Clonal plant species in a dry-grassland community: A simulation study of long-term population dynamics

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Ecological Modelling 96 (1997) 125-141

Clonal plant species in a dry-grassland community: A simulation study of long-term population dynamics Eckart Winkler a,*, Stefan Klotz b a Centrefi~r Environmental Research, Leipzig-Halle, Department of Ecological Modelling, P.O. Box 2, D-04301 Leipzig, Germany b Department of Community Ecology, D-06246 Bad Lauchstiidt, Germany

Received 29 December 1995; accepted 27 June 1996

Abstract An individual-based spatially explicit grid-based model is developed to simulate the simultaneous development of two clonally growing grassland plant species. The model is based on long-term permanent-plot observations in a low-cover Thymo-Festucetum grassland community which is characterized, besides of some low-abundant ('sparse') species, by the interaction between the perennial tuft grass Festuca cinerea and the stoloniferous rosette plant Hieracium pilosella. The grid-based model includes rules for seedling recruitment, diaspore exchange, mortality, tuft growth and rosette establishment, local interactions, and considers the dependence of population parameters on environmental factors (weather). The simulations give the characteristic spatial features of the community (aggregations of grass tufts and of rosettes) and the highly fluctuating species abundances. They allow the assessment of the importance of different factors which control the abundances in the community: reproduction modes, intra- and interspecific interactions, dependence of life-history processes on weather conditions, and overall climatic conditions. The mechanisms of the spatially explicit model are concentrated by averaging over local interactions into analytical models (stochastic difference equations) which form a basis for a general insight into community dynamics and for a large-scale study of heterogeneous grassland communities containing clonal plant species. © 1997 Elsevier Science B.V. Keywords: Grassland communities; Clonal plant species; Grid-based model; Analytical model

1. Introduction Grassland communities are known for their high species richness on a small scale. A lot of verbally formulated concepts try to explain different aspects of species coexistence and of the persistence of species in a community (Wilson, 1990; Van der Maarel and Sykes, 1993; Zobel, 1992; Palmer, 1994).

* Corresponding author. Tel.: +49-341-2352910; fax: +49341-2353500; e-mail: [email protected].

Besides this there are different attempts to formulate such concepts in the strict form of mathematical models in order to study the interaction of different mechanisms, to make predictions and to formulate testable hypotheses. Many models of plant community dynamics consider sexually reproducing species with seedling lottery or density dependent fecundity as decisive mechanisms (Watkinson, 1980; Chesson and Huntly, 1988). Only very few models take into account as well clonally growing species and the interactions between species having both reproduc-

0304-3800/97/$17.00 © 1997 Elsevier Science B.V. All fights reserved. PH S0304- 3800(96)00057-9

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E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

tion modes. The models of Crawley and May (1987) or Winkler and Schmid (1995) start from the life history of individual plants whereas other models in the form of cellular automata look at the dynamics of the occupation of microsites (Inghe, 1989; Herben, 1992; Silvertown et al., 1992; Oborny, 1994). Most population dynamic models work on a very small scale, with only few attempts to extend the spatial scale by the connection of different small plots via diaspore or module exchange (Weiner and Conte, 1981; Cz(tr(m, 1989; Perry and Gonzalez-Andujar, 1993). Despite of all these different approaches it is extremely difficult to analyze a complex grassland community given by empirical studies in all its dynamic aspects on different spatial scales. Therefore, a stepwise analysis is strongly recommended wherever possible which should start from rather simple and comprehensible cases. A Thymo-Festucetum grassland community was studied by Klotz and Winkler (in prep.) over 15 years by mapping of individuals in small plots. This community permanently shows a very low vegetation cover of only 30-50% and is rather species-poor because of highly unfavorable soil conditions which lead to a strong weather dependence especially of germination. These features make the community a good candidate for a study by a stepwise modelling approach. A slight disadvantage is the fact that it offers only few spatial or temporal patterns for an evaluation of model assumptions. In Winkler and Klotz (1996) a basic model analysis is presented. The main results are: (1) the intra- and interspecific control of the community is, above all, via a reduction by already established perennials of the area available for additional seedling recruitment; (2) the dominant species (the 'matrix' species) Festuca cinerea acts by this control mechanism on itself as well as on low-abundant ('sparse') species, but there is no significant reverse action of sparse species on the matrix; (3) the matrix species is persistent on a small area of only a few m 2 by a combination of clonal and sexual reproduction; (4) sparse species need a buffer to persist on a small scale, either a seed bank (mostly not present in this community), a sufficiently large area to cope with demographic fluctuations or a neighboring community with more favorable conditions for these species.

In the community there is one species, Hieracium pilosella, which does not strictly fit into the dichotomy of dominant and low-density species. Its main characteristics in the community are: (1) the abundance shows strong fluctuations over more than two orders of magnitude; (2) its life history is dominated by clonal reproduction, with weather dependent flushes of new seedlings; (3) occasionally it is able to occupy rapidly even a significant proportion of free area between the tuft aggregates of Festuca cinerea. In this study a spatially explicit individual based model of the population dynamics of the clonal herb Hieracium pilosella and its interaction with the perennial tuft grass Festuca cinerea in a ThymoFestucetum dry grassland community is presented. It focusses on the inclusion of clonal reproduction into cellular population dynamic models, and statements presented are supplemented by a comprehensive analytical presentation. These two modelling approaches serve to answer the following questions: (1) Which are the relative contributions of intraspecific density regulation, the interactions with the dominant species and of environmental factors on the control of the Hieracium pilosella population? (2) What would be the consequences of changing climatic conditions on the mean ratio between Festuca cinerea and Hieracium pilosella? (3) Which details of interspecific interactions are to be studied in future observations? 2. The model 2.1. Biological observations 2.1.1. Study area The study area is a relatively arid region near Halle, Central Germany (51035' N, 11050' E) at 120 m a.s.1, on porphyritic outcrops with shallow soils characterized by a mosaic of natural and seminatural dry and semidry grasslands within an agricultural landscape. Average annual rainfalls and temperature are 465 mm (extreme values: 258 and 640 mm in the period from 1980 to 1994, peak rainfalls in JulyAugust (Treffiich, 1995)) and 9°C, respectively. 2.1.2. Scheme of investigation In 1980, three independent permanent plots of I × 1 m were established in a Thymo-Festucetum

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

community (Thymo-Festucetum Mahn 59, Mahn, 1965) in the grassland mosaic and recorded once every year in April. The number and size of all individuals of all species were mapped; details of the observations are given by Klotz and Winkler (in prep.).

127

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2.1.3. General characteristics of the community The Thymo-Festucetum community under study is a permanent community with an average cover of only 30-50% on extremely shallow (10-15 cm), dry, nutrient poor and acidic soils. It is a remnant of the postglacial natural vegetation of the area (more than l O 3 years old) with no signs of succession processes and covers small areas of lOt-lO 3 m E within the mosaic of different communities. Environmental conditions are harsh, with water as the limiting factor. Disturbances are mainly by water and wind affecting seedlings and juveniles. The community is not managed, except of occasional grazing by sheep (less than once per year) which is not decisive for the long-term composition of the community. Animal disturbances are rare because most animals find better living conditions nearby. A seed bank within the community for the species under study was neither found by us, nor in other studies (Jackel, pers. comm.). Compared to other grasslands (e.g. Law et al., 1993) species diversity is low, with only 8 species (almost) regularly present in all plots over 15 years.

2.1.4. Main constituents of the community The dominant constituent as recorded in the permanent plots is Festuca cinerea, a long-living grass forming tufts which underlie a fragmentation and rejuvenation process. The matrix formed by this species gives rise to large interstices occupying much more than 50% of the whole area. These interstices are partly covered by individuals of other species: Hieracium pilosella, a stoloniferous rosette plant forming rosette aggregates with abundances fluctuating over more than two orders of magnitude (Fig. 1), some perennial grasses and herbs (especially Koeleria macrantha and Silene otites, present mostly with some individuals per mE), and, under favorable weather conditions, a number of spring ephemerals.

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Fig. 1. Abundances of Hieracium pilosella (including seedlings) in spring as observed over 15 years in 3 different 1 m 2 plots in a Thymo-Festucetum community.

The life history of F. cinerea and the hypotheses underlying its modelling are described by Winkler and Klotz (1996). The main facts relevant for the present study are: (1) The radius of the tufts only gradually increases (approximately 0.25 cm per year), and the maximum size of the tufts is determined by intrinsic factors and the unfavorable environmental conditions, but not by mutual competition; (2) flowering and seed production start after a delay of some years; (3) old tufts disintegrate into fragments, and these fragments give rise to rejuvenated tufts, where the process of fragmentation depends on local density; (4) weather conditions mainly influence seedling establishment and juvenile survival. Fig. 2 gives the main steps of the development of H. pilosella in a low-density community like the Thymo-Festucetum. To simplify the model we do not distinguish between juvenile rosettes successfully recruited from seedlings and from clonal reproduction. Under favorable weather conditions the rosettes flower in the second year, they give rise to stolons with new rosettes the fate of which depends on local density, and subsequently they die. Otherwise maturation is delayed for at least one additional year. As with F. ¢inerea we have a strong dependence of seedling establishment on weather conditions leading to a flush of seedlings in 'good' years, and a weather dependent mortality of juvenile rosettes.

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2.2. A grid-based model of the population dynamics of F. cinerea and H. pilosella The spatially explicit modelling of the population dynamics of the two clonal species F. cinerea and H. pilosella and of their interactions is part of the grid-based model described by Winkler and Klotz (1996) which follows the fate of plant individuals in space and time. An individual may be, according to the species and to the question, an individual genet, an individual module belonging to a genet or also a group of modules. An individual (e.g. a grass tuft or a rosette) may comprise more than 1 cell in the model plain as for both species of this study. The model grid consists of 100 × 100 cells of 1 cm 2, the basic time step is 1 year. The course of the annual events (seed production, seed dispersal, mortality, seedling establishment and competition, formation of new rosettes, growth of individuals) starts in summer when vegetative growth has largely been finished. The state of the community in this moment gives spatial representations exemplified in Fig. 5 and the data for time series as in Fig. 6. An individual in this model description is characterized by the position of its central cell, the developmental age ~(in years) and its radius r by means of which all .~ear

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cells are determined which belong to the given individual. One simulation run computes the state of the community in year t + 1 from the state in year t in a sequence of substeps. For the two species F. cinerea and H. pilosella they are implemented as follows:

2.2.1. Seed production Individuals produce seeds if age ~- is greater than ~'g, a delay in generative reproduction (given in developmental years which may differ from pure chronological ones). The reproductive capacity of an individual of species k is given by a k where a k relates to an area unit (i.e. a cell) of an individual. Hence total seed production sik of an individual i of species k is given by the product of a k with the individual area, i.e. the number of cells belonging to that individual. The actual number of seeds per individual is a random number obeying a Poisson distribution with sik as parameter. By this rule a density dependent fecundity can be expressed because in locally dense stands the actual individual size is often below its theoretically possible value because of interactions during growth. 2.2.2. Mortality In the model for each species k a series of age dependent mortalities m~k is defined. On the basis of these mortalities the death of an individual is treated as a random event. Additionally there are weatherdependent juvenile mortalities /x. The death of F. cinerea is combined with a fragmentation and rejuvenation process leading to tuft aggregates as described by Winkler and Klotz (1996). The outcome of this fragmentation, a mode of clonal reproduction, depends on local density. 2.2.3. Seed dispersal Each seed (or diaspore) is individually dispersed at random from its origin into another cell or, with probability e k, outside the plot. In addition to the internally produced seeds for each species seeds may be introduced from the outside of the plot. This abundance is given by a random number distributed according to Poisson with the parameter I k. The seeds remaining in the plot and the introduced ones are at random distributed over all cells of the plot with an equal probability for any cell to receive a diaspore.

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129

2.2.4. Seedling establishment and competition (1) All seeds deposited on cells occupied by parts of living individuals do not germinate and are lost (as a deposition in a seed bank plays no role in the community studied here). According to the observations an adult or a part of an adult of the two species cannot be replaced by a seedling. This rule gives an operational definition of the size of an individual: the individual area comprises all cells where a seed cannot germinate because of suppression by the already established individual. (2) In all free cells a seedling of species k successfully emerges with probability Pk. Under harsh conditions these probabilities may be very low and thus largely determine the fate of the species. A lottery competition (Chesson and Huntly, 1988) between seedlings plays only a marginal role in our community.

part of a F. cinerea tuft (or by another individual) the new rosette cannot establish itself in this cell and dies. But when the position is occupied by an individual of H. pilosella the new rosette can 'look' by one additional random search step for another position. This feature represents some plasticity in the establishment of new rosettes. These rules together express the intra- and interspecific local density dependence of rosette formation and thus of the clonal spread of H. pilosella. Especially in dense communities also the probability of maturation and the mean number n r of stolons may be density-dependent and there is a higher variability in stolon length as an answer to the spatial structure of the community (St~Scklin, pers. comm.). For our sparse community it is sufficient to concentrate all such features in the rules as given above.

2.2.5. Rosette formation A rosette of H. pilosella having reached the developmental age ~-= 2 produces new rosettes in some distance via stolon formation. The number of stolons is a Poisson distributed random number with p a r a m e t e r n r. New rosettes can root in 1 of 16 possible positions approximately 3 cm apart from the mother rosettes (see Fig. 3). This short distance corresponds to the observations in the low-density community with unfavorable growth conditions. If such a position selected at random is occupied by a

2.2.6. Growth of individuals In this programme step the F. cinerea tufts may add new cells (i.e. new tiller groups) to an individual according to the increase of its radius, and new H. pilosella rosettes reach their definite cover. (To simplify model rules it is assumed that a juvenile rosette reaches its full area already in its first year and that subsequent delays in its development due to unfavorable weather conditions only concern its ability to form new stolons and to flower.) Individuals compete against each other when growing. In our lowdensity community model competition occurs only for free, unoccupied cells (i.e. for free space), and adult individuals or parts of them cannot be replaced. The area of an individual is calculated using the radius r. But after having assigned new cells to the different individuals there are often free cells claimed by more than one plant. A decision is made as follows: (1) Seedlings just established can be eliminated, a competition often of minor importance; (2) all individuals claiming a free cell compete for it with a species-dependent 'module competition strength' c M~ according to a lottery rule. An alternative mode of interaction used in some simulation runs just allows for a replacement (an overgrowth) of parts of one species ( e . g . H . pilosella) by growing individuals of another species (e.g.F. cinerea). Consequently, it is assumed that the first species is also superior in the competition for free space. Consequences of such different assumptions about species

Fig. 3. Scheme of the establishment of new H. pilosella rosettes in a low-density community. The length of stolons (approximately 3 cm') is assumed to be independent of local conditions. If a position for a juvenile rosette which was selected at random is occupied by a F. cinerea tuft (dashed area) the establishment fails. If the position is occupied by another H. pilosella rosette (dotted area) a plastic reaction is assumed (search for another free position).

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E. Winkler, S. KIotz / Ecological Modelling 96 (1997) 125-141

interaction in a changing environmental situation are discussed in this study. After having completed the growth phase the state of the community is recorded and a new cycle begins. An important characteristic of this spatially explicit model is the consideration of different forms of clonal growth: a tuft growth by the addition of new tillers, the tuft fragmentation process, and the growth of stolons together with the formation of new rosettes. As different life histories of individuals are modelled it is not possible to formalize all these modes of clonal reproduction by one set of rules, even in a case of low vegetation cover.

Table 1 Model parameters for Festuca cinerea (F) and Hieracium pilosella ( H ) and their standard values for spatially explicit simulations

2.2.7. Stochastic processes (1) All demographic and interference processes are treated as random events; (2) environmental stochasticity manifests itself in form of climatic stochasticities which comprise a stochastic scenario of climatic events and the response of the system to the actual external conditions. To test general questions it is sufficient to have some abstract rules. The course of the weather is divided into two periods and into two quality classes of the weather. The first period ('spring') comprises seedling establishment and rosette formation, the second one ('summer') vegetative growth and mortality. In each model cycle and each of the two periods weather has a value /2 = - 1 o r / 2 = + 1 at random according to the two weather probabilities w_ 1 and w+ t. This weather value /2 is calculated independently for each period, and climatic events in subsequent cycles (i.e. years) are considered to be uncorrelated. It is assumed that weather mainly influences seedling establishment, maturation of rosettes, and juvenile mortality. Details are given in the next section.

A

2.3. Model parametrization As the study concentrates on long-term control of the community dynamics it is sufficient to deduce orders of magnitude of parameter values from empirical observation. Quantitative empirical findings concem life-span and mortality, flowering delay, number of successful seedlings, mean number of tuft fragments, maximum tuft radius, and mean number of stolons, and lead to the basic parameter set of

Parameters

Standard values for species F

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2.3.1. Weather scenario The altogether unfavorable climatic conditions of the community, mainly due to the low water-retention capacity of the soil, lead to the prevalence of 'bad' years. This fact is reflected in the simulations by weather probabilities w_ i = 0.75 and w+ ~= y . w_, = 0.25, unless stated otherwise. 2.3.2. Growth of individuals For F. cinerea growth curve parameters are used which lead to a sigmoid radius increase and a maximum radius of approximately 5 cm. An isolated rosette of H. pilosella is assumed to comprise 9 cm 2. This value may be somewhat lower than the total cover of a rosette in the community but it corresponds to the operational definition of individual size as given above. If competition of modules during growth is only for free space, as in the first (basic) competition scenario, we use CMF = C M H , i.e. we treat both species as having equal competition strength. The second competition scenario is charac-

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

terized by ¢MF >> CMtf, with an additional overgrowth of Hieracium by Festuca: the growth of Festuca tufts is not influenced by Hieracium rosettes.

2.3.3. Mortality The age-dependent mortalities as defined for Festuca lead to a decreasing survival for tufts older than 13 years and to a maximum tuft age of 20 years. Hieracium rosettes definitely die after having reached the developmental age z = 2. A part of juvenile mortality is largely independent of any weather scenarios and is included in the seedling establishment probability p~ (see below). For unfavorable weather conditions (12 = - 1 in 'summer') we have for Festuca an additional juvenile mortality o f / x = 0.5. The effect of different values for H. pilosella, i.e. the weather-dependence of population development, is a topic of the simulation study given below.

131

2.3.6. Rosette formation The value of the weather parameter g2 in 'spring' decides if a juvenile rosette with the developmental age z = 1 reaches the mature state (~-= 2) or if maturation is delayed for one further year. If 12 = + 1 then all rosettes mature, but if 12 = - 1 maturation occurs only with probability h = 0.5. We assume that in our community maturation is controlled by external conditions, not by local density. The parameter A is introduced to avoid an 'all-or-nothing'mechanism, i.e. to have some randomness in the stage transition. The mean number of stolons formed by 'mature' rosettes is n r = 2.0 according to our own observations and to Bishop and Davy (1994).

3. Results of model simulations

3.1. Long-term dynamics of clonal species 2.3.4. Fragmentation of Festuca tufts This fragmentation process is linked with the death of adults. The number of surviving fragments is determined as a Poisson distributed random number with nf = 1.3 as distribution parameter. Density regulation of fragmentation (Winkler and Klotz, 1996) needs no further parameter. 2.3.5. Seed production, distribution, seedling emergence For Festuca the parameters a k, I k, e k, and Pk are determined under the assumptions that we have 1-2 successful seedling per year in a 1 m 2 plot, that seed import approximately equals export, that 50% of internally produced seeds are distributed outside and that p~ is a very small magnitude, The assumptions for Hieracium are similar, but additionally Bishop and Davy (1994) give a value of approximately 70 seeds per flowering rosette. Because of unfavorable soil conditions the seedling establishment probabilities for both species have a very low average value, but the fluctuations of Pk depend on the actual weather parameter 12. If 12 = - 1, the Pk value of Table I is multiplied by "0j, and if 12 = + 1, by '02- According to the observations, we use a very sharp distinction between good and bad conditions: '0~ = 0 and "02 = 4 for both species.

These simulations reproduce the general pattern of the community, mainly the permanently sparse spatial structure with grass-tuft aggregations and the strongly fluctuating aggregates of H. pilosellarosettes, and the dependence of this pattern on different life-history responses to weather conditions. 'Weather' is a synonym for all the fluctuating environmental conditions influencing the fate of the community constituents. Basic simulation parameters are taken from Table 1. The asymmetric weather scenario with y = 0.333 corresponds to the general conditions in the community under study. The response of H. pilosella to weather fluctuations is expressed by its seedling recruitment probability, its maturation delay, and by the additional juvenile mortality /x in years with 'bad' climatic conditions in the vegetation period (see Fig. 2). Fig. 4 gives mean abundances and vegetation covers at different values of /x for Hieracium populations in pure stands and for a community of the two clonal species. Compared to the mean population size ( X ) of Hieracium from the data ( ~ 50) a value o f / x = 0.35 gives the most appropriate simulation result if it is taken into account that the field observations in spring largely do not register juveniles whereas the counting of rosettes in the model simulation gives all rosettes, adult plus juvenile ones. The mean number of adults in the simulation is 48.

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

132

A typical example of the spatial structure of the community resulting from the computer simulation is given in Fig. 5. F. cinerea shows aggregates of tufts due to fragmentation as explained by Winkler and Klotz (1996). Aggregates of H. pilosella originate from the short stolon length of only approximately 3 cm. A high percentage of aggregates has a life-span of only a few years so that there is a rather limited size of these aggregates (see below). The simulated structure fits well to the general pattern as described in Section 2.1. Fig. 6 gives an example for the course of species abundances (Fig. 6a) and of vegetation cover (Fig. 3500

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6b) over 300 years with /x = 0.35. Despite of the long-term stability of the community there are large short-term and long-term fluctuations in the time series. These fluctuations are especially pronounced for H. pilosella corresponding to the observations whereas F. cinerea shows limited short-term fluctuations because of its long life span and the low influence of weather on adult mortality. The large fluctuations of both species abundances in the simulated time series markedly wam of making predictions from observation series of very short range and to compare details of the simulated and observed time series. Fig. 4 reveals a high sensitivity of mean Hieracium population size to changes in/x in the range of /z = 0.25-0.4. In this range there are also great differences between mean abundances of Hieracium in pure stands and in mixtures with the matrix species Festuca. A small change in the sensitivity to weather conditions expressed by /z even leads to a reversal in the species dominance in the community. At /z = 0.4 (rather high sensitivity of Hieracium to weather conditions) we have a low population size of Hieracium with often an absence of Hieracium at all, and the Festuca population is unaffected by the

E. Winkler, S. Klotz/ Ecological Modelling 96 (1997) 125-141

presence of Hieracium, But already with /z = 0.3 the results are completely changed. Thus, we can understand that just at the 'standard value' of /x =

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0.35 larger random sequences of 'good' or 'bad' years have a great influence on the actual Hieracium-Festuca ratio. The more an overall change

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E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

134

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of climatic conditions (changes in the y-value) may lead to significant changes in the community composition (see below).

3.2. Long-term dynamics: Control of clonal reproduction

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=

.

0.2

~

"-

0.1

0.0 0.20

,

,

,

,

0.25

0.30

0.35

0.40

0.45

0.50

juvenile mortality parameter p

Fig. 8. Relative reduction of the number of juvenile H. pilosella rosettes during establishment due to (1) intraspecific interactions, and (2) interspecific interactions in pure stands (a) and in mixtures with F. cinerea (b) in dependence on the parameter/x of juvenile mortality during rosette maturation,

ter/x is independent of these factors. The percentage of juveniles eliminated by the juvenile mortality factor/x is given in Fig. 7, together with a theoretical estimation of this percentage (see last section). High mortality (/,~ = 0.5) alone would be sufficient to reduce the average number of descendants per rosette and year even below the desired ratio of 0.5 and would prevent a permanent presence of Hieracium in a small plot. The control of clonal reproduction by weather is overlapped by the reaction to local densities expressed by the model rules for the recruitment of new rosettes (Fig. 8). In the model, density effects are not directly influenced by weather conditions. But, on the other hand, species abundances highly depend just on this weather factor. Therefore, with the mortality value of /z = 0.35, the Hieracium abundance is very sensitive against changes in weather conditions as well as against the presence of other dominant species. This modelling result also corresponds to empirical findings on the weather dependence of the Festuca ovina-Hieracium pilosella ratio in the East Anglian Breckland reported by Watt (1981). Additionally, we have some seedling production, partly due to diaspores from the outside (independent of the state of the community, if no torus geometry),

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

partly from internally produced diaspores. The relative contribution of sexual reproduction to total reproduction and the importance of introduced diaspores, again in dependence on /z, is given in Fig. 9. The relative value of clonal and of sexual reproduction of Hieracium in the community is demonstrated by a computer experiment which follows the fate of populations emerging from one successful seedling. A Hieracium seedling is 'planted' at the start of each simulation run in the centre of a plot covered with approximately 35% by a dynamic Festuca population. Population development without any additional diaspore input was followed over 300 years at maximum under three different assumptions on the reproduction mode: (1) only sexual reproduction; (2) only clonal reproduction; (3) both reproduction modes. Survival curves are given in Fig. 10. Pure sexual reproduction gives rise to very short-lived populations. Also, with clonai reproduction the lifespan of the population is mostly short, but from time to time there is a survival of even decades. The formation of aggregates needs clonal reproduction, but for the initiation and perpetuation of such aggregates in the plot many origins by seedlings are necessary. The same result is given by computations on the fate of fully established Hieracium populations in mixed stand when diaspore input ceases (e.g. by a fragmentation of the habitat). 1.0

0.9 0.8 0.7

0.6

/

0.5 0.4

'Y

135

1.0

0.8

"Q 0.6

~

0.4

0.2

0.0

,

,

10

100

survival t i m e (years)

Fig. 10. Survival probabilities of H. pilosella populations (300 runs; /x = 0.35) from l seedling with different modes of reproduction: (l) only sexual reproduction (mean life span ( T ) = 2.1); (2) only clonal reproduction (rosette formation) ( ( T ) = 7.5); (3) both reproduction modes ( ( T ) = 12.5).

All simulations on the action of the different control factors together give the following result: (1) At a high response level of the population dynamics on weather conditions this environmental factor alone is sufficient to maintain the Hieracium population on a low level, and persistence of the population is mainly due to imported diaspores. (2) At a low response level the Hieracium population shows such a high rate of increase that it replaces other species and that its abundance finally depends only on intraspecific density control. This exclusion of other species is mainly not by a direct competition but only by the strong ability of Hieracium to occupy and to maintain space due to its life-history. (3) At an intermediate response level the presence or absence of other dominant species is of crucial importance (Fig. 8).

0.3

3.3. Influence of local interspecific interaction mechanisms

0.2

0.1

..-77.:..-7-Z-..:. . . . . -. . . . . : . . . . . . . .

0.0 0.20

i

i

i

!

i

0.25

0.30

0.35

0.40

0.45

0.50

juvenile mortality parameter p

Fig. 9. Relative contribution of sexually produced juveniles (a: all seedlings, b: proportion of seedlings emerging from seeds from the outside) in pure stands (1) and in mixtures (2) to the total progeny of H. pilosella in dependence on weather dependent juvenile mortality p,.

The results of Fig. 4 show that within a range of /x-values the presence of absence of Festuca has large consequences on the Hieracium populations. It is to be asked to what degree this consequence is modified by changes in the local interaction mode. The basic scenario starts from an equal local competition strength of Festuca and Hieracium for free

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

136

3.4. Long-term change of climatic conditions 1000

loo ¢1 "O e-1 J= ¢1

10

11 11

H F competition mode weather .333 ratio

H F

H F

a

The standard weather scenario with the quality ratio of w+ l / w _ l = Y = 0.33 contains sequences of random length of years with only good or only bad conditions but with an overall bias towards bad conditions. It was shown by Fig. 4 that population abundances rather sensitively depend on the response of the juveniles on the actual weather. Therefore it must be asked for the consequences of a change of the weather conditions themselves, e.g. to 7 = 1 with again /z = 0.35. This value means more years with

HF

5000

b 1.

.333

1.

Fig. 11. Stationary abundances (1500 years) of F. cinerea (F) and H. pilosella (H; with /x=0.35) in dependence on the local competition rule (a: both species equivalent; b: total superiority of F ) and on the ratio 3/ of 'good' and 'bad' weather conditions.

(a)

2000

1000 ~

500

a)

u c

~

21111 ~ .

5O space and there is no replacement of already occupied cells. This means that Festuca tufts are somewhat inhibited in their growth ability by the neighborhood of Hieracium rosettes but there is no direct mutual replacement. But it is difficult to base such a rule really on field observations. Therefore, it is necessary to study also the effect of a structural change in the model. This means a local superiority of Festuca: Festuca is much stronger than Hieracium in the competition for free space, so that it is not inhibited in its growth and can even partially overgrow already established rosettes of Hieracium. However, under the standard weather scenario these obviously strong modifications have almost no consequences on the long-term outcome of simulations (see Fig. 11). As long as the Hieracium population is low and locally fluctuating a Festuca tuft at a given position has only for a short period compared to its life span some contact to Hieracium rosettes. Thus, it is not necessary to perform the difficult observation which would allow to distinguish definitely between the two interaction mechanism. But, as it is shown below this is only valid under the present conditions of the community under study.

F

2O 0

50

i

i

i

!

100

150

200

250

300

time(yeam) 5000

/ (b)

2000 1

H

1000 o u r(o e.

•o .o

500 200 100 50 20

0

i

i

i

i

i

50

1O0

150

200

250

300

time (years)

Fig. 12. Dynamics of changes in population abundances of F. cinerea (F) and H. pilosella (/~ = 0.35) with different local interaction mechanisms ((a): both species equivalent; (b): total superiority of F) after a sudden change at t = 50 years of the global climatic conditions (transition from y = 0.33 to y = 1.0). (Averages from 20 runs.)

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

favorable conditions for Hieracium, as compared to 3, = 0.33, especially due to longer periods of humid years. It is not this assumption itself which is of interest but generally a change in climatic conditions at all. Indeed, on a long-term highly different mean population abundances and ratios between Hieracium and Festuca will result (Fig. 11). But the extent of the changes in the abundances strongly depends on the details of the local interspecific interactions as given above. Under the conditions of equal local competition strength we have a complete displacement of the Festuca population (mostly some individuals are still present in the simulation plot because of diaspore import). With a local superiority of Festuca we have an equilibrium between both species, and both species are present on the small plot with rather high abundances. Aggregates of Festuca tufts have a mean life-time of several decades (Winkler and Klotz, 1996) and therefore this species reacts only very slowly on changing conditions. In the scenario of Fig. 12, after 50 years of simulation the 3,-value suddenly changes from 0.33 to 1.0. Now, for again approximately 50 years (i.e. for a time much longer than even a long-term field observation) we have a significant increase of the Hieracium population level but, on the average, no changes for Festuca. Only after a still longer period Festuca decreases and the different local interaction mechanisms become manifest. Therefore, it must be concluded: (1) the response of a community to environmental changes may be very slow and not with the same velocity for the components of the community, and, as to be seen from Fig. 12b, the response may even start into the opposite direction; (2) it is very difficult to distinguish over some period of time between normal fluctuations and long-term changes; and (3) the prediction of the long-term outcome may highly depend on detailed mechanisms which are difficult to be observed and which may be, under standard conditions, also of minor importance.

4. Interpretation of results: Analytical equations The modelling study is looking for basic control mechanisms of grassland community dynamics which act behind the strong randomness of the results of a

137

15 years' observation period. An analytical, lumped theory for the two-species system F. cinerea and H. pilosella allows for a concise and general description of the population dynamics. The feasibility of averaging over spatial features should be checked against spatially explicit simulations. For F. cinerea (with abundance F ) only the comprehensive equations of Winkler and Klotz (1996), neglecting the age-structure, are given here, with some modification to include interactions with H. pilosella. For H. pilosella it is necessary to write down stochastic difference equations for the two developmental stages (abundances H l and H 2, with H=H~ +H2), as responses to random weather events play a significant role in the population development. The equation for the dynamics of F. cinerea reads as Ft+l = Ft + I F "PF "f + YF "aF "f'PF" (1 -- e v ) . F,

+ n'f'm v ' F , - m r.F, =F,+B+B' +Bf-M

(I)

with B for seedling recruitment from introduced diaspores, B' for seedling recruitment from internally produced diaspores, B e for recruitment of new tufts due to fragmentation, and M for mortality (explanation of other symbols see below). To develop the equations for the two stages H~ and H 2 of H. pilosella and for a temporary seed bank S, it is necessary, according to the spatial simulation programme, to divide the basic time step into three substeps. (1) Mortality; seed production and seed input H'l = H i , - / , ( / 2 )

"H,,,

(2a)

H ~ - H2,-(1 - mH),

(2b)

S' = (1 - e n ) " a H.yH "Hzt + In

(2c)

with m n - 1. (2) Stage transition H't' = HI - H't • W ( J 2 ) ,

(3a)

H i' --=H I - W ( O ) ,

(3b)

s = s'

(3c)

with

w( n ) = (T,(n) .(1- A) + r~( n)).

(3d)

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

138

(3) Rosette formation and seedling establishment

Hjt+ l = H'l' + ptt( J2 ) "f " ~' + n'r "H~',

(4a)

H2t+ 1 -- H2" '

(4b)

S,+ l = O.

(4c)

and (4) by the 'free area' f available for germination with f = (1 - { F . ( 1 - mr)"YF

In summary we get

H,,,+, =HI. , - I x ( a ) " H , . t - H , . , . (1 - Ix(g2)) • (1 - n'r)" W ( O )

+p~(~O).

(1 - e z )

•f . a H . y t y . H 2 . , + l u . f . p ~ ( S 2 ), H2.,+l = H , . , - ( I - / x ( ( 2 ) ) .

W((2)

(5a) (58)

with I for seed input, p for seedling establishment probability, f for 'free area' (Eq. (9)), y for mean individual size (number of cells per individual), a for seed productivity per individual cell, e for percentage of seed export, n'f for effective number of fragments per disintegrating Festuca tuft, m for adult mortality, Ix for juvenile mortality, A for transition delay probability under 'bad' conditions, and n'r for effective number of juvenile rosettes per parent rosette. Weather induced stochasticities are denoted by the weather parameter ~ the value of which is governed by the weather probabilities w_ 1 and w+ = w_ ~-3'. We have the response of H. pilosellaparameters as

pN(g2)={~h.pH if ~ = --1, 772"PH i f ~ = +1 Ixn(g2)=t,,.H/O

(6)

if O = - 1 if O = + 1

(7)

TI(O) = 1

T2(O) = 0

if g ] = - 1

T~(g2)=0

T2(O)=l

ifO=

+1

(8)

In the Festuca-Hieracium system intra- and interspecific interactions are expressed by: (1) a reduction of the mean individual sizes y with increasing abundances (yF=YF(F, H ) a n d yH=yn(F, H)); (2) a reduction of the mean number of Festuca fragments with increasing abundances (n'f= n'e(F, H)); (3) a reduction of the mean number of Hieracium rosettes per adult rosette (n'r = n'r(F, H));

+ H , " (1 - IXH)" yH}/N),

(9)

where N the number of cells in the grid-based model. (F_,q. (9) implies that germination of Hieracium occurs before the formation of new Hieracium rosettes.) For y, nf, and n r as functions of F and H, monotonically decreasing functions are used which can be parametrized according to results of simulations with the grid-based model (Caswell and John, 1992). As these functions average over rather complicated spatial rules there is no one-to-one relationship between the two model types. In general, one can consider both models as being independent from each other, each of them related only to the real system. But it is easier to formulate and to quantify along to the observations the rules of the grid-based model than the functions of the analytical model. In systems with spatial components it must be considered as the basic version. We have mutual relationships between the two model types: the grid-based one is the basis for the evaluation of local interactions whereas the analytical one allows for a comprehensive look on the role of the different species in the community. Though age-stages of Festuca are neglected in Eq. (1) the dynamics of the two species are rather complex. There are density-dependent control factors leading to intra- and interspecific regulation and additionally density-independent factors. The mechanisms for the control of the matrix species F. cinerea itself is described by Winkler and Klotz (1996). Important features of the interactions between the two species are: (1) Even if y, p, n r, and nf would be independent of interspecific interactions there is an important indirect relationship between the two species via the 'free area' f. In general the space available for seedling recruitment has great relevance for species coexistence and mutual exclusion of perennial plants. In our community high abundances of H. pilosella can thus reduce the sexual reproduction of F. cinerea, and in such situations H. pilosella cannot be treated simply as a 'sparse species'.

E. Winkler, S. KIotz / Ecological Modelling 96 (1997) 125-141

(2) In the spatial simulation model we have different interaction mechanisms which influence clonal growth and reproduction of the two species: (a) the local action of individuals on the clonal spread of H.

300

t

,

139

pilosella according to Fig. 3 is globally expressed in the analytical model by n'r= n'r(H, F); (b) both species also influence the mean fecundity YH of H.

pilosella; (c) basically, also the mean tuft size YF of ,

,

,

(a)

F.

cinerea-

20O

150

i00

I

,

:', ~

',', t,t

:i I

iit

I :I ~ ~ t~ I

50

'l

,

b

h

,.':

~ ,:

0

50

',~

"

'

, It'.;

i00

'. . . . . . . -, ,,,,", .,,, : ',./"',j-' ',t,. ¢ ,_ 150

200

250

300

40

35

30

25

20

15

10

:'~'!"4

:", ~',,,J:',,~ ,, ,,:,,!,, ,

', /,% 50

I00

150 Year

200

I ",,' 250

300

Fig. 13. Time series of a simulation over 300 years with the stochastic difference equation model of the dynamics of F. ¢inerea and H.

pilosella. ((a): abundances, (b): cover).

140

E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141

F. cinerea and, as a consequence, the fragmentation rate n~ may be influenced by both species. However, as to the third factor we discussed two different scenarios which may lead to markedly different consequences. In the analytical theory they can be expressed as follows: (a) basic scenario: Ye and n'f depend on both species; (b) superiority of Festuca: Yr and n'f depend only on F, thus giving a higher fecundity and lower mortality of Festuca and shifting the abundance ratio towards F. The presence or absence of dependencies of YF and n'f on H may have far-reaching consequences when average Hieracium abundances are high. (3) The juveniles H l from a cohort underlie in subsequent cycles a mortality/z until they are eventually transformed to adult rosettes H 2. The percentage of the reduction of the cohort should be independent on any densities. Taking the sequence of mortality and transformation the theory gives for the percentage of eliminated H 1 rosettes

Hl.elim = H~" ( 1 - M ) / ( 1 - M + T ' M )

(I0)

with M = ( 1 - w l ' / z ) and T = w l ' ( l - A ) + w+i). The results of this formula in dependence on /~ (see Fig. 7) are in good agreement with the results from the simulations with the grid-based model. In summary, the simulation scenarios and the analytical equations lead to the statement that Festuca acts on Hieracium mainly by the reduction of both clonal and sexual reproduction whereas the reverse action is, above all, due to a reduction of seedling recruitment. According to Winkler and Klotz 0996) sexual reproduction of F. cinerea can be neglected on a short term but is indispensable on a long term. Thus, short-range fluctuations of H. pilosella exert only a low influence on the community matrix. But in consequence of a change in external conditions or after long-range fluctuations there can be a pronounced reaction of H. pilosella on F. cinerea. Fig. 13 gives an example for time series in one plot over 300 years for the two species simulated by means of the analytical model of Eqs. (1) and (5). Here, the Festuca model was extended to consider different developmental stages, and for both species all birth, mortality, exchange and transition events are treated as stochastic processes. The overall features of these time series well agree with those of the

spatially explicit model (Fig. 6). Remaining differences in the properties of the time series are acceptable as there is no observation series of sufficient length for a decision between any points of controversy. The analytical theory reveals its full power when scale transitions are intended which extend the knowledge from small plots with a detailed modelling of local interaction mechanisms to an array of a great number of such plots linked by a dispersal of diaspores and characterized by locally varying conditions (Winkler and Klotz, in prep.). Compared to the literature (Soane and Watkinson, 1979; De Kroon et al., 1987; Watkinson and Powell, 1993) the model Eqs. (1) and (5) mark a progress in the analytical modelling of populations of clonal plants: they contain interspecific interactions, they average over spatial features and they allow for an individual-based stochastic approach. Thus, analytical models based on spatially explicit simulation models open a possibility to study intra- and interspecific interactions between clonal plants in a community, to include the effects of environmental conditions and to simulate processes over a long time and a large scale.

Acknowledgements The authors are indebted to Jiirg StScklin and Christian Wissel for encouraging discussions and valuable suggestions.

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E. Winkler, S. Klotz / Ecological Modelling 96 (1997) 125-141 Herbert, T., 1992. Coexistence and pattern diversity in communities of clonal organisms: A model based on cellular automata. Abstracta Bot., 16: 49-52. Inghe, O., 1989. Genet and ramet survivorship under different mortality regimes - a cellular automata model. J. Theor. Biol., 138: 257-270. De Kroon, H., Plaisier, A. and Van Groenendael, J., 1987. Density dependent simulation of the population dynamics of a perennial grassland species, Hypochoeris radicata. Oikos, 50: 3-12. Law, R., McLellan, A. and Mahdi, A,-K.S., 1993. Spatio-temporal processes in a calcareous grassland. Plant Species Biol., 8: 175-193. Mahn, E.-G., 1965. Vegetationsaufbau und Standortverh~altnisse der kontinental beeinflul3ten Xerothermrasengesellschaften Mitteldeutschlands. Abh. S~ichs. Akad. Wiss. Leipzig, Math. -Naturwiss. KI., 49: 1-138. Oborny, B., 1994. Growth rules in clonal plants and environmental predictability - a simulation study. J. Ecol., 82: 341-351. Palmer, M.W., 1994. Variation in species richness: Towards a unification of hypotheses. In: M. Zobel, M.W. Palmer, K. Kull, and T. Herben (Editors), Vegetation Structure and Species Coexistence. Opulus Press, Uppsala, pp. 85-101. Perry, J.N. and Gonzalez-Andujar, J,L., 1993. Dispersal in a metapopulation neighborhood model of an annual plant with a seedbank. J. Ecol., 81: 453-463. Silvertown, J., Holtier, S., Johnson, J. and Dale, P., 1992. Cellular automaton models of interspecific competition for space - the effect of pattern on process. J. Ecol., 80: 527-534. Soane, T.D. and Watkinson, A.R., 1979. Clonal variation in populations of Ranunculus repens. New Phytol., 82: 557-573. Trefflich, A., 1995. Die VerS.nderung der Bodenfeuchte im

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Zusammenhang mit der spontanen Vegetationsentwicklung auf Brachfl~ichen. Kiihn-Arch., 89: 87-102. Van der Maarel, E. and Sykes, M.T., 1993. Small-scale plant species turnover in a limestone grassland: The carousel model and some comments on the niche concept. J. Veg. Sci., 4: 179-188. Watkinson, A.R., 1980. Density-dependence in single-species populations of plants. J. Theor. Biol., 83: 345-357. Watkinson, A.R. and Powell, J.C., 1993. Seedling recruitment and the maintenance of clonal diversity in plant populations - a computer simulation of Ranunculus repens. J. Ecol., 81: 707717. Watt, A.S., 1981. Further observations on the effects of excluding rabbits from grassland A in East Anglian Breckland: The pattern of change and factors affecting it (1936-73). J. Ecol., 69: 509-536. Weiner, J. and Conte, P.T., 1981. Dispersal and neighborhood effects in annual plant competition models. Ecol. Modelling, 13: 131-147. Wilson, J.B., 1990. Mechanisms of species coexistence: Twelve explanations for Hutchinson's 'paradox of the plankton': Evidence from New Zealand plant communities. N.Z.J. Ecol., 13: 17-42. Winkler, E. and Klotz, S., 1996. Long-term control of species abundances in a dry grassland community: An investigation by mathematical modelling. J. Veg. Sci., in press. Winkler, E. and Schmid, B., 1995. Clonal strategies of herbaceous plant species - a simulation study on population growth and competition. Abstracta Bot., 19: 17-28. Zobel, M., 1992. Plant species coexistence - the role of historical, evolutionary and ecological factors. Oikos, 65:314-320.