The influence of differences in social experience on the development of species recognition in zebra finch males

The influence of differences in social experience on the development of species recognition in zebra finch males

Anim. Behav., i984, 32, 852-860 THE INFLUENCE OF DIFFERENCES IN SOCIAL EXPERIENCE ON THE DEVELOPMENT OF SPECIES RECOGNITION IN ZEBRA FINCH MALES BY C...

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Anim. Behav., i984, 32, 852-860

THE INFLUENCE OF DIFFERENCES IN SOCIAL EXPERIENCE ON THE DEVELOPMENT OF SPECIES RECOGNITION IN ZEBRA FINCH MALES BY CAREL T E N CATE, LIESBETH LOS & LEO S C H I L P E R O O R D

Zoological Laboratory, University of Groningen, Haren, The Netherlands Abstract. Zebra finch males were first raised by zebra finch parents and then placed in a group of

Bengalese finches between the ages of 30 and 60 days. A higher number of aggressive as well as nonaggressive initiatives by Bengalese finches towards young zebra finch males during this period was correlated with a more Bengalese-finch-directed sexual preference when these males were given a choice between a zebra finch and a Bengalese finch female as adults. Experiments in which a zebra finch male was exposed to Bengalese finches behind a wire screen or to Bengalese finch models gave corresponding results. The study shows that, in contrast to earlier findings, zebra finch males raised by their parents for 31 days can still develop a preference for Bengalese finches. Short term changes in preference are discussed. The results indicate that the behaviour shown by stimulus birds in studies on 'sexual imprinting' is important for the development of sexual preferences. zebra finches, involve a long period of several weeks of exposure to living objects. It may be expected that in such a situation not only the visual appearance of the surrogate parents is important but also their behaviour towards the young birds. To unravel the developmental process underlying sexual preferences, the influence of behavioural experience with stimulus birds needs therefore to be investigated. Such a study can only be carried out in conditions where birds are raised under roughly comparable conditions but behavioural interactions with parents or siblings are variable. One way of analysing the influence of behavioural differences is to compare the life histories of birds which vary in their later preferences. In studies on sexual imprinting (as in filial imprinting: Slucking 1972), individual differences in preference are regularly found between birds that are treated almost identically (e.g. Schutz 1965; Gallagher 1976). Recently, Immelmann (1979) and Immelmann & Suomi (1981) reported individual variation in preference between zebra finch males which had been raised by Bengalese finch foster parents for the same amount of time and subsequently placed for an equal amount of time with a group of conspecifics. Although they ascribe this variation to supposed genetical differences between individuals, differences in behavioural experience may also be involved, since it seems unlikely that the Bengalese finch foster parents and the zebra finches in the group of conspecifics all behaved identically to all zebra finch males. Another source of variation may have

Research on the development of sexual preferences is often conducted by raising young animals of species or morph A with adults of species or morph B. When A is mature, the preference for A or B is measured. Such experiments have clearly shown that early experience affects later partner choice (e.g. Warriner et al. 1963; Schutz 1965; Immelmann 1972a, b; Gallagher 1976). They give information on factors like the age at which the preference is established. Further, insight can be gained into the kind of objects, species or morphs to which sexual behaviour can be directed as a result of early experience. They may also give information about whether a preference for the own species or morph is stronger or develops more easily than one for a foster species. For instance, Immelman (1972a, b) came to the conclusion that the preference for zebra finch females in normallyraised zebra finch males is stronger than that for Bengalese finch females in zebra finch males raised by Bengalese finches. He considered this to be a consequence of a bias towards responding to characteristics of their own species. Preferences for objects of certain colours and/or shapes over others without prior exposure to them have also been found in filial imprinting (e.g. Slucking 1972). Such initial preferences may be the causal factor for an own-species bias too. However, the evidence for initial preference in filial imprinting is mostly based on experiments using a short exposure time and non-living objects as stimuli (e.g. Slucking 1972). In contrast, experiments on the development of sexual preferences, especially when carried out with altricial birds such as 852

TEN CATE ET AL.: ZEBRA FINCH SPECIES RECOGNITION been the number of siblings of the males used in their study. Kruijt et al. (1983), comparing the histories of differently-choosing zebra finch males, which were all raised by Bengalese finch foster parents for an equal amount of time, showed that the presence of siblings during rearing influenced their later partner choice. This sibling influence had hitherto not been recognized as important in the development of partner choice in zebra finch males. In addition to the analysis outlined above, another approach can be adopted in which birds, raised for the same period and with individuals of the same appearance, are exposed deliberately to different behaviour by their companions. An example of this is a series of experiments carried out by one of us on zebra finch males raised by pairs in which one parent is a zebra finch and the other a Bengalese finch. By manipulating the behaviour of the zebra finch parent the social experience of the young zebra finch males can be influenced (Ten Cate, in preparation). The present study investigates the influence of social experience on the development of sexual preferences in zebra finch males. Young males were raised for about 30 days by their own parents and then, for about another 30 days, placed in a group of Bengalese finches. These males showed a considerable variation in preference when given the choice between a zebra finch and a Bengalese finch female. The influence of the number of siblings before day 30 and of Bengalese finch group size and differences in experience with Bengalese finches between 30 and 60 days on the variation in preference are investigated. Another experiment was carried out by placing 30-dayold zebra finch males either in a group of six or seven Bengalese finches; or in a cage with such a group but separated from it by wire, or in a cage containing six or seven stuffed Bengalese finches. The effect of this experimental reduction of the behavioural experience with Bengalese finches is investigated. Immelmann (1979) has reported that some of the zebra finch males raised by Bengalese foster parents first and then given breeding experience with their own species as adults, in later preference tests showed a shift in choice from zebra finch to Bengalese finch. For this reason the short term stability in preference of the birds used in our study is also investigated. Methods Zebra Finches In identical breeding cages, each containing one zebra finch (Z) pair with young, young were

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sexed daily from day 25 onwards. As soon as male plumage characteristics were observed in a young bird, it was placed in one of three situations: (1) In a group containing only Bengalese (B) finches. The birds treated this way were designated the 'full contact group'. (2) In such a group but separated from the Bs by iron wire. Birds treated this way were designated the 'wire group'. (3) In a cage containing only stuffed Bs. Birds treated this way were designated the 'model group'. In most cases, day of transfer was 30 or 31 (day of hatching=day 0). The number of siblings present on day 25 was noted. Mostly, Z males stayed 28 or 29 days in such a group. Afterwards they were placed singly in small cages, visually isolated from each other. The isolation room contained only Z males and females. After reaching sexual maturity (about day 95) the males were tested for their preference between a Z and a B female. Full Contact Group Forty-seven Z males were placed in full contact with a group of Bs. The number of Bs per group varied between 1 and 55, however, most (40) groups contained either 3, 4, 6, 7, 11 or 12 Bs. Most groups consisted of B males and females, and contained both individuals raised by their own species and individuals raised by Zs. The B groups were all housed under comparable circumstances: artificial light (12L: 12D or l l L : 13D) and always more than one B group per room (care was taken that no visual contact could occur between different groups). Food and water were always available. Cage size varied according to group size. Groups consisting of four Bs or less were placed in iron wire cages measuring 50 x 50 x 50 cm; groups of five to 12 inclusive in cages measuring I00 x 50 x 50 cm; and groups of more than 12 ( N = 5) in larger cages of variable sizes. All cages contained a number of perches and sand and grit were present on the bottom. Wire and Model Groups The wire group consisted of 11 Z males. These were each placed in a U-shaped iron wire cage placed in the middle of a 100 x 50 x 50 cm cage containing six or seven Bs. The wire consisted of two parallel screens with a 3-cm space in between preventing physical contact. The model group consisted of nine Z males. Each male was placed in a 100 x 50 x 50 cm cage containing six or seven stuffed Bs, which were spread over the whole cage.

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The housing conditions of the wire and model groups were similar to those of the full contact group.

Behaviour Recorded In some of the groups containing four, six, seven or 12 Bs, and in some of the wire and model groups, observations were carried out on 3-4 days. An observation period usually lasted 2-3 h per day and was either in the morning or in the afternoon. In 10 B groups, each consisting of three Bs (one B male and one B female raised by Z, and one B female raised by B), the behaviour shown towards the young Z male was extensively recorded on 7-8 days (4 days in the first 10 days, 3-4 days in the rest of the period in the B group). On an observation day, the group was observed for five periods of 1 h, separated by periods of 1 h. In this way the effects of possible daily variations in the behaviour were the same for all birds and all observation days. Of the following behaviour patterns the frequency ( f ) and/or duration (d) were recorded. More extensive descriptions are given in Morris (1954) and Immelmann (1959, 1962). (1) Clumping ( f and d): two or more animals perching no more than 3-4 cm apart. It was noted which birds initiated clumping and which one broke off, (2) Allopreening ( f ) : this could only occur during clumping. It was noted which animal was the preener and which was the receiver. Every preening movement was scored. (3) Directed song ( f ) : this is only shown by male B and Z and is a behaviour involved in pair formation. Song consists of bouts of elements (strophes) mostly repeated several times. The number of song bouts was recorded. (4) Sexual behaviour ( f ) : copulation or attempted copulation (mounting). (5) Greeting (f). (6) Threatening (f). (7) Aggressive pecking (f). (8) Chasing and supplanting (f). These patterns of behaviour were only recorded when shown towards or by the Z male. Choice Tests For determining sexual preference, a male was put in a cage with two identical side-cages, one containing a Z female and the other a B female, both raised by Z parents. Each test lasted 30 rain; after 15 min the two side-cages were exchanged. Every male was tested two or three times per 14 days until he had sung in five tests. For each test the preference ratio was calculated in two ways:

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(1) song ratio = number of strophes to Z female total number of strophes to Z female + B female (2) time spent ratio = amount of time spent near the Z female total amount of time spent near both females 'Near' means in that quarter part of the test cage on the side of the female. The preference ratios of the five tests were averaged, giving a value between 1 (absolute preference for the Z female) and 0 (absolute preference for the B female).

Results (1) Full Contact Groups Choice tests of Z placed in normal B groups. Figure 1 shows the distribution of the song ratios of all Z males. Large individual differences were found: 16 birds sang exclusively to the Z female, 16 others sang to both but preferred Z over B and 15 had a preference for B over Z. The stability over the tests was analysed for the 31 birds singing for both females. For these males the mean song ratio over the first two tests was compared with the mean song ratio over the last two tests. According to Immelmann (1979), the influence of the first exposure period, i.e. to the Z parents in our study, is dominant. Therefore, an increase in song ratio was expected. This was found in 21 males, while 10 showed a decrease 22

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TEN CATE ET AL.: ZEBRA F I N C H SPECIES R E C O G N I T I O N

(two-tailed sign test: P = 0.10). A further analysis showed that males initially having a song ratio of i> 0.50 differed significantly from males having a ratio of < 0.50 in the direction of change (Table I, Fisher's test: P = 0.018, two-tailed). Males with a ratio of >/0.50 showed a significant increase in singing for Z over the series of tests (twotailed sign test: P = 0.002). No significant change was found in males with an initial song ratio of <0.50. Influence of experience with Z. In males having three or four siblings on day 25, the song ratio tended to be higher (0.80) than in males having no, one or two siblings (0.65; two-tailed M a n n Whitney U-test: P=0.087). N o evidence for different effects of male and female siblings could be found. Influence of experience in the B group. Although males out of a group of six Bs seem to have most interest in B females (Fig. 2), no significant relation between group size and song ratio could be found. Figure 2 also shows the considerable variation in song ratio existing among males placed in groups of the same size. Although the observations on the behaviour of groups of four, six and 12 Bs are limited in number, allowing no reliable quantitative analysis, they gave no indication of differences in amount of behaviour towards the Z males associated with group size. However, we observed that different B groups could show different behaviour towards Z males, for instance in some groups contact between Bs and Zs seemed to be mainly aggressive, in others little aggression and much dumping was observed. For this reason 10 Z males were observed in more detail. These males, which had all been placed in a group of three Bs, varied in song ratio between 0.34 and 1.0 with an average of 0.84. It was examined whether differences in experience with Bs among these males were correlated with differences in later song and time ratios (both ratios are correlated with each other r=0.933, P<0.01). The Table I. Direction of Change in Song Ratio Comparing the

Mean Song Ratio per Bird over Tests 1 and 2 with the Ratio over Tests 4 and 5 Mean song ratio

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ratios of the Z males were compared with the mean value per observation day for the different behaviour patterns shown towards the Z male by all Bs together. This was done for two periods: the first 10 days in the B group and the whole period. The first 10 days were chosen as a separate period since the work of Immelmann (1972a) indicated that experience with Bs before the age of 40 days has a much greater influence on the later preference than experience occurring later on. Some patterns of behaviour (greeting and sexual behaviour) occurred so infrequently that no relation to the preference ratios could be made. For the other activities shown by Bs to Zs the correlation coefficients over the first 10 days between the ratios and the behaviour, and of the different behaviours among each other are given in Table II. A significant negative correlation was found only between the number off d u m p i n g initiatives of Bs that were not broken off by Bs within 3 s and the choice ratios. All 9 showed no relation with the choice ratios, but a negative correlation is present if one bird with a song ratio of 1.0, which came from a B group in which the B male showed abnormal intensive all 9 behaviour, is left out. Over the whole period, all correlation coefficients between the ratios and the behaviour patterns were lower, except for directed song, which showed a significant negative correlation with both ratios (song ratio: r = - - 0 . 6 7 7 , P < 0 . 0 5 ; time spent ratio: r = - - 0 . 7 3 2 , P<0.01). So it seems that, especially in the first 10 days, the more behaviour

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TEN CATE ET AL. : ZEBRA FINCH SPECIES RECOGNITION

is shown by Bs towards the Z male, the more Bdirected the later choice is. However, the relation is only weak. A complicating factor in the analysis is the relations of the different behaviour patterns with each other. Aggressive behaviour (pecking, threatening and chasing and supplant together) shows a non-significant negative correlation with the choice ratios. It further shows a significant negative correlation with clumping (Table II). Non-aggressive behaviour (number of clumping initiatives; directed song; sexual behaviour and greeting together) shows a significant negative correlation with the choice ratios (Table II). A simple addition of aggressive and non-aggressive behaviour shows no better relation with the choice ratios than the separate behaviours do (Table Ii). This may be caused by differences between the effect of one aggressive and one nonaggressive contact on the later choice. This was investigated further by carrying out a multiple regression analysis on the effects of both behavioural types on the preference ratios. A strong relation between the ratios and both behaviour patterns was found (P < 0.01) being expressed for the song ratio as: song ratio = 1.45 -- 0.0029 x no. aggressive initiatives -- 0.0114 x no. nonaggressive initiatives and for the time spent ratio as: time spent ratio = 1.15 - - 0.0018 x no. aggressive initiatives -- 0.0073 x non-aggressive initiatives. The correlation coefficients between the number of initiatives shown by Zs towards Bs and the choice ratios were not significant (in both first and whole period: P > 0.10). When further analysed in the same way as has been done for the behaviour of Bs towards Zs, no better relation between the behaviour shown by Zs towards Bs and the later preference of the Z males could be found.

Figure 4 shows that the three groups differ not only in mean choice, but also in the short-term change over the five tests. Comparing the average song ratio per male in tests 1 and 2 with the ratio in tests 4 and 5, Z males from the wire group increased in song ratio (direction of change: plus,

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(2) Experimental B Groups Choice tests. The song ratios of the 11 Z males from the wire group and the nine males from the model group were compared with the song ratios of the 14 males that were placed in a normal group of six or seven Bs, and which thus had a number of Bs similar to that in the wire and model groups (Fig. 3). Birds exposed to models showed a higher song ratio than birds exposed to Bs from behind a wire screen (Mann-Whitney U-test, P < 0.001, one-tailed) or birds out of the normal B group (Mann-Whitney U-test, P < 0.025, one-tailed). The difference between males f r o m the wire group and birds from the full contact group was not significant.

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N = 1 0 ; minus, N = I ; sign test, P=0.006), whereas males out of the model and the full contact group did not (direction of change: plus, N = 2 ; minus, N = 1; no change, N = 6 and plus, N = 6; minus, N = 4 ; no change, N = 4 respectively). In every separate test the difference in song ratio between the model and the full contact group was significant: the wire group differed significantly from the model group in tests 1 and 2 and significantly from the full contact group in test 5 (Mann-Whitney U-test, in all cases P < 0.05, one-tailed). These results suggested that the three groups differed in average choice, as well as in shortterm change. As has been mentioned before, a shift in ratio may be related to the preference over the first two tests. Therefore the relation between mean ratio over tests 1 and 2 and the direction of change, comparing this ratio with the one over tests 4 and 5, was analysed for the wire and the full contact group (Table III). When analysed in this way, the two groups showed no difference. It may therefore be concluded that the difference in short-term change between these groups was a consequence of the difference in initial preference and not an independent variation caused by the different treatment of the males. B e h a v i o u r a l e x p e r i e n c e in e x p e r i m e n t a l groups.

Occasional observations were carried out on nine Z males in the full contact group (4-16 h/bird), on one male of the wire group (5 h) and on four males of the model group (8.5-12 h/bird). These observations were too few in number to use for a quantitative analysis, but gave some information about whether a certain behaviour was shown at all. Directed song was observed towards the Z male out of the wire group. It was also observed that the Z male and a B sat on the same perch, both against the wire separating them, in a way comparable to clumping. It was further noticed Table HI. Direction of Change in Song Ratio Comparing the Mean Song Ratio per Bird over Tests 1 and 2 with the Ratio over Tests 4 and 5

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that the Z male was attracted by a B approaching the cage and Bs as well were sometimes attracted when the Z male approached the wire. These observations suggested that, although the possibility of interaction was reduced, only the behaviour involving bodily contact (allopreening, pecking) did not occur in the wire group. All four observed Z males in the model group showed aggressive behaviour (pecking), allopreening and clumping towards the model. This was also the case for all nine observed Z males in the full contact group, although there the behavviours were directed towards living Bs. Directed song towards models was observed in three out of four Z males, and song towards living Bs in six out of nine Z males. The observations suggest that no differences were present between the behaviour shown towards models and towards living Bs. The only difference we noticed was that Z males in the model groups seemed to utter 'contact' calls more frequently than in any other group, birds in neighbouring cages often stimulating each other. Discussion

At least some of the Z males that were placed in a B group after day 28 became B-directed in their later preference. Our findings indicate that experiential differences in behaviour shown towards the Z young may be an important source of variation in the preference ratios. Whether, as the results suggest, an influence of siblings in the period when the Z are still with their parents is present needs further investigation. Especially important seems to have been the exposure to behaviour of Bs in the first 10 days after transfer to the B group. Both aggressive and non-aggressive initiatives from Bs are related to a more B-directed preference. Non-aggressive initiatives were more important than aggressive ones. The behaviour of Zs shown towards Bs showed no relation to the later preference. Whether the correlations may be interpreted as causal relations remains open for the moment. There are, however, some indications that this may be the case. First, if the relation between the behaviour shown by Bs and the later choice was based on some quality of the Z males, making them evoke behaviour by Bs, one would also expect a relation between the behaviour shown by Zs towards Bs and their later choice. N o such relation was found. Second, the findings in the experimental groups are as one would expect if a causal relation between the behaviour by Bs and the later choice was involved. In the wire group

TEN CATE ET AL.: ZEBRA FINCH SPECIES RECOGNITION only limited possibilities for interactions between the Z male and Bs were present and here a tendency for a more Z-directed preference was found. The preference was most Z-directed in the model group. Here Z males did show social behaviour towards the B models but these, of course, did not show any behaviour towards the Z males. I f the regression equations found in the groups of three Bs may be interpreted as a causal relation, a song ratio and a time spent ratio of 1.0 are expected in the model group. The average song ratio was 0.97 and the time spent ratio 0.79, which, at least for the song ratio, matches the predictions rather well. However, further experiments will be necessary to investigate the causal relations and furthermore, whether in that case the development of a preference is based on a combined effect of some specific behaviour patterns or of a more general effect of interactions involving approaching or just 'doing something' towards the young Z males. That exposure to models m a y still have some influence is indicated by three males f r o m the model group that showed some interest in the B female in the choice tests. This may indicate that the own behaviour of the Z male or the visual exposure to B models has some additional influence on the development. Functionally, an arrangement by which different aspects of the behaviour towards young Z have influence appears to be understandable. This may be the surest way to lead to a preference for the species rearing the young birds since the relations and the kind of behavioural interactions between parents and Z young change strongly during development (Ten Cate 1982). I f only parental care, or social behaviour like clumping and allopreening, or sexual, or aggressive behaviour was of importance, then only part of the interactions and a much more limited period during development would be suitable for the establishment of a preference with a larger risk of something going wrong. In contrast to our findings, it has been stated that when raised with its own species up tO day 20 (Immelmann 1972a) or day 22 (Immelmann & Suomi 1981) the preference for the own species is fixed. Several factors may be responsible for this difference. First, these conclusions are based on four males which were over 22 days old when transferred to Bs (Immelmann & Suomi 1981). Since in our study two-thirds of all males transferred to Bs on day 30 or 31 showed a preference for Zs over Bs, it may be that, if more birds had been used, they also would have found some B-

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directed males. An indication for this is that, of five males transferred on day 22, two showed a preference for Bs over Zs (hnmelmann & Suomi 1981). Second, they transferred a complete Z clutch, while we transferred one single Z male to a B group. The presence of siblings may have given rise to a more Z-directed preference in their experiments. Third, in the experiments reported by Immelmann & Suomi the males were transferred to one B pair, while we transferred a male to a B group of usually more than two individuals. The latter may have given rise to a more Zdirected preference since our results (Fig. 2) suggest that a decrease in ratio is present between males which had experience with one or two and those with six Bs. A fourth reason may be that the duration of exposure to Bs in our study was probably somewhat longer than in Immelmann's study, since the data he presented in 1972a show an exposure time to Bs of 16 days for three out of five males transferred after day 20 to Bs. In another experiment Immelmann (1979) and Immelmann & Suomi (1981) showed that Z males which were raised by B parents for about 30 days and subsequently transferred to Z females for periods of 3 to 60 days, were more strongly Z-directed the longer the exposure to the Z females lasted. It is likely that in the opposite situation, as realized in our experiment, the same will happen, so our Z males may be expected to be somewhat more B-directed (however, this is possibly partly counteracted by the later transfer from Zs to Bs in our study). Finally, in choice tests, we used B females raised by Zs, while Immelmann probably used normally-raised B females. We have some evidence that this difference may influence the preference, stimulating a more B-directed preference when B females raised by Zs are used. Over a series of tests a Z-directed shift in choice occurred during testing. This may be explained as a result of a dominating first exposure (Immelmann 1979; Immelmann & Suomi 1981), which was to Zs in our case. However, this shift was mainly shown by those males that already showed a preference for Zs over Bs for the first two tests. The males that had a preference for Bs over Zs remained on average stable in their choice. Therefore, alternative explanations may be that during testing the initial choice becomes more pronounced or that the birds respond more selectively to the cues provided by the stimulus birds. Such a change may have been caused by processes prior to and independent of testing, or by incorporating experience with the choice

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birds during the tests. That shifts in preference can, at least theoretically, occur independently of later experience is shown in a model developed by Bateson (1981). On the other hand Bischof (1979) mentions some experiments done by I m m e l m a n n which indicate that testing itself can have influence on the later preference o f Z males. That the shift is more clearly shown in originally Zdirected males compared with B-directed males m a y be due to differences in responses between Z and B females. We are doing some further experiments on this p h e n o m e n o n at this moment. The result that behavioural interactions seem to be important in developing sexual preferences leads to the conclusion that more attention must be given to the behaviour o f animals used as stimulus objects in imprinting studies. This is especially important when the preference for the own species of normally-raised animals is compared with that o f cross-fostered animals for their foster species. Behavioural differences between own and foster species may, rather than initial preferences o f the young, have been responsible for such an own-species bias. This was suggested by Ten Cate (1982) as possible for the Z-directed preference shown by most Z males raised by mixed pairs o f Zs and Bs. In these pairs Z parents showed more parental care and more aggression towards the Z y o u n g than B parents and most clumping occurred with the Z sibling. O u r present results indicate that clumping as well as aggression directed towards y o u n g Z males by Bs can indeed stimulate a later preference for individuals o f that species. Because o f the probable importance o f behavioural interactions for the development o f preferences, experiments on sexual imprinting should not only use the 'classical' imprinting experiment as outlined in the introduction, but also use description o f the development o f early social contacts, for instance in the way Hinde (1979) has suggested for the study o f relationships.

Acknowledgments We thank Professor D r J. P. Kruijt for discussions concerning this study. He and D r P. P. G. Bateson, D r I. Bossema and D r G. J. de Vos made helpful comments on the manuscript. F u r t h e r m o r e we thank J. van der Veen for his assistance in collecting the data, L. H o e k s t r a for preparing the models, A. Nolle and S. Veenstra for taking care o f the birds, D. Visser for preparing the figures and H. Lochorn-Hulsebos and J. Poelstra-Hiddinga for typing this and earlier versions:of the manuscript.

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