Searching for mechanisms of synchrony in spatially structured gamebird populations

Authors


Dr Isabella M. Cattadori, Institute of Biological Sciences, University of Stirling, Stirling FK9 4LA, Scotland, UK. Fax: 44 1786 464994. E-mail: imcc1@stir.ac.uk

Abstract

1. Time series data on five species of gamebird from the Dolomitic Alps were used to examine the relative importance of dispersal and common stochastic events in causing synchrony between spatially structured populations.

2. Cross-correlation analysis of detrended time series was used to describe the spatial pattern of fluctuations in abundance, while standardized time series were used to describe both fluctuations and the trend in abundance. There were large variations in synchrony both within and between species and only weak negative relationships with distance.

3. Species in neighbouring habitats were more likely to be in synchrony than species separated by several habitats. Species with similar density-dependent structure were more likely to be in synchrony.

4. In order to estimate the relative importance of dispersal and environmental stochasticity, we modelled the spatial dynamics of each species using two different approaches. First, we used estimating functions and bootstrapping of time series data to calculate the relative importance of dispersal and stochastic effects for each species. Second, we estimated the intensity of environmental stochasticity from climatic records during the breeding season and then modelled the dispersal rate and dispersal distance for each species. The two models exhibited similar results for rock ptarmigan, black grouse, hazel grouse and rock partridge, while contrasting patterns were observed for capercaillie.

5. The results suggest that environmental stochasticity plays the dominant role in synchronizing the fluctuations of these galliform species, although there will also be some dispersal between populations.

Introduction

A central objective of population ecology is to understand how populations are spatially structured. An informative way of looking at this is to describe how species abundance varies temporally and spatially and then to identify the mechanisms that can cause synchrony. A pattern common to many taxa is a decrease in synchrony with distance between populations (e.g.

Marcström, Höglund & Krebs 1990; Steen, Yoccoz & Ims 1990; Thomas 1991; Hanski & Woiwod 1993; Pollard, Van Swaay & Yates 1993; Ranta, Lindström & Lindén 1995a; Ranta et al. 1995b; Sutcliffe, Thomas & Moss 1996; Heino et al. 1997; Ranta et al. 1997a,b; Ranta, Kaitala & Lindström 1997c; Ranta, Kaitala & Lundberg 1998; Bjørnstad, Stenseth & Saitoh 1999). Two principal mechanisms have been identified as the possible cause of spatial synchrony. First, dispersal between spatially structured populations (Maynard Smith 1974) and second, the correlated effect of density-independent factors that synchronize populations with the same density-dependent structure, a process referred to as the Moran effect (Moran 1953; Hanski 1991; Royama 1992; Ranta et al. 1997a; Cattadori et al. 1999; Hudson & Cattadori 1999; Koenig 1999). There is also a third mechanism, where predator–prey interactions are responsible for synchrony in prey fluctuations. This may operate through the large-scale effect of nomadic avian predators on local prey populations or as a consequence of specialist predators shifting their attention to an alternative prey during the decline of the main prey (Ydenberg 1987; Korpimäki & Norrdahl 1989; Ims & Steen 1990; Small, Marcström & Willebrand 1993). The relative importance of each mechanism seems likely to depend to some extent on scale. At the local scale, dispersal between populations may well dominate, whereas at higher scales where distances exceed dispersal distances, synchrony is more likely to be caused by correlated stochastic factors (Moran 1953; Pollard 1991; Hanski & Woiwod 1993; Ranta et al. 1995a,b; Sutcliffe et al. 1996; Ranta et al. 1997a, 1998). Synchronized predation may operate at all scales but will only generate synchrony in the abundance of prey when operating at relatively large scales (Korpimäki & Norrdahl 1989; Ims & Steen 1990; Heikkilä, Below & Hanski 1994). While dispersal seems to operate principally at the local scale, recent theoretical studies have shown that populations with cyclic or complex to chaotic dynamics can exhibit broad-scale synchrony by local dispersal, two processes referred to as phase locking and fitness-dependent dispersal (Ruxton 1996; Blasius, Huppert & Stone 1999; Ruxton & Rohani 1999). Distinguishing between dispersal and common stochastic events is an important problem in population biology because it has repercussions on the persistence of local populations and the risk of global extinction (Heino et al. 1997; Heino 1998; Palmqvist & Lundberg 1998).

The only clear way to distinguish between the two principal processes is by experimentally preventing dispersal or by decoupling the environmental density-independent factors. Such experiments on natural populations are logistically difficult. Nevertheless, a study on populations of Soay sheep in the St Kilda archipelago was able to dismiss the possible role of dispersal because sheep populations were separated by several kilometres of lethal Atlantic Ocean (Grenfell et al. 1998). Analyses of population data, with modelling, demonstrated the important role of climatic perturbations in driving the synchronous fluctuations of these closed populations and identified that nonlinear density dependence can have a desynchronizing effect. Of course, dispersal and the Moran effect are not mutually exclusive and it seems likely that both may operate in many systems although the relative importance varies. At the current time the predation hypothesis is considered a special case. The parsimonious hypothesis is that large-scale synchrony can be caused by the Moran effect while local synchrony may be caused by a combination of the two. Ranta et al. (1995a,b) used a simulation model to examine the relative effects of the two mechanisms and concluded that both can independently drive synchrony but that superimposing the Moran effect on dispersal sharply improved the cross-correlations.

The experimental manipulation of natural populations to detect the mechanism of synchrony is usually logistically limited and the only solution is to apply statistical techniques that can indicate the relative importance of the mechanisms. In this paper, we examine this issue by looking at spatial synchrony within and between closely related species inhabiting the same area. We postulate that synchrony between species, particularly those inhabiting similar habitats, is probably caused by correlated environmental factors. By investigating the patterns of synchrony within and between species and by applying simple models, we argue that we should be able to obtain an estimate of the relative importance of dispersal and common environmental stochasticity.

The alpine gamebirds provide a suitable data set to examine problems of spatial synchrony. All the species are restricted to discrete mountain groups and exhibit a distinct altitudinal distribution, with the woodland grouse at the lower altitudes and the open-habitat species on the mountain plateaux. The data set is based on long-term hunting statistics, which provide a reasonable estimate of changes in abundance (Cattadori & Hudson 1999; Cattadori et al. 1999). Population data on gamebirds are particularly useful because they are collected in the autumn and exhibit large-scale fluctuations in abundance, which are driven principally by changes in productivity and particularly the mortality of chicks during the first few weeks of life. While a number of workers have highlighted the importance of climatic conditions in influencing survival of gamebird chicks, it is apparent that other factors, such as the availability of invertebrate food, the condition of the female or the effect of predation, will also play a role (Hudson 1986; Potts 1986; Potts & Aebischer 1994). Even so, harsh weather conditions are likely to have either a direct or indirect negative effect on the survival of chicks and we can expect these stochastic effects to be one of the principal synchronizing forces in gamebirds. The climatic data for Trentino is aggregated into different macroclimatic areas and this distribution avoids some of the confounding interactions between correlated weather and distance (Boato, Arrighetti & Osti 1988; Gafta 1994; Cattadori et al. 1999).

In this paper we specifically address three questions:

1. Do closely related galliform species exposed to common stochastic events exhibit similar patterns of synchrony?

2. How does synchrony vary between species relative to habitat differences?

3. Is dispersal or common stochastic events the cause of spatial patterns of synchrony observed in galliforms?

We reproduce the spatial patterns of synchrony using two spatially explicit models. First, we estimated both the dispersal and the effect of environmental perturbations using the Ricker model and estimating functions method (Godambe 1991; Lele, Taper & Gage 1998). Second, we applied the Ricker model assuming a priori the stochastic effect of a climatic variable and then estimated the dispersal rate and dispersal range of each species using the modifications applied by Ranta et al. (1995b, 1997c).

Materials and methods

Study area

Trentino (6250 km2) is an autonomous province situated in the Dolomitic Alps in north-east Italy. Altitude ranges from 65 m to 3750 m a.s.l. and the mountains fall into 18 discrete mountain groups separated by obvious valleys with orchards and vineyards (Fig. 1a). The climate within each mountain group is dominated by two rainfall patterns. First, the annual precipitation that divides the province into three distinct areas: an eastern and a western wet zone where precipitation exceeds 1000 mm per year, and a central dry zone with precipitation less than 1000 mm per year (Boato et al. 1988). Second, the seasonal distribution of the precipitation that divides the southern, prealpine, subcontinental area with an equinoctial peak in rainfall, from a northern area with continental conditions and a summer peak in rainfall (Gafta 1994). The combination of these two patterns determines the macroclimates of the province, which varies both from west to east and from south to north.

Figure 1.

(a) Map of the province of Trentino showing the 18 discrete mountain groups and (b) altitudinal distribution of the five gamebird species with respect to main habitat type in Trentino.

Climatic factors

We postulated that severe weather conditions during the period of brood rearing were likely to be the main density-independent feature determining synchrony in these data for three reasons. First, the data describe the variance in hunting statistics from one year to the next and it is well known that year-to-year variance in these data are influenced principally by chick survival (Bergerud, Mossop & Myrberget 1985; Potts 1990; Hudson 1992; Potts & Aebischer 1994). Second, harsh weather conditions are likely to be the main density-independent factor reducing chick survival. During the first few weeks of life chick growth rate is high, chicks become independent of the parents brooding behaviour and thus are vulnerable to exposure during wet, cold periods. Third, previous works on gamebirds in the Alps have highlighted the significance of summer rainfall when accounting for year-to-year variation in chick survival (Zbinden 1987; Klaus, Seibt & Boock 1991; Bernard Laurent, Leonard & Reitz 1992; Bernard Laurent 1994; De Franceschi 1994).

Climate data were collected from 1965 to 1994 from 31 meteorological stations distributed throughout the province and located at different altitudes (from 70 m to 2125 m). The stations were assigned to the mountain groups in which they resided and a monthly mean was estimated for each climatic variable and for each mountain group. Data were not corrected for altitude because we were not concerned with the mean but the variation of the variables between years, in particular the occasional extreme years that would synchronize populations. Following previous studies on gamebirds, we postulated that two climatic variables were likely to have a significant influence on chick survival: cold periods and summer rainfall storms (Potts 1986; Zbinden 1987; Meriggi et al. 1990; Bernard Laurent et al. 1992; Hudson 1992; Bernard Laurent 1994; De Franceschi 1994). Cold weather was measured as the average of the monthly minimum temperature, and rainfall storms as the total monthly millimetres of rainfall per days of rain. As rainfall was recorded for a longer period of time and from most of the climatic stations in the province, we used mean rainfall per day of rain in July as the stochastic climatic variable in the analysis. July is considered to be the crucial period of hatching for the majority of galliform species in the Alps, although annual changes in the climatic conditions can influence the spread of hatching between years (Brichetti, De Franceschi & Baccetti 1992). Climatic and population temporal variability in each mountain group was estimated using the coefficient of variation (Sokal & Rohlf 1981).

Species and hunting statistics

The five species of gamebird that inhabit the Dolomites exhibit an altitudinal distribution, associated with a change in habitat type (Fig. 1b). Hazel grouse (Bonasa bonasia) inhabit the lower and medium altitude woodland (700–1200 m average range) and are associated with a mosaic of deciduous trees and conifers in different aged stands. Capercaillie (Tetrao urogallus) (1100–1500 m average range) inhabit the mature, well structured coniferous forests at higher altitude, while black grouse (Tetrao tetrix) (1400–1900 m average range) are more widespread and can overlap with both capercaillie and the open landscape rock partridge. Above the timberline, the habitat opens out into typical rocky alpine prairies and meadows inhabited by rock partridge (Alectoris graeca saxatilis) (800–1900 m average range). Rock ptarmigan (Lagopus mutus) (2000–2400 m average range) are restricted to the high mountain plateaux in boulder screes (Artuso 1994).

Hunting statistics were obtained for each species from the 210 administrative hunting areas of the province between 1965 and 1994. Time series were summed within each of the 18 main mountain groups of Trentino (Cattadori & Hudson 1999; Cattadori et al. 1999). Shooting of hazel grouse ceased in 1987 and of capercaillie in 1989. A restriction on the number of animals shot per season was imposed in each of the hunting areas of the whole Trentino, except for hazel grouse, although the maximum limits were never reached (Anonymous 1991). Both sexes were hunted except for black grouse and capercaillie where hunting was restricted to the males. The hunting season started in mid-September and lasted to mid-December, and the number of days available for hunting each year was set between 22 and 44 hunting days for all species. Hunting was limited to local people. The Hunting Association of the Province of Trento monitors the number of animals harvested in each hunting area and provides hunting licences to local people, with no limit on the number of licences produced each year. The total number of hunters was recorded from 1974 to 1994, and the hunting effort was measured as the number of hunter*days each year. Further details on hunting strategy are presented elsewhere (Cattadori & Hudson 1999; Cattadori et al. 1999).

The number of grouse shot in Trentino varied between species and year. Hazel grouse was the species with the greatest number of animals shot (from the mountain groups: median = 111·5, min = 1, max = 717) followed by much lower numbers of rock partridge, black grouse and rock ptarmigan (from the mountain groups: median = 33·5, 26 and 17·5, min = 0, max = 298, 418 and 388, respectively). Few Capercaillie were shot (from the mountain groups: median = 9·2, min = 0, max = 109). For black grouse and rock partridge summer counts were available in sample areas between 1992 and 1997. The total number shot was linearly correlated with the summer counts for both species (variance explained by the model R2 = 0·13 and R2 = 0·33, respectively, P < 0·001).

Time series analysis

Each time series was log transformed log(x + 1) where x = numbers shot. Time series with more than five missing values or more than five zeros were ignored. In time series with less than five missing values, the points were interpolated by averaging the neighbouring data values. Because most of the time series exhibited a downward trend, this trend was removed by fitting a third-order polynomial model (xt= b0 + b1t + b2t2 + b3t?) and the residuals used for time series analysis. We restricted our analysis to 68 time series: 18 black grouse, 16 hazel grouse, 14 rock partridge, 10 rock ptarmigan and 10 capercaillie (Fig. 2).

Figure 2.

Detrended time series of hunting statistics for each species from each mountain group.

The pattern of density dependence was investigated by plotting population growth rate Rt(= logxt+1 − logxt) against abundance (xtand logxt) using the original detrended time series. The relationship between Rtand xt was linear in all species and similar to the relationship assumed in the Ricker model. As such, we felt the application of the Ricker model provided a suitable description of grouse dynamics (Fig. 3). The order and strength of direct and delayed density dependence was estimated using partial autocorrelation function analysis (Box & Jenkins 1976; Royama 1992) with significance determined from the lags greater than 2 standard errors of the white noise (Bartlett bar). This analysis was repeated using time series corrected and not corrected for hunting effort to determine whether the intrinsic structure is affected by hunting efficiency.

Figure 3.

The relationship between annual population growth rate Rt(= logxt+1 − logxt) and population abundance, xt, for each population of gamebird species in Trentino.

Spatial synchrony

The degree of spatial synchrony within each species was evaluated using cross-correlation analysis with bootstrapping at time lag 0. This procedure involved the random re-sampling of data pairs with replacement from each pair of original time series to generate new time series of the same size. Mean cross-correlation, standard deviation and confidence limits (95%) were estimated by bootstrapping the data with 1000 random resamples (Efron 1982; Efron & Tibshirani 1993). Cross-correlation was undertaken using detrended time series to investigate the strength of stochastic fluctuations in abundance of populations. Cross-correlation was again repeated using standardized time series to examine the combined strength of fluctuations and the general population decline. Basically, the log-transformed series were re-scaled to zero mean and unit variance, to remove specific differences both in population abundances and mountain groups, while maintaining the general characteristic of the data (Sokal & Rohlf 1981). The pattern of spatial synchrony was examined from the relationship of cross-correlations between populations on the Euclidean distance between the central points of each population in each mountain group. Because the mountain groups vary in size, altitudinal range and species composition it was not possible to measure the actual distance between populations. In the model we simplified Trentino to a grid where each intersection of the grid represented the centre of a mountain group and the distance between the intersections was the relative distance between the mountain groups. We assumed that the likelihood of movement between mountains was dependant only on relative distances and the relative abundance in both mountain groups.

Synchrony between species used the same techniques as estimating synchrony within species. We estimated the relative ‘habitat distance’ between species within mountain groups as the number of intervening habitats, ranging from 1, the distance between neighbouring species, to 4, the distance between hazel grouse in the deciduous woodland and rock ptarmigan on the mountain plateaux (Fig. 1b). Synchrony between species was repeated both for detrended series and standardized series.

Modelling the dynamics of spatially structured populations

To assess the relative importance of dispersal and common stochastic effects we applied two approaches. First, we estimated both the dispersal and the impact of environmental perturbations without any general assumptions using the Ricker model and estimating functions method with bootstrapping (Godambe 1991; Lele et al. 1998). Second, we assumed that specific climatic factors had an impact on chick survival and, using these data, we estimated dispersal rate and range again using the Ricker model.

Estimating dispersal and environmental stochasticity

The Ricker model was applied to the time series using the actual spatial structure of gamebird populations in Trentino and following the approach of Lele et al. (1998) the model was modified as follows:

image(eqn 1)

where r is the intrinsic growth rate and b is the impact of intraspecific competition on growth rate. Both these parameters were assumed to be spatially homogeneous. The environmental noise was εit at time t in the ith patch and for each patch it combined the effect of the local and the regional stochasticity. The environmental noise was assumed to be temporally independent but spatially correlated and decreased exponentially with distance according to the following covariance model:

image(eqn 2)

where σ2 is the variance of the perturbation, ρ correlation parameter with range [0–1) that describes the strength of correlation of the environmental noise between the mountain groups, such that the spatial covariance is directly related to ρ and decreases exponentially with the distance, ||si – sj||. The distance is calculated between the centre of mountain group i and mountain group j. The model was modified to include dispersal between mountain groups:

inline imageeqn 3

where k(si,sj) is the proportion of individuals that migrate from mountain group i to mountain group j, and k(sj,si) is the proportion of individuals that immigrated into i from j. We assumed that dispersal depends only on the distance between mountain groups. For each species we modelled dispersal in two ways: we first used a half exponential model (sensuLele et al. 1998):

image(eqn 4)

where δ is the dispersal parameter with values between [0,1) and ||sj − si|| is the distance between the mountain groups.

Second, we used a half Gaussian model (sensuLele et al. 1998):

image(5)

where, again δ is the dispersal parameter with values between (0, + ∞) and k(si, sj) is the proportion of individuals that migrate.

We opted for a general spatial model and instead of estimating 39 different demographic parameters for each species, we calculated only five demographic parameters r, b, σ2, ρ and δ. These parameters were estimated from the time series using the estimating functions method, and a mean value was calculated using bootstrap replicates of time series for each species (for details see Godambe 1991; Lele et al. 1998). The general approach of this technique consists of equating a set of linear functions to zero and solving the equations to select the parameters that satisfy the set of equations simultaneously. For each species, the estimated parameters were used to generate time series with bootstrap resampling procedures and the distribution of the parameters and the cross-correlation coefficients were estimated at 90% confidence intervals. We implemented 100 replicates for each pair of time series making no assumptions about the pattern of distribution of the parameters.

Estimating dispersal after assuming the pattern of stochasticity

We considered a simpler model with a reduced number of parameters but incorporating assumptions on the pattern of environmental stochasticity. Again, we applied the basic Ricker model without intraspecific competition on growth rate:

image(eqn 6)

where xit is the population size at time t in the ith mountain group and rit is the fecundity parameter at time t in the ith mountain group. Following the approach of Ranta et al. (1995a,b, 1997a) and Heino et al. (1997) the model was modified to include dispersal between mountain groups thus:

image(7)

where: i, j and k are mountain group indices, ||si − sj|| is the Euclidean distance between mountain group i and mountain group j, and c is an inverse parameter of dispersal distance (c > 0), such that when c approaches zero the probability that an individual will cover long or short distances is the same between the mountain groups. In Ranta's model, m was defined as the constant fraction of dispersing individuals from each patch (0 < m < 1), in our model dispersal mit was assumed to be density dependent because this is more relevant to gamebird populations (e.g. Potts 1986; Hudson 1992):

image(eqn 8)

where parameter M represents the fraction of migrants from an infinite population (x >> 0). From the simulations we estimated the mean dispersal rate between the populations of each species:

where T is the length of the time series and N the number of mountain groups.

Environmental stochasticity was considered at two levels: the local level of each mountain group, uit, and the regional level of all 18 mountain groups, zt. Local noise was considered to affect the growth rate as follow:

image(eqn 10)

where uit is assumed to be a sequence of independently and identically distributed random variables, uniformly distributed [– ui, ui], and r the maximum reproductive rate. Regional noise, zt, influenced population abundance at time t as:

image(eqn 11)

where the intensity of occurrence zt changes annually with a probability of occurrence p with range 0 ≤ p < 1 (Ranta et al. 1995b; 1997a). When the intensity deviated from zero in year t, the intensity was assumed to have a uniform distribution [z − σz, z + σz]. The lower zt the stronger the Moran effect (Ranta et al. 1995a,b; 1997a). To remove the amplifying effect of unit measure on the variance of the stochastic event, the parameters of regional and local noise were re-scaled. Basically, the climatic variables of each mountain group were multiplied to a constant parameter that removed the amplifying effect of the unit measure, while the relative effect between mountain groups remained the same. The re-scaled parameters were within the range of values reported for the environmental stochasticity by Ranta et al. (1995b).

The mean fraction of migrants m, and the range of dispersal, c, were estimated by fitting the model to the detrended time series of each species and minimizing the mean squared error. For each time series, 1000 simulations were carried out and a smoothed version of the mean squared error was obtained. Parameter M was calculated at 0·05 steps and parameter c at 0·25 steps and then selecting the value that minimized the smoothed model error.

For each species, we defined the parameters as follow:

r the log of the maximum reproductive rate taken as the maximum clutch size for each species in the Alps (Brichetti et al. 1992 and see Table 2),

Table 2. . Population parameters, dispersal and stochastic perturbations estimated using Ricker model with estimating functions method and half exponential dispersal. Bootstrap confidence intervals (90%) are shown in parentheses. The best fit, mean squared error of the model for each species is shown in Table 3
SpeciesGrowth rate
(r)
Intra-specific
competition (b)
Dispersal rate
(δ)
Variance in the
perturbation (σ2)
Correlation in the
perturbations (ρ)
Rock ptarmigan0·52 (0·362, 0·703)−0·56 (−0·786, −0·403)0·29 (0·164, 0·407)0·03 (0·019, 0·041)0·24(0·084, 0·368)
Rock partridge0·80 (0·704, 0·897)−1·12 (−1·253, −1·007)0·09 (0·000, 0·367)0·04 (0·030, 0·047)0·59 (0·468, 0·700)
Black grouse0·46 (0·342, 0·579)−0·56 (−0·711, −0·415)0·25 (0·151, 0·328)0·01 (0·008, 0·014)0·56 (0·439, 0·657)
Capercaillie0·62 (0·435, 0·759)−0·72 (−0·911, −0·525)0·15 (0·000, 0·629)0·03 (0·019, 0·047)0·51 (0·411, 0·597)
Hazel grouse0·86 (0·664, 1·003)−1·17 (−1·369, −0·951)0·14 (0·000, 0·363)0·08 (0·061, 0·091)0·60 (0·491, 0·687)

||si − sj|| Euclidean distance between the 18 mountain groups of Trentino,

uit variance of local noise, that is, variance in the July rainfall per days of rain from each of the 18 patches (re-scaled uit= 0·034–0·085, see Table 2),

p equal to 1/P where P is the period of monthly July rainfall per day of rain from all the province (p = 0·02),

zt regional mean stochastic events: mean monthly July rainfall per days of rain from the whole province (re-scaled zt = 0·359, see Table 2),

inline image variance of regional noise; the variance in the monthly July rainfall per day of rain from the entire province (re-scaled inline image= 0·05, see Table 2).

Results

Hunting statistics

There were no consistent differences in the strength of the second-order density dependence between time series corrected and not corrected for hunting effort (for all Wilcoxon matched pairs sign test: P > 0·05). Further details on the evidence of a weak influence of hunting effort on the long-term pattern of time series are reported elsewhere (Cattadori & Hudson 1999; Cattadori et al. 1999). Because more data were available for hunting time series than hunting effort time series (30 vs. 20 years), and these results indicate no significant effect of hunting, we used the complete hunting time series as representative data of the annual change in abundance and long-term pattern of galliform populations in Trentino.

Spatial synchrony within species

There were differences between species in the temporal variability of population abundance (Kruskal–Wallis anova by ranks test on detrended time series: P < 0·001, Fig. 2). Hazel grouse populations, that live in the low altitude woodlands where seasonal variation in climatic conditions is relatively small, exhibited relatively low levels of variation between mountain groups (CV = 29·73 ± 2·67 SE). In contrast, rock ptarmigan, that inhabit the mountain plateaux, with large seasonal variation in climate, exhibited the highest variation between populations (CV = 55·41 ± 7·41 SE). Rock partridge, capercaillie and black grouse were intermediate (CV = 49·78 ± 1·93 SE; 48·12 ± 2·86 SE; 39·08 ± 3·47 SE, respectively).

With the exception of capercaillie, all species exhibited large variation in synchrony for both detrended (i.e. year-to-year variations) and standardized time series (i.e. trend plus year-to-year variations, Table 1). Cross-correlations were consistently higher in standardized than detrended time series for all the species (Wilcoxon matched pairs sign test for all: P < 0·01; Table 1) with the exception of rock ptarmigan (Wilcoxon matched pairs sign test: P < 0·40; Table 1). This suggested that both population trend and population variability were spatially correlated.

Table 1. . Mean ± SE of spatial synchrony and percentage of positive and significant cross-correlation within each species using detrended and standardized time series. Wilcoxon matched pairs sign test between the percentage of positive and significant cross-correlation of the two data sets in each species
SpeciesMean ± SE
cross-correlation
of detrended series
Percentage of
significant positive
cross-correlations
in detrended series
Mean ± SE
cross-correlation
of standardized series
Percentage of
significant positive
cross-correlations
in standardized series
P
Rock ptarmigan0·21 ± 0·04350·20 ± 0·0427NS
Rock partridge0·23 ± 0·03530·51 ± 0·0279< 0·01
Black grouse0·33 ± 0·02480·38 ± 0·0254< 0·01
Capercaillie0·62 ± 0·03890·70 ± 0·0395< 0·01
Hazel grouse0·18 ± 0·03280·38 ± 0·0354< 0·01

Different spatial patterns were observed between species, although there was a general weak negative relationship between synchrony and distance for both data sets (Fig. 4). The variance explained by a negative exponential model was, in general, very low both using detrended (between 14·87% and 0·25%) and standardized time series (between 23·34% and 0·87%). Almost 90% of pairs of capercaillie populations exhibited significant synchrony (Table 1) and the correlation remained high even between populations more than 60 km apart (Fig. 4). The other four species showed larger variation, with all exhibiting both strong positive correlations and weak negative correlations at distances of less than 20 km. For black grouse and hazel grouse detrended series, a significant negative relationship was observed in synchrony with distance (bootstrapped cross-correlation vs. distance between pairs of populations r = − 0·20, n = 153, P < 0·05; r = − 0·39, n = 120, P < 0·001, respectively).

Figure 4.

Spatial synchrony in numbers harvested in relation to distance between populations for each species using: (a) detrended time series, and (b) standardized time series.

Relative importance of synchronizing mechanisms

Estimating dispersal and environmental stochasticity

Using the Ricker model with the half exponential pattern of dispersal and applying the estimating functions method with bootstrapping, we estimated both dispersal rate and the effect of environmental perturbations using the time series of all species (Table 2 and Fig. 5). The simulations indicated a high rate of dispersal in rock ptarmigan and black grouse (δ = 0·29 and 0·25, respectively), while rock partridge exhibited a relatively sedentary pattern (δ = 0·09). The results for capercaillie and hazel grouse showed a tendency for a relatively low dispersal rate (δ = 0·15 and 0·14, respectively). According to the statistical model, strongly correlated common environmental perturbations between mountain groups accounted for the spatial pattern of time series of rock partridge, black grouse, capercaillie and hazel grouse (Table 2). In contrast, the strength of stochastic correlation between mountain groups had to be weak to account for the rock ptarmigan time series (Table 2). These results suggest that common perturbations positively influence the pattern of synchrony in four out of the five species examined. In general, the variation in the stochastic perturbations was relatively low between mountain groups, although the effect was greatest for hazel grouse time series (σ2 = 0·074) and weakest for black grouse time series (σ2 = 0·014). The pattern of synchrony on distance produced by the model was comparable with the observed data sets for the majority of the species. The simulation for capercaillie produced large variation in the strength of synchrony but no apparent trend with distance (Fig. 5).

Figure 5.

Spatial synchrony in numbers harvested estimated in relation to distance between populations for each species using: (a) Ricker model in which both dispersal and environmental stochasticity are estimated, and (b) Ricker model with environmental stochasticity taken as July rainfall and dispersal estimated. Compare data with Fig. 4.

When the simulations were repeated with dispersal described by the half Gaussian model there was no improvement in the fit of the model over the half exponential pattern of dispersal. The half exponential dispersal model also provided a better representation of the spatial dynamics than a model with no dispersal (Table 3). A significant improvement was observed for rock ptarmigan, black grouse and hazel grouse, while for rock partridge and capercaillie no significant differences were observed (Table 3).

Table 3. . Mean squared error of the best fit using the Ricker model and estimating functions method with half exponential dispersal (A) for each species. Also shown is the percentage improvement in the mean squared error (MSE) using Ricker model with estimating functions method and half Gaussian dispersal (B) and, Ricker model with estimating functions method and no dispersal (C). Analysis of deviance between model (A) and model (C) is reported
SpeciesA
Ricker and half
exponential dispersal
MSE
B
Ricker and half
Gaussian dispersal
improvement of MSE (%)
C
Ricker with no
dispersal
improvement of MSE (%)
A vs. C
analysis of deviance
P
Rock ptarmigan0·021−7·00−8·00< 0·001
Rock partridge0·022−0·24−0·24NS
Black grouse0·009−5·30−5·40< 0·001
Capercaillie0·019−5·00−10·00NS
Hazel grouse0·034−2·30−2·32< 0·05

Estimating dispersal assuming the pattern of environmental stochasticity

The mean rainfall per day of rain in July was used to estimate the local and regional environmental stochasticity, and was then added to the Ricker model to estimate the dispersal rate and the dispersal range that minimized the mean squared error (Table 4). As with the previous model, the simulations indicated that a relatively high proportion of rock ptarmigan tended to disperse (m= 0·23) with movements over long distances (c = 0·75). Capercaillie and black grouse exhibited a high mean dispersal rate (m= 0·32 and 0·18, respectively) but the range of the movements was restricted to neighbouring mountain groups (for both the species c = 3·0). Simulations carried out on rock partridge and hazel grouse showed similar dispersal patterns with a tendency to be more sedentary (for both the species: m= 0·08) and when dispersing, to move to the nearest mountain group (c = 4·0). As observed in the previous model a comparison of the spatial pattern of synchrony on distance produced by the model compared with the observed data sets was reasonable for most species with the exception of hazel grouse (Fig. 5).

Table 4. . Dispersal rates and dispersal distance estimated from the Ricker model with July rainfall, as environmental stochasticity, and growth rate taken from previous works. The best fit, mean squared error (MSE), for each species is shown
SpeciesMSEMaximum growth
rate (r)
Local stochasticity
(min–max)
Regional stochasticity
xz, inline image , p
Mean dispersal rate
( ± SE)
Maximum dispersal
rate (M ± SE)
Dispersal distance
(c ± SE)
Rock ptarmigan0·0612·30·034–0·0850·359, 0·05, 0·20·23 ± 0·050·50 ± 0·070·75 ± 0·11
Rock partridge0·0392·60·034–0·0850·359, 0·05, 0·20·09 ± 0·040·20 ± 0·054·00 ± 0·32
Black grouse0·0342·50·034–0·0850·359, 0·05, 0·20·18 ± 0·030·40 ± 0·073·00 ± 0·25
Capercaillie0·0392·30·034–0·0850·359, 0·05, 0·20·32 ± 0·070·65 ± 0·063·00 ± 0·35
Hazel grouse0·0532·30·034–0·0850·359, 0·05, 0·20·08 ± 0·030·20 ± 0·064·00 ± 0·17

Spatial synchrony between species

Cross-correlation analysis between species within mountain groups showed an inverse relationship with the relative altitudinal distance between species. A significant negative relationship with the number of intermediate habitats was observed between species for the detrended series but not for the standardized series (Spearman rank correlation on bootstrapped cross-correlations data, r = −0·27, n = 102, P < 0·01; linFig. 6).

Figure 6.

Spatial synchrony in number harvested in relation to relative distance between species habitats within mountain groups. Detrended time series are used.

Density dependence and synchrony between species

The order of density dependence within each population was determined from the detrended time series. Significant, density-dependent regulation was identified in just 46% of the gamebird populations and this was dominated by first-order density dependence (32·5%), while delayed intrinsic structures were relatively scarce (Partial Autocorrelation Function (PACF) second order = 3%, third order = 4·5% and fourth order = 6%; Table 5).

Table 5.  Order of density dependence in each population using PACF analysis on detrended time series. The first five temporal lags were considered, zero indicates no significant density dependence within these five lag periods. The shaded background represents the pattern of significant and positive intraspecific synchrony within each mountain group. A similar shade represents population in positive synchrony. A population with two patterns overlapped is in synchrony with populations showing the two different patterns. *Indicates populations not in synchrony with each other but with other populations of the mountain group. Bootstrap cross-correlation on detrended time series, P < 0·05
Mountain groupsRock ptarmiganRock partridgeBlack grouseCapercaillieHazel grouse
1 00 0
2 01 0
311*1*14*
421*11*0*
5 00 0
60111*0*
70*110*0
8 4111
9 00 0
100201*0*
110 0
12001*1*0*
13  0 4
14 00*10*
15 3003
163 100
17100
184 0 0

Discussion

In general, our results on the spatial dynamics of gamebird populations in the Italian Dolomites implied that common, environmental stochastic factors are one of the principal causes of regional patterns of synchrony between populations. Specifically, we posed three questions about the spatial patterns of synchrony and we will examine each of these in turn.

Do closely related species exposed to common stochastic events exhibit similar patterns of synchrony?

Unlike many previous studies on spatial synchrony in animal populations (Hanski & Woiwod 1993; Lindström 1996; Sutcliffe et al. 1996; Heino et al. 1997; Ranta et al. 1995a,b, 1997a,b), the galliform birds in Trentino do not exhibit a strong negative relationship between synchrony and distance. In this study the species either showed no clear relationship with distance or a weak negative relationship with large variations in the degree of synchrony between neighbouring populations. Capercaillie was an exception in that populations showed consistently strong synchrony with no decrease in the correlations with distance. Previous modelling studies have shown that when dispersal is the dominant cause of synchrony a strong negative relationship between cross-correlations and distance can be expected but this does not occur when stochastic events are the driving force (Lindström 1996; Ranta et al. 1995b, 1997a, 1998). However, two factors can confound this general pattern. First, we may observe broad scale synchrony when a small amount of local dispersal occurs between populations with cyclic, complex or chaotic dynamics (Ruxton 1996; Blasius et al. 1999; Ruxton & Rohani 1999). Second, a negative relationship can be detected when the stochastic perturbations or the correlations between common stochastic events decrease with distance. One of the characteristics of the data set from the Dolomites is that the populations exhibit a weak tendency to cycle so the broad effect of local dispersal is unlikely (Cattadori & Hudson 1999; Cattadori et al. 1999). Another characteristic is that the climatic data of Trentino fall into 11 distinct macroclimatic zones (Gafta 1994) where there is only a weak relationship between climatic variables and distance so this confounding effect is avoided. For example, July rainfall, the variable we postulated would be an important synchronizing climatic factor, exhibited high positive correlations but large variations in synchrony between neighbouring areas and a very weak decrease in the correlation with distance (negative exponential model R0 = −0·142, variance explained = 0·020%, Fig. 7). In this respect, the spatial patterns observed in the gamebirds of Trentino imply that common stochastic events are probably the main driving force of large-scale synchrony between populations, although dispersal seems to contribute to affecting this pattern in some species. Strictly speaking we have no evidence to refute the possibility of synchrony being caused by a predator–prey interaction. For a predator to operate at the scale of this study it would have to be a raptor but there is no clear and obvious candidate.

Figure 7.

Spatial pattern of synchrony in July rainfall in relation to distance between meteorological stations in Trentino.

As expected, synchrony exhibited a stronger and positive relationship when both the strength of fluctuations and the general population decline were considered. A likely explanation of this increase in synchrony is a consequence of the widespread and correlated decrease in abundance of the majority of the gamebirds of Trentino since the fifties associated with the loss of suitable habitat (De Franceschi 1994; Meriggi et al. 1998). A relationship between synchrony in abundance and decline of suitable habitats has also been noted in species of arable land in Britain, where changes in agricultural practises have influenced species abundance over a wide area (Paradis et al. 1999). The lower correlations observed in the standardized time series of rock ptarmigan of Trentino appeared unrelated to the changes in the habitat of the mountain plateaux but to the large variations between populations, probably caused by a combination of intrinsic and environmental factors.

In contrast to this study, work in Finland on the same species of woodland grouse, recorded large-scale synchrony in the cyclic grouse populations but a clear decrease in cross-correlation with distance (Ranta et al. 1995a,b; Lindström 1996). Simulations of this spatial pattern indicated the principal role of dispersal but with an additional impact of common environmental events. The Finnish data differ from these data in two important respects. First, the populations exhibited clear cyclic dynamics, whereas the signal is relatively weak in the Italian populations (Lindén 1989; Lindström 1996; Cattadori & Hudson 1999; Cattadori et al. 1999). Second, the Finnish habitats are relatively homogeneous over large areas and the environmental data are highly synchronized over large regional scales (Heino 1994; Lindström 1996). Such synchrony by local dispersal is more likely to occur in Finland, although it would be difficult to disentangle the confounding effects of climate and dispersal.

How does synchrony vary between species with respect to habitat differences?

The finding that species with similar density-dependent structure and inhabiting neighbouring habitats exhibited a higher tendency to synchrony than species separated by several habitats, provides further support for the hypothesis that common environmental factors influence the pattern of synchrony observed, as, clearly, dispersal between species is not possible. However, an alternative hypothesis, which could account for synchrony between species is that common natural enemies could cause this pattern. Synchronous fluctuations between predators and their prey have been reported in a number of studies on grouse species at northern latitudes (Angelstam, Lindström & Widén 1985; Lindén 1988; Royama 1992; Small et al. 1993). Two possible mechanisms can generate this pattern; first, the variations in predation pressure that occur through nomadic avian predators and, second, the shift in predator diet to alternative prey during the decline of the preferred prey species (Ydenberg 1987; Ims & Steen 1990; Steen et al. 1990; Heikkilä, Below & Hanski 1994). Neither of these explanations can be refuted, although this aspect cannot be investigated in detail because of the lack of large-scale surveys on the abundance of the common predators in Trentino.

Is dispersal or stochastic events the cause of synchrony?

The modelling of the spatial population dynamics to investigate the effect of dispersal and common stochastic perturbations, provides supporting evidence for the dominating role of environmental stochasticity in determining the spatial patterns of synchrony within species. The application of estimating functions method demonstrated that common environmental events accounted for the patterns of synchrony observed in four out of five species. The rock ptarmigan was the exception, and simulations showed a weak synchrony between the common stochasticity of the mountain groups. One explanation is that ptarmigan inhabit the high mountain plateaux where they are more exposed to very localized environmental conditions which are not reflected at the larger scale; for example July rainfall, recorded at climatic stations located at more than 1500 m a.s.l., exhibited a very low spatial correlation (r0 = 0·07 n = 36 P = 0·664). An alternative explanation is that heavy snow or winter sports may push the birds from the high tops so they mix with birds from other mountain areas and this could lead to increased dispersal and weaken the effect of environmental events.

In the second model, we selected rainfall per day of rain in July as the environmental synchronizing factor, following the findings of previous workers. This provided reasonable outputs in comparison with the observed patterns for all species, with the exception of capercaillie. The pattern of synchrony on distance in capercaillie provided a reasonable comparison to that observed but the model predicted high dispersal rates of individuals over short distances (Table 4 and Fig. 5). This seems unlikely in capercaillie because the males tend to occupy the same home range in consecutive years and even the more active subadult males tend not to move far from the leks during the year (Storch 1993, 1995). An alternative explanation is that July rainfall was not the only factor involved.

In general, the pattern of dispersal from the modelling of the spatial dynamics of the galliforms in Trentino, reflected the pattern recorded in natural populations (Cramp & Simmons 1980; De Franceschi 1992a–d). Previous studies on dispersal, using marked animals, have suggested a higher tendency of rock ptarmigan and black grouse individuals to disperse, while caparcaillie, hazel grouse and rock partridge tend to be relatively sedentary (De Franceschi 1992a,b,c,d; Storch 1993; Bernard Laurent 1988, 1991). Mean dispersal rates estimated from the two models were similar for all species, with the exception of capercaillie (see the previous explanation), suggesting that the models captured the general pattern of movements. Mean dispersal rate, estimated from estimating functions, varied from 9% to 29% between species, which is the correct order of magnitude in galliform birds, and represents the immature individuals of the year that tend to disperse. However, data are scarce and usually have insufficient sample sizes to make reasonable estimates.

The Ricker model with half exponential dispersal provided a more acceptable fit to the observed patterns than the model with half Gaussian dispersal or no dispersal at all. Moreover, we suspect that without good data on the precise combination of environmental factors that influence changes in abundance, then the best approach for identifying the importance of stochastic events is to use the estimating functions method. This technique has not previously been applied to questions of synchrony. Using estimation functions and bootstrapping for the galliform species in Trentino it was possible to estimate the confidence intervals of the parameters without assumptions on the distribution of the demographic and stochastic variables. Furthermore, because we took into account the geographical distribution of the populations and related their pattern to the spatial structure of the environmental events, we were more likely to capture the processes in natural populations. While the estimating functions method avoids many of the general assumptions of a modelling procedure, the investigation of a complex spatial system such as the galliform populations in Trentino required simplifying assumptions. Despite this, we captured the important patterns of each species in a spatiotemporal system.

The biggest limitation must be the use of hunting statistics as measures of relative abundance and breeding production. In fact, while the linear relation between hunting statistics and population abundance was observed, the variance explained by the model was low (see Methods), suggesting that, despite the correction of the data for the hunting effort, some stochasticity caused by sampling error may have affected the general pattern observed. Previous work has emphasized that hunting effort has no major influence on the intrinsic structure of these populations, although hunting effort probably influenced amplitude of fluctuations (Cattadori & Hudson 1999; Cattadori et al. 1999).

In summary, these data provide evidence that common environmental factors are important in causing synchrony between populations, although dispersal occurs in all species to some degree, and affect the synchronous pattern of some populations. The use of statistical tools can help to improve the understanding of this pattern. These results have important implications for the management of wild animal populations because if common stochastic events are the main cause of synchrony, then the local extinction of fragmented populations may not be followed by recolonization for a relatively long time interval.

Acknowledgements

We would like to thank the Hunting Association of Trentino, which provided the hunting statistics. We are particularly grateful to Esa Ranta, Ottar Bjørnstad, Mick Crawley, Tim Benton and an unknown referee for constructive comments on an earlier manuscript. The Centro di Ecologia Alpina supported this work financially.

Received 12 May 1999;revisionreceived 14 December 1999

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