1 For many clonal plant species, the density of shoot populations makes it almost impossible to determine genet natality directly. We identified genets by a randomly amplified polymorphic DNA (RAPD) method and used their size and spatial pattern, together with demographic parameters (genet spreading rate and mortality rate of shoots) determined in the field to estimate natality rates for Festuca rubra (red fescue).
2 In each of two sites (a species-rich and a species-poor site in a mountain grassland) three plots were established. Each plot contained two 1 m × 3.3 cm transects, composed of 3.3 × 3.3 cm square cells. Estimates of genet number per plot (18–49 and 27–33, respectively, in the two sites) were based on a randomization test. Mean genet size (1.2–1.6 cells) was not significantly different between the sites, nor was the spatial pattern of genets significantly different from random at either site. Interactions between genets therefore appeared to be negligible.
3 A spatial simulation model was developed for the genet population. Values estimated from the growth and demographic data over several years for the genet spreading rate (0.2–0.3) and for the mortality rate of shoots per cell (0.2–0.3) were among those used in the simulation. When a constant genet natality rate of 3–7 genets m–2 year–1 was included in the model, the simulation generated numbers and size frequency distributions of genets that were similar to those found in the field.
4 In this mountain grassland, F. rubra appeared to show repeated seedling recruitment, instead of the initial seedling recruitment following disturbance that is thought to be typical of many grasses. Founder effects were immaterial at the rates of seedling recruitment apparent in these populations. A stable population was achieved with the values of genet spreading rate and mortality rate of shoots per cell observed in the field, and repeated seedling recruitment. However, genet natality rates may vary if environmental conditions fluctuate.
Genetic diversity is often high within populations of many plant species that are apparently predominantly clonal (Ellstrand & Roose 1987; Eriksson 1993; Widén et al. 1994). This is surprising because clonal growth is an entirely vegetative process that itself does not increase genetic diversity. To determine the relative contributions of clonal growth and seedling recruitment to the genetic diversity of clonal populations, data are needed on non-reproductive demographic processes, including rates of spread and mortality of genets. Clonal growth has two major effects on the genetic structure of a population: it generates many genetically identical individuals and extends the life span of genets. Therefore, even if seedling recruitment is infrequent, it can be important over a long time scale to increase genetic diversity (cf. Parker & Hamrick 1992). The balance between clonal growth and genet natality may depend on the morphology of the species (Eriksson & Jerling 1990) and on the frequency of seedling recruitment, the importance of which is difficult to assess because of the problems in identifying genet establishment events in the field, especially in dense populations (Eriksson & Bremer 1993). Apart from being technically difficult, counting seedlings in the field provides only short-term estimates of the genet natality rate, and these are often highly variable in time (Eriksson 1993). The long-term natality rate, which determines the genet dynamics of a clonal plant population, has to be determined by indirect means.
Genet natality may vary over the life span of a population. Eriksson (1993, 1997) identified two extremes. With initial seedling recruitment (ISR), little or no recruitment occurs after establishment of the first cohort of genets (e.g. Antennaria dioica and Prunella vulgaris;Eriksson 1997), whereas with repeated seedling recruitment (RSR), new genets are repeatedly recruited, even after the first cohort of genets has established (e.g. Trifolium repens;Eriksson 1997).
In field populations of clonal plants, genet natality and mortality rates determine total genet number and average genet life span; spatial spreading rate determines genet sizes given the average genet life span. This relationship could be used for indirect estimation of genet natality, because the remaining variables are relatively easy to determine. Ramet-level variables (spreading rate and ramet mortality) can be measured directly; of the genet-level variables, genet mortality can be inferred more easily than genet natality, because it is a probabilistic summation of mortality risks at the ramet (shoot) level, and could thus be determined on the assumption that mortality risks of individual shoots are not correlated (Watkinson & Powell 1993).
Our aim in this study was to determine the role of genet natality in the development and maintenance of populations of the clonal plant Festuca rubra L. (red fescue) in a mountain grassland. A spatial simulation model for the development of genet populations was parameterized using data collected from the field, assuming that natality and spread of genets and mortality of ramets (shoots in the case of F. rubra) are directly related to numbers and size distributions of genets. We applied a randomly amplified polymorphic DNA (RAPD) method to sampled shoots, and then used their fine-scale position to determine the spatial pattern and size distribution of the genets identified. We estimated genet spread and shoot mortality from demographic data collected over several years from permanent plots, and used these values to infer a genet natality rate and to determine whether F. rubra shows ISR or RSR.
Materials and methods
The two study sites were located in the grassland of the Krkonoše Mountains, North Bohemia, Czech Republic: Janovy boudy settlement (J site) lies 3.75 km east-south-east of the centre of Pec pod Sněžkou (50 41′ 28′′ N, 15 47′ 35′′ E, 880 m a.s.l.), and Severka settlement (S site) is approximately 3 km north-west of Pec pod Sněžkou (50 41′ 42′′ N, 15 42′ 25′′ E, 1100 m a.s.l.). Species richness was 13–18 species m–2 and 32–36 species m–2 at the S and J sites, respectively. All species except Euphrasia spp. at site J were perennial. Traditionally, the meadows have been mown in summer, grazed late in autumn, and manured every 2–3 years. Although there are no precise historical data available, both sites are 300–400 years old, having developed during the late Middle Ages when the Krkonoše Mountains were extensively colonized and cleared for producing hay and keeping cattle.
There are pronounced differences in length of growing season and soil parameters between the two sites. At the more species-rich J site, the growing season begins in mid-April after snow melt and lasts until November, whereas at the S site snow melts in mid-May and growth ceases at the beginning of October. The soil in the J site is richer in calcium and magnesium than that in the S site (2.40, 0.54 mg g–1 and 0.65, 0.06 mg g–1, respectively), and soil pH is also higher. However, the sites do not differ in maximum above-ground biomass (approximately 170–190 g dry weight m–2). All F. rubra plants are hexaploid at both study sites (F. Krahulec, unpublished data).
Shoots of the same genet should exhibit an identical band pattern when analysed by the PCR-RAPD polymerace chain reaction (PCR) randomly amplified polymorphic DNA (RAPD) method. In order to test this, band patterns of physically connected shoots outside the experimental plots were analysed. Nineteen genets were transplanted to pots in the laboratory of Tokyo Metropolitan University in February 1994 and used to provide control samples.
Three 1 × 1 m plots were set up at each site using a stratified random approach (plots J1, J2 and J3 and S1, S2 and S3). Two perpendicular transects were established across the centre of each plot. Each transect was 3.3 cm wide and was divided into 30 cells, each 3.3 cm long. This cell size was the same as in previous studies in this grassland (Herben et al. 1993a, 1995). All the F. rubra shoots within each cell were sampled in May 1994 at the J site and in June 1994 at the S site. Connections between shoots were carefully traced and shoots within a cell that were visibly connected by stolons were kept together. These connected shoots, which clearly belong to the same genet, are termed ‘shoot clusters’.
DNA of shoots sampled from the six plots was analysed to allow identification of genets (Table 1). All sampled shoots were carefully washed and transported at 0 °C to Tokyo Metropolitan University, Tokyo, Japan. Total DNA was extracted from approximately 100 mg of shoot tissue according to the modified method of Milligan (1992).
Table 1. Numbers of Festuca rubra samples collected at each site, numbers subject to RAPD analysis and numbers of genets identified. The numbers of shoot clusters that showed clear band patterns are given in parentheses (1 cell = 3.3 × 3.3 cm, 1 plot = two 1 m × 3.3 cm transects)
No. of cells with shoots
No. of shoot clusters
No. of shoots
No. of shoot clusters analysed
No. of genets identified
No. of genets per plot
Only 60% of shoot clusters in this plot showed clear band patterns.
For all plots except J1 and S1, the number of genets per plot was estimated on the assumption that the ratio of number of shoot clusters per plot to number of genets per plot is constant within a site (see text).
A modified version of the PCR-RAPD procedure of Williams et al. (1990) and Levitan & Grosberg (1993) was used. Amplification reactions were performed in 10 mm Tris–HCl (pH 8.3) containing 50 mm KCl, 2 mm MgCl2, 0.001% gelatine and 100 µm each of the four dNTPs (TaKaRa BIOMEDICALS, Oohtu, Japan). Each 20 µl reaction volume also contained 1.2 pm of a primer (either OPA-1 or OPA-10, selected from the 40 available in KIT A and KIT B from Operon Technologies Inc., Alameda, CA), 20 ng sampled DNA and 0.8 U Taq DNA polymerase (TaKaRa BIOMEDICALS, Oohtu, Japan) and was passed through 45 cycles, each 1 min at 94 °C, 1 min at 35 °C and 2 min at 72 °C in a programmable thermal controller, model PTC-100-60 (MJ Research Inc., Waltham, MA, USA). Amplification products were analysed by electrophoresis in 8% polyacrylamide gels and DNA bands were detected by staining with silver (Tegelström 1992).
In August 1994, DNA was extracted and analysed from 2–6 shoots from each of the six control genets that had produced more than two shoots. Shoots derived from a single control genet should exhibit identical band patterns. To check whether the method provided such reproducible results a further two DNA samples were extracted from each shoot of the six control genets and amplified independently.
The gels for the six experimental plots were run in September and December 1994. One plot at each site was chosen at random (J1 and S1) and all shoot clusters were analysed for genet identification. In the remaining plots, all shoot clusters were analysed in a randomly chosen subsample of cells, and one randomly chosen shoot cluster was analysed in every other cell along the transect. Shoot clusters exhibiting unclear band patterns or no band patterns were excluded from further analyses. Each sample was allocated to a particular genet on the basis of the bands seen in the gels.
For each of the partially analysed plots, the numbers of genets over the whole plot were estimated statistically. The basic assumption in the bootstrap procedure was that the ratio of the total number of shoot clusters to the total number of genets was the same for each plot within a site. This ratio was known for the fully analysed plot at each site. For example, for the partially analysed J2 plot, the proportion of shoot clusters analysed was 46/174 (Table 1). We selected 113 shoot clusters at random from plot J1 and counted the number of genets in this sample. The number of genets obtained was then multiplied by 174/113 to give an estimate of the number of genets present in the whole of plot J2. For each plot, we repeated this procedure 1000 times to obtain a mean and 95% confidence interval for the number of genets present.
Genetic differences between shoots in the studied sites might also be due to somatic mutation or other causes. Our measurements of genet natality rates would then tend to overestimate the contribution of sexual reproduction (i.e. seedling recruitment) to the populations. Therefore, we necessarily defined the genet as a genetically distinct individual, irrespective of how it was generated, and assessed natality rates on this basis. Although there are no data available on the rate and frequency of non-sexual genetic differentiation in F. rubra or related species, band patterns from physically connected shoots were always the same (see the controls above), and we therefore assumed that the somatic mutation rate in F. rubra is very low.
Estimation of genet size
Genet size was calculated as the number of cells occupied by the genet. For each plot the mean genet size was estimated using bootstrap procedures based on all identified genets and all sampled shoot clusters (Efron & Tibshirani 1993). Two procedures were applied to the fully analysed plots (J1 and S1). In method G, the basic unit for bootstrapping was the genet, and shoot cluster structure within a genet was ignored. In contrast, shoot cluster structure was taken into account in method S, and the basic unit was the shoot cluster. Only method S was applicable to the partially analysed plots. When a shoot cluster selected randomly during the bootstrapping did not belong to the group analysed for DNA, it was not included in the calculation of mean genet size. Furthermore, mean genet size was calculated only for those shoot clusters selected. Thus, a genet demonstrated by DNA analysis to be present in N cells would have a genet size of 1 if only one shoot cluster was selected during bootstrapping (and the other N – 1 shoot clusters were not selected), but a genet size of N if shoot clusters in N different cells were selected. In all cases, 1000 bootstrapping iterations were carried out to obtain means and 95% confidence intervals of genet size.
Spatial pattern of the number of genets per cell
Means and variances of the number of genets observed per cell were calculated for the fully analysed plots J1 and S1. We then examined whether genets were distributed randomly in a plot, using a randomization test in which the cell positions of each genet were assigned randomly in each run, but the number of cells occupied by a genet was taken from the field data. Mean and variance of the numbers of genets per cell were calculated in each run, and the mean of randomized variances was obtained from 1000 runs. If the observed variance fell in the 2.5% tail at either end of the randomized distribution, it was considered to be significantly different (at P < 0.05) from the randomly generated distribution.
Structure of the simulation model
The spatial patterns and size distributions of F. rubra genets were simulated on the basis of a spatially explicit model. The model was spatially discrete with a matrix of 120 × 120 cells (i.e. 1 cell = 3.3 × 3.3 cm, as in the field), covering an area of 4 × 4 m. The grid was assumed to have a toroidal shape (‘wrapped around boundaries’), although a pilot study showed that the results differed little from those obtained from a flat grid with absorbing boundaries when realistic parameter values were used. Rates are expressed per simulated time step (i.e. per year). We determined the effects of three parameters (genet natality rate, mortality rate of shoots and genet spreading rate) on the genet number and size (see Table 2 for values used in simulations).
Table 2. Parameter values used in the simulation model for the development of Festuca rubra genets
Values used for simulations
Genet natality rate per 14 400 cells per year
5, 10, 20, 50, 70, 100, 150
Mortality rate of shoots per cell per year
0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35
Genet spreading rate per year
0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35
1 Genet natality rate: the number of seedlings establishing per year over the simulation area, i.e. 14 400 cells = 16 m2.
2 Mortality rate of shoots (genet fragments) per year: the probability per year that a cell becomes empty (because all F. rubra shoots in the cell die).
3 Genet spreading rate: the probability per year that a genet will colonize a neighbouring cell as a result of horizontal movement of a shoot (or shoots) into the cell.
Apart from the seedling establishment rate, all parameters were kept constant throughout one simulation run. The behaviour of each genet was simulated independently and each cell could therefore be occupied simultaneously by several genets. Thus there was also no upper limit on the potential number of genets that could coexist within the simulation area.
At establishment, a genet occupied one cell, the position of which was determined within the area of 120 × 120 cells by a random number generator. RSR was modelled using a constant natality rate throughout the development of the population (values in Table 2); for ISR, an initially high natality rate (200 genets year–1) was replaced after 1 year by a zero natality rate for the rest of the simulation. In addition, a simulation with high ISR for the first 3 years followed by low annual RSR was also modelled.
It was assumed that a genet shows perfectly circular growth and that the probability of it spreading into those adjacent cells in which it is not already present is equal to its genet spreading rate (for values see Table 2). Empty cells not adjacent to colonized cells had zero probability of being colonized during each time step.
The mortality of shoots was assumed to occur in a strictly local (per cell) fashion: each genet had a constant probability of dying within each cell at each time step (year). This probability was independent of the behaviour of the genet in other cells.
Because it was assumed that there were no interactions between genets (see the Discussion for the validity of this assumption), natality, spreading and mortality rates of a particular genet in each cell were independent of whether the cell was occupied by any other genet.
To model the sampling scheme used in the field, two perpendicular sampling transects of 30 cells were positioned in the centre of the simulation grid. Only those genets reaching these transects were ‘sampled’ and included in calculations of genet number; genet size was measured as the length of these transects over which each genet had spread. Simulated values could therefore be compared directly with field data.
In a pilot study, we found that most parameter combinations led to stable population states within 150 years (for an example see Fig. 1). Five runs of 200 years were therefore simulated for each combination of the parameters in Table 2. Runs of this length are consistent with the estimated age of these grasslands. The size distribution of sampled genets was recorded at the end of each run.
Parameter estimation for the simulation model
The mortality rate of shoots per cell was estimated by two independent methods: (i) from previous data on F. rubra shoot demography (Herben et al. 1993b; F. Krahulec et al., unpublished data) combined with our observed field shoot densities; and (ii) from the permanent plots with a fine-scale recording system (Herben et al. 1993a, 1995).
Mortality rates of approximately 0.4 and 0.6 shoot–1 year–1 have been reported at the J and S sites, respectively (Herben et al. 1993b; F. Krahulec et al., unpublished data). Numbers of shoots per cell ranged from 1 to 40, with means of 9.0, 7.6 and 3.5 (plots J1, J2, J3, respectively) and 3.6, 4.6 and 6.2 (plots S1, S2, S3, respectively). Distributions were skewed, with many cells having small numbers of shoots and a few cells with very large numbers of shoots. If the probabilities of death of individual shoots were assumed to be independent, application of these distributions to shoot-based mortality rates yielded mean cell-wise mortality rates of 0.13 (J) and 0.22 (S).
The permanent plots had a grid of 3.3 × 3.3 cm cells and all vegetative shoots of all grasses were counted every year from 1985 to 1994 (parts of these data are used in Herben et al. 1993a). The per cell mortality rate can thus be expressed directly as the proportion of the cells containing F. rubra in one year that did not contain F. rubra in the subsequent year. This yielded mortality rates ranging from 0.1 to 0.7 cell–1 year–1, with a mean of 0.34 (0.342 for the J site and 0.339 for the S site).
The estimates of per cell mortality rate from the permanent plot data were thus higher than those determined from shoot demography. We believe that the latter method may lead to an underestimate of per cell mortality rate because it assumes that shoot mortalities are uncorrelated, and that the former method may overestimate this value because it does not allow for shoot mobility, whereby shoots can be lost from a cell by growing out of it. Therefore we used the permanent plot estimates as maximum values and the shoot demography estimates as minimum values of per cell mortality rate.
The shoot spreading data were based on 3 years of observation of 27 small tussocks of F. rubra at the J site and 15 small tussocks at the S site (F. Krahulec et al., unpublished data). The change in spatial position of the living ends of marked shoots was measured directly at half-year intervals, using a pantograph system from fixed rods. The mean distance between the positions of shoots in successive years was 1.21 cm and 1.33 cm at the J and S sites, respectively, corresponding to mean cell-wise spreading rates of 0.27 and 0.33. Using a regression approach, Law et al. (1997) analysed data from fine-scale permanent plots at the S site (cell size 3.3 cm) recorded over 12 years and found that the mean probability of a single F. rubra shoot moving to a neighbouring cell was 0.066. Assuming that shoots are independent of each other, the spreading rates of 0.24, 0.29 and 0.34 (for 4, 5 or 6 shoots in a cell) determined by Law et al. (1997) are very similar to the estimates given above.
‘Genet establishment’ essentially refers to a transition from a seedling to a small plant that can immediately spread horizontally. No account is taken of processes specific to the seedling stage, in particular to higher mortality risk due to both small shoot size and the absence of effective spatial spreading during the early life of a seedling. However, these processes can be summarized into an aggregate parameter that covers all processes from germination to formation of a small mature plant. A large range of values was used for genet natality rate (Table 2) to allow for the absence of reliable estimates.
Polymorphic band patterns were reproducible and robust. Both primers produced about 15 bands sample–1. Identical bands were seen when two samples from the same shoot were separately extracted and independently amplified. Identical patterns were obtained when different shoots from the same control genet were compared. We therefore assume that shoots exhibiting different patterns for either or both of the primers belonged to different genets.
All but one of the shoot clusters in plot J1 showed clear band patterns, and examination of the 28 and 31 polymorphic bands produced by the OPA-1 and OPA-10 primers, respectively, allowed identification of 32 genets (Table 1). All the shoot clusters in plot S1 showed clear band patterns and 27 genets were identified (Table 1). Forty per cent of shoot clusters in plot J3 did not show clear band patterns, perhaps due to poorly preserved samples, and the number of genets identified was therefore much lower than in the other partially analysed plots (Table 1).
The bootstrap procedure provided estimates of genet numbers in partially sampled plots that agreed well with the observed values (Table 1). Mean values (with 95% confidence intervals) were 23.4 (7.6) for plot J2, 8.7 (3.0) for plot J3, 22.0 (5.9) for plot S2 and 28.4 (9.6) for plot S3. Of various assumptions tested, ‘constant ratio’ gave the closest correspondence between the observed and estimated values. The estimates of total number of genets per plot (two 1 m × 3.3 cm transects) in Table 1 are therefore based on this assumption.
Size and spatial pattern of genets
The two methods of bootstrapping used to estimate mean genet size in fully analysed plots gave similar results (Table 3). This validates the results for the partially analysed plots (where only method S was applicable). There was little difference in genet size between the J and S sites (Table 3).
Table 3. Estimates of genet size (the number of occupied 3.3 × 3.3 cm cells) of Festuca rubra by bootstrap procedures. See text for explanation of G and S methods of bootstrapping
For partially analysed plots (J2, J3, S2 and S3), observed means were calculated only for identified genets.
1.429 (± 0.245)
1.444 (± 0.152)
1.494 (± 0.276)
1.595 (± 0.281)
1.569 (± 0.332)
1.447 (± 0.214)
1.198 (± 0.263)
1.280 (± 0.194)
The randomization test revealed that genet spatial distribution was not significantly different from random (P > 0.05) at either the J or S sites (Table 4), although plot J1 showed a weak tendency (P = 0.082) towards aggregation of genets.
Table 4. The results of a randomization test for the spatial pattern of genets of Festuca rubra. The mean and variance of the number of genets per cell (3.3 × 3.3 cm) are given. The P-value indicates the significance level of the difference in the spatial pattern between the observed and randomized variances
J site, plot J1
S site, plot S1
Simulation of genet dynamics
The number of genets sampled within the simulation area was sensitive to all three variables in the time model (Figs 2a and 3a), whereas mean genet size depended on the per cell mortality rate and genet spreading rate, but was almost independent of the genet natality rate (Figs 2b and 3b). When RSR occurred, changes in per cell mortality and genet spreading rates had opposite and interacting effects on both the number and size of genets. When the values of their parameters differed by more than 0.1, either very large (if genet spreading rate > per cell mortality rate) or very small genets (if genet spreading rate < per cell mortality rate) were produced, and, for a given natality rate, the number of genets increased as the ratio of the spreading rate to mortality rate increased (Fig. 2a). Increasing natality rate increased the total number of genets present, particularly when mortality and spreading rates were low (Fig. 3a where the two rates are equal in any particular run). If ISR was simulated, the patterns were qualitatively similar, although this produced much larger genets for most combinations of the cell mortality and genet spreading rates, and stronger responses of genet number and size to the per cell mortality and genet spreading rates (Figs 2 and 4).
The simulations of RSR produced realistic numbers of genets if the ratio of mortality rate to genet spreading rate was close to 1. If both these rates were 0.3, natality rates of 70–100 (Table 2) gave values similar to those found in field (five independent runs gave 27–34 genets with mean sizes of 2.0–3.0 cells), whereas if mortality and spreading rates were equal to 0.2, a natality rate of approximately 50 gave 27–45 genets of mean size 2.8–5.6 cells. No realistic values were predicted when lower rates of mortality and spreading were simulated. Mean genet sizes were always slightly larger than those found in the field (Figs 2b, 3b and 5).
If per cell mortality rate exceeded genet spreading rate by 0.05 year–1, the qualitative picture remained the same, although the number of genets decreased slightly and the mean genet size fell so that it was closer to that found in the field. Thus, when per cell mortality rate = 0.3, genet spreading rate = 0.25 and genet natality rate = 150, the prediction was for 23–49 genets of mean size 1.9–2.4 cells, and when per cell mortality rate = 0.2, genet spreading rate = 0.15 and genet natality rate = 50–100, 28–50 genets of mean size 1.6–2.8 cells were predicted.
Under the ISR regime, per cell mortality and genet spreading rates greater than 0.1 resulted either in no genet survival at year 200 (if per cell mortality rate > genet spreading rate) or in mean genet sizes greater than 10 cells (if per cell mortality rate < genet spreading rate). Realistic numbers and sizes of genets were therefore obtained only for per cell mortality and genet spreading rates smaller than 0.1. However, independent field estimates for these parameters were much higher than this (commonly about 0.3, see the Methods).
An initially high genet natality rate followed by a lower but non-zero annual natality rate (combined seedling recruitment; Fig. 6), hardly influenced the final number and mean size of genets (compare Figs 3 and 6). Only when the per cell mortality rate fell below 0.1 (i.e. when values were much lower than those estimated in the field) did the large initial natality rate substantially affect the number and mean size of genets.
Our simulation results indicate that ISR could not sustain the F. rubra genet population at observed densities and mean genet sizes unless both the genet spreading and per cell mortality rates were much lower than those found in the field. Furthermore, even small increases in either parameter value, particularly in genet spreading rate, made the simulated genet sizes much greater (> 6 times) than those seen in the field (cf. Watkinson & Powell 1993). However, if natality rates were maintained through time, at around 50–100 genets every year (equivalent to 3–7 genets m–2 year–1), realistic numbers and sizes were predicted for the genet populations (Fig. 3) at rates of genet spreading and per cell mortality rates similar to those observed in the field. We can thus conclude that in this mountain grassland F. rubra shows RSR and that even if there had been a burst of initial seedling recruitment, it would be undetectable after 200 years of grassland development (cf. Watkinson & Powell 1993).
Although ISR has been suggested to occur in many grass species (Zhukova & Ermakova 1985) there are still very few data available to support this contention. For example, although Calamagrostis canadensis, another perennial grass, displayed extensive genetic variation, MacDonald & Lieffers (1991) found no evidence for seedling recruitment. They argued that although disturbed sites were colonized primarily by sexually produced seedlings, populations seemed to be maintained during later successional stages by vegetative reproduction. The genet natality rate estimated for F. rubra was higher than that for C. canadensis, probably because the populations of C. canadensis were not mown. Such disturbance may enhance seedling recruitment in semi-natural pastures (Eriksson & Eriksson 1997).
The use of two response parameters in the model (number and size of genets) increases the precision with which genet natality rate can be inferred. Realistic values of both parameters could be obtained for particular combinations of mortality and genet spreading rate (Figs 2–6). Genet natality rate was the only demographic parameter not estimated directly from the field data. The model further predicts a close relationship between genet spreading rate and per cell mortality rate. Observed genet spreading rates of 0.2–0.3 year–1 lie between the values yielded by the two methods used for per cell mortality estimation.
As newly established seedlings do not spread spatially from their place of germination for some time and are subject to higher mortality risk than established genets, there is a lag period between seedling establishment and the beginning of effective spatial spreading. The genet natality rate is therefore more likely to be subject to variations in response to environmental conditions than the genet spreading and per cell mortality rates. In the field this may be reflected in a very high genet natality rate in favourable years that compensates for the absence of seedling recruitment in unfavourable years.
Our simulation model showed that if seedling recruitment occurs repeatedly, natality rate has little effect on the size of genets at year 200. This suggests that F. rubra populations will be stable, even if varying environments affect the genet natality rate, because it is likely that genet spreading and per cell mortality rates will remain at the moderate values found in the field. Although the assumption that there is no between-year variation in any parameter except for genet establishment rate makes the model less realistic, temporal variation is likely to be within the range of mean values tested and thus unlikely to change the qualitative predictions. Unfortunately, variation in natality rate cannot be estimated using the current model or data set.
The spatial model presented in this paper does not include any explicit processes of inter- or intraspecific interactions between genets or between shoots within a cell, as included in Watkinson & Powell's (1993) model for Ranunculus repens. It should be noted, however, that all our model parameters were obtained in the field in a closed sward and must therefore be ‘post-competitive’ values, which also include the effects of physiological integration. Thus the model parameters employed correspond to the mean values applicable if there are interactions with neighbouring genets, or more likely with neighbouring shoots.
However, little difference was found in the number and size of genets between the J and S sites (Tables 1 and 3 and Fig. 5a) and the spatial pattern of genets was not significantly different from random in either site (Table 4). Both biotic and abiotic parameters differed between the sites, suggesting that the genet dynamics of F. rubra are rather independent of such parameters. A uniform spatial pattern is often assumed to be the end result of competition (Mohler et al. 1978; Cannell et al. 1984) and the random distribution is consistent with the absence of interactions between genets as found by Hara & Herben (1997) for F. rubra shoots > 1 year old.
However, several studies have shown a decrease in the number of genets in populations of clonal species during stand development (studies cited in Cook 1985; Turkington 1989), indicating either competitive exclusion of genets or differential success of individual genets under different environmental conditions. This pattern is likely to hold under the ISR regime or where seedling recruitment rate is very low in the later stages of population development and interclonal competition is pronounced (Sebens & Thorne 1985). However, it does not explain the large number of F. rubra genets in this fairly old grassland (300–400 years old). Large numbers of genets, which have also been reported in other studies (Harberd & Owen 1969), could simply result from a continuing abundance of germination opportunities, even in a densely occupied grassland, together with absence of competition at the genet level.
As in populations of other clonal plant species (Maddox et al. 1989; MacDonald & Lieffers 1991; Parker & Hamrick 1992; Eriksson 1993; Parks & Werth 1993), genetic variation in these F. rubra populations was considerable. Most other studies, however, have inferred very low genet natality rates (i.e. rare seedling recruitment), although some have found both very few large genets and many small ones at the same site (Cook 1985). The similar pattern seen in our results (Fig. 5a) appears to be due to a recruitment regime in which sexual reproduction, which generates genetic diversity, continues to occur from time to time.
Such RSR should generate a large number of new genotypes upon which selection may operate. Given the high spatiotemporal environmental variability of grasslands (Silvertown et al. 1989; Jackson & Caldwell 1993; Tang & Washitani 1995), selection pressures are also likely to vary in space and time and may contribute to the maintenance of genetic variation within the population. There is indeed large genetic variation in the physiological parameters of F. rubra genets in this population (Skálová & Krahulec 1992; Skálováet al. 1997). These selection pressures might even have caused stabilization of the genet spreading and mortality rates to around values of 0.2–0.3 which lead to the stable persistence of the population. The lack of an effect of initial conditions on the final number and size of genets indicates the greater importance for F. rubra of short-term processes (e.g. spatiotemporal variations) rather than of long-term processes (e.g. competition and founder effects) (Chesson 1986; Hara 1993).
This study was supported by a grant for international collaboration from the Japan Society for the Promotion of Science (JSPS), a Czech Academy grant (60555), the GACR grant (205/98/1533) and partly by a grant for young scientists from the JSPS and a JSPS Fellowship for Research Abroad to J. Suzuki. We thank Věra Hadincová and Sylvie Pecháčková for help in the field and for providing us with unpublished data. We are also grateful to Karin Kottovaˇ and Masako Kato for help in the laboratory. The DNA analysis was carried out at the Department of Biology, Tokyo Metropolitan University, Japan. We are grateful to Monica Geber, Mike Hutchings, Josef F. Stuefer, Beáta Oborny, Jan van Groenendael, Lindsay Haddon and an anonymous referee for valuable comments and suggestions on the manuscript. This paper was read at the 4th Clonal Plants Workshop held in Visegrád, Hungary, in May 1995, and at the Conservation Biology Symposium of the 43rd Annual Meeting of Japanese Ecological Society (JES) held in Tokyo, Japan, in March 1996, and we thank the participants for useful discussions. Yoh Iwasa kindly sent us a preprint of his paper.
Received 3 November 1998 revision accepted 2 April 1999