Two methods for quantifying the development of dominance ...

Anita. Behav., 1987, 35, 1113 1128

Two methods for quantifying the development of dominance hierarchies in large groups with applications to Harris' sparrows I V A N D. CHASE* & S I E V E R T R O H W E R t

* Department of Sociology and Graduate Program in Ecology and Evolution, State University of New York at Stony Brook, Stony Brook, New York 11794-4356, U.S.A. q;Department of Zoology and Burke Museum DB-IO, University of Washington, Seattle, Washington 98105, U.S.A. Abstract. Two new methods for quantitatively describing behavioural processes of hierarchy formation in large groups are introduced. These methods supplement those already available with the jigsaw puzzle approach to hierarchy formation (Chase 1980, 1982, 1985) and they examine behaviourat sequences in component triads, subgroups of three individuals, making up the larger group. The first method gives a new procedure for counting various kinds of attack sequences in component triads, and the second traces how relationships evolve in triads. Used together, the procedures can help explain the development of dominance structures, and in particular, what kinds of interactions produce those that are linear or nearlinear. The methods are illustrated by applying them to large flocks of Harris' sparrows, Zonotrichia quereula, having 12-17 members, during hierarchy formation. This application indicates that different behavioural mechanisms may be involved in hierarchy formation for large and small groups and that some configurations of interactions in triads are much more stable than others, namely, transitive ones are much more resistant to reversals than intransitive ones. These findings suggest that earlier and later interactions may not be independent and raise a number of interesting questions about individual-level mechanisms operating during hierarchy formation.

When brought together in small groups, individuals in a broad range of animals will readily form social relationships, a term that simply indicates a clear trend in behavioural interactions or acts across time (Hinde 1976, 1979; Altmann 1981). Intriguingly, social relationships and interactions in small groups frequently form characteristic patterns. For example, friendship networks in humans often involve hierarchically organized cliques of individuals (Davis 1970; Holland & Leinhardt 1970, 1971; Feld & Elmore 1982; Johnsen 1985), and dominance hierarchies in animals and children frequently show a high degree of linearity (see Chase 1980, 1982, 1985 and the literature reviewed therein). If interactions and relationships formed at random, their structures would not be typically restricted to a few similar types. In particular, strongly linear dominance hierarchies would be highly improbable even in groups of modest size (Landau 1951; Chase 1974; Appleby 1983). The jigsaw puzzle approach developed by Chase (1980, 1982, 1985) describes how hierarchy structures, especially strongly linear ones, emerge from

patterns of interaction among individuals. Just as a jigsaw puzzle is assembled from interlocking pieces put together in the right way, the structure of a dominance hierarchy is seen as emerging from the aggregation of behavioural sequences in component triads of a group. Triadic units of analysis have also proved effective in a series of innovative studies in animal behaviour (Kummer 1975; Mason 1978; Seyfarth et al. 1978; Stammbach 1978; Vaitl 1978; de Waal 1982, 1984; Hinde 1983) and human sociology (Davis 1970; Holland & Leinhardt 1970, 1971; Fisek 1974; Hallinan 1974; Barchas & Fisek 1984; Johnsen 1985).

The Jigsaw Puzzle Approach Current methods available with the jigsaw puzzle approach examine how the first dyadic interaction in a triad relates to the second one. The interactions in question can be dominance relationships (Chase 1982), single aggressive acts (Chase 1985), or even non-agonistic behaviours (Barchas & Mendoza 1984). Four patterns are possible when one dyad in a triad has an interaction and then one member of

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Animal Behaviour, 35, 4

this pair has a second interaction with the bystander or third member of the triad (Chase 1980, 1982, 1985). By convention, A and B are the first dyad to interact, and A dominates or attacks B, depending upon whether the formulation is for dominance relationships or single aggressive acts. The second interaction is between one of the original combatants and the bystander C. The four possible patterns are produced by the alternative directions of interaction in the second dyad. For example, using the formulation for single aggressive acts (Chase 1985), when A and C are the second dyad and A attacks C, the Double Attack sequence results. But i f C attacks A, the Attack the Attacker sequence is produced. Alternatively, when B and C are the second dyad and B attacks C, the sequence is termed Pass On, and when C attacks B it is called Double Receive. If dominance interactions occurred randomly, then all four of these sequences would be equally likely. However, together Double Attack and Double Receive, and their analogues in dominance relationship formulation, Double Dominance and Double Subordinance, are much more common than the other two patterns in chickens, Gallus gallus, rhesus macaques, Macaca rnulatta, Java monkeys, M. fascicularis and Japanese macaques, M.fuscata (Chase 1980 in a reanalysis of data in de Waal et al. 1976; Chase 1982, 1985; Mendoza & Barchas 1983; Barchas & Mendoza 1984; Eaton 1984). This is important because these common patterns have a crucial implication for linear hierarchies. To have a perfectly linear hierarchy, the dominance interactions in every component triad must, by definition, be transitive. In a triad with a transitive dominance interaction, A attacks or dominates B (depending upon the type of interaction), B attacks or dominates C, and A attacks or dominates C. Non-linear hierarchies contain at least one component triad with an intransitive relationship: A dominates or attacks B, B dominates or attacks C, and C dominates or attacks A to form a cyclical arrangement. The more intransitive triads there are, the further a hierarchy departs from linearity. Both Double Attack and Double Receive, as well as their analogues using dominance relationships, Double Dominance and Double Subordinance, guarantee transitive triads regardless of the direction of interaction in the third and last dyad in the triad. The other possible sequences, Attack the Attacker and Pass On, and their dominance analogues, Bystander Dominates

Initial Dominant and Initial Subordinate Dominates Bystander, do not guarantee transitive triads but can produce either transitive or intransitive ones depending upon the direction of the interaction between the third pair (see Chase 1982, 1985 for a detailed explanation). Chase (1980, 1982, 1985) originally developed this jigsaw puzzle approach for the investigation of dominance behaviour using groups with only three or four members. As we explain in the Methodological Results section, the earlier method (Chase 1982) for examining sequences of single aggressive acts cannot be applied to larger groups without modification. Therefore, in this paper we develop a new counting method for attack sequences that is applicable to groups of any size, and we also introduce a procedure for following how interactions in component triads develop and become stabilized or change over time within larger groups. With these new methods the patterns of attack sequences which are responsible for the great amount of transitivity we observed in several fully developed hierarchies can be described. We illustrate these methods by analysing dominance interactions in groups of Harris' sparrows, Zonotrichia quereula, containing 12-17 members.

METHODS Animals The ideal data set for applying our two new methods would consist of a continuous, sequential record of all aggressive interactions among previously unacquainted members of newly assembled, large groups from the moment of introduction until all members had interacted and the direction of interaction between pairs had become relatively stable, probably a period of from 1 to several days. At this time, we do not have a data set that meets all these requirements, but we do have one that meets some of them. While our data set is somewhat compromised, as will be described below, we feel that it is instructive to use actual data presently available in showing how the methods work and what kinds of information they can supply. However, the reader should keep in mind that our findings are only tentative and suggestive until confirmed, if they are, by analysis with completely adequate data sets. The Harris' sparrows were captured in midDecember 1982 at several areas in north-central

Chase & Rohwer: Hierarchies in large groups

Kansas and taken about 80 km south to the Konza Prairie Research Natural Area near Manhattan, Kansas where our observations were made (Kansas State permit no. 82-173, U.S. Fish and Wildlife Service permit no. PRT 2-0348-PT). We marked the birds with coloured leg bands and kept them in outdoor aviaries for several days before observations began (Federal banding permit no. 20157). Food and water were available ad libitum. We assembled four experimental flocks segregated by age and sex class: one of adult males, one of adult females, one of young (juvenile) males, and one of young (juvenile) females. The method for assignment of age and sex classes is described in Rohwer et al. (1981). About half the young males and females were dyed to replicate the appearance of adult males in an investigation of the statussignalling hypothesis (Rohwer 1975); see Rohwer (1985) for experimental details. Each experimental flock consisted of two subgroups which were combined for observations, and each subgroup constituted, within one bird, half of an experimental flock. Members in the different subgroups of an experimental flock were captured in different locations. Thus individuals in different halves of an experimental flock were strangers to one another, but members within a subgroup may have been previously acquainted in the wild and were housed together several days before our experiments began. We released members of each subgroup simultaneously into a neutral aviary and made our observations there. Upon introduction we observed each flock continuously for periods of up to 2.5 h: 151 min for adult males, 108 rain for adult females, 124 min for young males and 95 rain for young females. After the initial periods, we made observations periodically over several days for each group: approximately 8 h and 30 min over 3 days for adult males, 9 h and 25 min over 7 days for adult females, 4 h over 5 days for young males, and 3 h and 50 rain over 3 days for young females. During the initial observation sessions, two observers dictated interactions and a third recorded them. Inter-observer reliability appeared to be high, but no measures were calculated. In initial observation periods we attempted to record all possible dominance interactions, but in subsequent periods somewhat more emphasis was placed upon recording information for pairs not previously observed. We recorded five types of dominance interac-

l I 15

tions: active supplants (displacer makes a short rush towards supplanted bird), avoidances, holds (remaining stationary) against approaches, jump fights and supplants with pursuit. Over 9 0 % of the interactions consisted of the first two types, and we lumped all types of interactions together as attacks in the following analyses.

METHODOLOGICAL

RESULTS

Counting Procedure for Attack Sequences The assumption behind Chase's (1980, 1985) original method for counting attack sequences was that any particular attack between initiator and recipient influenced the very next attack that occurred chronologically in that group. While this assumption may be acceptable for very small groups, its validity would appear to diminish rapidly as group size increases. In large groups many individuals will independently pursue their own aggressive agendas or become involved in those of other individuals, and they will not be able to monitor or respond to all of the other attacks taking place in a group. Thus the original method leads to two differences when applied to larger groups: (1) the percentage of Disjoint sequences (Chase 1985), where successive attacks show no relationship to one another (completely different pairs are involved in the two attacks), is likely to increase with group size and (2) all sequences in which the second attack follows the first with great rapidity would be counted in artificially inflated proportions. Our new counting procedure redistributes attacks (in chronological sequence) into all the relevant possible triadic combinations of individuals within a group. For example, consider a group with five members A, B, C, D and E. The very first attack is A on B. This attack is placed under all possible component triads that include A and B as members: [A, B, C]; [A, B, D]; [A, B, E]. The second attack in the raw data record is D on E, and this is likewise placed under all its possible component triads: [A, D, E]; [B, D, E]; and [C, D, E]. This technique is repeated for all the attacks in the raw data record. When this operation is complete, all attacks will have been rearranged under their respective component triads with chronological order preserved within each triad. This new procedure is thus

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analogous to the one used for examining patterns of dominance relationship formation (Chase 1982). This recasting of attacks into component triads eliminates Disjoint sequences and the bias towards analysing only those sequences that follow each other quickly. Once sequences are classified, the researcher can tabulate and examine the distribution of sequence occurrence in triads across a group. He or she can now ask, for example, whether some kinds of sequences are more common than others and how initial sequences set the stage, if they do, for the great amount of transitivity often observed in component triads of a group.

Method for Following the Developmental History of Triads We now introduce a method, which uses the same data record as our counting procedure, for following the developmental pathways by which triads achieve their final transitive or intransitive states. This method allows us to investigate the following types of questions. What are the different ways in which triads become transitive or intransitive? Are some developmental pathways more common than others? Once triads reach transitivity or intransitivity, are these destinations stable or do triads change back and forth from one configuration to another? To follow the history of a triad, we need a way to characterize it as it develops. We call these characterizations at various points in time states, and they are based on the possible structural configurations of attacks through which a component triad can pass. A total of seven states are possible. U p o n introduction, the individuals have not yet interacted and the triad is in the no-attacks state; when the first dyad interacts, the triad moves to the (attack between) one-pair state. When a second dyad interacts, the triad moves to one of three possible states involving two pairs. (1) Attack-Two (A2): the state where one animal has attacked the two other animals. (2) Receive-Two (R2): the state where one animal has received attacks from the two other animals. (3) Attack One Receive One ( A I R 1): the state where one individual has attacked the second but has been attacked by the third individual. When the third dyad interacts, the triad moves to either the transitive or intransitive state for which definitions have been given in the Introduction. While there is an obvious resemblance between

these states and the attack sequences within the triad, they should not be confused. The states are static configurations, snapshots at a point in time, indicating graphically the direction, but not the temporal order, of attacks that have occurred previously. Sequences, in contrast, show the order of attacks in time; it is the various sequences that move a triad from one state to another. Figure 1 shows the various possible pathways by which triads can reach an initial state of transitivity or intransitivity. Tracing the development of a set of triads with Fig. 1 would produce a display of frequencies in the various states corresponding to the destinations of those triads (the frequencies in Fig. 1 are from analyses described below and will be discussed later). Arrows that originate from the top of a shape and then loop back to it symbolize sequences that keep a triad in that particular state. Arrows between shapes indicate sequences that can move a triad from one state to another; many of these involve the reversal of the immediately previous direction of attack between a particular pair and these are so marked. Usually two or more kinds of sequences can move a triad from one state to another or keep it in a particular state. Note that the only possible way to reach initial intransitivity is via the A1-R1 state. Once a triad has reached either an initial transitive or intransitive state, reversals in the previous direction of attack between pairs can send it further into other states, while attacks that are not reversals keep the triad in its initial state. A triad in the initial transitive state having a reversal can go on to either the intransitive state or a state we call Rtransitivity, the R indicating a triad that remains transitive despite a reversal of a previous attack. F o r example, consider a transitive triad in which A attacks B, B attacks C, and A attacks C. If a reversal between A and C occurs, the triad goes to intransitivity. However, if a reversal occurs between either A and B or B and C, the triad will remain transitive, but with a new ordering among the members. Thus, given an initial transitive triad, reversing one of the attacks will send it to intransitivity, while reversing either of the other two will send it to R-transitivity. The situation is more straightforward for a triad in the intransitive state: the reversal of any attack will convert it to transitivity. Figure 2 shows all these various possibilities. This diagram continues where Fig. 1 stopped: the further development of all triads that reached

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9 Figure 1. The possible developmental pathways for triads starting with no interactions and reaching initial states of transitivity or intransitivity during the first observation sessions. The states for no-attacks, one-pair and all two-pair attacks are indicated by circles, transitivity by hexagons and intransitivity by squares. The names for two-pair and three-pair states are abbreviated: A2 for Attack-Two, R2 for Receive-Two, A 1-R 1 for Attack One-Receive One, Tr for transitivity and Intr for intransitivity. Arrows indicate how triads can move from one state to others by various kinds of attack sequences. The numbers in the various states indicate the frequencies of triads reaching those states during the course of first observation sessions for all groups combined. The frequencies indicate end points: the numbers of triads reaching particular states by the end of the first observation sessions. A triad can be in only one state at a time, and once it has moved to a new state it is only counted there, and the frequency in its previous state is reduced by one. See the text for further explanation.

initial transitivity or intransitivity in Fig. 1 are followed, respectively, in the top a n d b o t t o m branches. Because h u n d r e d s of possible triads exist for each g r o u p of sparrows (In!/3! ( n - 3 ) ! ] , where n is group size), we used finite state m a c h i n e theory as the basis for a c o m p u t e r p r o g r a m to follow the triad p a t h w a y s to transitivity a n d intransitivity.

A l t h o u g h apparently n o t previously applied to behavioural studies, finite state machine theory (covered in m a n y s t a n d a r d c o m p u t e r science texts, such as H o p c r o f t & U l l m a n 1979) provides standard algorithms by which processes can be followed as they move t h r o u g h various specified states along possible pathways, such as those indicated for the triads in Figs 1 and 2. (A copy of the

Animal Behaviour, 35, 4

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F•

Reversal

r-

Sloles Combined~ .

~ ~.1

.~ .... IReversol/T. \

Reversal

Figure 2. The further possible developmental pathways for triads reaching states of initial transitivity and intransitivity during the first observation sessions. See Fig. 1 for details.

program we used for this procedure and the counting method for attacks is available from the first author.) In addition to greatly facilitating the writing of computer programs for following behaviour in triads, this methodology can be readily adapted to explore the developmental course of other kinds of behaviour in individuals or groups.

EMPIRICAL

RESULTS

Attack Sequences in Component Triads Using the new procedure for counting attack sequences in the first observation periods, we have categorized all possible triads into the four possible sequences (Double Attack, Double Receive, Pass on and Attack the Attacker) which, barring reversals, set the stage for transitivity or intransitivity. Some triads could not be so categorized because of insufficient interactions; thus, four additional con-

ditions apply in the initial observation periods: no attacks within a triad, repeated unidirectional attacks between one dyad (A attacks B two or more times in a row), and an interchange of attacks between one dyad (A attacks B and B counterattacks A). All four types of sequences involving two dyads (Table I, columns 1-4) were relatively c o m m o n in all groups except adult females. F o r sequences involving only one dyad, Repeats far outnumbered Interchanges (columns 5 6); thus attackers frequently went on to attack the same individual again, but the sparrows rarely exchanged aggressive acts. Two of the four groups contained moderate percentages of triads in which one member attacked another only once (column 7), and in the adult females nearly half of the triads had no attacks at all (column 8). Table II shows the distributions of the four sequences involving two dyads alone (P < 0.01 for all groups using Z2). (The expected distribution is calculated under the assumption that the attacks in either direction for dyads are equally likely, and this results in an equiprobable distribution for the four sequence types. See Chase 1982 for more details using equivalent assumptions for dominance relationships.) Double Receive was the most c o m m o n sequence in the two juvenile groups, and Double Attack the most c o m m o n in the two adult groups. The abundance of Double Receives in juveniles is most probably due to the fact that the undyed birds in these two groups conspicuously avoided the dyed birds in their first encounters (see Rohwer 1985). These two sequences, ensuring transitivity, together account for modest majorities of all sequences from a low of 55" 1% in adult males to a high of 70-7% in juvenile females. Additional

Table I. Percentage distributions of initial attack sequences involving two or fewer dyads in component triads of sparrow groups during the first observation sessions Involving two dyads Group

Double Attack

Adult males 20.7 Adult females 6.2 Juvenile males 20.9 Juvenile females 23.6

Fewer than two dyads

Double Attack Inter- Only one Total number Receive Pass On the Attacker Repeat change attack No attack of triads* 15-2 2.4 41.5 37.7

10.5 3.1 16.5 9.5

t8.8 3'8 16.3 15-9

* Numbers for calculating each group's percentage distribution.

9.8 11'5 2.2 10.9

2.3 1"9 0.0 0.0

14.6 26.6 1.8 2.3

8.0 44.6 0-9 0-0

560 680 455 220

Chase & Rohwer." Hierarchies in large groups

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Table II. Percentage distributions of initial attack sequences involving two dyads only in component triads of sparrow groups during the first observation sessions Group

Double Attack

Adult males Adult females Juvenile males Juvenile females

31.8 40.0 21.9 27.2

Double Receive PassOn 23.3 15.2 43.6 43-5

16.2 20.2 17.3 11.0

Attack the Atacker

Total number of sequences involving two dyads*

28.8 24.8 17.1 18-3

365t I05:~ 4337 191~

* Numbers for calculating each group's percentage distribution. t P