Positive correlations of brood size with some parental activities [vigilance (in females), approaching young (in males and females), and attack (in males)] and a negative correlation of female feeding time with brood size were found in a sample of 23 semicaptive Bar-headed Goose (Anser indicus) families. Detailed examination of these correlations suggests that some components of parental care in geese represent "shared parental investment" (Lazarus and Inglis 1978, 1986). The benefits of parental care are divided among the offspring, so that in precocial birds, as in altricial birds, clutch size may be adapted to selection pressures that act after the young hatch. Received 27 October 1986, accepted 4 May 1987.

Max-Planck-Institut far Verhaltensphysiologie, D-8131 Seewiesen, West Germany CLUTCH size in altricial birds appears to be a compromise between the number of young that could be raised to breeding age and the costs of parental care in terms of the parents' future reproduction or survival (Perrins 1965, Char- nov and Krebs 1974, Stearns 1976, Drent and Daan 1980). Models usually assume an increase of parental effort with brood size. They seem inapplicable to the post-hatching period in pre- cocial birds that do not feed their young and for which parental care after hatching is gen- erally assumed to be "unshared" (Lazarus and Inglis 1978, 1986). In this case the total benefit of a parental act (vigilance, defense, etc.) is gained simultaneously by each of the young. Unshared components of parental care should thus be independent of brood size. Wittenber- ger (1979) used. the terms "shareable" (for "un- shared") and "non-shareable" (for "shared"), which may give rise to serious semantic con- fusion. We adhere to the terminology of Lazarus and Inglis. In the precocial Semipalmated Sandpiper (Calidris pusilla) the number of hatchlings the parents can ra:ise is limited (Safriel 1975), but there is still no clear evidence that the amount of parental activities varies with brood size in precocial birds. Such variation can indicate shared components of parental care where the benefit of a parental act is divided among the offspring so tlat each receives only a portion of it. Trends of increased parental vigilance and decreased feed.ing time with brood size were reported for Greater White-fronted Geese (An- To whom reprint requests should be sent. ser albifrons; Madsen 1981) and for the Southern Lapwing (Vanellus chilensis; Walters 1982), but no such relationships were found in the Pink- footed Goose (Anser brachyrhynchus; Lazarus and Inglis 1978) (for a review see Winkler and Wal- ters 1983). We sought correlations between parental ac- tivities and brood size in Bar-headed Geese (An- ser indicus) to test the assumption of unshared post-hatching parental care. Pains were taken to differentiate between parental ability influ- encing brood size and parental effort conse- quent upon brood size. METHODS The semicaptive flock of about 100 individually banded, unpinioned birds lived on the Max Planck Institute lake (7.2 ha) in southern West Germany. A fenced area of about 1,000 m 2 of grazing land was available, and ad libitum pellet food provided in a trough was located near the lake (further details were given by Lamprecht 1986). Summer correlations.--We watched the tame birds from 10-20 m distance from May to July. Time-budget data for 14 pairs were collected in 1981 and for 9 pairs, including 4 from the previous year, in 1982. For each of the 23 pairs, 3-h observations were made at 4-day intervals from day 2 to day 30 after the brood hatched, then at 5-day intervals until day 50, when the young were close to fledging. Thus, each pair was observed for 36 h in total. Roughly equal morning and after- noon observations were assigned for each pair to avoid any effects of diurnal activity changes. During the 3-h observations we recorded the fol- lowing activities for each parent after each 5-min in- terval: feeding (head low with intermittent pecking at grass or food pellets), head up (head raised, bill held horizontal or lower), threatening (all neck positions from extreme head up with bill raised high to head- 2.0 1.5 1.0 0.5 0 6O 40 2O 40 20 Mean brood size Mean brood size Fig. 1. Significant relationships of activities of female (left) and of male (right) parents with mean brood size. Each dot or cross represents the data of one parent. Solid lines connect data points of the three pairs in different years; crosses refer to a fourth pair with the same brood size in both years. For correlation coefficients see Table 1. forward posture directed toward another bird), preen- ing, sleeping (bird motionless, underside of bill touch- ing breast or back), brooding (covering young with wings), swimming, walking, standing, and lying. The last four categories were not exclusive of the others. We determined the percentage of each activity in all 12 observations for each parent (i.e. 36 h; Table 1, Fig. 1) or in different intervals of the entire rearing period (Table 2). This provided a relative measure of the time attributed to the various activities. Short- term events like attacks (dash at another bird with head held forward) and approach young (clearly ori- ented movement toward own offspring more than 2 m away or distress calling) were recorded as they occurred, and frequencies per hour determined for each parent. Finally, we correlated the duration of long-lasting behaviors and the frequencies of short-term events with the mean number of young that accompanied each pair on all observation days (Table 1) or during the respective intervals (Table 2). Brood size was not constant because some goslings died. One to 4 well-developed eggs (which later hatched in an incubator) were removed from three nests. In contrast to this reduction of brood size, one pair did not hatch young but adopted 4 goslings (3 survived), another pair adopted 2 young in addition to their own 3, and a third pair with 3 young adopted 1 gos- ling. An estimate of a pair's "potential mean brood size" was obtained by adding the number of surviv- ing incubated goslings to the actual mean brood size, and subtracting the number of young adopted. Thus, TABLE 1. Spearalan rank correlations between mean brood size and parental behaviors during the rear- ing period. a Values in parentheses are correlations with the estimated potential mean brood size. TABLE 2. Spearman rank correlations between some parental behaviors in summer and actual brood size in different intervals of the rearing period. a n = 23 pairs. Behavior Males Females Feeding -0.13 -0.57*** (-0.31) Head up 0.21 0.43* (0.34) Threatening -0.34 -0.20 Preening 0.24 - 0.08 Sleeping 0.17 0.24 Brooding -- 0.15 Walking - 0.004 -0.04 Standing -0.29 -0.15 Lying 0.30 0.21 Swimming -0.03 -0.002 Attacks 0.49** (0.19) 0.31 Approach young 0.64*** (0.39) 0.54*** (0.49**) . * = P < 0.05, ** = P < 0.02, *** = P < 0.01. actual brood size differed from potential brood size in 6 pairs, actual to potential mean brood size being 1 to 2, 1 to 3, 1 to 5, 3.36 to 3, 4 to 3.14, and 3.1 to 0. The durations and frequencies of parental behavior significantly related to actual mean brood size were correlated with potential brood size. This was to test whether these behaviors were predictive of potential rather than actual brood size, thus indicating parental ability rather than brood-size-dependent parental ef- fort. Spring correlations.--We investigated whether be- havioral differences between pairs in spring could be used to predict brood size. We collected time-budget data for pairs in March 1983, before laying. Three to 5 times daily, with intervals of at least i h, each pair was located in a pre-set order and the activity (feed- ing, head up, attack, or threat) of each mate noted after 1 min. Any threats or attacks were also noted during the following minute. Each was obserxed for 60-80 min. We expressed head up and feeding as the percentage of observation minutes starting with this behavior, and tee frequencies of attacks and threats as the percentage of observation minutes containing at least one such event. The behavior durations or frequencies in the 13 successfully breeding pairs were correlated with sbsequent brood size measured when the family left the nest. All P-values for Spearman rank correlation coeffi- cients are two-tailed. RESULTS Summer correlations.--Brood size correlated positively and significantly with approach young and attack rates in male parents and with time spent head up and rate of approach young in females, and negatively with female feeding time (Table 1'). These relationships also Age of young (days) Behavior 2-14 18-30 35-50 Female Feeding time (%) -0.54 .... 0.49** -0.12 Head up time (%) 0.55*** 0.24 0.38 Approach young/h 0.20 0.52** 0.40 Male Attacks/h 0.41 0.36 0.30 Approach young/h 0.64*** 0.62*** 0.31 ß ** = P < 0.02, *** = P < 0.01. applied to all three pairs with different brood sizes in the 2 yr (connected points in Fig. 1). The values of one pair that had the same num- ber of young in both years tended to be re- markably similar. Except for approach young in females, Spearman correlations for the five parental behaviors above with potential brood size were not significant (P > 0.05; Table 1) and were lower than the correlation between actual and potential brood size (r = 0.56, n = 23, P < 0.01). For these five parental behaviors, correlations with mean actual brood size were calculated separately for three parts of the rearing period (Table 2). Except for female approach young, correlations were higher when goslings were young. Spring correlations.--Only female head up and threats correlated significantly with subsequent brood size (Table 3). All other correlations were not significant. DISCUSSION Parental age was not related to actual or po- tential brood size (maximum Spearman corre- lation coefficient r = 0.16, P > 0.2) and cannot account for our results. Correlations with brood size do not indicate directly that behavior du- rations or frequencies are consequences of brood size. This interpretation is suspect if a spring behavior correlated significantly with future brood size just as it did in summer, and if the behavior in summer correlated higher (or equally high) with potential than with actual brood size. We found that only three parental behaviors, female feeding time, male attack rate, and mal rate of approaching young, met these criteria. They are more likely to be conse- quences than determinants of actual brood size, and their dependence on brood size is indica- tive of shared components of parental effort (see introductory paragraphs). Only these three be- haviors will be discussed further. Relationships between parental effort and brood size will affect clutch size only if the parents incur costs in terms of survival, future reproductive success, or both. Male approaches toward young and attacks were infrequent (Fig. 1). Although these activities expend energy, and attacks may also induce injury, male parental costs may be too small to affect the evolution of clutch size. In females, however, brood-size- dependent costs of parental care may be linked with substantially reduced feeding time (see Fig. 1) and thus induce a slower or incomplete re- placement of nutrients lost during incubation. In some goose species, female feeding rates and nutrient reserves are important for subsequent reproductive success (Ryder 1970, Harvey 1971, Ankney and Macinnes 1978, Aldrich and Rav- eling 1983, Prop et al. 1984, Teunissen et al. 1985). Reduced feeding time in large families does not mean necessarily that females eat less. At least three alternatives exist. (1) Females feeding more efficiently may build up more reserves, and consequently lay larger clutches (Ankney and Macinnes 1978), breed more effectively (Aldrich and Raveling 1983), or both. Such birds would have more young while needing less time to feed. We found that clutch size did not correlate with brood size (rs = 0.04, n = 23; see also Lamprecht 1986). Further, the body mass of paired females mea- sured in January (1982 and 1983) or March (1983) did not correlate with the number of young leaving the nest in early summer (January 1982: rs = 0.03, n = 24; January 1983: rs = -0.08, n = 29; March 1983: rs = 0.19, n = 27). We believe this lack of correlation was due to a supera- bundance of food. (2) If females with large families selected the more nourishing pellet food over grass, they could reduce feeding time. The correlation be- tween the number of young and the proportion of time females fed on pellet food (measured only in 1982) was not significant (rs = -0.10, n = 9) and contrary to expectation. (3) If large families tended to feed in less exploited areas, the females might need less time to become satiated. Time spent in less frequent- ed areas with higher grass was not correlated with brood size (r = 0.05, n = 23), however. TABLE 3. Spearman rank correlations between pa- rental behaviors in March and subsequent brood size. Behavior Males Females Feeding 0.20 - 0.03 Head up -0.21 0.65** Threats - 0.18 0.57' Attacks - 0.09 - 0.27 a * - p < 0.05, ** = P < 0.02. None of the alternative explanations hold, and we believe females with more young have higher nutritional costs that may limit brood size to a level below the maximum possible. It would be inappropriate to generalize re- suits from one field population to another when environmental conditions are different. We thus cannot be confident that our results, obtained under conditions of semicaptivity and super- abundance of food, also apply to geese in the wild. In fact, the superabundance of food in our flock apparently obscured the positive relation- ship between female feeding time in spring and subsequent reproductive success, which was demonstrated for Barnacle Geese (Branta leucop- sis) in the field (Prop et al. 1984). We also found no relationship between male attack rate in spring and future brood size (Table 3), but it is difficult to imagine how, under the same con- ditions, the dependence of brood size on female feeding time and male attack rate could arise as an artifact in summer. Some justification for a more general validity of our results comes from the few field studies available. The correlations of parental vigilance and feeding with brood size reported for Greater White-fronted Geese and Southern Lapwings agree with our findings, in spite of the low numbers of individuals and possible influence of parental ability. In addition, the "sitting time" of parents decreased with brood size in Snow Geese (Chen caerulescens caerulescens) (Lessells in press). Lazarus and Inglis (1978) found no such correlations in a field study of Pink-footed Geese, probably because observations began at a gos- ling age of about 4 weeks. We found that cor- relations of female feeding time and head up and of male attacks and approach young with brood size tended to be higher early in the rear- ing period and decreased over time (Table 2). Brood sizes observed in the two years of our study (see Fig. 1) were within the normal range of the flock, for which brood size upon leaving the nest averaged 2.58 young (range 1-6, n = 130 broods in ] 975-1986). Mean gosling mor- tality until fledging was 22.3%. Field records of brood sizes in Ear-headed Geese are rare: Schi- fer (1938) counted 3-8 well-developed eggs per clutch and observed that only 1-3 young (more rarely 4-5) fledged. Clutch sizes of 4-8 eggs (mostly 4-6) were reported by Dementiev and Gladkov (1967) and of 2-10 eggs (mostly 4-5) by Kydyraliew (1967), but no information on brood size or hatching rate was given. Lessells (1986) found in Canada Geese (Branta canadensis) that from one molt to the next, fe- males with larger broods had lost more mass (or gained less) than those with smaller broods. She was unable to show, however, that brood size affected parental survival or future fecun- dity in the stat:[onary population studied. In the migratory Tundra Swan (Cygnus colum- bianus bewickii) both males and females accom- panied by cygnets had a lower return rate to the wintering grounds than adults with no off- spring (Scott 1980: table 2). Although these dif- ferences were not quite significant, they sug- gest some survival costs of parental care. Proof is still wanting, but in migrating populations brood-size-dependent energy costs and food deficits may lower the parents' survival, future reproductive success, or both. Clutch size in such nidifugous birds may be adapted to selec- tion pressures acting after hatching, as is ap- parently true in altricial birds. In geese, selection pressures that limit clutch size might be counteracted by the effect that larger families tend to be more dominant in wild flocks (Bc.yd 1953, Hanson 1953, Raveling 1970). In competitive situations females of dom- inant pairs feed more and will breed more suc- cessfully in the following season (Teunissen et al. 1985, Lami?recht 1986). Successful adults, however, do not adopt stray goslings to increase family size. Orphans older than a few days are always rejected. by other families, indicating that the optimum brood size is smaller than maxi- mum (Black and Owen 1984). As no effect of sibling competition was found (Black and Owen 1984, Lessells 1986), reluctance to adopt gos- lings may be clue to the costs involved in rear- ing additional young. ACKNOWLEDGMENTS We thank A. Wosegien for help with the collection of the spring data. J. M. Black, H.-U. Reyer, U. Safriel, F. Trillmich, P. Watson, W. 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