An analysis of weight changes in the Mute Swan Cygnus olor

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1 Bird Study ISSN: (Print) (Online) Journal homepage: An analysis of weight changes in the Mute Swan Cygnus olor P. J. Bacon & A. E. Coleman To cite this article: P. J. Bacon & A. E. Coleman (1986) An analysis of weight changes in the Mute Swan Cygnus olor, Bird Study, 33:3, , DOI: / To link to this article: Published online: 05 Nov Submit your article to this journal Article views: 249 View related articles Citing articles: 8 View citing articles Full Terms & Conditions of access and use can be found at

2 Bird Study (1986) 33, An analysis of weight changes in the Mute Swan Cygnus olor P.J. BACON Institute of Terrestrial Ecology, Merlewood Research Station, Grange over Sands, Cumbria LA11 6J11 A.E. COLEMAN 67 Park Lane, Bonehill, Tamworth, Staffordshire The weights of Mute Swans contain useful information on individuals' prospects for survival and breeding but to interpret them one needs to know what 'typical' weights would be. This paper uses multiple linear regression to predict such 'typical' weights: 1968 zveighings of 957 Mute Swans, from south Staffordshire, England, are analysed with respect to sex, age, moultstage, month of capture and breeding status. Because of marked sexual dimorphism, knowing a swan's sex is fundamental to interpreting its weight; age from hatching and stage of primary feather growth affect cygnets' weights near fledging; weights of young swans change with age during their first years of life; primary feather moult significantly depresses the weights of first year males but not, in this study area, of older males or females; monthly, seasonal changes are generally small; breeding adults are significantly heavier. The results and their biological implications agree well with other, less comprehensive, analyses. The method described could facilitate both the identification of other factors that should be investigated and comparisons between different study areas. W eight is a simple and informative measure to take of birds in the field and many studies have shown that weights can be usefully used as indices of a bird's condition. In the Mute Swan, Cygnus olor for example, heavier cygnets survive better (Andersen- Harild 1981), older swans are heavier (Reynolds 1972), heavier males and females are more likely to breed (Reynolds 1972) and lighter swans are more likely to be suffering from lead poisoning (Simpson, Hunt & French 1979). 'Heavy' and 'light' are relative terms and it would be useful to be able to predict what the weight of a swan ought to be, in terms of sex; age, breeding status, moult stage, etc., and thereby quantify the weight discrepancy. For example: the paper by Simpson et al. (1979) on lead poisoning did not separate swans by sex, yet an 8 kg swan could be a healthy young female, a sick male or even a sick breeding female. Another difficulty arises in making comparisons between the weights of cygnets ringed prior to fledging: it is impractical to catch all broods at the same age for comparison, so it is common to estimate expected weight at some standard age by assuming linear growth, a crude assumption which can be improved. An analysis of Mute Swan weights is presented here using multiple linear regression analysis (MLR) to predict weights from a set of commonly recorded attributes with the aim of predicting typical weights based on those attributes. Given such a regression equation and a set of measured attributes for a single swan, its expected weight can be ca lculated; the difference between this and its recorded weight is the amount by which it is heavy or light (termed the 'residual'). The results of this MLR analysis conform well with previous analyses of Mute Swan weights, but MLR has two advantages over previous methods. First, the residual weight differences provide a convenient and sensitive way to investigate the effects of other factors on

3 146 P.1. Bacon and A.E. Coleman swans' weights; for example, lead-poisoned swans might have large negative residual weights. Second, the formulae resulting from this analysis provide an initial method whereby other workers could compare their results from different study areas with our area; for example, swans moult at different times in different areas and the formulae could predict approximately what a swan might have weighed if it had moulted a month earlier or later. METHODS The study area comprises a 1440 km= region of south Staffordshire, England, where Mute Swans have been studied intensively for about twenty years (Minton 1971; Coleman & Minton 1980). Between 1978 and 1982 samples of nonbreeding swans were caught each month, chiefly from the large urban flocks at Tamworth and Burton-on-Trent. Failed breeders and families that had joined the urban flocks were also represented in these samples. Breeding adults were sampled less regularly: a few were caught at nests in early spring but the majority of breeding adults were caught with their families in August and September. An important feature of the study is an annual round-up of a moulting flock, typically of 50 to 120 swans, in July or August each year. Over 95% of swans in the study area are of precisely known age and have been sexed by cloacal examination (Hochbaum 1942). The bulk of the weight data analysed in this paper, 1968 weighings of 957 individuals, were collected between 1979 and 1981 inclusive. Some additional weights spanning the short but very cold spell of winter weather in 1981/82 are discussed in relation to the previous milder winters. Finally, and most importantly, it is emphasized that lead poisoning is uncommon in this study area; estimated and measured lead levels are low (A.E. Hunt, T.R. Birkhead and J. Sears, pers. comm.) and swans from the Burton flock comprise the 'unpolluted control area' in table 1 of Simpson et al. 1979); thus lead poisoning is unlikely to depress the swans' weights noticeably below the normal 'healthy' level, nor will suffering or recovering from lead poisoning be an explanation for more than a few weight changes. All swans caught were weighed and measured as described below and this information, plus date of capture and ring numbers, was entered on to computer files. A program was written to check the records for consistency in ageing and sexing, and another to extract suitable sub-sets of the data for analysis. Sexual dimorphism is very marked in Mute Swans and seasonal changes of weight are likely to be different between the sexes, while cygnets of different sexes clearly have different growth patterns. Hence a fundamental tenet of this analysis was to estimate all effects separately for each sex. Swans of uncertain age provided only about 5% of the data and, as analyses of them conformed closely with the findings from the precisely aged birds, data on them have been omitted from this paper. Weights were recorded to the nearest 0.1 kg. When considering the accuracy of these, or of expected weights, it should be remembered that fresh droppings from swans, including large cygnets, weigh around 0.1 kg (about 1% of body weight). Swans usually defaecate on capture, and may defaecate two or three times more between capture and processing (because of the time taken to process family parties or flocks at round-ups), so the recorded weights could vary by around kg. Further, the gut contents of Mute Swans weigh several hundred grams, so that a period of starvation, perhaps induced by lead poisoning, could produce a drop of around 1.0 kg in weight. Similarly, a full set of flight feathers, simultaneously lost at the start of moult, weighs around 0.15 kg. A computer program read the basic data file and, for the appropriate sex, re-coded the information into a form suitable for MLR analysis. Re-coding was necessary for two types of factors. First, some relationships are known not to be straight lines but curves, for example a sigmoid curve for the relationship between cygnet weight and age. Such nonlinear effects were catered for by including squared and cubic terms of these factors to allow MLR to estimate a curve. Cubic equations were used as they were likely to approximate reasonably to all the expected relationships and are technically straightforward; in all cases linear and quadratic functions were tried first and the cubic term retained only if it improved the fit of the curve to the data.

4 Analysis of Mute Swan weights 147 Second, some data items, such as 'breeder', are categories rather than quantitative values; these were incorporated using the standard technique of scoring 0 or 1 depending on whether the factor was absent or present. Readers requiring further insight into MLR analysis should consult a standard text such as Draper & Smith (1981) or Chatterjee & Price (1977). The predictor variables used were incorporated into the MLR analysis as follows. (1) Adult age. Swans were assumed to fledge on 1 October in their year of hatching and age was coded in years from 1 October in the year of hatching to the day of capture, including fractions of years. The regression used terms for age, age squared and age cubed to estimate curved relationships between weight and age. Note that these adult ages could be slightly negative for cygnets caught before October, which were also given a 'cygnet age' (see below). It may, initially, seem a little curious that cygnets were given both an adult and a cygnet age, but there are good reasons for doing this. The aim was to devise a single method which would cope with cygnets of both known and unknown hatching date. There are also inherent difficulties in defining a change from cygnet to adult; broods of different ages fledge at different times of year and fledging is often accompanied by behavioural and habitat changes that make cygnets that have not yet joined urban flocks almost impossible to catch; unfortunately, as broods from different quality territories leave them at different times during autumn and winter (Scott 1984), it cannot be assumed that either late-fledging cygnets or those joining flocks early are representative of the population. We attempted to circumvent these problems by allowing a period of a few months with two 'ages', thereby, for the average cygnet, being able to interpolate between two large, reliable data sets instead of extrapolating at the probably unrepresentative ends of both sets. This procedure could, in principle, cause problems of interpreting such an analysis, but with these data the effects of other cygnet variables on their weights were so much larger than those of their negative 'adult ages' that interpretation problems were unimportant. (2) Cygnet age. The cygnets' ages from the approximate day of hatching (usually known to within 4-7 days) were recorded as fractions of years and used in the regression as linear, squared and cubic terms. These three cygnet age terms were all set to zeros for adults (a statistical technique to conform to the requirements of the regression model and ensure that for adults' weights the meaningless factor of 'cygnet-age' had no effect). If cygnets' ages were not known to within 4-7 days the above cygnet age terms were ignored (set to zeros) and a binary factor used to allow a comparison to be made between the averages for aged and unaged cygnets (see statistical references for details). (3) Month of observation. There were no good grounds for assuming gradual changes of weight during the year, as might be adequately reflected by a simple smooth curve. Accordingly a set of binary variables was used to represent the months, with 0 = not in that month and 1 = in that month; each binary variable tests for consistent weight differences for that month from those expected on the basis of sex, age, moult, etc. As every observation must be in some month, knowing whether the observation was made or not is necessary for only 11 months, information on the twelfth being redundant; January was arbitrarily chosen for omission. The effect ot this is that January serves as a reference month, with zero deviation by definition, and the deviations for other months are measured relative to January. (4) Wing moult and feather growth. Since swans moult and regrow all their primaries simultaneously a simple scoring system can be used to describe the stage of moult. The original records coded a moult score of 0 as 'No primary'; 1 for less than a quarter grown; 2,3,4 as less than half, three-quarters and fully grown; 5 as fully grown new feathers; and 9 for old unmoulted feathers (following the BTO system). Although this visual estimate is not accurate it is highly correlated to measured feather lengths. To conform with MLR analysis, the moult-score was re-coded by adding 1 to any moult score from 0 to 5 and using zero to represent birds not in moult. Squared and cubic terms of these scores were also used to allow estimation of curved relationships. Separate sets of regression

5 148 P.J. Bacon and A.E. Coleman parameters were assigned to feather growth in cygnets and moult in adults. In cases where the moult was not recorded in the period July to September (when birds might be in moult) a separate binary parameter which was otherwise 0 was set to 1, as a check for possible sampling biases due to whether or not moult was recorded. (5) Breeding. Breeding status was originally recorded as Non-breeding, Paired, Territorial, Nesting, Clutch or Brood. Because of a paucity of observations of paired birds in some months such subdivision in the analysis was unjustified, particularly as it had not been possible to cross-reference the breeding records fully to ensure that all failed breeders had been correctly designated every time. Accordingly, a single binary parameter was used, with 0 = Non-breeder (acquiring zero deviation by definition) and 1 = Breeder. The majority of breeders weighed were adults with broods in August and September !!! Males Females RESULTS OF MAIN ANALYSIS Before starting MLR analysis the data were first summarized graphically by plotting weights against age for males and females separately (Fig. 1). The graphs indicate an overall increase of weight with age (in males to age 3 years at least but in females only until 18 months), with some seasonal fluctuations, especially a loss of weight by young males in July. Regression models of increasing complexity were then devised, starting with adult age only and progressing to the multiple factor model described below. The final model showed all the variables recorded to be useful in predicting Mute Swans' weights: while many alternative formulations and some further refinements could easily be suggested, such changes would stretch the present data beyond their bounds without an appreciable increase in biological understanding. The relationships for the separate factors, as deduced from MLR analysis, are described below but the reader is asked to remember that prediction of any one weight requires a complete set of factors and that some relationships cannot be sensibly interpreted in isolation (e.g., cygnet age and cygnet wingfeather growth). For simplicity we begin by describing, for each sex, how the weights of Age (years) Figure 1. Weights of male and female Mute Swans according to their age from 1 October in year of hatching. Points represent means and vertical lines their 95% confidence limits. Single points are means of only a few observations. The age axis is truncated at three years, above which sample sizes are too small for averaging. fledged swans vary with age, as adult age is the factor which most simply and directly establishes a base-line of meaningful weights. The effects of other factors are then expressed as deviations from this base-line. Adult age Figure 2 clearly shows that average weights increase with age but that weights and the

6 Analysis of Mute Swan wei 14() patterns of increase differ between the sexes. The average male weighs 9.5 kg at fledging and average weights rise by about 0.5 kg per year for the next 2 years. Thereafter, male weights change only slowly, so that an average 8-yearold male is only 0.5 kg heavier than an average 4-year-old. There is a tendency for males between 10 and 20 years old to be much heavier, but the sample size is too small (c. 30) to investigate this further, especially as it refers mainly to adults with broods so that other factors, such as especially favourable territories, may be the reason for the greater weights. Cygnet age The curves of Fig. 2 indicate the weight of average cygnets hatched at the average date as their ages approach 1 October (= zero on the age axis of Fig. 2). However, as hatching dates differ between broods, younger cygnets might be expected to be lighter than older ones caught on the same date. Figure 3 shows the average expected deviation in weight from that predicted by Fig. 2 in relation to cygnet age. These cygnet age corrections improve weight predictions very significantly (Table 1). During the ages spanned by the data (70 to 120 days from hatching), the weights of males increase more rapidly than those of females (about 1.5 versus 1.0 kg). The binary variable representing cygnets of unknown age had no significant effect, which suggests that such birds, at least in this study, are typical of the average cygnet of known age; thus no overall correction can be made and lack of cygnet age data will impair accuracy of weight prediction. Age since hatching (days) Figure 2. Predicted weights of Mute Swans according to their ages when weighed since I October in year of hatching, restricted to data for birds whose exact year of hatching is known I I I Males The pattern for females is slightly different. The average female weighs 8 kg at fledging and average weights reach a normal level of 8.5 kg by about age 2 (0.25 kg per year). There is a suggestion that 4-year-old females may be slightly heavier than 8-year-olds, and, as with males, females older than 10 years are even heavier, but the sample size is again only c. 30, mainly birds with broods. Note that these are average changes: they could, in theory, arise from selective mortality of lighter birds, a process which could elevate the average weight even if the weights of the survivors did not change. However, present mortality data, although sparse, do not in any way support the possibility that swans which are unusually low in weight have particularly high mortality so we conclude that the changes in average weight most probably result from similar changes in most individuals. 3 ales Figure 3. Deviations of cygnets' weights from those predicted from Fig. 2 in relation to their age since hatching. Cygnet primary feather growth The stage of cygnets' primary feather growth is a useful predictor of their weights (Table 1). The binary variable representing cygnets whose feather growth was unrecorded had no significant effect, probably both because there was no consistent difference (such cygnets could be either better or less developed) and also because our data rarely omit -feather

7 150 P.J. Bacon and A.E. Coleman Table 1. Significance levels of predictor variables used in the multiple linear regression analysis. Data for exactly aged swans only Predictor variable Age categories of male swans All ages Less than 1.0 years 1.0 years and older Female swans (all ages) Adult age *** *** Adult age squared *** *X.* Adult age cubed *** *** Cygnet age Cygnet age squared Cygnet age cubed *** *** *** ** ** n.a. n.a. n.a. *** *** *** February March April May June July August September October November December *** *** Cygnet primary growth n.a. Cygnet primary squared *** * * n.a. Cygnet primary cubed *** * * n.a. *** Adult primary moult Adult primary squared Adult primary cubed Breeding adult ** X ** X *** n.a. * * * *** Percentage variance explained Mean weight (kg) Standard deviation (kg) 'Standardized' unexplained variation (kg) Key to symbols (Significance levels of individual coefficients.) n.a. not applicable * p < 0.05 x p < 0.20 " p < 0.01 y p <0.10 ***p <0.001 For the monthly factors note that the probability of getting a significant individual value should be assessed against the probability of getting 1 or more out of 11. These are: individual p = 0.01 gives 1/11 = 0.10; individual p = gives 1/11 = growth. However, as cygnet primary feather length is linearly correlated with age from hatching (Mathiasson 1981, Fig.3) the resulting coefficients need interpreting with some caution, as MLR analysis requires (for interpretation but not prediction) that the predictor variables are uncorrelated. Examination of the scatter plot of cygnet feather growth with age, illustrated for female cygnets in Fig. 4, shows a broad scatter of points with a significant but

8 Analysis of Mute Swan weights I Age since hatching (days) Figure 4. Scatter diagram of primary feather growth of female cygnet against their ages from hatching. See text for scoring system for feather growth. weak correlation (p < 0.01, but linear regression explains only 16% of the variance), in contrast to the tight relationship implied by Mathiasson's graph. A likely explanation of the broad scatter in our data is that primary feather growth starts at a particular stage of development, so that cygnets growing at different rates Figure 5. Deviations of cygnets' weights from those predicted from their ages plotted against their stage of primary feather growth. Dotted portions of lines indicate where feather growth score is non-linear. See text for explanation of feather growth score and interactions of feather growth with age. reach this stage at different ages. Primary feather growth could then act as a measure of growth stage: rapidly growing cygnets would be expected to have longer primaries and be heavier than 'standard' cygnets of average feather growth and age. The deviation of feather growth from the average might then predict the likely weight deviation. The calculated 'correction curves' (Fig. 5) show that, relative to a mean feather growth score of 3.5 for both sexes, the relationships are consistent with the above argument: long-feathered cygnets were heavier and short-feathered cygnets lighter. The precise shapes of the curves are unimportant (they will be affected both by interactions with cygnet ages and by non-linearity at the ends of the moult-score scales). If cygnet age and feather growth had been uncorrelated, an alternative explanation of the relationship between feather growth and weight would have been that food resources were diverted from body growth to feather growth, causing weight to increase less rapidly when feather growth started. It is possible that both these effects occur, but the age correction needs accounting for independently before this can be ascertained and growth stage cannot at present be defined with sufficient accuracy to achieve this. Seasonal variations, by months Figure 6 shows average monthly weight deviations throughout the year after allowing for sex, age, moult and so on (recall that January has zero deviation by definition). Although first-year males respond differently from older males when moulting their primary feathers (see below) the good correspondence between two sub-sets of ages within the sexes, evident from Fig. 6, indicates that seasonal changes of weight among non -breeders probably do not alter with age. The magnitude of these seasonal effects is around 0.75 kg for both sexes, with no obvious sudden changes. Male weights are significantly lower in March than in January and thereafter rise slowly, reaching a peak in late winter, with November and December weights being significantly higher than in January. Weights of females remain relatively constant from January to October, followed by a sig-

9 152 Pl. Bacon and A.E. Coleman +1 1 Females it /I + Months of year 41 ft # i 4 # Figure 6. Deviations of Mute Swans' weights from those otherwise expected from their ages, moult stages and breeding status plotted against month of weighing. Points are means, solid lines 95% confidence limits; dotted lines are 95% limits based on small sample sizes which may be unrepresentative; missing points indicate no data at all; January deviations are defined as zero. All data are for exactly aged birds: solid points are means for all ages; open circles indicate a sub-set of swans that were two years or older when weighed. nificant weight gain of about 0.75 kg in November and weights are still high in December. 1st year Males Figure 7. Deviations of adult Mute Swans' weights from those expected from their ages, dates of capture and breeding status plotted against their stages of primary feather moult. Dotted portions of curves indicate where the change in moult score becomes non-linear. were generally small and moult score is usually recorded. Breeding status Among precisely aged swans the average breeding male was 1.4 kg heavier and the average breeding female 0.8 kg heavier than non-breeders. Amount of variance explained Males..., Females Adult primary feather moult The effects of moult in adults are not complicated by correlations with adult age, as swans of all ages can have all possible moult scores. The results of the analyses are a little complicated, however, as the effect of moult differs between the sexes and changes with age. There is a highly significant effect of moult on the weights of first-year males (Table 1, Fig. 7). First-year males lose about 1.5 kg of weight at the start of moult, which they regain towards the end of moult, followed by some further loss as moult is completed and flight resumed. There were no significant effects of moult stage on the weights of males older than one year or on the weights of females, although it is unlikely that moult stage had no effect at all on the weights of first-year females. For older females the calculated changes in weight were actually within the expected limits of a set of grown wing feathers. There was no significant effect of the binary variable for unrecorded moult score, as might be expected if the weight changes due to moult The proportions of variance explained by the above analyses are shown at the bottom of Table 1. The highest proportions of variances explained naturally occur in those age groups that include cygnets and first-year birds, as it is in this period that weights change most, so there is more variation to explain. The bottom line of Table 1 gives the unexplained variance (approximately standardized into kilograms by taking its square root) for the different age and sex classes: this is about 1.0 kg in each case. Accepting a maximal likely accuracy of ±0.3 kg due to defaecations and other 'errors', this leaves an average of some 0.7 kg unexplained by the analyses. SOME EXAMPLE ANALYSES OF RESIDUAL WEIGHT DIFFERENCES Some further analyses of the differences between observed weights and the weights expected from the above MLR analysis are presented here, both to illustrate how this can be done and to indicate other factors that may

10 Analysis of Mute Swan weights 153 merit further investigation. A procedure to calculate approximate expected weights according to the regression parameters derived from the analysis is given in the Appendix. Individual's residuals Of 1968 weighings of 957 swans, 61% of captures were swans caught only once, 15% twice and 8, 5, 3, 2, 2, 1, 1 and 1% caught 3, 4,.. more than 10, times, respectively. If some swans were consistently heavier than others it would be expected, for example, that the residuals for one particular individual might, on average, always be about 1.4 kg heavy, while the residuals for another might always be about 0.9 kg light, and so on. If there was complete consistency of differences then an examination of the relationship between residuals at successive weighings would give a regression line of slope +1.0 and intercept 0.0: If individuals' weights were no more consistent than expected for any bird typical of their age and sex, there would be no correlation between successive residuals. Analysis of the repeated weighings of 368 individuals (of which 228 were caught three times or more) shows a highly significant relationship (p < 0.001) with a slope of 0.52 and an intercept not appreciably different from 0.0 (= 0.05 kg). This implies that heavy birds tend to remain heavy and light ones to remain light but that deviations from the average are not maintained in the long term. Effects of cold weather in winter During December 1981 and January 1982 there were two periods of intense cold when temperatures dropped nightly to below 10 C and many areas of open water normally used by swans were frozen continuously for many days, preventing access to the birds' normal foods. The urban flocks from which the weight samples were taken were entirely dependent on bread fed to them by people during these periods. During prolonged spells of much colder weather in 'ice-winters' in Denmark Mute Swans can lose about 2 kg in 2 months (Andersen-Harild 1981). A traditional analysis of the Staffordshire data for these cold spells, with the decreases relative to November weights averaged and plotted against date, Males } 1980/81 10 Females Males 20 Nov Dec Jan Feb Mar Females j1981/82 Figure 8. Changes in mean weights in Mute Swan flocks during two winters, relative to mean November weights. Dotted portions of lines are based on small samples. suggests weight decreases of 10-15% (about 1 kg) for the average male and female (Fig. 8). However, such a presentation takes no account of the altered age structure of the flock during this period, when families and juveniles were forced out of frozen rural sites and into the flocks. To allow for this, the regression equations (which had been derived from independent data) were used to predict the expected weights of all birds caught and the deviations of the observed from predicted weights examined (Table 2 and Fig. 9). In contrast to the implications of Fig. 8, it can be seen that weight losses estimated by the MI.R method are only a few hundred grams, not around a kilogram. Thus, the main reason tor the drop in average weight of swans in the flock (Fig. 8) was an influx of lighter birds: individuals' weights declined only slightly compared to the appropriate expectations and, while some swans in the flock were in very poor condition (1, 1, 4 and 19 wereyespectively 4, 3, 2 and 1 kg underweight) others were in very good condition (1, 3 and 5 were respectively 3, 2 and 1 kg overweight). DISCUSSION We have investigated several factors as predictors of Mute Swans' weights, with the aim of using the predicted weights and deviations from them as indices of the swans' conditions. The weight of a swan changes most when it is a growing cygnet and in its first year or so of life, but thereafter age is not particularly important, at least in our study area. Cygnets of unknown hatching dates have weights that agree closely

11 154 P.J. Bacon and A.E. Coleman Table 2. Effects of a short period of cold winter weather on the weights of male and female swans in flocks. Data for birds of known age only Month of 1982 males females N Mean C.R. N Mean C.R. Jan * Feb Mar N is the number of observations. Mean is the mean deviation (kg) from the weights predicted from sex, age and month. C.R. is the 95% confidence range on either side of the mean. An asterisk indicates that the mean is significantly different from zero (p < 0.01) * 1-, Moles Fern ales * ; Days from 1st January with the expected means for cygnets of known hatching age, implying that coverage of the area does not selectively miss late nesting pairs. The stage of primary feather growth gave useful additional information about expected weights of cygnets. Primary feather growth is interpreted as a factor that varies with, and is thus an indirect measure of, the stage of growth attained by cygnets. Scott & Birkhead (1983) found that skull length was not a useful predictor of the weights of cygnets of known age. There are several likely causes of this difference. First, poorly growing cygnets may be more able to delay feather growth than reduce skull growth. Second, skull growth has nearly stopped at the ages when cygnets are ringed, whereas the primaries are still growing rapidly at this time (e.g., Mathiasson 1981) so very accurate measures of skull length but only rough measures of primary lengths might be needed to detect the same change in growth stage. Third, Scott & Birkhead did not allow for non-linear relationships of weight with age, which have been shown here to be important. Finally, the precision of Scott & Birkhead's results will have been impaired by their use of mean weights per brood instead of weights of Figure 9. Deviations of measured weights during the cold weather in 1982 from weights predicted from the swans' ages and months of capture; predictions are based on independent data from 1978 to Dots represent single observations, crosses multiple ones.

12 Analysis of Mute Swan weights 155 individual cygnets, a procedure that not only reduces sample sizes but, because of variations of brood composition by sex, introduces additional uncontrolled variation. In many adult waterfowl growth of primary feathers is linear with time (e.g. Owen & Ogilvie 1979) and this is true of adult Mute Swans (Mathiasson 1973; Andersen-Harild, pers. comm.). One-year-old male swans in our study area lose weight during moult but older males and all females do not. This finding is in contrast to studies elsewhere: for example 'there is a significant weight loss during moult' (Wiley & HaIla 1972: N.B. several variables given in Willey's paper are in the wrong units (cm/mm) or wrongly converted (1b/kg)); 'moulting swans of all ages are low in weight' (Andersen-Harild 1981 and pers. comm.). Many studies of moulting rely on weight changes of individuals recaught during moult. While such data can provide unequivocal evidence of changes in individuals' weights, they are prone to bias either if the catching process stresses the bird or if some categories of birds are harder to recatch. The MLR method uses birds caught only once to infer the average change in weight during moult. It would be useful to compare the two methods and it is unfortunate that we could not get an adequate sample for such a comparison. If we accept the results at face value, in Denmark Mute Swans of all ages, especially those feeding on poor quality food, lose between 10 and 20% of their weight during moult (Andersen-Harild 1981 and pers. comm.) but moult has negligible effect on the weights of fully grown adults in Staffordshire (including both birds in the moulting flocks at Alvecote Pools and breeding pairs). It is likely that this difference is, at least in part, brought about by the preferred, richer foods in Staffordshire (typically pond weeds such as Elodea canadensis, Pot omogeton pectinatus and Zannichellia palustris) than in Denmark (typically various algae: Zostera, Ulva, Chara, Fucus spp.; Mathiasson 1973; Andersen-Harild 1981). It is interesting that first-year males in Staffordshire do show a significant drop in weight as moult commences when they are still growing; if food availability is limiting for growing first-year males then the diversion of food resources to feather growth might well cause such a loss in weight. Note that there is no corresponding loss of weight either for first-year females or in older birds, which are growing less and seem able to grow new feathers without losing weight. Thus, additional stresses, such as lead poisoning, during moult might be expected to cause higher mortality in first-year males than in first-year females (death from lead poisoning is caused by starvation (Birkhead 1983)). The data show that weights of swans varied only slightly with the season (months of year) after the effects of age and moulting had been accounted for, but that breeding birds were very significantly heavier than non-breeders of the same age. Reynolds (1972) showed that neither male nor female Mute Swans bred unless they attained minimum weights in spring of 10.6 kg for males and 8.8 kg for females. Our results show that Mute Swans in Staffordshire attained such weights, on average, at ages of about 3-4 years (males) and 2-3 years (females). Previous papers (Coleman & Minton 1980; Bacon 1980a, b) document cases of Mute Swans breeding at these young ages in recent years but such early breeding was formerly less common in Britain (Minton 1971; Coleman & Minton 1980; Bacon 1980a, b) and is at present uncommon in Denmark in areas of saturated populations or poorer food quality than in our Staffordsh ire study (Andersen-Harild, pers. comm.). Corn pa red with the previous situation reported by Min toii (1971) in Staffordshire, swan numbers are now down, with more vacant territories, suggesting that lack of competition may have permitted more rapid growth, earlier maturity and ea rlier first breeding attempts in recent years. It is unfortunate that weight data are not available for the early years of studies in Staffordshire. Our data do not allow us to decide whether the higher weights of breeding swans is a result of them being heavier when they take up their territories,or of better food quality on territories compared with non-breeding sites, or both. Female swans are smaller than males and thus require about 25% less food for body maintenance (Kendeigh 1970). Presumably there is some advantage to males in being larger, despite their appreciably greater food demands for growth and maintenance. Both the quality and quantity of available food have direct effects on Mute Swans' weights (Andersen-Harild 1981). When feeding is poor,

13 156 P.J. Bacon and A.E. Coleman females might be expected to show less weight loss than males because their needs are lower, although direct competition for food may penalize the lighter, subordinate swans, i.e. unpaired females and young birds (Scott 1981; K.M. Lessells, pers. comm.). Cygnets require energy both for maintenance and growth, moulting swans for maintenance and feather growth, and breeding females for maintenance and egg production. It is possible that selection has favoured not only males who maximize their size and competitive ability, but also females who maximize their rates of food intake and egg production; such differences could lead to the observed marked sexual dimorphism of body size in the Mute Swan, as argued by Belovsky (1978) for the Moose Alces alces and by Reiss (1982) for large animals generally. Interpreting predictions made from this or similar models should be done with caution. For example, this model adjusts the prediction of cygnet weight using the stage of growth, as indicated by primary feather lengths. However, factors such as lead poisoning might actually reduce cygnet growth, so that poisoned cygnets might not have extremely low residuals because their low weights, though caused by lead poisoning, might be consistent with the reduced growth evident from the primary feather data. In such circumstances one would do better to compare two predictions, one estimating the growth stage reached (from data on body measurements and body weight) and a second estimating whether this stage was consistent with typical cygnet development rates, based on the ages of the same birds. We hope shortly to indicate how such comparisons could be done for the Mute Swan (Bacon, Coleman and Andersen-Harild, in prep.). Many previous papers with information on Mute Swans' weights give too little information on exactly how the data were analysed for detailed comparisons to be made between them. As a comprehensive analysis requires many hundreds of weights, such comparison or analysis should be done by computer. Several methods would allow other data to be compared with our results. First, and preferably, other data sets (measured and encoded exactly as here) should be analysed by MLR and the resulting coefficients compared statistically with ours. Second, a simple computer program could calculate 'Staffordshire predicted' weights from other data sets and the resulting residuals should average zero if there were no differences: however, this second approach will be less informative as to why any differences occur; copies of encoding and predicition programs can be obtained from PJB. Third, for readers interested in making a few approximate calculations a set of instructions is given in the Appendix for deducing the approximae predictions from the graphs in this paper. The temptation to quote 'typical weights' (e.g., for cygnets 'at fledging') for the Staffordshire swans is deliberately avoided as differences between different studies, both in field techniques and in the swans' environments, cause so much variation about such 'typical' weights as to make them more misleading than helpful. It is encouraging that a comprehensive analysis of a large set of Mute Swan weights not only explains much of the variance of those weights but also produces interpretations closely consistent with many less detailed analyses from several other studies. Use of similar methods for data from other areas would greatly strengthen the rigour of comparisons. The calculated residual weights from such MLR analyses may also be useful in guiding further work. It is recognized that these data under-represent breeding birds at some seasons, and that more complete data sets would merit modified regression models. Application of MLR analysis (perhaps slightly modified) in areas where Mute Swans lose weight during moult might be especially fruitful. Measurements of primary feather lengths would improve accuracy over the moult-scores used here. ACKNOWLEDGMENTS We are most grateful to many people who helped with field-work over the years, especially Mr J. Coleman, Mr and Mrs F. Hollis, Mr J. Robinson, Mr and Mrs I. Taylor and Mr A. Whitmore. Many local landowners, especially the Alvecote Pools Committee, the Staffordshire Trust for Nature Conservation, Warwickshire County Council and Drakelow Power Station Nature Reserve (Mr T. Cockburn), have kindly permitted repeated access to their land. George and Maurice

14 Analysis of Mute Swan weights 157 Arnold provided information on the typical vegetation of Alvecote Pools, Mr E. Hopkins furnished data on Kingsbury Water Park pools and Mr J. McMeeking and Mr N. Lewis have, for many years, assisted greatly with the roundup at Alvecote Pools. The Wildfowl Trust provided the coded colour rings. We thank P. Andersen-Harild, D.K. Lindley, Jane Sears and Drs Brenda Howard, T.R. Birkhead, C.M. Perrins and three referees for constructive comments on earlier drafts. Finally, we would like to thank our wives, not only for their effective and enthusiastic help in catching swans but also for their understanding of two wayward swan-catchers who should often have been occupied with domestic tasks rather than up to their knees in river water. REFERENCES Andersen-Harild, P. (1981) Weight changes in Cygnus olor. In: Matthews & Smart (1981), pp Bacon, P.J. (1980a) Population genetics of the Mute Swan (Cygnus olor). DPhil thesis, University of Oxford. D 32193/80 (BLLD F). Bacon, P.J. (1980b) Status and dynamics of a Mute Swan population near Oxford between 1976 and Wildfowl, 31, Belovsky, G.E. (1978) Diet optimisation in a general herbivore: the Moose. Theor. pop. biol. 14, Birkhead, M.E. (1983) Lead levels in the blood of Mute swans (Cygnus olor) on the river Thames. J. Zool. Loud. 199, Chatterjee, S. & Price, B. (1977) Regression Analysts by Example. Wiley, Chichester. Coleman, A.E. & Minton, C.D.T. (1980) Mortality of Mute Swan progeny in an area of south Staffordshire. Wildfowl, 31, Draper, N.R. & Smith H. (1981) Applied Regression Analysis, 2nd ed. Wiley, Chichester. Hochbaum, H.A. (1942) Sex and age determination of waterfowl by cloacal examination. Trans. 7th North American Wildlife Conf., Ontario, Kendeigh, S.C. (1970) Energy requirements for existence in relation to size of bird. Condor, 72, Mathiasson, S. (1973) A moulting population of nonbreeding Mute swans with special reference to flight-feather moult, feeding ecology and habitat selection. Wildfowl, 24, Mathiasson, S. (1981) Weight and growth of morphological characters of Cygnus tor. In: Matthews & Smart (1981), pp Matthews, G.T.V. & Smart, M. (Eds) (1981)Second Int. Swan Symp. Sapporo, Japan, February International Waterfowl Research Bureau, Slimbridge, England. Minton, C.D.T. (1971) Mute swan flocks. Wildfowl, 22, Owen, M. & Ogilvie, M.A. (1979) Moult, weight changes and measurements of Barnacle geese Branta leucopsis in Spitsbergen. Condor, 81, Reiss, M. (1982) Males bigger, females biggest. New Sci. 96, Reynolds, C.M. (1972) Mute swan weights in relation to breeding. Wildfowl, 23, Scott, D.K. (1981) Social behaviour of wintering Cygnus columbianus bewickii. In: Matthews & Smart (1981), pp Scott, D.K. (1984) Winter territoriality or Mute Swans Cygnus olor. Ibis, 126, Scott, D.K. & Birkhead, M.E. (1983) Rt-sourt.inil reproductive performance in Mute,,wait,.1/N1111, olor. J. Zoo!. Lond. 200, Simpson, V.R., Hunt, A. L. & French, M.( (1079) Chronic lead poisoning in a herd ot Mute swan,. Environ. Pollut. 18, Willey, C.H. & Halla, B.F. (1972) Mute swans ot Rhode Island, Rhode Island Department of Natural Resources, Wildlife Pamphlet no. 8. (MS received 2 July 1985; revised MS received 6 March 1986) Note: Appendix follows overleaf.