Behav Ecol Sociobiol (1993) 32:349-354 Behavioral Ecology and Sociobiology © Springer-¥erlag 1993

A method for the detection of non-random associations among flocking birds and its application to sanderlings CMidris Mba wintering in N.E. England Gilbert Roberts ~ and Peter R. Evans

Department of Biological Sciences, University of Durham, South Road, Durham DH1 3LE, UK

Received March 30, 1992 / Accepted December 17, 1992

Summary. Indices of association are frequently used in studies of social behaviour. Observed association indices may be compared with those obtained from computer randomizations of the data in order to test whether any two individuals in a population tend to occur together more than would be expected by chance. Data for indi- vidually-identifiable colour-ringed sanderlings Calidris alba are presented to illustrate the importance of the assumptions on which such null models are built. When each individual was given an equal chance of appearing in each flock associations differed from those expected by chance. But when the different numbers of times that each individual occurred at the study site were taken into account associations were not different from those expected by chance. Hypotheses relating association lev- els to a number of factors were tested. None of the fac- tors examined had significant and appreciable effects on association levels. In particular, there was no evidence for sanderlings moving around in stable groups. Taking into account the different distributions of different indi- viduals, the population of birds present on any day rep- resented a random sample from the population of birds seen during the winter.

Introduction

A common question which arises in studies of social behaviour is how often any two particular individuals occur together in the same groups. This question may be addressed by recording the individual composition of groups on a number of occasions. An association index may then be calculated for every possible pairing as some function of the numbers of sightings of each individual together and apart.

One such index has been referred to by several au- thors (Myers 1983; Whitfield 1985; Metcalfe 1986) as

* Present address: Computing Service, South Road, Durham DH1 3LE, UK

Correspondence to: G. Roberts

Ekman's index (Ekman 1979). It has also been referred to as Jaccard's index (e.g. Southwood 1978) and as the twice-weight index (Cairns and Schwager 1987). It is given by the number of times that two individuals are seen together as a fraction of the number of times that one or both of them are seen. If n A B is the total number of sightings of A and B together and nA and nB are the total numbers of sightings of A and B respectively, whether together or apart, then Ekman's index is:

n A B EA'B = nA + nB- - nAB"

The association levels obtained using such an index must be interpreted by comparison with some other as- sociation levels. Studies of associations may aim (1) to establish whether there are non-random associations, and if so to find the magnitude of the difference from random so that its biological meaning can be interpret- ed; (2) to compare observed associations of different pairs; or (3) to compare observed associations in differ- ent situations.

In order to find the levels of association which may be expected by chance, computer randomizations can be carried out in which each bird actually seen is re- placed by one picked at random from the population. This method was first used by Myers (1983) and was followed by Whitfield (1985) and Metcalfe (1986). This paper is concerned with the methods used in carrying out such computer randomizations.

The simplest null hypothesis is that there is an equal chance of any bird appearing in a flock. According to this hypothesis the birds in a flock constitute a random sample from the local population. This was the approach adopted by Myers (1983) and followed by Metcalfe (1986) and by Whitfield (1985). Alternatively, the ob- served sighting frequencies of each individual can be tak- en into account. That is, a bird seen twice as often is given twice as great a chance of appearing in the com- puter-generated flocks. The null hypothesis is that the birds in a flock constitute a random sample from the local population weighted by the overall occurrence fre- quencies of individual birds.

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T h e s e t w o p r o c e d u r e s w e r e a p p l i e d to d a t a f r o m a s t u d y o f s a n d e r l i n g s Calidris alba a t T e e s m o u t h , N . E . E n g l a n d , in o r d e r to i n v e s t i g a t e t he i m p o r t a n c e o f t he a s s u m p t i o n s bu i l t in to nu l l m o d e l s o f a s s o c i a t i o n levels. F u r t h e r tes ts w e r e t h e n ca r r i ed o u t to d e t e r m i n e w h e n s a n d e r l i n g s t e n d e d to m o v e a r o u n d t o g e t h e r a n d o c c u r in t he s a m e f locks a n d t h e r e b y to u n d e r s t a n d the m o v e - m e n t s o f s a n d e r l i n g s a r o u n d T e e s m o u t h .

Materia l and methods

Observations

The main part of the fieldwork was carried out around Redcar, N.E. England, between October 1986 and May 1987 on days when reasonable weather coincided with a daylight low tide. Observa- tions were made on 36 days with 1 or 2 days of observations in most weeks. Observations covered a predominantly rocky area (Redcar Rocks) and an adjoining stretch of sandy beach (Coatham Sands). At low tide, sanderlings concentrated to feed on Redcar Rocks. As the tide rose to cover this area, the birds moved off onto the sandy beach. Observations were carried out either on foot or from a vehicle using 8 x 40 binoculars and a 15-60 x 60 telescope. An observer standing in the open caused no apparent disturbance. A total of 2803 sightings were obtained for 91 colour- ringed birds. Additional data (1377 sightings) were collected in the winters 1987-1988 and 1988-1989. In these additional data the presence of birds at a site on a day was recorded but complete checks of each flock were not made.

For each flock encountered, a complete check was made of all individually-identifiable colour-ringed sanderlings present. Birds were ringed with four rings of the colours green, blue, black, white, red, orange and yellow. Approximately one in five sanderlings pres- ent at any one time were colour-ringed. The mean number of col- our-ringed birds per flock was 4.88 (_+0.19 standard error) with a maximum of 40. Where the distance between birds was more than 10 m, birds were considered to be in different flocks. The rocky substrate at Redcar often imposed constraints on flock spac- ing, especially where areas were cut off by water channels, while on the sands patchy wrack or coal dust and mussel deposits often supported discrete flocks. The 10-m criterion was therefore used flexibly when other factors appeared to delineate flocks more meaningfully. Flocks were differentiated in time as well as in space. Since birds were continually free to move between groups, every flock recorded was considered to be a separate sample. Rather than specifying an arbitrary time interval within which observa- tions were considered to be dependent and outside of which they were considered to be independent, no criterion was set and the time interval between sightings remains as a factor potentially af- fecting recorded association levels. In practice, few repeat checks were made within 15 min, an interval during which several move- ments of birds between flocks typically occurred, usually as a result of a disturbance or because of a rising tide.

There were almost always other people present, mainly exercis- ing dogs but also riding horses, riding motor-cycles, launching boats, playing, flying microlight aircraft, bait-digging, searching the strandline, collecting coal-dust, or simply walking and jogging. The extent of this disturbance was greatest at weekends, which were therefore avoided as fieldwork days. Disturbance, especially by dogs chasing the birds or by horses being ridden along the water's edge, often prevented me from recording all of the marked birds in a flock. In such cases the data were recorded as being incomplete and were not included in the analyses presented here.

Analysis

From the sighting records, indices of association were calculated for every possible pairing. Indices were also calculated after corn-

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Fig. 1. The sighting frequency distribution for the observed data (and for the randomization in which sighting frequencies were re- tained) (blank columns) compared with that for the randomization in which all birds had approximately equal sighting frequencies (shaded columns)

puter randomization of the data. Two randomization procedures were used.

Method 1. The number of birds in each observed flock was retained while their identities were substituted randomly, (by using a ran- dom number to specify a bird from a list of all individuals) subject to the constraint that no bird could appear more than once in the same flock. Because each bird was considered to be equally ' available' for the computer randomization, the frequency distribu- tion of sightings had a small standard deviation: all were ' seen ' approximately the same number of times.

Method 2. The second procedure retained not only the frequency distribution of flock sizes (as in method 1) but also the number of sightings of each individual. This was achieved by using a ran- dom number to specify an individual from a list of all sightings. The randomization was again subject to the constraint that no bird could appear more than once in any flock.

The difference between the observed sighting frequency distri- bution and that in the data generated using the randomization which assumed that all birds were equally available was appreciable (Fig. 1). The randomization in which all birds were considered equally 'available' produced a sighting frequency distribution with the same mean (30.80) but a much smaller standard deviation (2.41) than that of the observed data (18.07).

Birds seen fewer than six times were excluded from the data before randomization. One reason for this exclusion was that it is unlikely that reliable indices of association could be obtained on the basis of few sightings. Furthermore, the possibility that such birds might have been erroneously recorded is difficult to discount since only a small percentage of errors can give rise to an appreciable number of additional birds being recorded as pres- ent.

Results

O b s e r v e d a s s o c i a t i o n s d i f f e red f r o m t h o s e e x p e c t e d w h e n e x p e c t e d a s s o c i a t i o n s w e r e c a l c u l a t e d f r o m a r an - d o m i z a t i o n o f the d a t a in w h i c h e a c h b i r d was g i v e n an e q u a l c h a n c e o f a p p e a r i n g in e a c h f l ock ( o b s e r v e d

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800 ~ Random 2

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 >15

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Fig. 2a, b. Frequency distributions of association indices for ob- served data (blank columns) compared with a a randomization in which all birds had approximately equal sighting frequencies; and b a randomization in which actual sighting frequencies were re- tained (shaded columns)

median=4.54%, n=4095 pairs; random median= 5.26%, n=4095 pairs; Kolmogorov-Smirnov two-sam- ple test on a random sample of 2300 pairs, Dma x-= 0.20, Z = 4.78, P < 0.00005; Fig. 2 a). In fact, observed associa- tions tended to be lower than expected; there were more pairs than predicted with very low association levels and fewer with medium values of the association index. But observed associations did not differ from those expected if the observed frequencies of occurrence of each individ- ual were taken into account in the randomization (ran- dom median=4.44%, n=4095 pairs; Kolmogorov- Smirnov two-sample test on a random sample of 2300 pairs, Dmax=0.05, Z=1.13 , P = 0 . 1 5 ; Fig. 2b). Those pairs seen most frequently were most strongly associated (Table 1), but these associations were no stronger than expected given the birds' sighting frequencies.

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Table 1. Associations among pairs of sanderlings seen different numbers of times

Sighting Observed Random Pairs Dma x Z frequency

All 4.55 4.41 4095 0.05 1.14 0.15 > 30 8.05 8.57 946 0.03 0.80 0.54 >40 9.26 9.79 406 0.03 0.62 0.84 > 50 10.89 10.88 120 0.04 0.91 0.37

The sighting frequencies refer to each individual bird. Median values of the association index are given for the observed data and for the randomization in which sighting frequencies were re- tained. Significance levels were obtained using Kolmogorov-Smir- nov two-sample tests

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Fig. 3. Frequency distributions of association indices calculated from the birds' daily pressences or absences. Observed median = 27.27, n=4005 (blank columns); random median=27.59, n=4005 (shaded columns). Kolmogorov-Smirnov 2-sample test, D~ax= 0.020, Z=0.501, P=0.959

Daily occurrences

If individuals moved around between sites with particu- lar other individuals but mixed randomly while at a site, then associations might not be found at the level of flock membership but might be found at the level of co-occur- rences at a site on a given day. A test of this hypothesis, retaining observed sighting frequencies in the null model, resulted in a good fit between the data and the null model (Fig. 3).

Assortment among flocks

Observed associations were tested against those obtained using a null model in which each bird's sightings were reshuffled randomly amongst the flocks present on each of the days on which it was seen. That is, the null model retained both the actual days on which a bird was seen and the number of times on each of those days. No

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Observed Random

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Association index (%)

Fig. 4. Observed frequency distribution (blank columns) of associa- tion indices for all pairings tested against a null model prepared by randomizing sightings among flocks while maintaining the days of the sightings (shaded columns). Observed median=4.545, n= 4095; random median=4.348, n=4095 pairs; Kolmogorov-Smir- nov 2-sample test, Din,x=0.031, Z=0.662, P=0.778

Table 2. Observed and random median association indices for (a) Redcar and Coatham and (b) sandy areas and rocky areas (a)

Observed Random Dmax Z P

Redcar 4.40 4.26 0.04 1.58 0.0l Coatham 4.17 4.26 0.02 0.71 0.70 Dm,~ 0.13 0.10 Z 5.68 4.44 P <0.01 <0.01

(b)

Observed Random Dm,x Z P

Sandy 3.85 3.70 0.03 1.48 0.03 Rocky 3.57 4.35 0.05 2.07 <0.01 D~.ax 0.02 0.04 Z 0.72 1.75 P 0.68 <0.01

The sample size was approximately 4000 pairs for each data set. Probabilities were obtained from Kolmogorov-Smirnov 2-sample tests

evidence was found of non-random assortment among flocks within days (Fig. 4).

Associations in relation to feeding site and substrate

Associations of birds visiting Redcar were compared with those of birds visiting Coatham Sands. The sites differed in substrate type, and consequently food supply, but also in degree of disturbance, exposure period and variations thereof, and proximity to roost sites.

Associations differed from random at Redcar (Table 2 a), but the difference was only slight and would appear to be of little biological significance. Comparing sites, there were significant differences both for the observed data and for the random data.

Substrate effects were addressed more specifically by considering only data for the Redcar area and compar- ing associations of birds feeding on sandy areas with those of birds feeding on rocky areas. Within each habi-

tat significant differences between observed and random were found but, as in the case of comparisons between sites, the differences were small (Table 2b).

Associations in relation to distributions and vagility

Associations between individuals on the south side of the estuary in winter 1986 1987 were examined in terms of the frequencies of occurrence of those individuals on the north side in the previous winter. This was done by finding the numbers of sightings of each individual on the north side in winter 1985-1986 as proportions of the numbers of observation days in that winter. Most birds (17) were seen on fewer than 5% of observation days (group A); 8 birds were seen more frequently (group B). This classification was arbitrary in that there was no clear bimodality in the distribution of sighting frequencies. Association levels within and between the distribution classes were compared with those expected

Table 3. Median association indices by (a) distribution classes and (b) vagility levels

(a)

Distribution Observed Random n pairs Oma x Z P

Both group A 3.90 3.97 190 0.10 0.92 0.36 Both group B 5.67 5.65 300 0.06 0.74 0.65 Different groups 4.93 4.20 500 0.07 1.14 0.15

(b)

Vagility Observed Random n pairs Oma x Z P

Both low 1.61 1.61 153 0.09 0.80 0.54 Both high 5.09 5.66 666 0.08 1.37 0.05 Different 3.73 3.57 666 0.03 0.49 0.97

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using the association indices calculated for overall flock membership (Table 3 a). No differences from random- ness were found.

Vagility is a measure of the extent to which a bird moves between sites. An index of vagility was computed as the number of status changes made over the maxi- mum possible number of status changes given the arrival and departure dates. Pairs were divided into three vagi- lity classes: (1) where both members of a pair had vagili- ties less than the mean; (2) where both had vagilities above the mean; (3) where one bird's vagility was below the mean and the other's above. Although a significant difference from randomness was found for the high-vagi- lity birds (Table 3 b) the magnitude of the difference was small and it appears that the null models give a good fit to the data.

Correlations between associations in different periods

Sightings were divided into three periods: October-No- vember; December-February; and March-May. Rando- mizations of the data were carried out separately for each period. Association indices for each pair were com- puted and the difference between observed and random calculated. This gave three difference values for each pair which were then used to compute correlations be- tween the difference values in different seasons. There were no significant correlations and therefore there was no evidence of any consistency in the non-randomness of any pair's associations.

Discussion

Studies of associations are important in that they can indicate the types of behavioural interactions and the degree of social organization to be expected in a popula- tion (e.g. Myers 1983). However, a number of methodo- logical problems arise when trying to measure and inter- pret association levels.

In this study it has been shown that differences be- tween the sighting frequency distributions for the ob- served data and the randomized data may lead to appar- ently non-random association levels being recorded. The simple randomization technique used by Myers (1983) is a poor null model because the value of the index used depends on the ratio of the number of sightings to the number of flocks. As the average number of sightings per bird in relation to the number of flocks increases, so the association level increases. The theoretical limit of this process comes where all birds are seen in all flocks and all index values become 100%.

This dependence on the number of sightings is not important if what is being tested is the difference be- tween observed data and random models;~t-ovided that the random model is generated by a method which pre- serves the frequency distribution of sightings. However, previous studies have not used such models. In the null models used each bird has had an approximately equal number of sightings. Any differences from random that

are found may simply be due to differences between the sighting frequency distributions of the observed and randomized datasets. Such differences may be of interest in showing that patterns of occurrence can give rise to associations which are non-random at the simplest level of analysis, but this explanation has not been recognized explicitly.

There has been a tendency to follow the methods of other workers in order to compare the index values obtained with those obtained in previous studies. How- ever, this is invalid if the relationship between the number of sightings and the number of flocks is not controlled for. Comparisons between studies should be confined to differences between observed frequencies and expected random frequencies: comparing the abso- lute values of the indices obtained may be meaningless.

Myers (1983), Metcalfe (1986), and Whitfield (1986) all excluded birds seen fewer than four times from their analyses on the grounds that sampling error would give unreliable estimates of association when sighting fre- quency was low. If such a minimum sighting frequency is set then the frequency distribution of index values obtained may be affected, whether for the random data or for the observed data. The introduction of a minimum criterion raises the average number of sightings per bird in relation to the number of flocks and thereby affects the index values obtained.

Furthermore, these authors used randomizations in which all birds had approximately equal sighting fre- quencies. This meant that few if any birds were excluded from the randomized data. For example, in one test Myers (1983) had 58 individuals (giving 1653 pairings) in the random data, but only 49 individuals (giving 1176 pairings) in the observed data. Myers obtained a better fit to the null model than was found in this study. This may have been because he excluded rarely seen birds from the observed data but not from the random data, and so most of the pairs with low associations would have been removed from the former but not the latter data.

If association is defined in terms of common member- ship of a group, then, using the index used in this study, higher levels of association will be found where flock size is greater as a proportion of the population being studied. This illustrates the difficulty of making cross- study comparisons of absolute association levels. One answer is to ignore absolute association levels and in- stead to confine the analysis to the difference from a null model. Another would be to derive an index which was not dependent on the relationship between flock size and total population size. Cairns and Schwager (1987) reviewed a number of different association indices and derived maximum likelihood estimators which they found to be less biased and to have lower variance than other association indices. However, we found their pro- cedure impractical because of the difficulty of estimating the number of flocks that the entire local population was subdivided into at any given time.

The question of how individuals are assembled into flocks is analogous to that of how species are assembled into communities on islands. In island biogeography null

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models have been used to test whether observed assem- blages are different from those which would be observed if communities were random collections of species un- structured by competition (e.g. Strong et al. 1984). A problem in such studies is whether to incorporate into the null model the observed number of islands, the ob- served number of species, the observed number of occur- rences for each species, and the observed number of species on each island. This is analogous to the question of whether to incorporate the observed flock sizes and the observed number of sightings for each individual.

No evidence was found of non-random associations among sanderlings at Teesmouth. This finding is consis- tent with that of Myers (1983) for sanderlings in Califor- nia despite a number of differences between the two areas in terms of the ecology and behaviour of the birds.

In particular, Teesmouth sanderlings appeared to have a wider range of choices of where and on what to feed than did sanderlings in California. Birds could choose between sites and within sites whether to forage on rocky areas; on the banks of wrack occasionally washed ashore; by probing in sand for worms; by pec- king items from the surface of sand; or by taking crusta- ceans from the water. There was no evidence for the hypothesis that non-random groupings may have re- sulted from shared foraging site or substrate preferences.

Furthermore, although the predictability of food sup- plies is thought to be an important factor affecting socia- lity (e.g. Pulliam and Caraco 1984) no evidence was found of a link between the non-randomness of associa- tions and the apparent predictability of the food supplies exploited by sanderlings. The sandy areas appeared to be highly unpredictable, in particular due to the occa- sional occurrence of wrack beds, but association levels on sandy areas were approximately as expected by chance.

Teesmouth sanderlings had a wider range of distribu- tion patterns than their Californian counterparts with some birds moving around to a considerable extent (Ro- berts 1991). In addition, the population size at a site was much less stable between days than in California. Although Myers (1983) found no evidence of non-ran- dom associations within a population, Myers et al. (1989) found that there was a high degree of between- population structuring. Teesmouth sanderlings did not form such discrete populations (Roberts 1991). Birds visiting the study site showed a range of preferences for different sites and showed a range of degrees of itiner- ancy. Evans (1981) hypothesised that there might be groups of highly mobile birds which move around to- gether and groups of more sedentary birds. However, no evidence of birds moving around together was found: birds which used one side of the estuary to similar ex- tents did not show a greater than expected tendency to visit the other side together. Furthermore, there was no evidence of a link between the level of itinerancy and the occurrence of non-random associations. This contrasts with the finding of Metcalfe (1986) that in- creasing vagility among turnstones caused individuals to come into contact with more other individuals and raised average levels of association.

Thus, despite being gregarious, the sanderlings stud- ied at Teesmouth appeared to behave independently in that they responded to the choices available to them in terms of where and when to feed in ways which may have depended on what other birds were doing but did not depend on the behaviour of any other particular individuals or of any sub-groupings of the population. Although they frequently moved around in flocks, these did not represent stable groups. Birds which shared simi- lar distributions appeared to have independently reached similar decisions in terms of how to distribute their time between sites. That there was no difference between ob- served and random association indices suggests that there were neither consistent preferences for being with particular individuals nor shared preferences for particu- lar feeding sites or methods.

It follows from this that when the number of sander- lings at a site peaked there was simply a larger random sample from the local population present, weighted by overall sighting frequencies. That is, sanderlings did not use sites independently of each other (because on some days there were large numbers and on others few) but there was no tendency for birds to arrive with particular other individuals beyond that due to their overall fre- quencies of occurrence.

Acknowledgements. G.R. was supported by a Natural Environment Research Council studentship.

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