/s), as measured by the gradient of the respective line(Fig. 2a, Appendix, Table A1). Therefore, the meanduration of movement and its 95% confidence intervalfor each brood type could be calculated as the reciprocalsof the rate over time and its 95% confidence interval.

We calculated the mean linear distance of broodmovement by ants using the same method. The linearregression model fitted well the log-survivorship plot ofthe linear distance data, pooled over all five colonies, foreach of the five brood types, for each of the two phasesand over the whole period (Fig. 2b, Appendix, Table A2).This means that individual ants were putting down brooditems of each type at a constant rate over linear distance(probability/mm), as measured by the gradient of therespective line (Fig. 2b, Appendix, Table A2). Therefore,the mean linear distance of movement and its 95%confidence interval for each brood type could be calcu-lated as the reciprocal of the rate over linear distance andits 95% confidence interval.

The weight of each of the five brood types was estimatedas the cube of its mean length (mm). The mean length(mm) of each brood type was based on data in Franks &Sendova-Franks (1992), Table 2, Colony D, column ‘Itemlength: Mean’. The brood weights estimated in this waywere the following: eggs and small larvae: 0.40522;medium larvae: 2.62807; prepupae: 5.92974; pupae:5.83200; large larvae: 7.41487 (length3 mm). Therefore,the order of brood types according to estimated weightwas the same as their order from the centre to theperiphery of the sorted brood pattern.

Frequency of Movement

We calculated the relative frequency, R, with which antspicked up brood items, for each brood type for each of thetwo phases and for the overall period in each of the fivecolonies. For each brood type in each colony and in each

Table 2. Number of brood movements by ants according to brood type, experimental colony and phase

Phase

Number of movements for brood type

4 6 8 9 10 Total

1 2 All 1 2 All 1 2 All 1 2 All 1 2 All 1 2 All

Colony1 1 63 64 15 95 110 18 24 42 2 19 21 4 6 10 40 207 2472 4 2 6 3 34 37 11 11 22 0 1 1 12 6 18 30 54 843 3 40 43 9 154 163 8 65 73 4 34 38 6 18 24 30 311 3414 5 9 14 9 35 44 18 23 41 16 28 44 29 41 70 77 136 2135 6 6 12 4 8 12 6 2 8 0 1 1 7 11 18 23 28 51

Total 19 120 139 40 326 366 61 125 186 22 83 105 58 82 140 200 736 936

For brood type codes see Table 1.


phase as well as over the whole period, RZmi=Mni=N

, where mi

is the number of movements of items of brood type i, M isthe total number of brood movements by ants (Table 2), niis the number of items of brood type i and N is the totalnumber of brood items (Table 1).To test the null hypothesis of no difference in the

frequency with which the different types of brood aremoved, we applied a Friedman’s test to the data for eachphase and for the overall period with colony as theblocking factor. When the test was significant we identi-fied the medians that were significantly different from oneanother with Nemenyi’s test for pairwise comparisons ofmedians with no rank ties (Zar 1999, page 267).

Brood Sorting through Differential Diffusion

A convenient measure of spread in a diffusion process isthe root-mean-square displacement (RMSD), Cx2ðnÞD1=2

(Berg 1993). To explain the meaning of RMSD, we consider

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Figure 2. Examples of log-survivorship plots from which the mean

duration or the mean linear distance of movement for each type of

brood for each phase and overall were estimated: (a) plot for the

duration of movement of eggs and small larvae in phase 2,ln(cumulative proportion) Z 0.185 � 0.016 ! duration, R2 Z99.2%, F1,118 Z 15 051.99, P! 0.001, see also Appendix, Table

A1; (b) plot for the linear distance of movement of large larvae in

phase 2, ln(cumulative proportion) Z 0.211 � 0.264 ! linear dis-tance, R2 Z 99.5%, F1,121 Z 26 782.65, P ! 0.001, two outliers

were excluded from the analysis, see also Appendix, Table A2.

a one-dimensional random walk. Let xi(n) be the position(distance from start) of a brood item i of a particular typeafter n steps (executed in a time t Z nt). We average thesquare of this displacement rather than the displacementitself to avoid negative numbers. The mean-square dis-placement for items of this type is therefore Cx2ðnÞDZ1N

PNiZ1x

2i ðnÞ. Since xi(n) Z xi(n � 1)G d, and therefore,

xi2(n) Z xi

2(n � 1) G 2dxi(n � 1)C d2, it follows that themean-square displacement is Cx2ðnÞDZ1

N

PNiZ1

�x2i ðn� 1ÞG

2dxiðn� 1ÞCd2�ZCx2ðn� 1ÞDCd2Z Cx2ð0ÞDCnd2. Now, the

mean-square displacement for nZ 0 is Cx2ð0ÞDZ0 becausexi(0) Z 0 for all items i of a particular brood type.Therefore, we can simplify the equation for the mean-square displacement to Cx2ðnÞDZnd2. It follows that theRMSD is Cx2ðnÞD1=2Zn1=2d. In two dimensions, assumingthat movement is independent in the two directions, themean-square displacement distance from the origin (0,0)to the point (x,y) is Cr2ðnÞDZCx2ðnÞDCCy2ðnÞDZnd2Cnd2Z2nd2 and the RMSD is (2n)1/2d. Therefore, the RMSD foreach brood type is proportional to ðnÞ1=2CdD and that iswhat we used for our calculations. RMSD can also be ex-pressed through the diffusion coefficient, i.e. ð2nÞ1=2dZð2t

td2Þ1=2Zð2td2t Þ

1=2Zð2tDÞ1=2, which gives equivalentresults.

RESULTS

Direction Switch in Brood Movement

There was a clear switch in the behaviour of brood-sorting ants between (1) moving brood towards the farshort wall of the nest opposite the nest entrance (Fig. 1) inphase 1 and (2) moving brood in a random direction inphase 2 (Fig. 3). In all five colonies, the directiondistribution of brood movement in phase 1 was signifi-cantly different from uniform (Table 3) and had a meanclose to 180 � (Fig. 3). This was the direction towards theshort wall of the nest opposite the entrance (Fig. 1).By contrast, the direction distribution of brood move-

ment in phase 2 was not significantly different froma uniform distribution in four of the five colonies(Rayleigh test, Table 3). This explains why the estimatedvalues for the 95% confidence interval of the meandirection may be unreliable for phase 2 (Fig. 3).The significant values of the chi-square test comparing

the direction distributions for phase 1 and 2 were reliablein four of the five colonies (Table 3). This confirms thatthe mean direction of brood movement by ants isdifferent in the two phases. Since phase 2 follows phase1, a direction switch in brood movement by ants musthave occurred.Such a switch is further evidenced by the analysis of the

linear displacement of brood relative to the long walls ofthe nest (i.e. along the X coordinate of their positions,compare Figs 1 and 4). In phase 1, brood items wereclearly displaced towards the far short wall of the nest(compare Fig. 4a, b). There is also some evidence that thesmaller items were sieving through gaps between thelarger items in this phase of clustering. The small larvaewere put down closest to the far short wall of the nest


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followed by the medium and large larvae with theprepupae and pupae in between (Fig. 4b). By contrast, inphase 2, there was little noticeable change in the displace-ment of brood items relative to the long nest wall (Fig. 4).This result was to be expected on the basis of the uniformdistribution of the direction of brood movement in phase2.The timing of the switch varied considerably between

the colonies. The duration of the interval between the endof transport during colony emigration and the beginningof phase 2 of brood sorting was 21 min (Colony 3), 1 h38 min (Colony 2), 3 h 9 min (Colony 1), 8 h 9 min(Colony 5) and 13 h 19 min (Colony 4).

Diffusion Coefficient, Movement Durationand Distance

Before we consider the diffusion coefficient for thedifferent brood types, we examine the relationship ofeach of its components, duration and linear distance ofmovement, with brood weight. Ants carried lighter brooditems for longer than heavier brood items. There wasa negative exponential relationship between duration ofbrood movement by ants and brood weight for the fivedifferent types of brood in phase 2, spacing (Fig. 5b). Thismeans that the duration of brood movement by ants waslongest for the small larvae, followed by the mediumlarvae, the prepupae and pupae, while the duration ofmovement for the large larvae was the shortest.

Table 3. Direction of brood movement by ants: the Rayleigh test ofuniformity and the chi-square test for comparing the two phases

Colony Phase

Test

Rayleigh Chi-square

r N P c df P

1 1 0.73 40 !0.001 35.07 5 !0.012 0.06 207 0.48

2 1 0.62 30 !0.001 19.98 4 !0.012 0.20 54 0.13

3 1 0.38 30 0.01 13.19 4 !0.012 0.11 311 0.02

4 1 0.65 77 !0.001 48.03 5 !0.012 0.14 136 0.07

5 1 0.60 23 !0.001 12.95* 3 !0.012 0.19 28 0.37

*Value may be unreliable (more than 20% of the classes haveexpected frequencies less than 5, class width cannot be greaterthan 90 �).
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Figure 4. Example plots of the distribution of the X coordinate ofbrood position inside the nest (see Fig. 1) when (a) picked up and (b)

put down, for all brood types in phases 1 and 2, colony 1; 4: eggs

and small larvae, 6: medium larvae, 8: large larvae, 9: prepupae, 10:

pupae; the value 0 for the X coordinate corresponds to the positionof the far short wall of the nest (see Fig. 1). C: outliers, defined as

points beyond the end of the whiskers drawn to the nearest value

within 1.5 times the interquartile range.

Figure 3. Distribution of the direction of brood movement by ants with mean vector direction G 1.96 SE: (a) Colony 1, phase 1:

179.32 � G 13.88 �; (b) Colony 1, phase 2: 201.62 � G 92.18 �*; (c) Colony 2, phase 1: 165.22 � G 20.48 �; (d) Colony 2;phase 2: 335.94 � G 54.61 �*; (e) Colony 3, phase 1: 170.72 � G 36.30 �; (f) Colony 3, phase 2: 341.68 � G 40.34 �*; (g) Colony 4, phase 1:

187.36 � G 12.11 �; (h) Colony 4, phase 2: 300.48 � G 48.59 �*; (i) Colony 5, phase 1: 165.78 � G 24.77 �; (j) Colony 5,

phase 2: 10.93 � G 78.11 �*; *indicates value of 95% confidence interval may be unreliable because distribution not different from uniform;

for interpretation of direction relative to nest geometry see Fig. 1.


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Figure 5. Mean duration (s) of brood movement by ants with 95% confidence interval against estimated brood weight (length3 mm): (a)phase 1; (b) phase 2, linear regression: ln(mean duration) Z 4.048 � 0.082 ! estimated weight, R2 Z 79.9%, F1,3 Z 11.90, PZ 0.041; mean

linear distance (mm) of brood movement by ants with 95% confidence interval against estimated brood weight (length3 mm); (c) phase 1, (d)

phase 2: C: eggs and small larvae; &: medium larvae; A: large larvae; :: prepupae; ;: pupae.

With the exception of pupae, the duration of broodmovement by ants in phase 1 comprised only a proportion(50–80%) of the duration of brood movement by ants inphase 2 (Fig. 5a, b). This suggests that, in phase 1, ants putdown brood items before they were fatigued by the weightof the item. It supports the idea that in phase 1, ants putdown brood items at a rate that is a function of encoun-tering other brood items or the wall rather than asa function of brood weight, as in phase 2. This couldexplain the noisier relationship between duration ofbrood movement by ants and brood weight in phase 1(Fig. 5a).Despite the noise associated with the data for prepupae

and pupae, there was a tendency for linear distance ofbrood movement to decrease exponentially with broodweight in both phases with the notable exception of largelarvae (Fig. 5b, c). Items of this largest of brood typestended to be displaced disproportionately further for theirweight.The diffusion coefficient for the large larvae was signif-

icantly greater than the diffusion coefficient for either thesmall or the medium larvae (Fig. 6a, b). Their 95%confidence intervals did not overlap in either phase 1 orphase 2 (Fig. 6a, b). This is consistent with the order ofthese brood types along the radial distance from thecolony centre in the sorted brood pattern. In both phases,the diffusion coefficients for prepupae and pupae were the

smallest (Fig. 6a, b). This suggests their positions in thenest did not change much. In the sorted brood pattern,the positions of prepupae and pupae vary but usually theyare situated between the medium and large larvae.

Frequency of Movement

The movement of brood items of the same type by thesame individual ant is a very rare event. The rate ofputting down a brood item of any type is 1.80 per min(Sendova-Franks et al. 2002). This is equivalent to a meaninterval of 0.56 min between picking up a brood item andputting it down. The within-bout rate of picking upa brood item is 0.06 per min (Sendova-Franks et al.2002). This is equivalent to a mean interval of16.67 min between putting down a brood item andpicking up another one. Therefore, the mean intervalbetween two successive instances of the same individualant picking up a brood item is 17.23 min (0.56 minC16.67 min). Assuming that an ant is equally likely to pickup any of the five brood types, she would pick up a brooditem of the same type again after on average5 ! 17.23 minZ 86.15 min. Furthermore, this is an un-derestimate because it does not take into account intervalsbetween bouts of moving brood (interbout intervals).Indeed when we followed individual ants, they did not


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Figure 6. Diffusion coefficient (mm2/s) of brood with 95% confidence interval against estimated brood weight (length3 mm): (a) phase 1; (b)

phase 2; root-mean-square displacement (mm) of brood with 95% confidence interval against estimated brood weight (length3 mm): (c)phase 1; (d) phase 2; for symbol key see Fig. 5.

pick up a brood item of the same type again even afterseveral hours.We estimated any such differences through the ratio R

measuring the relative frequency with which ants pickedup brood items of a particular type for each of the twophases and for the overall period. There was a significantdifference in R between at least two brood types over thewhole period (Friedman’s test, colony as blocking factor:S4 Z 12.32, PZ 0.015). The two pairs of brood typesaccounting for this difference were the medium andsmall larvae (q6–4 Z 3.960, P! 0.05, the critical valueof q for this and all other pairwise comparisons of Rmedians was q0.05,N,5 Z 3.858) and the prepupae andmedium larvae (q9–6 Z �4.243, P ! 0.05). There was alsoa significant difference in R between at least two broodtypes in both phases 1 and 2 (Friedman’s test, colony asblocking factor: S4 Z 15.20, P Z 0.004 and S4 Z 11.68,PZ 0.020, respectively). In phase 1, a single pair ofbrood types accounted for this difference: large and smalllarvae (q8–4 Z 3.960, P! 0.05). In phase 2, two pairs ofbrood types accounted for this difference: the mediumand small larvae (q6–4 Z 4.243, P! 0.05) and the pre-pupae and medium larvae (q9–6 Z �3.960, P ! 0.05).Note that the differences we found in phase 1 may, atleast in part, be accounted for by the majority of eggs andsmall larvae having been moved close to the far shortwall of the nest by the transporters who first broughtthem into the nest.

In sum, any detected differences were consistent withthe relative positions of brood types in the sorted broodpattern.

Brood Sorting through Differential Diffusion

As a measure of spread in the hypothesized differentialdiffusion process, the RMSD for the different brood typeswas consistent with their relative positions in the sortedbrood pattern with the exception of medium larvae inphase 2 (Fig. 6c, d). In the second phase, the RMSD formedium larvae was greater than the RMSD for large larvae(Fig. 6d). Its value was influenced by the high relativefrequency with which medium larvae were moved (seeabove). The RMSD calculation does not take into accountthe interactions between the movements of differentbrood types. This is evidence to suggest that differentialdiffusion is a plausible underlying mechanism for broodsorting in ants, but such a diffusion mechanism clearlyinvolves interactions.

DISCUSSION

We showed that during brood sorting associated withcolony emigration to a new nest site, there is a clear switchin the direction ants move brood. Oriented movementswitches to movement in a random direction. This switch


marks the end of a first phase of clustering (Deneubourget al. 1991; Franks & Sendova-Franks 1992) and thebeginning of a second phase of spacing brood items out.The particular direction of the oriented movement is likelyto be dependent on nest geometry. In our experiments,the oriented brood movement was in the direction of theshort wall (opposite the entrance, Fig. 1) probably becausethe nest was rectangular and the nest entrance was themissing short wall. The presence of oriented movement,however, is unlikely to depend on nest geometry becausebrood clustering occurs in association with colony emi-gration to nests of different geometry.As our log-survivorship analysis revealed, ants have

a giving-up time for carrying items of each brood typeand this giving-up time is longer for lighter brood items.In other words, lighter brood items are carried for longer.We found that ants move medium and large larvae more

frequently than small larvae or prepupae and that thediffusivity of the large larvae is higher than that of eithersmall or medium larvae. The large larvae also spread outmost. These results are consistent with the order ofdifferent brood types in the sorted brood pattern andtherefore with our differential diffusion hypothesis. Suchdifferential diffusion of different brood types is clearlyinterdependent.In phase 1, the diffusion coefficients of all brood types

are greater than in phase 2 because the linear distances ofmovement are longer while the durations of movementare shorter. By the end of phase 1, not only is the broodclustered but there is also evidence that the relative orderof different brood types is beginning to appear. The eggsand small larvae are closest to the far short wall of thenest, the large larvae furthest and the remaining broodtypes are in between.Our interpretation is that in phase 1, an ant is more

likely to pick up a brood item of any type if it is isolated(Deneubourg et al. 1991) and more likely to put downa brood item of any type if she encounters another brooditem or the wall. Given the higher diffusivity of all brood inphase 1 than in phase 2, ants carrying brood are likely toencounter another brood item or the wall before thegiving-up time for the type of carried brood item has beenexhausted. In our experiments, the first ants bringingbrood items into the new nest were likely to encounterthe far short wall of the nest as their first obstacle and putdown their load there. Note that such events were notanalysed in our study because without a picking-up timeand place they did not constitute brood movements insidethe nest. Subsequent brood movements inside the nestfollow the same direction very closely because ants aremore likely to put down brood items next to other brooditems. Recall that the direction of brood movement is thedirection of the item’s linear displacement between thepositions where it was picked up and put down irrespectiveof total path length. A muesli-type effect (Barker &Grimson 1990) could explain the order in the brood clusterat the end of phase 1. The ants carrying the smallest broodsuch as the eggs and small larvae manage to sieve throughthe small gaps between the larger brood items and aremorelikely to encounter the wall or a brood item closer to thewall as their first obstacle and put down their load there.

In phase 2, brood movement is in a random directionand therefore heavier brood items, with higher diffusivity,diffuse outwards more quickly than lighter brood items.Any earlier appearance of the relative order of the fivebrood types is consolidated and the shape of the sortedbrood structure appears. The light eggs and small larvaeend up in the middle and the heavy large larvae are on theperiphery with annuli of the intermediately heavy medi-um larvae, prepupae and pupae in between.

Our interpretation is that in phase 2, an ant is morelikely to pick up a brood item of any type if it is too closeto its neighbours to allow any tending. Once the item hasbeen picked up, the ant moves it in a random directionand puts it down after the specific giving-up time for itsbrood type and in the first available space. Giving-up timeas an inverse function of weight would be sufficient toexplain our results. All the mean giving-up times forbrood movement inside the nest in phase 2 are greaterthan 25 s, the average time of item (brood or nestmate)transport at a distance of 6 cm between the new and theold nest (Sendova-Franks et al. 2002). The more brooditems are moved in this way the more different fromclustered the brood pattern becomes. Note that only theeggs, small larvae and, occasionally, the medium larvaetend to be nonrandomly distributed (clustered) in thesorted brood pattern (Franks & Sendova-Franks 1992). Ifa brood item has sufficient space around it for an ant totend it, it is unlikely to be picked up again and vice versa.Furthermore, different brood types require differentamounts of space. Indeed, medium and large larvaerequire greater domains of care than either small larvaeor prepupae and pupae, which do not need feeding(Franks & Sendova-Franks 1992). Spacing according tofeeding requirements also gives a mechanism for thediffusion outwards to slow down or even stop eventuallyso that no brood items end up around the nest wall oreven outside the nest. Indeed, brood sorting slows downeven within the first 48 h after the start of emigration(Sendova-Franks et al. 2002).

The mechanism we have just described could link thecollective level phenomenon of brood sorting in Lepto-thorax ant colonies to a simple algorithm of individualbehaviour at the level of the single ant (Camazine et al.2001) in each of two phases. What is the underlyingmechanism of the switch between these two phases? Oneof the more parsimonious possibilities is that individualsreceive a local cue about the global status of the brood.This local cue could come from other ants or the broodthemselves. For example, the slowdown in the activitylevel of workers following the end of transport from theold to the new nest (Sendova-Franks et al. 2002) may actas a local cue for ants that the relocation of the wholecolony to the new nest has been completed and theemergency of the emigration is over. This would entailswitching from looking after the needs of brood in anemergency by clustering them to looking after the brood’severyday needs, such as grooming and feeding, by spacingthem out. Our results show that the duration of theinterval between the end of transport and the beginningof phase 2 is very variable. This is not surprising, however,given the high variability of behaviour at the colony level,


such as the duration of transport, as well as our discretemethod of defining the two phases. This activity levelscenario implies that the clustering phase is only presentwhen brood sorting is associated with colony emigration.Both the present and the earlier (Franks & Sendova-Franks1992) studies of Leptothorax brood sorting were carried outon brood sorting associated with colony emigration toa new nest site. We are currently carrying out manipula-tive experimental studies that dissociate the process ofbrood sorting from the process of emigration. They shouldbe able to determine whether clustering is a necessarycondition for sorting.Another possibility is that the brood themselves give

out a local cue for the switch. For example, when thebrood are not actively requiring attention, ants clusterthem and when they do actively require attention, antsspace them out. This makes sense in the context of theexpansion and contraction of the sorted brood pattern indifferent seasons (Sendova-Franks & Franks 1995).Throughout this study we have not made any reference

to task specialization among the workers. It is possible thatdifferent individual ants perform brood sorting in the twophases. For example, ants specializing in extranidal tasksmay be more likely to perform brood sorting in phase 1,whereas ants specializing in intranidal tasks are morelikely to perform brood sorting in phase 2. Individualsthat transport brood or nestmates from the old to the newnest are likely to spend at least a few seconds inside thenew nest after they have put down their load. Within thatperiod they are likely to move a brood item inside the newnest. Indeed, Sendova-Franks et al. (2002) found that 32%of brood sorters were also transporters in the emigration.However, this possibility of task specialization does notexplain the underlying mechanisms of the switch be-tween the two phases.Brood sorting in Leptothorax ant colonies is an example

of collective problem solving (Camazine et al. 2001).However, as with other examples of collective problemsolving, a single ant following the underlying algorithm ofindividual behaviour can solve the problem, but thesolution would be much less efficient and/or more proneto error (Deneubourg et al. 1991). Furthermore, followingsimple algorithms of behaviour does not mean thatindividuals lack sophistication (Deneubourg et al. 1999).In this study we have been guided by the search for the

most parsimonious mechanism for brood sorting that isconsistent with the data. This does not necessarily meanthat such a mechanism is the only one that ant coloniesuse. It is possible that there is more than one mechanism.Each of them could lead to brood sorting on its own buttogether they give the colony robustness. Sometimes ‘themost parsimonious mechanism’ could mean more sophis-ticated ants but no rules of behaviour or information inthe environment that explicitly code for the pattern. Forexample, the mechanism for brood sorting of differentialdiffusion following initial clustering that we describe heredoes not involve such explicit information. By contrast,another mechanism could involve a global centre thatants use as a pivot for orientation or as a source ofa template that represents explicit information in theenvironment and indicates to ants where to drop brood

items of each type (Sendova-Franks & Franks 1999). Weare currently performing manipulative experiments to testwhether a gaseous template or the source of a gaseoustemplate acting as a pivot are each a necessary conditionfor brood sorting.Finally, we think that the best possible algorithms

inspired by animal behaviour and applied in computerscience or robotics come from the understanding of thebiology. For example, most computer sorting algorithms(e.g. quick sort) are efficient when applied to random databut perform particularly badly on partially or totallyordered data (Knuth 1973). Similarly, here we havesuggested that brood sorting in ants may be more efficientif the brood are clustered before they are sorted. Suchinitial clustering would allow sorting to take place what-ever the initial spatial distribution of the items. Onlyinsights like this would allow us to learn most from thesesuccessful organizations honed by evolution throughnatural selection over tens of millions of years. Theapplication of such lessons to robotics, for instance, couldin turn lead to examples of how biology could learn fromrobotics (Webb 2000).

Acknowledgments

A.S.F., S.S. and C.M. gratefully acknowledge the EPSRC forsupport. N.R.F. and A.S.F. are grateful to the LeverhulmeTrust. We thank Jay Denny, Anna Dornhaus, ElizabethLangridge, Scott Powell and Matthew Wilson for helpfulsuggestions and discussions.

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AppendixTable A1. The slopes of the log-survivorship plots from which themean duration of movement for each type of brood for each phaseand overall were estimated

Phase

Brood

type N

MeanGSE rate ofbrood dropping

by ants over

time (per s) P R2 (%)

1 4 18 0.021G0.00099 !0.001 96.21 6 40 0.047G0.00096 !0.001 98.41 8 60 0.040G0.00073 !0.001 98.01 9 22 0.042G0.00300 !0.001 90.51 10 57 0.028G0.00075 !0.001 96.22 4 120 0.016G0.00013 !0.001 99.22 6 324 0.024G0.00020 !0.001 97.82 8 120 0.032G0.00044 !0.001 97.72 9 79 0.023G0.00050 !0.001 96.62 10 82 0.030G0.00058 !0.001 97.0Overall 4 139 0.017G0.00014 !0.001 99.0Overall 6 364 0.025G0.00018 !0.001 98.1Overall 8 181 0.034G0.00030 !0.001 98.7Overall 9 101 0.026G0.00045 !0.001 97.1Overall 10 140 0.031G0.00030 !0.001 98.8

Table A2. The slopes of the log-survivorship plots from which themean linear distance of movement for each type of brood for eachphase and overall were estimated

PhaseBroodtype N

MeanGSE rate of

brood dropping by

ants over lineardistance (per mm) P R2 (%)

1 4 19 0.088G0.00366 !0.001 97.01 6 40 0.130G0.00203 !0.001 99.11 8 56 0.116G0.00102 !0.001 99.61 9 22 0.141G0.00536 !0.001 97.11 10 53 0.126G0.00229 !0.001 98.32 4 120 0.211G0.00346 !0.001 96.92 6 326 0.262G0.00125 !0.001 99.32 8 123 0.264G0.00161 !0.001 99.52 9 81 0.350G0.00718 !0.001 96.72 10 77 0.381G0.01103 !0.001 94.0Overall 4 138 0.181G0.00275 !0.001 96.9Overall 6 365 0.221G0.00093 !0.001 99.4Overall 8 186 0.185G0.00079 !0.001 99.7Overall 9 103 0.241G0.00381 !0.001 97.5Overall 10 140 0.171G0.00285 !0.001 96.3

brood sorting by ants: two phases and differential diffusion

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