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Population dynamics of Scottish Rock Ptarmigan cycles.

INTRODUCTION

Cyclic fluctuations of northern rodents, hares, and grouse were an early problem in population ecology (Chitty and Elton 1940), yet the mechanisms remain unresolved (Keith 1963, Lindstrom 1994). Simple model populations with delayed density-dependent growth suggest that cycles may be special cases of unstable dynamics, which include damped oscillations, limit cycles, and chaotic fluctuations (May 1975). Most workers have studied 3-4 yr cycles in rodents, with less attention to long cycles such as the 10-yr ones in grouse (Tetraonidae) and hares (Keith 1963). Here, we show that (1) Scottish Rock Ptarmigan (Lagopus mutus) cycle with a period of 10 yr, and (2) their cycles are influenced both by physical factors, such as soil and weather, and by intrinsic factors, such as feedback of density on breeding success and population growth.

There have been three main approaches to the study of long cycles. One is to show that they occur, mostly with secondary data such as fur records and shooting bags, which provide the long runs necessary for statistical demonstration of cycles. This has seldom been done with primary data, because most population studies have not lasted long enough. Watson (1965) found cycle-like fluctuations in Rock Ptarmigan on the Cairngorms massif of Scotland, but his 21-yr study covered only one full fluctuation. Here, we analyze a 53-yr run from the same massif.

The second approach considers population dynamics on defined study areas. Most hypotheses involve time lags in interactions between trophic levels such as food - consumer or predator - prey, or between different parts of a population structured by age or phenotype (Krebs 1985). We document population dynamics and assess food, weather, and predation as possible causes of population fluctuations.

The third approach considers geographical variations, such as differences in amplitude and cyclicity in snowshoe hares (Lepus americanus) across continental North America (Smith 1983). However, many factors vary on such a geographical scale, so the causes of cycle variation are confounded. Here, we present population data on areas with different soils in the same geographical region.

STUDY AREAS

The bird and its food

Scottish Rock Ptarmigan occur on arctic-alpine land (called alpine hereafter) and eat mostly heath species (Ericaceae), mainly crowberry (Empetrum nigrum), ling (Calluna vulgaris), and blaeberry (Vaccinium myrtillus) in winter (Watson 1964), and mainly blaeberry in spring (Moss and Watson 1984). As alpine vegetation is very short, boulders provide the main cover.

After being in flocks in fall-winter, Rock Ptarmigan pair on territories in spring (Watson 1965). They breed in their first year (Rae 1994). Hens lay eggs in May-early June, the timing varying with altitude and snow lie. After hatching in June, most broods move to flushes, where chicks [less than or equal to]2 wk old eat invertebrates to supplement their mainly plant diet.

[TABULAR DATA FOR TABLE 1 OMITTED]

Study areas

The two massifs studied were the Cairngorms and the Mounth, both near Braemar, 80 km west of Aberdeen, Scotland ([ILLUSTRATION FOR FIGURE 1 OMITTED], Table 1). Valleys unoccupied by Rock Ptarmigan separated the massifs, and side valleys separated submassifs within each massif. One of us (AW) noted numbers of ptarmigan seen on walks on two submassifs in the Cairngorms and two in the Mounth, and did total counts on smaller study areas on each submassif for fewer years. When choosing study areas, he favored high densities, which maximized sample sizes. In retrospect, probably all were "sources" and none "sinks" (Pulliam 1988).

Watson (1965) described study area D on Derry Cairngorm (submassif DS). He cut his original 500-ha area in 1965 to 131 ha; all data from D reported here are from the 131-ha area. He also did counts on area B on Beinn a' Bhuird (submassif Bs), area L on Lochnagar (on LS), and on area C (on CS). Area C was composed of two parts: 20 ha at Cairnwell and 20 ha at Meall Odhar, 2 km away, separated by moorland unoccupied by ptarmigan. Ski lift wires on both parts of area C killed ptarmigan, but not enough to affect numbers materially (Watson 1979). Counts were also done on Carn a' Gheoidh (C a' G) to check variability within CS.

Bedrock, soils, and climate

Because all areas lay above the upper limit of deep, glacial deposits and extensive, thick peat, bedrock had a major effect on soils. Alpine granite soil is coarse, incohesive, and barren, whereas mica schists and basic rocks lead to more silty, compact soils with thicker topsoil (Heslop 1974). Most of the Cairngorms massif and its submassifs DS and BS are of granite, as is submassif LS (although it has some schist and diorite), but the CS submassif is mostly schist with some limestone (Johnstone 1974).

Plant cover on CS exceeded that at a similar altitude and aspect on granite. Food plants (especially blaeberry) at D had lower ground coverage and nutrient contents than at C (Moss 1968, Moss and Watson 1984). Both D and C were mostly freely drained, but the higher D had more flushes, streams, and snow patches providing summer irrigation.

The climate was subarctic-oceanic, with snowfalls in any month and frequent winter thaws. Because there were no weather data on alpine land (above 760 m) in most years, we used monthly mean precipitation and air temperature at 339 m in a valley at Braemar for 1912-1995 (Meteorological Office). The natural upper woodland limit is [approximately] 600 m.

Bird shooting, grazers, and predators

Hardly any Rock Ptarmigan were shot on DS, but many were shot on BS in 1971-1991, and at CS and LS in some years (Appendix A). Alpine land was near-natural, grazed lightly by red deer (Cervus elaphus) and mountain hares (Lepus timidus), and moderately by sheep summering on C and CS (Watson 1965, 1979). Short-tailed voles (Microtus agrestis) were locally at high density on C, but at lower densities on D (Nethersole-Thompson and Watson 1974), as were hares (Watson and Hewson 1973).

There were no specialist predators. Generalists were red fox (Vulpes vulpes), stoat and weasel (Mustela erminea and M. nivalis), Golden Eagle (Aquila chrysaetos), Peregrine Falcon (Falco peregrinus), and Carrion Crow and Common Raven (Corvus corone and C. corax). Gamekeepers killed foxes and crows on low ground. (For details, see Watson 1965, 1979, 1996, Moss and Watson 1984, Watson at al. 1989.)

METHODS

Ptarmigan and blaeberry

Watson (1965) described methods for total counts on study areas of Rock Ptarmigan cocks and hens in spring (April-early May) and of cocks, hens, and big young in late summer (late July-early August), and for recording adult numbers seen on transect walks in summer (May-August), called "walk data." Walks were not systematic or random, and could have involved counting some birds more than once in a summer, but results were closely related to density. We also used early observers' notes (Appendix B) to lengthen data runs.

As AW found few nests in some years (n = 156 nests at C, range 3-15 nests per year; and n = 94 nests at D, range 1-6 nests per year), analyses with clutch size are less reliable than those with young. We enlarged the sample of hatch dates by backdating from estimated ages of broods, but some samples were still small (n = 219 hatch dates at C, range 2-25 dates per year; and n = 100 dates at D, range 2-45 per year). Because hatch dates were skewed, we used medians. Calculations of medians excluded a small peak of late hatches that indicated renesting after nest predation or desertion; analyses that included this peak gave the same conclusions.

Brood age was estimated as in Red Grouse, Lagopus lagopus scoticus (Parr 1975, Watson and Miller 1976), and was tested on young of known age by us and by Brockie (1993). Methods for assessing causes of death in Red Grouse (Jenkins et al. 1963, Watson and Miller 1976) apply to Rock Ptarmigan. In a summer trial with ptarmigan corpses on area C, most were found (Appendix A).

The onset of unfolding of blaeberry leaves was noted to the nearest week in May-early June. Dates varied within and between areas, depending on altitude, snow lie, and aspect, so each record was an average for a study area.

Numerical analysis

Time series analyses. - We removed trends in walk and other data by fitting polynomials with up to 10 terms and removing insignificant (P [greater than] 0.05) terms by a step-down procedure. Smoothing with running means gave similar results, not presented here. Because no linear trends emerged, the main effect of detrending was to remove variation in the heights of different peaks and troughs. We did autocorrelations on residuals (Box and Jenkins 1970). If residuals from untransformed data were not normally distributed, we obtained normal residuals by square-root transformation of the original data and by fitting another polynomial.
TABLE 2. Definitions of population terms for Rock Ptarmigan.

Sym-
bol                   Term             Explanation

[N.sub.t]   Spring number       Number in late April-early
                                May, shortly before nest-
                                ing, in year t.

[N.sub.c]   Spring cocks        Superscript defines sex; con-
                                vention applies throughout.
[N.sub.h]   Spring hens
C           Population change   ([N.sub.t]/[N.sup.I-1]) - 1.
                                Subtracting 1
                                made C vary about zero,
                                so that increases were pos-
                                itive and declines negative.

[dagger]   Spring sex ratio     [N.sup.c]/[N.sup.h].

A          August adults        Number of adults in early August.

Y          August young         Number of young in early August.

B          Breeding success     Y/2A. [B.sup.c] is Y/2[A.sup.c and
                                [B.sup.h] is Y/2[A.sup.h].

[dagger]   Young per hen        Y/[A.sup.h].

E           Clutch size         Mean number of eggs in nests.

[L.sub.s]   Summer loss         (N - A)/N. Negative values
                                signify net gains.

[L.sub.w]   Winter loss         [((A + Y).sub.t] -
                                [N.sub.t+1])/[(A+Y).sub.t].
                                Negative values are net gains.

Ph          Phase               Sign of C.

[dagger] No symbol for this term.


We did spectral analyses of log-transformed residual Rock Ptarmigan numbers by the SAS (1989) SPECTRA procedure, and tested significance by Fisher's Kappa (designed to detect one sinusoidal component embedded in "white noise" by comparing the ratio of the largest periodogram ordinate with the average of all ordinates). Spectral analyses detect sine waves in "white noise," but ptarmigan numbers and residuals fluctuated more abruptly than sine waves. Log-transformation reduced abruptness and, thus, better fitted the assumptions of the analysis.

Population dynamics. - Table 2 defines terms and symbols. Change (C) in spring population size (N) from one year to the next was completely determined by summer loss [L.sub.s], breeding success B, and winter loss [L.sub.w].:

[N.sub.t] = [N.sub.t-1] (1 - [L.sub.s]) (1 + B) (1 - [L.sub.w])

C + 1 = (1 - [L.sub.s)(1 + B)(1 - [L.sub.w).

C, and [L.sub.s] each include [N.sub.t-1] in their definition, and [C.sub.t] and [L.sub.w] include [N.sub.t]. Hence, significance tests for correlations between these variables are not strictly valid, but we use them as informal guides to the relative importance of each loss to population change.

In seven of 27 years at D, August counts were only samples, precluding estimates of [L.sub.s] and [L.sub.w]. Some analyses had phase (increase or decrease) as an explanatory class variable. To help avoid circular argument, we used the hens' phase when analyzing cock population change, and vice versa. In fact, most rises and falls coincided in both sexes (Figs. 2 and 3).

Density dependence in population trajectories was characterized by autoregressive models (Royama 1992), which relate present to past numbers:

[log.sub.e][N.sub.t] = [k.sub.0] + [k.sub.1][log.sub.e][N.sub.t-1] + [k.sub.2][log.sub.e][N.sub.t-2] . . .

+ [k.sub.n][log.sub.e][N.sub.t-n] + [Epsilon]

where k are constants and [Epsilon] is error. Although we use the term "density dependence," density is unlikely to limit numbers (e.g., if resources differ between areas, the same bird density involves different resource amounts per bird). Hence, we use numbers for analyses, except when comparing density between areas. Annual data for all walk data, counts, phenology, and weather are on file at our correspondence address.

RESULTS

Long-term patterns in spring numbers

Consistency of count and walk data within massifs. Walk data came from large areas of ground with both high and low mean densities of Rock Ptarmigan. They fluctuated more widely than did spring counts from the study areas, which were smaller and chosen for their high density (Study areas). Nonetheless, within granite submassifs, spring counts [ILLUSTRATION FOR FIGURE 3 OMITTED] and walk data [ILLUSTRATION FOR FIGURE 4 OMITTED] were closely related on BS (r = 0.91, P = 0.0003, n = 10), DS (r = 0.91, P [less than or equal to] 0.0001, n = 28), and LS (r = 0.95, P = 0.0003, n = 8).

Within the more fragmented schist submassif CS, spring counts on the two separate parts of C and on C a' G were closely related [ILLUSTRATION FOR FIGURE 2 OMITTED]. To swell the sample of broods in years of low numbers, we combined the two parts of C. This was justifiable, because their spring numbers were highly related (r = 0.94 for cocks, r = 0.92 for hens, each P [less than or equal to] 0.0001), and their population change, summer loss, and winter loss were similar. Spring counts and walk data at CS were more weakly related (r = 0.69, P [less than or equal to] 0.0001, n = 26) than on granite.

Synchrony. - Walk data were low at all four submassifs in the mid 1940s and fluctuated every [approximately] 10 yr, with peaks in the early 1950s, troughs in the late 1950s, and peaks in the early 1960s [ILLUSTRATION FOR FIGURE 4 OMITTED]. All four sets remained high through the 1960s, a period of warm summers. Until 1964, they resembled each other more closely within massifs (BS resembling DS, and CS resembling LS), than between massifs (Table 3). After 1964, synchrony among submassifs BS, CS, and DS lessened (there were too few years to analyze LS).

Cock numbers [ILLUSTRATION FOR FIGURE 3 OMITTED] in the same years at areas D and C were unrelated (r = 0.14, P = 0.61), and hen numbers were only weakly related (r = 0.47, P = 0.08). Population change at D and C was unrelated (cocks: r = -0.031, P = 0.92; hens: r = 0.31, P = 0.27).

Cyclicity. - The longest run of walk data (at DS) showed cycles with peaks in 1951, 1962, 1971, 1980, and 1990 [ILLUSTRATION FOR FIGURE 4 OMITTED]. Autocorrelation [ILLUSTRATION FOR FIGURE 5 OMITTED] and spectral analysis (Fisher's Kappa = 12.6, M = 26, P [less than] 0.01) confirmed the period ([approximately]10 yr).
TABLE 3. Correlations among ptarmigan numbers (walk data) at four
submassifs.

Submassif

Sub-
massif             DS       BS           CS          LS

DS                         0.72(**)    0.46(***)    0.21
BS                0.05                 0.59(*)      0.45(***)
CS               -0.03     0.30                     0.76**(***)

Notes: See Table 1 for sample sizes. Correlations up to 1964 are
given above the diagonal; correlations after 1964 are below the
diagonal. There were too few data from LS to calculate meaningful
correlations after 1964.

(****) P [less than] 0.1, * P [less than] 0.05, ** P [less than]
0.01, *** P [less than] 0.001.


Walk data at BS [ILLUSTRATION FOR FIGURE 4 OMITTED] showed cycles with peaks in 1951, 1962, 1972, 1981, and 1989. Autocorrelation [ILLUSTRATION FOR FIGURE 5 OMITTED] and spectral analysis (Fisher's Kappa = 6.90, M = 25, P [less than] 0.05) indicated a period of [approximately]9 yr. After the 1981 peak, the BS and DS trajectories drifted farther apart, associated with heavy shooting at BS from 1971 onwards, but not at DS (Appendix A).

Walk data at CS [ILLUSTRATION FOR FIGURE 4 OMITTED] were more erratic than at DS, both year-to-year and in the longer term, with peaks in 1953, 1964, 1970, 1977, and 1987. There were 10-11 yr fluctuations at the start and end, with two fluctuations of 6-7 yr between. Autocorrelation [ILLUSTRATION FOR FIGURE 5 OMITTED] confirmed this more complex pattern. Spectral analysis (Fisher's Kappa = 6.2, M = 22, P [less than] 0.05) showed a primary period of [approximately]11 yr and a secondary one of [approximately]6 yr. The interposition of two 6-7 yr fluctuations resulted in the first and last 10-11 yr fluctuations being out of phase with each other.

Walk data at LS [ILLUSTRATION FOR FIGURE 4 OMITTED] showed peaks in 1954 and 1964-1968 (no data for 1965-1967), with very high numbers in 1968. The run was too short for reliable spectral analysis, and a suggestion of a 12-yr period from autocorrelation [ILLUSTRATION FOR FIGURE 5 OMITTED] should be treated cautiously.

Other observers' information for the Cairngorms in 1909-1964 (Appendix B) was from partly different areas. Even so, it fitted DS walk data in overlap years (1943-1964), with a 1945 trough (1944 by DS walks), a 1951 peak, a 1957 trough, and a 1962-1964 peak (1962 at DS). Overall, it showed peaks in 1912, 1923, 1934, 1940, 1951, and 1962-1964 (no information for 1915-1918). The 11-yr intervals 1912-1923, 19231934, and 1940-1951 resembled the 10-yr period in walk data at DS in 1943-1995. The single 6-yr interval in 1934-1940 was like the two 6-7 yr fluctuations at CS. Two independent observers noted it, and the 17-yr period 1923-1940 could not accommodate two 10-yr fluctuations.

Density dependence. - Second-order autoregressive density dependence ([k.sub.2] significant, delayed density dependence with a lag of 1 yr) occurred in walk data at DS, BS, and LS, but not at CS (Table 4). Adding the logarithm of shot birds at BS, CS, and LS (there was negligible shooting at Ds) as an explanatory variable improved [R.sup.2] insignificantly by [less than] 1% for each submassif.

The lack of significant second-order density dependence at CS does not prove that its dynamics differed from that of other submassifs, because [k.sub.2] did not differ significantly. However, there was evidence of fourth-order (lag 3) density dependence on granite (DS, BS, LS), but not on schist (CS). An omnibus model (SAS GLM procedure) combined walk data from all submassifs, with [N.sub.t-1], [N.sub.t-2], [N.sub.t-3], [N.sub.t-4], and rock type (granite or schist) as explanatory variables (Table 4). It showed significant values for [k.sub.2] and rock x [N.sub.t-4] interaction (P = 0.045), with [k.sub.4] significant on granite, but not on schist.

Hence, the population trajectory on the schist submassif CS differed from granite submassifs in not showing fourth-order density dependence. At D, but not C, a similar 3-yr lag occurred in the relationship [TABULAR DATA FOR TABLE 4 OMITTED] between breeding success and past population size (below).

Spring density and sex ratio

Mean spring density in common years (1964-1978) for cocks at C (48 [+ or -] 3 cocks/[km.sup.2], mean [+ or -] 1 SE) exceeded that at D (18 [+ or -] 2 cocks/[km.sup.2]), and likewise for hens (45 [+ or -]3 vs 16 [+ or -] 2 hens/[km.sup.2]). Cocks often outnumbered hens at D and C [ILLUSTRATION FOR FIGURE 3 OMITTED], as some had no hens; however, hens occasionally outnumbered cocks, as a few cocks had two hens. At D, an excess of males occurred during declines, but the sex ratio came close to 1:1 during increase years and the 1960s plateau. At C, the excess of males was lower, on average, and tended to occur during population increases, when there were unmated cocks on small territories.

Breeding success and losses as causes of population change

Correlations with population change. - Population change at D was strongly related to intervening breeding [TABULAR DATA FOR TABLE 5 OMITTED] success and summer loss (Table 5). At C, too, it was related to breeding success, but less strongly to summer loss. However, the relationship with breeding success at C [ILLUSTRATION FOR FIGURE 6 OMITTED] depended largely on two years of very good breeding ([greater than]6 young per hen), without which the correlations were very low (r = 0.05 and r = 0.10 for cocks and hens, respectively).

Although large and variable, winter loss (Table 6, Appendix A) accounted for little of the variation in population change. Indeed, it was positively related to prior breeding success (suggesting compensation) at D, and likewise at C, although with a weaker correlation. Summer and subsequent winter losses of hens at C were negatively correlated, again suggesting compensation.

Numbers of Rock Ptarmigan shot at D were negligible (Appendix A). Associations at C between numbers shot (both sexes combined) and either winter loss (r = 0.31, P = 0.15) or population change (r = 0.32, P = 0.14) were weak; even so, they depended largely on one point when winter loss was 95 birds and 77 birds were shot (when we excluded this point, r = 0.04 and r = 0.16, respectively). Adding the number of birds shot to the regression of [log.sub.e[[N.sub.t] (both sexes) upon [log.sub.e][N.sub.t-1] increased [R.sup.2] insignificantly by [less than] 1%.

Density dependence. - Breeding success at D showed [TABULAR DATA FOR TABLE 6 OMITTED] no direct density dependence (Table 7), but good evidence of delayed density dependence, with poor breeding after high numbers, strongest at lag 3 (equivalent to fourth-order autoregressive density dependence). [TABULAR DATA FOR TABLE 7 OMITTED] Summer loss showed delayed density dependence, again strongest at lag 3. Winter loss showed negative delayed density dependence, with low loss after high numbers, strongest at lag 3.

At C, no significant delayed density dependence occurred in breeding success, summer loss, or winter loss (Table 7). Hence, the differences between D and C in the lag 3 density dependence of population change, [TABULAR DATA FOR TABLE 8 OMITTED] summer loss, breeding success, and winter loss paralleled differences (Table 4) in fourth-order autoregressive density dependence on granite (DS, BS, and LS) and schist (CS) submassifs.

Breeding success and recruitment. - Breeding success was the strongest correlate of population change (Table 5). One idea is that variations in breeding success and proportional changes in recruitment drive population change (Bergerud 1988). If so, one might expect the relationship between breeding success and population change [ILLUSTRATION FOR FIGURE 6 OMITTED] to be the same in both increase and decline phases.

To test this, we did analyses of covariance (Table 8), which explained population change in terms of breeding success, area, and phase. The relation between population change and breeding success had a significantly steeper slope in the increase than in the decrease phase (difference for cocks 0.68 [+ or -] 0.27 and for hens 0.60 [+ or -] 0.18). Overall, these data at D and C were consistent, and separate area-specific models gave similar results for each area, except that differences between slopes were insignificant for cocks at C ([F.sub.1,15] = 3.39, P = 0.086) and for hens at D ([F.sub.1,19] = 3.44, P = 0.079). These results go against the idea that variations in breeding success and proportional changes in recruitment were insufficient to explain population change.

Immediate determinants of breeding success

Breeding success (number of young reared per hen) involves the proportion of brood hens (those with young in late summer) and brood size (number of young per brood hen). Broodless hens can result from [TABULAR DATA FOR TABLE 9 OMITTED] loss of a whole nest or brood, whereas brood size depends partly on hatch-ability (the annual mean is always [greater than]90%; Watson 1965, Rae 1994), but mostly on clutch size and number of young lost. Nest loss can occur by desertion or predation, and chick loss by predation or other factors, such as starvation or chilling.

Differences between D and C. - At the infertile study area D, mean breeding success was lower than at C (0.98 [+ or -] 0.25 vs. 1.62 [+ or -] 0.32 young per hen, n = 14, paired t = 2.01, P = 0.066), as was brood size (2.04 [+ or -] 0.32 vs. 3.22 [+ or -] 0.52 young per brood hen, t = 2.39, P = 0.033). However, clutch size (6.37 [+ or -] 0.17 vs. 6.49 [+ or -] 0.18 eggs per nest) did not differ significantly, nor did the proportion of brood hens among total hens (0.60 [+ or -] 0.30 vs. 0.55 [+ or -] 0.29 brood hens). Breeding success at D and C was insignificantly related (r = 0.40, P = 0.16), as was brood size (r = 0.46, P = 0.18).

Nest predation and broodless hens. - Foxes took 20% of 30 clutches followed at D in 1946-1963 (Watson 1965) and 8% of 64 clutches in 1964-1978 (plus two clutches taken by crows). In 1964-1988 at C, 7% of 156 nests were taken (including the exceptional year 1971, when crows preyed on seven of the eight nests monitored; Moss and Watson 1984).

If nest-robbing reduces breeding success, the proportion of broodless hens will be higher. For each year, we classified this proportion as low ([less than]30%), middling (30-65%), and high ([greater than]65%). We used study area, broodless hen class, and the year 1971 at C as explanatory variables in a stepwise logistic regression, the dependent variable being the number of nests robbed out of the number of nests followed each year. This showed more robbing at D than C (15% vs. 3%, P = 0.0014). The robbing rate was unrelated to the proportion of broodless hens in all years but the exceptional 1971 at C (P [less than or equal to] 0.0001). Hence, nest predation was not a major, general cause of variation in the proportion of broodless hens.

Relationships within areas. - At D and C, breeding success each year was related to clutch size, brood size, and the proportion of brood hens (Table 9). The partial correlation between clutch size and brood size was strong when we kept the number of brood hens constant, but that between clutch size and brood hens became insignificant when we kept brood size constant. Also, the relationship between clutch size and breeding success at D and C (r = 0.77 at both, Table 9) lessened little when we kept the proportion of brood hens constant (r = 0.66, P [less than] 0.001 and r = 0.64, P [less than] 0.01 at D and C, respectively). In addition, population change was correlated with clutch size at D (cocks: r = 0.55, P = 0.003; hens: r = 0.35, P = 0.078) and C (cocks: r = 0.58, P = 0.003; hens: r = 0.61, P = 0.001), although correlations at C depended largely on two points with big clutches and big population increases.

From the previous correlations, we infer that clutch size, brood size, breeding success, and population change had a common antecedent cause. The proportion of brood hens, however, seemed to be affected by additional factors.

Clutch size, brood size, and the proportion of brood hens each showed delayed density dependence at D, but not C (Table 10). Hence, their inferred common antecedent cause seems to have been related to population density up to three years previously at D, but not C.

[TABULAR DATA FOR TABLE 10 OMITTED]

Young reared and recruited per egg laid. - During years of increase at D and C, breeding success rose with clutch size [ILLUSTRATION FOR FIGURE 7 OMITTED] at a rate faster than one young reared per egg laid (2.33 [+ or -] 0.34 young per egg; for [H.sub.o] = 1, [t.sub.34] = 3.86, P [less than] 0.001), but not during declines (Table 11). Area-specific models gave similar results at D and C separately, except that the clutch size x phase interaction was insignificant at C ([F.sub.1,15] = 3.59, P = 0.078).

Cock population change was related to clutch size in increase years, but not in decline years ([ILLUSTRATION FOR FIGURE 8 OMITTED] and Table 12), as was hen population change at C, but not D. Area-specific models showed similar results at D and C, except that the difference in slopes was insignificant for cocks at C ([F.sub.1,15] = 3.36, P = 0.087) and hens at D ([F.sub.1,19] = 2.08, P = 0.17).

Thus, bigger clutches in increase years were associated with more young reared per extra egg laid and either more recruits per extra egg, or fewer adult hens lost per extra egg laid, or both. In short, the hens' average return on investment (fitness per extra egg laid) was higher in years of increase than in declines.

Breeding success, clutch size, hatch date, timing of food plant growth, and weather

Variations in food and weather are likely to affect breeding success and clutch size, irrespective of any separate effects of population phase or past densities.

Blaeberry growth and spring temperature. - The timing of blaeberry growth at D and C was unrelated (n = 9, r = -0.14, P = 0.72). Growth at the higher D began later, and was affected by different weather. Therefore, the date of growth was more strongly related to mean April temperature at Braemar for area C and to May temperature for D. At D and C, respectively (n = 21 and 26), April values were r = -0.36 and r = -0.57 (P = 0.11 and 0.0027); May values were r = -0.48 and r = -0.18 (P = 0.027 and 0.39); and April-May values were r = -0.56 and r = -0.35 (P = 0.0089 and 0.10).

In years of early blaeberry growth at D, hatching was early, clutches were large (Table 9), and breeding success was high (r = 0.79, P [less than or equal to] 0.0001). At C, early blaeberry growth was again related to early hatching [TABULAR DATA FOR TABLE 11 OMITTED] (r = 0.70, P [less than or equal to] 0.0001), but not to significantly larger clutches or better breeding.

We did an analysis of covariance (SAS GLM, [R.sup.2] = 0.75), with median hatch date as the dependent variable and date of blaeberry growth and area as explanatory variables. The ANCOVA showed earlier hatching in springs with early blaeberry growth (4.0 [+ or -] 0.6 d earlier hatching per week of earlier growth, mean [+ or -]1 SE; [F.sub.1,43] = 50.1, P [less than or equal to] 0.0001), and later hatching at D than at C (4.3 [+ or -] 1.8 d; [F.sub.1,43] = 5.81, P = 0.02).

[TABULAR DATA FOR TABLE 12 OMITTED]

June weather. - Most chicks hatched in June. At D, breeding success was related to June temperature when we kept the date of blaeberry growth constant (Table 9). Other partial correlations suggested that June temperature affected both brood size and the proportion of brood hens at D. At C, which had a lower proportion of poorly drained ground than D, partial correlations (Table 9) indicated a positive effect of June rain on breeding success, acting through larger brood size, not a higher proportion of brood hens.

Cycles, plant growth, and weather

Cycles in plant growth? - The timing of blaeberry growth at D, but not C, showed apparent delayed density dependence on Rock Ptarmigan numbers at lag 3 (Table 10). There was evidence of a 12-yr cycle in growth timing at D (autocorrelation coefficient [r.sub.lag6] = -0.70 for raw and [r.sub.tag6] = -0.69 for detrended data, P [less than] 0.05), but it was inconclusive because of only 21 yr of data. This raises the possibility that a cycle in the timing of plant growth at D caused the observed cycles in clutch size and breeding success. However, hatch date did not show the significant delayed density dependence (Table 10) that one would expect from this possibility. Also, residuals from a regression of breeding success on blaeberry growth gave evidence of 10-yr cycles (autocorrelation coefficient [r.sub.lag5] = -0.49, n = 21, P [less than] 0.05), as did residuals from a similar regression for clutch size ([r.sub.lag5] = 0.50, n = 21, P [less than] 0.05). Thus, there was evidence of 10-yr cycles in breeding success and clutch size at D, independent of the timing of plant growth. Also, there was no indication of cycles in April or May temperature. Hence, the evidence is not consistent with the hypothesis that cycles in the timing of plant growth cause ptarmigan cycles at D.

Cycle timing and weather. - Peaks in Rock Ptarmigan walk data in 1943-1995 at DS came 1-2 yr after five of the seven years when mean June temperature at Braemar was [greater than]12.5 [degrees] C (1950, 1960, 1970, 1976, 1979, 1988, and 1992). This was unlikely (exact P = 0.0015), on the null hypothesis that June temperatures were in random order. A similar relationship occurred for BS in 1945-1995 (P = 0.0018).

Other observers' information for 1909-1942 showed four ptarmigan peaks (1912, 1923, 1934, and 1940; Appendix B). In 1900-1942, Braemar June temperatures [less than] 12.5 [degrees] C occurred only in 1933 and 1940 (no data in 1906-1911). Adding the early information to the DS walk data gave eight ptarmigan peaks from 1919 to 1995, six of which followed June temperatures [greater than] 12.5 [degrees] C by 1-2 yr (for six or more coincidences P = 0.0011; for seven out of eight ptarmigan peaks following 0-2 yr after June temperatures [greater than] 12.5 [degrees] C, P = 0.0032). However, a ptarmigan peak came in 1923 despite no June temperature [greater than] 12.0 [degrees] C in the period 19121932. This counters the idea that June temperatures alone caused ptarmigan cycles.

Overall, June temperatures (1912-1995) showed evidence of 10-yr cycles ([r.sub.lag10] = 0.28, P [less than] 0.05, no trends detected). The shape of the autocorrelogram [ILLUSTRATION FOR FIGURE 9 OMITTED] confirmed that the temperature cycle was due largely to a 1-yr spike in each decade, rather than a sinusoidal fluctuation.

The generally high numbers at all four submassifs in the 1960s coincided with a long run (1962-1970) of above-average ([greater than or equal to] 11.3 [degrees] C) June temperatures. The next longest runs of such temperatures were 1932-1937, 1992-1995, 1913-1915, and 1978-1980. Because summer loss was related to population change at D, low summer loss associated with warm Junes may have contributed to the lack of a marked decline in the 1960s. However, summer loss was not significantly related to Braemar June temperature ([r.sub.20] = -0.22 and [r.sub.20] = -0.18 for cocks and hens, respectively).

Sunspots. - Sinclair et al. (1993) suggested that sunspots, acting via weather and plant growth, entrained snowshoe hare cycles by phase-locking in periods of high sunspot activity (i.e., the 10-yr cycles occur irrespective of sunspots, but sunspots influence the timing). They noted that recent sunspot peaks were in 1969, 1979, and 1990, and hare peaks in 1971, 1981, and 1990. In the Cairngorms, Rock Ptarmigan peaked in 1971, 1981, and 1990 at DS, and in 1972, 1981, and 1989 at BS.

Although the annual mean sunspot number has peaked once every [approximately]10 yr since 1900 (1905, 1917, 1928, 1937, 1947, 1957, 1969, 1979, and 1989), peak sunspot activity (U.S. Department of Commerce 1986) was not consistently related to peak June temperature at Braemar. However, the first three sunspot peaks were the lowest (Mann-Whitney U = 0, P = 0.012), so the lack of a warm June at the 1923 ptarmigan peak occurred in a period of low sunspot activity. We will discuss cycle entrainment further.

DISCUSSION

Population trajectories on the four submassifs

Synchrony. - Agreement among counts and walk data showed fairly synchronous fluctuations within submassifs. Walk data ([ILLUSTRATION FOR FIGURE 4 OMITTED] at all four submassifs were low in the mid-1940s and late 1950s, but synchrony among submassifs lessened after generally high numbers in the mid-1960s (Table 3).

At DS, the 1944 trough was lower (2 adults/10 km) than later ones (5, 6, and 9 adults/kin). Gordon (1956) wrote that ptarmigan in the Cairngorms were scarcer in 1945 than he had ever known. Deep lows in the 1940s occurred in bags of Red Grouse in Scotland, England, and Ireland, Rock Ptarmigan in Scotland, Black Grouse (Tetrao tetrix) and Capercaillie (Tetrao urogallus) in Scotland (Mackenzie 1952), and Willow Ptarmigan (Lagopus lagopus) in Finland (Siivonen 1948). Because deep declines in Fennoscandia began at about the same time as in Red Grouse, Siivonen suggested a common cause such as weather. This agrees with the idea that irregular events such as bad weather may reduce different populations simultaneously, bringing them into a synchrony (Moran 1953, Ranta et al. 1997) that vanishes in more favorable times.

Cyclicity. - There was significant cyclicity at DS, BS, and CS, and probably at LS, although the latter had a short data run. The typical period length was -10 yr, but there were three intervals of 6-7 yr, one between 1934 and 1940 at DS, and two between 1964 and 1977 at CS. These coincided with years of general tetraonid abundance. Red Grouse bags were exceptionally high in Scotland in the 1930s (Mackenzie 1952, Hudson 1992) and very high in the late 1960s and early 1970s, when Rock Ptarmigan numbers [ILLUSTRATION FOR FIGURE 4 OMITTED] and Capercaillie bags (Moss 1993) were also high. The 6-7 yr period was associated with high densities, possibly caused by good summer weather such as the warm Junes of 1932-1937 and 1962-1970. Another response to good weather may be a rise in equilibrium density (as suggested by a run of high numbers in the 1960s at DS and BS).

As expected from model cycles generated by time-lagged equations (Royama 1992), walk data at DS, BS, and LS showed delayed density dependence, due to time lags between density and subsequent changes in number. Second- and fourth-order density dependence were detected from autoregressive equations (Table 4), the latter being confirmed by the 3-yr lag between breeding success and past density at D (Table 7). At C, in contrast, no delayed density dependence was detected by autoregression, it did not occur in breeding success, and cycles were more erratic.

Soil fertility

Food differed among submassifs, because the richer CS soils had a higher coverage of more nutritious food plants (Moss 1968, Moss and Watson 1984). High Rock Ptarmigan densities and brood sizes at C resembled those of Red Grouse on rich moors (Jenkins et al. 1967, Moss 1969, Moss et al. 1975). Like Red Grouse (Moss et al. 1988), cock ptarmigan tended to outnumber hens in declines at the poor-quality D, but not at C. The male excess in increase years at C, however, has no documented parallel in Red Grouse.

At both D and C, early hatching followed early blaeberry growth. At D, but not C, we detected associated increases in clutch size and breeding success. The boost to the laying hens' nutrition from early blaeberry growth presumably had more effect at D, where food plants were less nutritious. Chicks were intrinsically more viable at C than at D, high chick viability followed early plant growth, and chick viability could largely explain variations in breeding success in 19681971 (Moss and Watson 1984).

Clear 10-yr cycles occurred on poor soils, but a more erratic mixture of 10- and 6-yr cycles occurred on rich soils. Hence, differences in soil fertility may affect animal productivity, thereby contributing to geographical variations in cyclicity, such as the shorter period and lesser regularity of vole cycles from north to south Fennoscandia (Hansson and Henttonen 1988, Bjornstad et al. 1995).

Good breeding on rich soils should allow fast population growth. Models of populations with delayed density-dependent growth rate can show cycles that, with increasing intrinsic growth rates, first double in frequency and then become chaotic (May 1975). Rock Ptarmigan breeding success at D was lower than at C, and the 10- and 6-yr cycles at C are reminiscent of cycle doubling, as is the 1934-1940 cycle in the Cairngorms massif. Both model and observation suggest that greater intrinsic population growth rates (perhaps due to better food or weather) are associated with less stable population fluctuations.

Immediate demographic causes of population change

Population change, by definition, resulted from breeding success, summer loss, and winter loss. At D and C, it was correlated with breeding success (Table 5, [ILLUSTRATION FOR FIGURE 6 OMITTED]), albeit depending on two extreme years at C. At D, it was also related to summer loss, mostly emigration. Hence, declines at D may have been due partly to summer emigration, as in Red Grouse (Watson et al. 1984), and not simply to poor breeding. Although summer loss was less strongly related to population change at C, it varied at least as much as at D (Table 6). This indicated as much emigration at C as at D, given the few summer deaths noted (Appendix A).

Population change in Rock Ptarmigan was only weakly related to winter loss at D and C, in contrast to Red Grouse (Lance and Lawton 1990). As in Red Grouse, however, evidence of compensation in winter loss implied that shortage of potential recruits did not usually limit numbers. On a 500-ha area including D, emigration caused much winter loss after a spring rise of territorial behavior (Watson 1965). It is possible that birds took big territories following poor breeding, causing more emigration, which we recorded as winter loss.

Factors affecting breeding success

Food and weather. - The timing of blaeberry growth at D was related to hatch date, clutch size, and breeding success, but only to hatch date at C. Because C had a lower proportion of poorly drained ground than D, the flushes favored by downy chicks (Rae 1994) may have depended more on rain at C, explaining the unexpected positive association of June rain and brood size at C. Rain was less likely to be limiting at D, where warm Junes may have boosted plant and invertebrate production on flushes and ground irrigated by melting snow, thus explaining the association of temperature and breeding success there.

The timing of blaeberry growth at D and C was unrelated. Breeding success was related to the timing of growth at D, but not C, and to June temperature at D, but to June rain at C. We suggest that differences in hen and chick nutrition among submassifs, due to differences in altitude, soil, weather, and their interactions, contributed to population fluctuations being out of phase.

Other factors. - Predation of eggs and chicks had little effect on variations in breeding success. Hens laid more eggs and reared more chicks per extra egg laid in increase years than in declines ([ILLUSTRATION FOR FIGURE 7 OMITTED], Table 11), although the correlation depended on two extreme years at the more erratically fluctuating C. We infer that a hen's state largely determined her breeding success via clutch size and chick survival. State may involve diet, condition (Myrberget 1985), parasites (Hudson 1992), quality (Weeden and Theberge 1972), genotype (Page and Bergerud 1988), and stress (Boonstra and Singleton 1993). It may also involve fitness costs and benefits (Oksanen and Lundberg 1995), such that adults invest in more, better quality eggs and rear more young in increase years, when each chick's probability of being recruited is greater.

Population cycles, weather, and sunspots

June temperature at Braemar was cyclic and tended to spike 1-2 yr before ptarmigan peaks at DS and BS, with imperfect fit. However, phase-locking of ptarmigan cycles to a cycle in June temperature, perhaps via effects of warm Junes on breeding success, would not require a perfect fit (see Sinclair et al. 1993). Because June temperatures and breeding success were unrelated at C, there was no obvious mechanism for phase-locking on submassif CS.

We refuted the idea that June temperatures were in random order and that the association of peak June temperatures and ptarmigan peaks at DS and BS was random. This does not exclude the possibility of two separate, unlinked 10-yr bird and weather cycles (for two perfectly regular 10-yr cycles, the probability of each possible time association occurring by chance is quite high at 0.1).

The 10-yr cycle in June temperatures at Braemar was inconsistently related to sunspots, but sunspots might affect June temperature indirectly via climate cycles, thereby introducing extra variability into any relationship between sunspots and animal performance. In short, our data are consistent with the idea (Sinclair et al. 1993) that sunspots entrain the 10-yr cycle of wildlife, but only on poor soils.

Refuting hypotheses on the cause of population cycles

There is still no consensus on the biological causes of population cycles. Most ecologists agree that cyclic population trajectories should show delayed density dependence, but even this is questionable, as we could not detect density dependence in the cyclic population at CS. However, progress has been made by refuting specific hypotheses as necessary causes in particular cases. In Red Grouse, for example, four hypotheses are so refuted (Moss et al. 1996): (1) predator-prey relationships, (2) maternal nutrition, (3) host-parasite (cecal threadworm Trichostrongylus tenuis) relationships, and (4) a later version of Chitty's (1967) genetic hypothesis.

Our data on breeding success confirm that predator-prey interactions are unlikely to cause Scottish Rock Ptarmigan cycles. Furthermore, simple predator-prey oscillations probably require specialist predators (Hanski 1987), but all predators in our study were generalists. Work on a separate area (A. Watson and R. Moss, unpublished data) shows that artificially increased numbers of generalist predators (crows) dampen, rather than cause, Rock Ptarmigan cycles.

Maternal nutrition affected ptarmigan chick viability and breeding success (Moss and Watson 1984). We cannot refute the possibility that cycles in maternal or chick nutrition caused population cycles. However, the evidence countered the idea that cycles in spring temperature cause Rock Ptarmigan cycles via plant growth and breeding success.

Most Scottish Rock Ptarmigan have no cecal threadworms or other internal macroparasites; hence, these cannot cause ptarmigan cycles (Watson and Shaw 1991). The viral (Flavivirus) disease "louping ill" kills Red Grouse (Duncan et al. 1978), but the sheep ticks (Ixodes ricinus) that transmit it have not been recorded on Scottish Rock Ptarmigan (Watson and Shaw 1991).

The hypothesis of Chitty (1967) is a specific case of the idea that unstable dynamics result from interactions between different parts of a structured population. Another hypothesis is that cycles are due to differential behavior between kin and non-kin (Mountford et al. 1990, Watson et al. 1994). Testing of both hypotheses requires marked animals, which we did not have.

Possible role of parental investment

The evidence of compensation in winter loss suggests that there is no shortage of potential recruits on the study areas, which were probably all "sources" (Study areas) with net emigration. In particular, summer emigration contributed to cyclic declines at D, as in Red Grouse (Watson et al. 1984), where cyclic declines involved summer emigration of entire families, the parents returning in fall without young.

Hens at D laid more eggs in increase years, when proportionately greater fitness benefits followed ([ILLUSTRATION FOR FIGURE 7 OMITTED] and 8). There might be a trade-off between investment and survival, such that adults survive better when investing less in breeding (Steen and Unander 1985). We suggest that breeding is poor in cyclic declines primarily because hens invest less in eggs and chicks; this causes poor breeding, which may contribute to declines, but is not sufficient to cause them.

Spring sex ratios may reflect hen investment on cock territories. There were fewer hens per cock in springs of decline at D. Perhaps young hens left with their families in summer and invested breeding effort where fitness benefits were high, possibly in rising populations. In Red Grouse, too, there were fewer hens per cock in declining populations on infertile ground (Moss et al. 1988). This did not occur at the richer C area, perhaps because better food allowed relatively more hen investment in periods of both decline and increase.

The suggestion that cycles are due to differential behavior between kin and non-kin (Mountford et al. 1990, Watson et al. 1994) involves neighboring cocks being more closely related during the increase phase, with relatedness facilitating recruitment. Relatedness is therefore a correlate of population change. Thus, hens could invest more in breeding in years of high cock relatedness, which would be followed by more recruitment and increased population density.

Wider comparisons

Cycle period can vary within grouse species (Watson and Moss 1979, Lindstrom 1994). Frequently reported periods are 3-4, 6-7, and 10-11 yr. Because 6-7 and 10-11 yr fluctuations can occur in the same population (Weeden and Theberge 1972, Moss et al. 1996; present study), it is possible that the same mechanism causes them. The 3-4 yr cycles may be due to predators switching from their main rodent prey to grouse prey when rodents are scarce (Angelstam et al. 1984, Lindstrom et al. 1994). However, in his 24-yr island study of 3-4 yr cycles in Willow Ptarmigan, Myrberget (1982) found that three out of five vole crashes occurred without mustelids or other predators that could switch to eggs and chicks.

Myrberget's (1984a, b, 1985, 1986, 1988, 1989) data resemble ours in that: (1) clutch size was related to breeding success, which (2) was the main correlate of population change; (3) the proportion of young that recruited next spring was lower in periods of decline; and (4) there was compensation, with low winter loss after poor breeding. Thus, all four features occurred in 3-4 and 10-yr cycles.

Rock Ptarmigan 10-yr cycles have been studied in Alaska (Weeden and Theberge 1972) and Iceland (Gardarsson 1988). In Alaska, parallel variations in clutch size, nest loss, and winter loss of young birds combined to raise or reduce numbers. In Iceland, winter loss of young was the main cause of population change, and breeding success was always high compared with that in Scotland. In Scotland, parallel variations in clutch size, breeding success, and seemingly disproportionate losses of young in decline phases [ILLUSTRATION FOR FIGURE 6 OMITTED] caused population change. There was evidence, in all three countries, that the proportion of young reared in summer and recruited into the breeding population by next spring was lower in declines. This applied also to the 10-yr cycle of Willow Ptarmigan in Newfoundland (Bergerud 1970) and to Red Grouse in Scotland (Moss et al. 1996). We suggest that cyclic declines in these populations had a common mechanism, whereby a lower proportion of young was recruited into the spring population, and that differences between populations were incidental.

There is no need to invoke natural enemies to explain our results; in particular, the data are inconsistent with hypotheses involving predation, as Gudmundsson (1960) concluded for Icelandic Rock Ptarmigan. Our hypothesis is that Scottish Rock Ptarmigan show unstable dynamics, driven by intrinsic positive feedback between recruitment in successive years, regulated by negative feedback between recruitment and population density, and modified by nutrition, which, in turn, is affected by the physical factors of soil fertility and weather.

ACKNOWLEDGMENTS

We thank W. Bain, S. Cumming, R. Hepburn, and P. Ord for bag records, A. J. Sinclair and C. J. Krebs for sunspot data, P. Rothery for statistical advice, D. Elston for a computer program, K. Goodsir and A. Webb for Fig. 1, and A. T. Bergerud, X. Lambin, S. Redpath, P. Rothery, N. Picozzi, and an anonymous referee for comments.

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Weeden, R. B., and J. B. Theberge. 1972. The dynamics of a fluctuating population of Rock Ptarmigan in Alaska. Proceedings of the International Ornithological Congress 15: 90-106.

APPENDIX A

DEATHS AND LOSS

Shooting

Data (Table A1) for submassifs CS, BS, and LS were of Rock Ptarmigan shot on areas covered by walk data [ILLUSTRATION FOR FIGURE 1 OMITTED]; those for area C came from a bigger area that included C.

Summer deaths and loss

During nest searches and summer counts at D, a dead cock and a dead hen were seen in 1952, two dead hens in 1964, and a dead hen in each of four other years. At C, three cock corpses and a dead hen were seen, the most in a summer being two dead cocks. On 24 July 1995, SR broke up six ptarmigan corpses and put their remains out on C. He simulated 18 deaths (15 corpses, or parts thereof, and three feather clumps in holes such as a fox makes), in places and numbers unknown to AW, and he saw a corpse of a wild bird. AW and a fairly inexperienced, young dog found 11 corpse units and three feather clumps in a replicated area count on 31 July and 7 August, and three more corpse units on the next count in spring 1996; AW checked numbers and locations later with SR. In total, 89% of the 19 corpses were found. Therefore, most adult summer deaths were likely to be seen, especially as all counts up to July 1995 involved two or three highly experienced dogs. Because most summer adult deaths were found, most summer loss (Table 6) entailed emigration.

Summers with total counts at D showed no cock gains and only one extra hen in 1955 and 1957. In 1952, 1954, and 1955, when several counts were done each spring, many territorial and nonterritorial birds vanished over short periods as late as May, without dead ones being seen, so Watson (1965) inferred emigration. At C, small summer gains of up to 21% for cocks (14 plus 3) and 14% for hens (14 plus 2) occurred in 1969, but losses were more usual, up to 78% for cocks and 72% for hens.

Winter mortality and loss

Feathers were conspicuous on the short vegetation, but blew away on hard snow, so the proportion of winter deaths seen may have been lower than in summer. At D, 117 deaths were noted from mid-August to April: 58 deaths attributed to foxes, 30 to fox or eagle, 28 to eagle, and one to a Peregrine Falcon. The most in a winter was eight deaths. No ptarmigans were shot in 1951-1993, except 16 birds in winter by AW, the most in a winter being 12 birds in early 1952 (Watson 1965).
TABLE A1. Number of Rock Ptarmigan shot.

Year       CS(*)       C(**)       BS(***)       Year       LS(****)

1966         45           41          0          1945         6
1967         77           77          0          1951        73
1968         10            2          0          1952        53
1969          0            0          0          1953        33
1970          2            0          0          1954         1
1971         17           17         55          1962        40
1972          0            0         38          1963        82
1973          2            2         71          1964        95
1974          0            0        114          1965        33
1975          0            0          6          1966        37
1976         13           13         92          1983        16
1977          0            0          0
1978         29           29         28
1979          3            0         97
1980         28           28         41
1981         19           19        105
1982         16           16         30
1983         21           21        183
1984          4            4        124
1985         24           24         31
1986         37           37         46
1987         19           19         35
1988         63           33         41
1989         55           55         16
1990         40            8         99
1991         99           81         59
1992         28           20         28
1993         17           17         10
1994         14           14          2
1995         16           16          0

* Including the Rhiedorrach beat (Carn Mor, Cairnwell, Glas Choire
Mhor, County boundary) and the Glen Shee beat. Data before 1966 are
incomplete.

** Data for C were from the Cairnwell and the Glen Shee beat, bigger
areas that included C.

*** No ptarmigan were shot in 1940-1951, four were shot in 1951, and
none were shot until 1971.

**** No ptarmigan were shot in intervening years.


Winter deaths seen at C totalled 68 ptarmigan. Predators took 35 birds (26 by fox, seven probably by fox, and two by eagle), 31 flew into ski lift cables, one flew into a car, and one showed no sign of violence. The greatest winter loss was in 1988-1989 (eight accidents and seven predator kills). Numbers shot on and near C were noted (mean 16, range 077 ptarmigan), about two-thirds of them being shot on C.

Winter loss at D (Table 6) varied between years, in cocks from an 8% gain to a 67% loss, and in hens from a 45% gain to a 63% loss. Winter gain implied immigration, but might have been due to summer emigrant adults returning. In 1968, however, few or no adults emigrated and no young were reared, so the winter loss of 0% males and only 9% females indicated compensation.

Winter loss at C varied from a 29% gain to a 75% loss for cocks, and from an 80% gain to an 80% loss for hens. Although no young were reared in 1975 and 1979, and there was no material net adult emigration in these summers, winter loss of hens and cocks was zero, indicating compensation. Again, despite no young being reared in 1975 and 1976, spring numbers in 1975-1976 rose from 12 to 22 cocks and from 12 to 15 hens, and in 1976-1977 from 15 to 18 hens. We infer that immigration contributed to population change.

APPENDIX B

OTHER OBSERVERS' INFORMATION

The ordinal information (Table B1) was from Gordon (1912, 1915, 1923, 1925, 1931, 1943, 1951, 1956; personal communication) for the Cairngorms massif generally, and from D. and C. Nethersole-Thompson (personal communication) for the massif's north side. Table B 1 gives Gordon's records for 1909-1927 and the Nethersole-Thompsons' [TABULAR DATA FOR TABLE B1 OMITTED] for 1928-1964. Gordon noted the 1930 trough, the 1934 peak, and the following decline. He reported "high" numbers in 1940, "quite good" in 1941, "still fair" in 1942, "very scarce" in 1943, and scarcer at war's end than he had ever known. He recorded a rise from 1945 to a peak in 1951, and a fall in the mid-1950s.
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Date:Jun 1, 1998
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