Behavioral Ecology
doi:10.1093/beheco/arq062
Advance Access publication 10 May 2010
Unavoidable limits on group size in a body
size-based linear hierarchy
Tzo Zen Ang and Andrea Manica
Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK
Competition between individual group members is a key force in shaping social group structure and size. In animal societies,
within-group competition may be structured by linear dominance hierarchies, which can be stable if there are minimum differences in competitive ability between adjacently ranked individuals. This requirement constrains maximum group size because
only a certain number of clearly differentiated ranks can be fit into the range of competitive abilities between the top and bottom
of the hierarchy. We investigated this hypothesis in the body size-based linear dominance hierarchy of the angelfish Centropyge
bicolor. Unlike in previous studies, we found that maximum group size in natural C. bicolor groups was not always strictly limited by
the range of possible body sizes and the average size difference between adjacent ranks. Oversized groups displayed a compressed
body size hierarchy with smaller size differences between adjacent ranks, less effective regulation of subordinate foraging rates to
maintain size differences, and greater spatial segregation between adjacently ranked individuals. Our results suggest that when
spatial segregation compromises the regulatory mechanisms that maintain clear size hierarchies, groups can become larger than
expected by slotting more individuals into a compressed size hierarchy. However, we also found that oversized groups tended to
fission into smaller groups, suggesting that they are transient entities and that ultimately the group size limits imposed by the
need to maintain a well-defined hierarchy are unavoidable. Key words: Centropyge bicolor, group size, linear dominance hierarchy,
maximum group size. [Behav Ecol 21:819–825 (2010)]
any animals spend part or all of their lives in social
groups, which can vary widely in size from pairs, for example, bobucks (Martin et al. 2007), Western Australian seahorses (Kvarnemo et al. 2000), to enormous aggregations for
example, American flamingos (Schmitz and Baldassarre 1992),
unicolonial ants (Helantera et al. 2009). Group size may be
limited by external constraints such as increasing conspicuousness of large groups to predators (Vine 1973; Andersson and
Wiklund 1978; Ioannou and Krause 2008) or the disturbance
that large groups cause reducing the ability of individuals to
surprise prey (Goss-Custard 1976), but for many animal societies limits on maximum group size may be more urgently affected by competition and conflict within the group. The total
food available in a resource patch or group-defended territory
must be shared between group members, and unless food is
superabundant per capita consumption will eventually fall with
increasing group size (Caraco and Wolf 1975; Major 1978;
Pulliam and Caraco 1984; Schmidt and Mech 1997). In addition
to environmental resources such as food and shelter, group
members also compete over access to reproduction, and in
large groups, weaker competitors may gain little or no reproduction at all, raising the likelihood that they will leave the
group entirely given the chance (Vehrencamp 1983; Reeve
and Emlen 2000; Clutton-Brock et al. 2008).
Competition for food, shelter, and reproduction within
groups may be structured by a linear dominance hierarchy
in which dominant individuals gain a disproportionate share
of resources (e.g., paper wasps [Cant and Field 2001], cleaning
gobies [Whiteman and Côté 2004], and brown hyaenas [Owens
and Owens 1996]). Subordinates in such systems may be making the best of their poor competitive ability (Pulliam and
Caraco 1984) or may be queuing to inherit higher rank when
dominants disappear, and staying in the group in order to reap
M
Address correspondence to T.Z. Ang. E-mail: [email protected].
Received 17 December 2009; revised 15 February 2010; accepted 27
March 2010.
The Author 2010. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved.
For permissions, please e-mail: [email protected]
future benefits despite currently losing out in within-group
competition (Wiley and Rabenold 1984; Kokko and Johnstone
1999). Group size in linear dominance hierarchies is often
particularly limited. A strict linear dominance system may require significant differences in resource holding power (RHP)
between each dominant and its subordinate (Pusey and Packer
1997) such that dominants have enough power to prevent subordinate rank challenges that destabilize the system. The biologically possible RHP range between the most dominant
individual and the most subordinate places a limit on the number of ranks that can be slot in between while maintaining
significant RHP differences between each rank. For example,
in a body size-based dominance hierarchy, the maximum group
size can be determined by the difference in body size between
the largest (most dominant) individual and the smallest mature
individual, divided by the typical size ratio that must be maintained between adjacent ranks for stability of the linear hierarchy (Buston and Cant 2006). Group size limits imposed by this
requirement of minimum size differences (analogous to earlier
ideas about limits on species diversity and niche differences
[Hutchinson 1959; MacArthur and Levins 1967]) have been
little investigated despite being an important link between individual behavioral and growth decisions, and emergent social
organization at a larger scale (Buston and Cant 2006; Kohda
et al. 2008).
Body size-based linear dominance hierarchies in fish have
recently emerged as a model system for understanding hierarchy formation and maintenance (Heg et al. 2004; Buston and
Balshine 2007; Wong et al. 2007). Stability in these hierarchies
is achieved by maintenance of body size differences between
adjacent ranks, via regulation of subordinate growth and foraging (Buston 2003b; Heg et al. 2004; Wong et al. 2008; Ang
and Manica 2010), which is in turn enforced by the threat of
eviction from dominants should subordinates become too
large (Wong et al. 2007; Ang 2010). These body size differences can be remarkably consistent in strict hierarchies and
place limits on maximum hierarchy length in the clown anemonefish Amphiprion percula (Buston and Cant 2006). By
Behavioral Ecology
820
assuming that body size ratios between adjacently ranked individuals were converging on a particular size ratio (obtained
from the mean size ratio in their study population), Buston
and Cant (2006) were able to successfully predict the maximum group size of natural A. percula groups based on the size
of the most dominant fish. However, recent work on a less
specialized but similar system has shown that differences between adjacently ranked individuals are not always strictly
maintained: when regulatory mechanisms are compromised,
compression of the size hierarchy can result with adjacently
ranked fish closer in size than one would normally expect
(Ang and Manica 2010). Such compression has clear implications for group size limits, and in this paper, we conduct
a quantitative analysis of the interplay of group size, compression, and its causes and consequences in the dwarf angelfish
Centropyge bicolor.
Centropyge bicolor is a protogynous coral reef angelfish that
lives in haremic groups of 2–8 mature individuals, consisting of
a large dominant male and several breeding females arranged
in a linear dominance hierarchy with stepwise decreases in
body size down the ranks (Aldenhoven 1984). The male guards
a group territory of up to 200 m2, within which the females
have overlapping smaller home ranges. The hierarchy is also
a breeding queue: when the male disappears, the top-ranked
female will change sex and take over the harem, whereas the
remaining females grow and move up in rank (Aldenhoven
1984). In previous work, we showed that adjacently ranked
individuals are usually maintained at a body size ratio of
0.85–0.95 (i.e., the subordinate’s standard length [SL] is usually 85–95% the SL of the dominant), by means of regulated
subordinate foraging and growth rates (Ang 2010).
In this paper, we show that unlike in A. percula, maximum
group size in C. bicolor is not perfectly predicted by the size of
the dominant. We go on to investigate the mechanisms enabling some groups to be larger than predicted (oversize
groups), testing the following hypotheses: 1) oversize groups
are able to fit more mature individuals into the group by
compressing the body size hierarchy such that adjacently
ranked fish are closer in size; 2) the behavioral regulatory
mechanisms that help to maintain clearly defined size hierarchies (specifically the foraging reduction of subordinates
when they approach their immediate dominants too closely
in size) are less effective in oversize groups; 3) compromised
regulatory mechanisms are in turn enabled by high spatial
segregation in oversize groups. Finally, we consider the consequences of size hierarchy compression for oversize groups
because a compressed body size hierarchy with reduced competitive asymmetries between ranks may be expected to have
reduced stability.
Our results suggest that a small proportion of natural groups
may increase in size beyond the predicted maximum if spatial
segregation makes it more difficult for group members to enforce a rigid body size hierarchy. However, compressed size hierarchies are unstable, and oversize groups eventually fission
into smaller well-defined dominance hierarchies. Ultimately,
the requirement for clear RHP differences in linear dominance hierarchies places a limit on group size that is inescapable in the long term.
MATERIALS AND METHODS
Study population and general methods
Thirty-five social groups of C. bicolor were studied at 4 study
sites around Lizard Island (lat 1440’S, long 14528’E) on
Australia’s northern Great Barrier Reef, between March
2007 and February 2009. Each group consisted of a dominant
male, 1–7 breeding females, and 0–4 juveniles (,5 cm SL, no
gametes expelled when squeezed, not observed to spawn),
arranged in a linear body size-based dominance hierarchy.
Group size was defined as the number of mature fish in the
group. The male defended a large home range (up to 200 m2)
within which the females had individual overlapping home
ranges. Mature fish were individually identifiable by location,
size, distinctive patterns in the borders between blue and yellow body coloring, and visible implant elastomer tags (Northwest Marine Technology). All mature fish were caught at the
beginning of each field season by surrounding a small coral or
rock shelter the fish was in with handnets, and spraying a small
amount of 1:4 clove oil:ethanol anesthetic solution (Munday
and Wilson 1997) into the shelter after which the fish could
be gently encouraged into the net and then transferred to
a sealable plastic bag, through which tagging and measuring
could be done in situ. On release, fish were observed to resume normal foraging behavior within 5–10 min.
Body sizes (SLs) of all fish were measured to the nearest 0.5
mm using vernier calipers. Fish were assigned ranks based on
their relative sizes in the group as dominance is known to be
rigidly size based in this species (Aldenhoven 1984; Ang 2010)
and size ratios between adjacently ranked fish calculated as
the SL of the subordinate divided by the SL of the dominant.
All procedures were conducted according to institutional
guidelines and approved by the Animal Ethics Committee of
James Cook University in Australia where the work was carried
out.
Behavioral observations
Field behavioral observations were carried out on all mature
individuals in the study population using a standardized focal
watch technique. Each individual was observed using three
15-min focal watches, with one focal watch in the morning
(8–11 AM), one at midday (11 AM to 2 PM), and one in the
afternoon (2 PM to 1 h before sunset). The 3 focal watches
were spread out over several days with no more than one focal
watch in a single day on the same fish. During the focal watch,
the observer counted the total number of foraging nips the focal fish took and used a stopwatch to record the total time (to
the nearest second) that the fish was visible to the observer. A
foraging rate for each focal watch was then calculated as the
total number of nips divided by the visible time, given as number of nips per minute. The observer also stayed directly above
the focal fish at all times, carrying or towing on a taut line
a Garmin global positioning system (GPS) 72 unit attached to
a surface buoy, which recorded GPS fixes every 10 s. GPS
data were combined for the 3 focal watches (270 fixes over
the 45 min; standard bootstrapping procedures were used to
check this number of points adequately covered the home
range) to calculate a home range estimate for each individual.
As recommended by Getz et al. (2007), we used the ‘‘adaptive sphere-of-influence’’ a-LoCoH method to calculate home
range. a-LoCoH (local convex hull) is a nonparametric
kernel-based method of home range estimation particularly
useful in patchy environments with hard habitat-type edges,
such as a coral reef. It produces home ranges by first considering each observed location and identifying all the neighboring points within a radius a such that the distances of all
points within the radius to the reference point sum to a value
less than or equal to a. A minimum convex polygon (local
hull) is first produced for each point from the selected neighboring points. After arranging the hulls in increasing order of
size, they are merged until the required proportion of points
is included (e.g., 50% of points are included in the 50th
percentile isopleths) to produce the home range. The lower
isopleths represent the most used part of the home territory
(i.e., the densest area in terms of points). The radius a was
selected following the ‘‘minimum spurious hole covering’’
Ang and Manica • Group size limits in a linear hierarchy
821
rule (Getz et al. 2007). We used the 50% density isopleth
throughout to estimate the home range (as recommended
by Börger et al. 2006). Home ranges were calculated using
the adehabitat package in R. Kernel shapefiles were exported
to ArcView 9 (Environmental Systems Research Institute) to
calculate the area of overlaps between individuals’ home
ranges. The overlapping area of adjacently ranked fishes’
home ranges was expressed as a percentage of the subordinate’s total home range area for analysis.
Statistics
All statistical analyses were carried out in R (Ihaka and
Gentleman 1996). Most of the tests used in this study were
simple nonparametric Spearman’s rank correlations due to
nonnormality of data such as overlap extent. Foraging rate
and size ratios were, however, analyzed by building a generalized linear mixed model (GLMM) using the lme4 package so
that we could account for the effect of random factors such as
group and individual identity. In the foraging model presented here, we retained only those random factors that were
significant. However, including all the nonsignificant random
factors that we dropped resulted in no qualitative change in
the results. In the size ratio models, we retained the random
factor group regardless of its significance to control for the
nonindependence of size ratios from the same group. We
tested the significance of model terms using analysis of variance (ANOVA) to compare alternative models with and without each term. We also used an alternative test by Markov chain
Monte Carlo sampling the posterior distribution of the coefficient values generated from the model algorithm (using
the function mcmcsamp from lme4) and checking that the
95% confidence interval for the coefficients did not include
zero, indicating a significant effect. Only the ANOVA test
results are presented as the 2 approaches gave the same results.
RESULTS
Predicting maximum group size from the size of the
dominant
Following Buston and Cant (2006), we predicted maximum
group sizes (number of mature fish in the group) by assuming
that there was a convergence on a body size ratio of 0.88
between adjacently ranked individuals (0.88 6 0.06 standard
deviation [SD] was the mean of the distribution of observed
size ratios in the field) and that the smallest mature group
members were 5.0 cm in SL. From these 2 assumptions, we
were able to predict the maximum group size (gmax) for
a range of dominant male sizes: male SL 5–5.67 cm, gmax ¼
1; 5.68–6.45 cm, gmax ¼ 2; 6.46–7.33 cm, gmax ¼ 3; 7.34–8.33
cm, gmax ¼ 4; 8.34–9.46 cm, gmax ¼ 5; 9.47–10.75 cm, gmax ¼ 6.
We compared the observed group size with the predicted
maximum group size for 36 natural groups (Figure 1). Eight
of the 35 groups were larger than the predicted maximum
group size.
Do oversize groups display a compressed body size
hierarchy?
We considered whether larger than predicted group sizes were
correlated to a compressed body size hierarchy such that adjacently ranked fish were closer together in size and more ranks
could be fit into the range of sizes available between the smallest group member and the largest. We tested for a correlation
between the average size ratios between adjacently ranked
group members (calculated as subordinate SL/dominant
SL) and the difference between observed and predicted maximum group sizes for that group.
Figure 1
The relationship between the observed group size and the predicted
maximum group size (n ¼ 35 groups). Maximum group size was
predicted assuming that body size ratios were maintained at 0.88.
The line represents the 1:1 relationship such that groups falling
above the line were larger than predicted. Numbers next to points
indicate the number of groups at each point.
Average size ratios between adjacently ranked group members increased with the difference between the observed group
size and the predicted maximum group size (Spearman’s rank
correlation, q ¼ 0.72, P , 0.001, n ¼ 35 groups, Figure 2). This
indicated that in oversize groups, adjacently ranked group
members were closer in size and the group body size hierarchy
was compressed.
We then considered whether the compression occurred
evenly across the hierarchy, using linear mixed models of size ratios between adjacently ranked individuals. Size ratios were log
(x 1 1) transformed for normality, and group was included as
a random factor. In oversize groups, compression occurred particularly toward the bottom of the hierarchy with size ratios increasing with rank number (decreasing with dominance rank;
GLMM: v21 ¼ 9.21, P ¼ 0.002, n ¼ 34 ratios), whereas in groups
that were no larger than predicted, there was no relationship
(GLMM: v21 ¼ 0.03, P ¼ not significant [NS], n ¼ 72 ratios).
Are subordinate foraging rates less well regulated in
oversize groups?
Body size-based hierarchies may be maintained by regulation
of subordinate foraging rates such that subordinates reduce
their foraging and growth if they approach their immediate
dominants too closely in size (Ang and Manica 2010; Wong
et al. 2008). The compression in oversize groups may have
resulted from a compromised foraging regulation mechanism. We tested whether the regulation of subordinate foraging rates by size ratios to their immediate dominants was
mitigated by the difference between observed and predicted
maximum group size.
We built a linear mixed model of subordinate foraging rate,
with size ratio to the immediate dominant and the difference
between observed and predicted maximum group size as fixed
factors, controlling for the random effects of site, group,
822
Figure 2
Average size ratios between adjacently ranked group members
increase with the difference between observed and predicted
maximum group size, indicating that groups which are larger than
predicted have more compressed body size hierarchies. Size ratio is
calculated as the SL of the subordinate/SL of the dominant.
observer, and field season. We found that there was a significant
interaction effect (GLMM: v21 ¼ 4.84, P ¼ 0.028, n ¼ 349): in
groups that were the same size or smaller than the predicted
maximum group size, relatively large subordinates had reduced foraging rates (GLMM on data subset: v21 ¼ 5.60, P ¼
0.018, n ¼ 240, Figure 3a), whereas this foraging reduction
was lost in groups that were larger than the predicted maximum group size (GLMM on data subset: v21 ¼ 1.65, P ¼ NS,
n ¼ 109, Figure 3b). Oversize groups therefore had less wellregulated subordinate foraging rates. In the mixed models for
the data subsets, group and observer were the only significant
random effects.
Behavioral Ecology
Figure 3
There is a significant interaction of the size ratio between adjacently
ranked pairs and the difference between the observed and predicted
maximum group size in determining foraging rates of the
subordinates in the field. Data are split into groups that were the
same size or smaller than the predicted maximum, where there is
a significant decrease in foraging with SL ratio (a) but no such
relationship was found in groups that were larger than predicted (b).
Foraging rates are corrected for group and observer effects as
estimated by the mixed models.
small dominant males with less control over subordinate foraging and size, due to their smaller absolute size. However, we
found that there was no difference in the size of males leading
oversize groups and males leading groups that were no larger
Are oversize groups more spatially segregated?
In previous work, we showed that the behavioral mechanisms
maintaining clear body size hierarchies could be compromised
when individual group members were spatially segregated
(Ang and Manica 2010). Here, we ask whether the reduced
foraging regulation and body size compression enabling oversize groups might therefore be linked to higher spatial segregation in those groups. We tested for a correlation between
the average percentage of a subordinate’s home range which
was overlapped by the home range of its immediate dominant
(only the female hierarchy was considered as the male home
range encompasses all female ranges) and the difference between the observed and predicted maximum group size for
that group. The average overlap extent between adjacently
ranked group members decreased as the difference between
observed and predicted maximum group size increased
(Spearman’s rank correlation, q ¼ 20.39, P ¼ 0.021, n ¼ 35
groups, Figure 4), indicating that spatial segregation was
higher in oversize groups.
We also considered the alternative hypothesis that compressed hierarchies in oversized groups might be caused by
Figure 4
Average percentage home range overlaps between adjacently ranked
group members decrease with the difference between observed and
predicted maximum group size, indicating that groups which are
larger than predicted are more spatially segregated.
Ang and Manica • Group size limits in a linear hierarchy
than predicted (Mann–Whitney U test, W ¼ 150, P ¼ NS, n ¼
35 groups), suggesting that absolute size of dominants has no
discernible effect on their ability to control relative subordinate size.
Are oversize groups more unstable?
We considered whether oversize groups were more likely to fission into 2 separate groups during the study period or display
a branching harem structure indicating imminent fission
(Sakai and Kohda 1997). We found that the difference between the observed and predicted maximum group size was
significantly smaller in groups that were stable than in groups
that were about to undergo fission (Mann–Whitney U test:
W ¼ 15, P ¼ 0.004, n ¼ 35 groups). Twenty-six of the 27
groups that were at or smaller than the predicted maximum
group size were stable, whereas only 4 of the 8 oversize groups
were stable (Fisher Exact test: P ¼ 0.006), that is, oversize
groups were significantly more unstable than groups that were
at or smaller than the predicted maximum.
DISCUSSION
In a body size-based linear hierarchy, one might expect that
group size or hierarchy length will be limited by the number
of ranks that can be fit into the range of body sizes between the
largest and smallest individual, while maintaining a consistent
minimum size difference between adjacently ranked members.
Buston and Cant (2006) showed that in the clown anemonefish A. percula, maximum group size can indeed be accurately
predicted from the size of the largest individual (assuming
a certain size ratio between adjacently ranked members), with
no groups exceeding the predicted maximum. Our results
differ from theirs, with 8 out of 35 of our C. bicolor groups
larger than the maximum group size predicted using the same
method, due to compression of the body size hierarchy in
these groups enabling more ranks to be fit into the range of
available body sizes. The C. bicolor system differs from that of
A. percula in being less specialized and therefore perhaps
a more representative indicator of how size hierarchies in
a wider range of species may influence group size.
Reproductive skew in C. bicolor is lower than in A. percula,
with multiple-breeding females in the haremic system of the
former (Aldenhoven 1984) compared to a single breeding
pair with multiple nonbreeding subordinates in the latter
(Allen 1972). The ability of subordinate C. bicolor females to
obtain at least a small measure of current reproductive success
reduces the selective pressure on them to challenge for higher
rank rather than peacefully waiting to inherit (Cant et al.
2006; Wong et al. 2007). Subordinates are discouraged from
challenging by the maintenance of large size differences between adjacent ranks, which make challenges not worthwhile
due to the very low chance of success (Maynard Smith 1983;
Wong et al. 2007). In a lower skew system with lower pressures
on subordinates, we might expect that the rigidity with which
size hierarchy spacing is enforced becomes less imperative for
hierarchy stability. This is reflected in the average size ratios
between adjacent ranks, which are less widely spaced and
more variable in C. bicolor (0.88 6 0.06 SD) than in A. percula
(ca. 0.79 6 0.01 SD [Buston and Cant 2006]). Larger variability in size ratios may help to explain why some C. bicolor groups
in our study displayed compressed body size hierarchies that
enabled them to exceed the predicted maximum group size,
whereas the very strictly enforced A. percula system showed no
such flexibility in size ratios and group size (Buston and Cant
2006). Mating systems with some subordinate breeding are
widespread in fishes (Robertson 1972; Fricke and Holzberg
1974; Bauer JA and Bauer SE 1981; Koltes 1993; Wong et al.
823
2005) and other taxa (Stacey and Koenig 1990; Keane et al.
1994; Clutton-Brock et al. 2001), and we expect that in these
other relatively open systems, maximum group size may also
not be perfectly predictable from size ratios and the size of the
dominant.
A second major difference between the C. bicolor and A. percula
systems is ecological: Group home range sizes in A. percula,
confined to a single anemone (Allen 1972), are much smaller
than the generalist ranges of C. bicolor, which extend up to 200
m2 over the reef (Aldenhoven 1984; Eagle et al. 2001). The
size of the C. bicolor range enables individual female group
members to become spatially segregated from each other
within the larger group home range. In a previous paper, we
showed that such spatial segregation can lead to reduced effectiveness of the regulatory mechanisms that maintain a clear
size hierarchy in the group (Ang and Manica 2010). Our results from this study suggest that in groups that become spatially segregated, subordinate foraging rates are less well
regulated to maintain size differences between adjacent ranks,
leading to a compressed body size hierarchy and the possibility of an oversized group. Given its important effects on social
structure, the factors that lead to spatial segregation within
groups present an avenue for further research. The type of
substrate may play an important role as habitat that is poorer
in food or shelter may be less able to support spatially
overlapping individual home ranges and so encourage greater
spatial segregation. In our study, 6 of the 8 groups that
were larger than the predicted maximum came from a single
study site, which was unusual in having a higher proportion of
shelter- and food-poor flat rock in the substrate than the other
sites. Patchiness of the habitat may also be important if it
limits group ranges; inhospitable open sand ‘‘corridors’’ in
the reef may act as barriers on group home ranges, enforcing
high spatial overlap within groups. Finally, population density
may also impact on the potential for spatial segregation as an
environment that is saturated will provide less opportunity for
spatial expansion and segregation than one that has a lower
population density (Woolfenden and Fitzpatrick 1978).
Although lower skew and the potential for spatial segregation may allow some C. bicolor groups to become larger than
predicted, our results suggest that these groups are unstable,
with a high likelihood of either fissioning into 2 separate
groups during the study period or displaying a ‘‘branching’’
harem structure (Sakai and Kohda 1997) indicating a potential imminent fission event. Such instability may be due to
a compressed body size hierarchy wherein asymmetries in
RHP between adjacently ranked individuals are reduced such
that subordinates may find it worthwhile to challenge dominants and destabilize the group (Wong et al. 2007; Ang and
Manica 2010). Ultimately, the limits on group size imposed by
the need to maintain a clearly separated size hierarchy may
be unavoidable, with oversize groups only a transient phenomenon. Ideally, a future longitudinal study on C. bicolor
or a similar system would be able to show the progression
from a well-defined small social group, through a spatially
segregated and compressed oversized group that eventually
fissions back into 2 smaller well-defined groups.
We have discussed the causes and consequences of oversized
groups from the point of view of group stability but note that
the optimal group size for individual group members is not
necessarily stable (Sibly 1983). In a simple situation with equal
competitive ability, observed group sizes may often be larger
than the optimum because it pays individuals to join a group
even if in doing so the average payoff to each group member
falls due to increased competition (Sibly 1983; Pulliam and
Caraco 1984). In the C. bicolor system, however, there is significantly greater complexity caused by the dominance hierarchy
which is also a social queue, and optimum group size is likely
824
different for different ranks (Pulliam and Caraco 1984). Small
groups may be preferred by subordinates because they offer
higher current reproductive shares (Ang and Manica 2010)
and a shorter wait for the dominant position. Large groups
may be preferred by the dominant male so long as he can
maintain his rank because they provide more females to mate
with. The dominant female might prefer a larger group because it will provide more mates when she takes over but this
might be outweighed by the benefits of harem fission into
smaller groups as she would then achieve the male position
sooner (Sakai 1997) (albeit with a smaller number of females
to mate with). As dominants in these systems appear to have
a large measure of control over group size through their ability to aggressively evict subordinates (Buston 2003a; Wong
et al. 2007; Ang 2010), we expect that the main point of
conflict in an oversized group will occur between the dominant male’s preference for a large stable group and the dominant female’s preference for harem fission. This conflict
might be reflected in changes in aggressive and spatial relationships between the dominant male and female as group
size increases.
In conclusion, the need to maintain size differences between
adjacent ranks in the body size-based C. bicolor linear hierarchy
limits maximum group size. On occasion, spatial segregation
may allow some flexibility in the system, with compression of
the size hierarchy enabling some groups to become larger
than predicted, but such oversized groups are probably only
transient as they are unstable and fission into smaller groups.
Body size-based linear hierarchies are increasingly becoming
a useful model system for understanding how within-group
competition and conflict shapes social structure (Hamilton
et al. 2005; Buston and Balshine 2007; Wong et al. 2007;
Ang and Manica 2010). We expect that the group size dynamics uncovered in this study may be generalized to other linear
dominance hierarchies, whether they are based on body sizes
or on other correlates of RHP.
FUNDING
Yousef Jameel Scholarship and Edith Mary Pratt Musgrave
Fund to T.Z.A.
We thank C. Luder, H. Hedworth, T. Ismail, H. Salomonsen, A. Lutz,
and T.T.A. for support in the field.
REFERENCES
Aldenhoven JM. 1984. Social organization and sex change in an angelfish Centropyge bicolor on the Great Barrier Reef [PhD thesis].
North Ryde New South Wales (Australia): Macquarie University.
Allen GR. 1972. The anemonefishes: their classification and biology.
2nd ed. Neptune City (NJ): T.F.H. Publications.
Andersson M, Wiklund CG. 1978. Clumping versus spacing out—
experiments on nest predation in fieldfares (Turdus pilaris). Anim
Behav. 26:1207–1212.
Ang TZ. 2010. Social conflict resolution in groups of the angelfish
Centropyge bicolor [PhD thesis]. Cambridge: Cambridge University.
Ang TZ, Manica A. 2010. Aggression, segregation and stability in
a dominance hierarchy. Proc R Soc B Biol Sci. doi: 10.1098/
rspb.2009.1839.
Bauer JA, Bauer SE. 1981. Reproductive biology of pigmy angelfishes
of the genus Centropyge (Pomacanthidae). Bull Mar Sci. 31:
495–513.
Börger L, Franconi N, De Michele G, Gantz A, Meschi F, Manica A,
Lovari S, Coulson T. 2006. Effects of sampling regime on the mean
and variance of home range size estimates. J Anim Ecol. 75:
1393–1405.
Buston P. 2003a. Forcible eviction and prevention of recruitment in
the clown anemonefish. Behav Ecol. 14:576–582.
Behavioral Ecology
Buston P. 2003b. Size and growth modification in clownfish. Nature.
424:145–146.
Buston PM, Balshine S. 2007. Cooperating in the face of uncertainty:
a consistent framework for understanding the evolution of cooperation. Behav Processes. 76:152–159.
Buston P, Cant MA. 2006. A new perspective on size hierarchies in
nature: patterns, causes, and consequences. Oecologia. 149:
362–372.
Cant MA, Field J. 2001. Helping effort and future fitness in cooperative animal societies. Proc R Soc B Biol Sci. 268:1959–1964.
Cant MA, Llop JB, Field J. 2006. Individual variation in social aggression and the probability of inheritance: theory and a field test. Am
Nat. 167:837–852.
Caraco T, Wolf LL. 1975. Ecological determinants of group sizes of
foraging lions. Am Nat. 109:343–352.
Clutton-Brock TH, Brotherton PNM, Russell AF, O’Riain MJ, Gaynor
D, Kansky R, Griffin A, Manser M, Sharpe L, McIlrath GM, et al.
2001. Cooperation, control, and concession in meerkat groups.
Science. 291:478–481.
Clutton-Brock TH, Hodge SJ, Flower TP. 2008. Group size and the
suppression of subordinate reproduction in Kalahari meerkats.
Anim Behav. 76:689–700.
Eagle JV, Jones GP, McCormick MI. 2001. A multi-scale study of the
relationships between habitat use and the distribution and abundance patterns of three coral reef angelfishes (Pomacanthidae).
Mar Ecol Prog Ser. 214:253–265.
Fricke HW, Holzberg S. 1974. Social units and hermaphroditism in
a pomacentrid fish. Naturwissenschaften. 61:367–368.
Getz WM, Fortmann-Roe S, Cross PC, Lyons AJ, Ryan SJ, Wilmers CC.
2007. LoCoH: nonparametric kernel methods for constructing
home ranges and utilization distributions. PLoS One. 2:e207.
Goss-Custard JD. 1976. Variation in dispersion of redshank Tringa
totanus on their winter feeding grounds. Ibis. 118:257–263.
Hamilton IM, Heg D, Bender N. 2005. Size differences within a dominance hierarchy influence conflict and help in a cooperatively
breeding cichlid. Behaviour. 142:1591–1613.
Heg D, Bender N, Hamilton I. 2004. Strategic growth decisions in
helper cichlids. Proc R Soc B Biol Sci. 271:S505–S508.
Helantera H, Strassmann JE, Carrillo J, Queller DC. 2009. Unicolonial
ants: where do they come from, what are they and where are they
going? Trends Ecol Evol. 24:341–349.
Hutchinson GE. 1959. Homage to Santa Rosalia or why are there so
many kinds of animals? Am Nat. 93:145.
Ihaka R, Gentleman R. 1996. R: a language for data analysis and
graphics. J Comput Graph Stat. 5:299–314.
Ioannou CC, Krause J. 2008. Searching for prey: the effects of group
size and number. Anim Behav. 75:1383–1388.
Keane B, Waser PM, Creel SR, Creel NM, Elliott LF, Minchella DJ.
1994. Subordinate reproduction in dwarf mongooses. Anim Behav.
47:65–75.
Kohda M, Shibata JY, Awata S, Gomagano D, Takeyama T, Hori M, Heg
D. 2008. Niche differentiation depends on body size in a cichlid
fish: a model system of a community structured according to size
regularities. J Anim Ecol. 77:859–868.
Kokko H, Johnstone RA. 1999. Social queuing in animal societies: a dynamic model of reproductive skew. Proc R Soc B Biol Sci. 266:571–578.
Koltes KH. 1993. Aspects of the reproductive-biology and socialstructure of the stoplight parrotfish Sparisoma viride, at Grand Turk,
Turks-and-Caicos-Islands, B.W.I. Bull Mar Sci. 52:792–805.
Kvarnemo C, Moore GI, Jones AG, Nelson WS, Avise JC. 2000. Monogamous pair bonds and mate switching in the Western Australian
seahorse Hippocampus subelongatus. J Evol Biol. 13:882–888.
MacArthur R, Levins R. 1967. The limiting similarity, convergence,
and divergence of coexisting species. Am Nat. 101:377.
Major PF. 1978. Predator–prey interactions in 2 schooling fishes, Caranx ignobilis and Stolephorus purpureus. Anim Behav. 26:760–777.
Martin JK, Handasyde KA, Taylor AC, Coulson G. 2007. Long-term
pair-bonds without mating fidelity in a mammal. Behaviour.
144:1419–1445.
Maynard Smith J. 1983. Game theory and the evolution of cooperation. In: Bendall DS, editor. Evolution from molecules to men. Cambridge: Cambridge University Press. p. 445–456.
Munday PL, Wilson SK. 1997. Comparative efficiency of clove oil and
other chemicals in anaesthetization of Pomacentrus amboiensis, a coral
reef fish. J Fish Biol. 51:931–938.
Ang and Manica • Group size limits in a linear hierarchy
Owens D, Owens M. 1996. Social dominance and reproductive patterns in brown hyaenas, Hyaena brunnea, of the central Kalahari
desert. Anim Behav. 51:535–551.
Pulliam HR, Caraco T. 1984. Living in groups: is there an optimal
group size? In: Krebs JR, Davies NB, editors. Behavioural ecology:
an evolutionary approach. 2nd ed. Oxford: Blackwell Scientific Publications. p. 122–147.
Pusey AE, Packer C. 1997. The ecology of relationships. In: Krebs JR,
Davies NB, editors. Behavioural ecology: an evolutionary approach.
4th ed. Oxford: Blackwell Publishing. p. 254–283.
Reeve HK, Emlen ST. 2000. Reproductive skew and group size: an
N-person staying incentive model. Behav Ecol. 11:640–647.
Robertson DR. 1972. Social control of sex reversal in a coral-reef fish.
Science. 177:1007–1009.
Sakai Y. 1997. Alternative spawning tactics of female angelfish according to two different contexts of sex change. Behav Ecol. 8:372–377.
Sakai Y, Kohda M. 1997. Harem structure of the protogynous angelfish, Centropyge ferrugatus (Pomacanthidae). Environ Biol Fishes.
49:333–339.
Schmidt PA, Mech LD. 1997. Wolf pack size and food acquisition. Am
Nat. 150:513–517.
Schmitz RA, Baldassarre GA. 1992. Correlates of flock size and behavior of foraging American flamingos following hurricane Gilbert in
Yucatan, Mexico. Condor. 94:260–264.
825
Sibly RM. 1983. Optimal group-size is unstable. Anim Behav. 31:
947–948.
Stacey PB, Koenig WD. 1990. Cooperative breeding in birds. Cambridge: Cambridge University Press.
Vehrencamp SL. 1983. Optimal degree of skew in cooperative societies. Am Zool. 23:327–335.
Vine I. 1973. Detection of prey flocks by predators. J Theor Biol.
40:207–210.
Whiteman EA, Côté IM. 2004. Dominance hierarchies in group-living
cleaning gobies: causes and foraging consequences. Anim Behav.
67:239–247.
Wiley RH, Rabenold KN. 1984. The evolution of cooperative breeding
by delayed reciprocity and queuing for favorable social positions.
Evolution. 38:609–621.
Wong MYL, Buston P, Munday PL, Jones GP. 2007. The threat of
punishment enforces peaceful cooperation and stabilizes queues
in a coral-reef fish. Proc R Soc B Biol Sci. 274:1093–1099.
Wong MYL, Munday PL, Buston PM, Jones GR. 2008. Fasting or feasting in a fish social hierarchy. Curr Biol. 18:R372–R373.
Wong MYL, Munday PL, Jones GP. 2005. Habitat patch size, facultative
monogamy and sex change in a coral-dwelling fish, Caracanthus
unipinna. Environ Biol Fishes. 74:141–150.
Woolfenden GE, Fitzpatrick JW. 1978. The inheritance of territory in
group breeding birds. Bioscience. 28:104–108.