Introduction

Long-term studies of plant populations have been mainly concerned with annuals, biennials (Symonides, 1987; Watkinson, 1990), and perennials of lowland ecosystems (Inghe and Tamm, 1985; Falinska, 1991; Willems and Bik, 1991; Bengtsson, 1993, 2000; Svensson et al., 1993; Woodward, 1997; Menges and Dolan, 1998). Populations of alpine or arctic species have rarely been studied for longer periods (Callaghan, 1976; Carlsson and Callaghan, 1991; Diemer, 1992; Forbis and Doak, 2004). For long-lived species, conclusions based on only 1 or 2 years of study may be misleading, and the importance of long-term demographic studies has frequently been stressed. Long-term observations enable critical stages of population development and environmental factors causing population changes to be detected (Bengtsson, 2000). Population development and/or extinction can then be predicted.

In arctic and alpine environments, recruitment by sexual reproduction is less frequent compared to other ecosystems (review in Carlsson and Callaghan, 1990), and the dominant clonal graminoid species rely mainly on vegetative propagation. However, flowering itself may influence the population dynamics of shoots if they are monocarpic. Additionally, vegetative shoots may die due to environmental stress.

The dynamic state of a population may change in the long run due to changes in environmental factors, e.g., changing competitive pressure from other species or intraspecific density effects. Thus, a population initially growing vigorously may eventually reach a stationary state or even become at increasing risk of local extinction. This risk will be enhanced by the effect of environmental and demographic stochasticities.

In the alpine zone, there is a lack of information on population dynamics, even for dominant species. Therefore, from 1990 to 1992, the shoot numbers of long-lived clonal sedges—Carex curvula ssp. rosae and Carex curvula ssp. curvula—were recorded during the growing seasons in permanent plots in order to observe population development and to understand the species' dynamics in different alpine grassland types (Erschbamer, 1994). In 2002, the sites were re-visited and the numbers of shoots were recorded again.

The objective of the present study was to compare the data from 1990–1992 with the return visit to the sites in 2002. Based on the first observation period, a model for shoot population growth was developed and parameterized. The main model parameter was the annual rate of shoot population increase, comprising the annual shoot birth and death rates. This model was used to predict development until 2002. Parameterization of the model on the basis of the complete observation interval 1990–2002 was used to examine extinction risks for further periods. Analysis of temporal dynamics was accompanied by an evaluation of the spatial population structure. The main questions to be answered were: (1) Is there a correlation between the size, dynamic state, and spatial structure of the populations? (2) What predictions on population development for a 10-year period result from the short-term observations of 1990–1992? (3) What conclusions can be drawn about changes in site conditions and population state from comparing predictions with empirical verification? (4) What are the extinction risks of the populations at different sites?

Study Area, Material, and Methods

MODELING OF POPULATION GROWTH

The recording of shoots distinguished between vegetative and generative shoots. As shoot labeling was not possible in the field, the transition rates between these two stages could not be determined. The separate record of generative shoots served the estimation of shoot mortality. Growth modeling pooled all shoots in one plot. The temporal development of the number X of shoots in a plot was described by the growth equation

where X_t = number of shoots in year t in the plot, λ = annual finite rate of population increase, b = shoot birth rate (vegetative reproduction), and d = shoot death rate. This growth model considered all shoots to be independent of each other, i.e., it neglected the tussock structure of the species and hence any correlated shoot mortality.

DETERMINATION OF RATES

If shoot numbers X were recorded in subsequent years, the rate of population increase was calculated from the records by

In the general case where the interval between records was n years, the average rate of population increase λ(n) was given by

Weighted values and standard deviations from m different rates of population increase λ_i (i = 1, … , m) were calculated in a simplified manner by arithmetic averaging:

The weights n_i were given by the number of annual steps n that featured in the calculation of λ_i values via Equation 3.

Death rates (and indirectly birth rates, via Equation 1b) were estimated from the proportion of the monocarpic generative shoots, neglecting other causes for mortality. The following values were used for the percentage of generative shoots in order to estimate death rates d (Erschbamer, 1994):

• (A) Pioneer 5% d = 0.05

• (B) Pisa 1 8% d = 0.08

• (C) Oberholz 10% d = 0.10

• (D) Pisa 2 8% d = 0.08

• (E) Valsorda 5% d = 0.05

PATCHINESS INDEX

The spatial structure of the shoot population within one plot was characterized by Lloyd's Patchiness Index (Lloyd, 1967; Pielou, 1977). This patchiness index C of a 25 × 25 cm plot with 5 × 5 cm subplots as counting units was calculated by:

The mean shoot density m in a plot sums over all subplots:

where y_i is the shoot numbers in the subplots (N = 25).

“Mean crowding” m* is determined by:

If C = 1, all individuals are distributed randomly over the area, whereas C > 1 denotes an aggregation of shoots within some subplots. The maximum patchiness value is given by C = N = 25, when all shoots are concentrated within one subplot.

PATCH OCCUPANCY

The proportion of occupied subplots in a plot was calculated by:

where z = number of subplots with at least one shoot, and N = total number of subplots (N = 25). In our context, patch occupancy f varied between 0.04 and 1.0.

Results

Discussion

The study addressed the problem of evaluating long-term population development on the basis of observations over periods that are significantly shorter than the mean lifetime of individuals. Usually, population dynamics are recorded over 2 or at most 3 years. Observations allow population development to be projected into the future via simulation modeling, so that the risks of population extinction can be calculated. Such projections can be done by simple rate models if all the individual shoots are pooled together, or age- or stage-based matrix models (Caswell, 2001) if the transition rates can be determined. Simulations should include all the knowledge available on stochastic aspects (demographic and environmental stochasticities). The range of stochastic projection outcomes may be rather large: many new observations will fit into this interval and thus may validate the projection. On the other hand, significant deviations between projections and verifications will not disqualify the model forecast, but will elucidate gradual changes in external conditions for the population, e.g., caused by disturbance or succession. When there are several observations under similar conditions, even modest differences between projections and observations may enable some general trends to be elucidated.

One-year values for the rate of population increase λ were scattered over a broad interval of λ = 0.4–1.50, denoting high temporal and site-dependent stochasticity in growth conditions. By contrast, almost all the averaged values were within a small interval of λ = 0.95–1.05. These long-term rates of population increase of the Carex curvula subspecies were similar to those reported for long-lived perennials which reproduce by vegetative means, also remaining close to the equilibrium value of 1.0 (Callaghan, 1976; Fetcher and Shaver, 1983; McGraw and Antonovics, 1983; Callaghan, 1984; Svensson and Callaghan, 1988; Carlsson and Callaghan, 1991; Jonsdottir, 1991; Nault and Gagnon, 1993; Silvertown et al., 1993; Wikberg et al., 1994). If λ remains more than 1.0, it may be assumed that the population size can be steadily maintained by clonal reproduction (Shimizu et al., 1998). Clonality has already been recognized as one of the essential features of plants growing under harsh arctic and alpine conditions (Callaghan, 1988; Stöcklin, 1999).

Parallel to the determination of size and the actual dynamic state of populations, the spatial structure of the plot populations was also evaluated. Shoot populations varied spatially depending on the grassland type they occupied. This suggests that population dynamics may change as a result of natural changes in the grassland within the course of succession to denser swards. Similar results were found by Valverde and Silvertown (1998) for Primula vulgaris in different forest canopies.

Small, decreasing populations were on average more aggregated than large populations in an expanding state. These correlations are rather plausible: a growing population increasingly fills a plot and thus lowers shoot patchiness. The increase in aggregation parallel to a decrease in size corresponds to theoretical conclusions: patchiness arises when population densities become low, and dispersal occurs only over short distances and where interactions between individuals are localized (Freckleton and Watkinson, 2002). Short vegetative “dispersal” distances are due to the phalanx growth form of the Carex species. At best, a dispersal of shoots was only observed between neighboring subplots of 5 × 5 cm.

The results showed that patchiness can serve as a measure of the dynamic state of a population: from Figure 2b it can be deduced that a population increases (λ > 1) whenever more than 50% of all patches have at least one shoot (f > 0.5). Values for patch occupancy f can be determined in the field much easier than for patchiness C or even the increase rate λ (which needs at least a 2-year observation period) and may be used for a screening of the population state. However, it should be borne in mind that such structural values can only serve as a snapshot: a strict relationship between λ and C or f will not hold over longer periods of population development (Winkler and Matthies, unpub.).

The correlation found in Figure 2 cannot hold any longer when new subpopulations arise from established seedlings. Here, initial aggregation may be high even though such a population will be in a growth state (λ > 1). However, during the research period, seedlings were never recorded for either Carex rosae or Carex curvula (Erschbamer, 1994). On the other hand, the potential to recruit by seedlings has to be assumed at least occasionally, as seeds of both subspecies were found for instance in the soil of a central alpine grassland site (Niederfriniger Schlag, unpubl.). The degree to which populations can be rejuvenated by occasional successful germination remains uncertain.

Predictions for 2002, over 10 years, were made from observations of size changes and of aggregation over two annual steps 10 years before. These predictions were compared with the empirical findings and judged in the light of general knowledge about the conditions at the observation sites.

Site A—Pioneer. Initially there was a large potential for expansion: the overall cover of the vegetation was lower than in closed grassland, with low interspecific competition and open gaps. This is reflected by the average values for the plots of the site: λ = 1.037 ± 0.166 and f = 0.72 ± 0.08. They seemed to be strong indicators of an increase in population size, the population growing in its optimum environment. However, the high average λ may be due to the “outlier” λ₂ of A5 (average λ without this value is 0.997). Indeed, in the period until 2002, the plot populations did not change in size. On average, λ was a better predictor of development than f: all the relevant values in Figure 2a lie above the regression line. The population evidently left the growth stage in the last decade and approached a stationary state. Similar to Carex curvula which does not exceed a certain density of shoots per plot (Grabherr, 1987), intraspecific regulation may be suggested for Carex rosae, too.

Site B—Pisa 1. In this grass sward, high competition between Carex rosae and Kobresia myosuroides has to be assumed. Hence, the Carex tussocks were smaller, with lower shoot density. The average plot values were λ = 1.036 and f = 0.55 (for all plots and both annual steps). They still indicated a tendency for population growth. However, stronger competition compared to site A was reflected by the much lower value for f. Indeed, the population size decreased (Fig. 1a), and the shoot values observed were lower than those predicted using the growth model (Fig. 3). Here, patch occupation f was a better indicator of population development and a valuable addition for determining λ.

Site C—Oberholz. Strong competition by other species (Carex sempervirens, Sesleria albicans, Kobresia myosuroides, Festuca norica) allows only small tussocks of Carex rosae. Due to its thin leaves, a low aboveground biomass was found for C. rosae (Erschbamer et al., 1998), and the species may be assumed to be a weak competitor. Both λ and f (0.936 and 0.34) indicated population decline. Indeed, the population did decline, albeit significantly less rapidly than expected (Fig. 3).

Site D—Pisa 2. Both λ and f (0.955 and 0.29 on average) predicted population decrease. These values may reflect strong competition. However, no observations were available for 2002. Sites D and C represent the lower distribution limits of C. rosae and fitness may be reduced, as was found for several other species growing at the margins of their distribution area (Bengtsson, 2000; Gaudeul et al., 2000).

Site E—Valsorda. Following all λ and f values (average values 1.21 and 0.74) population sizes of Carex curvula should strongly increase. This may be the typical situation of a dominant species close to carrying capacity. However, the short-term observation 1990–1992 could not include all relevant external effects. In the last decade the whole area was strongly affected by tourists and by grazing. Although the predictions could be compared only in one case with the actual state, a remarkable decline in population size compared to the initial observations was detected. It must remain open if this deviation between prognosis and verification is due to an increasing competitive stress in the course of community development not reflected in the first observation period or simply due to disturbance by tourists.

On a short term, within the next decades, the risk of the various populations going extinct is still very low (Fig. 4). However, the populations of the species-rich climax grasslands will decrease, probably even below some critical threshold. Only the populations at site A (“Pioneer”) seem to be far-removed from any danger of population decline. Inevitably, such prognoses depend on different preconditions. Because of the phalanx growth form of the Carex curvula subspecies, the simulation Equation 1, which assumes independent shoots, is unlikely to hold when populations become small. Moreover, we had to assume that environmental conditions will remain in the same state as averaged over the period 1990–2002. It is unlikely that this will really be the case. Therefore, a continuous monitoring of population development of long-living species combined with an updating of prognoses must be a task for future research.

Conclusions