vegetation change in semiarid communities

Vegetatio 125: 169-183, 1996. 169 © 1996 KluwerAcademic Publishers. Printed in Belgium.

Vegetat ion cha n g e in semiar id c o m m u n i t i e s

Simulating probabilities and time scales

T. Wiegand I & S. J. Milton 2 1Department of Ecological Modelling, UFZ-Centre of Environmental Research, Permoserstr. 15, Leipzig, 04318, Germany; 2 FitzPatrick Institute, University of Cape Town, Rondebosch 7700, South Africa

Received 17 October 1995; accepted in revised form 13 May 1996

Key words: Event-driven dynamics, Grid based model, Grazing, Individual-based simulation model, Karoo

Abstract

In arid regions, the effects of grazing or sparing management on natural communities of long-lived plants generally take decades to become evident. Event-driven dynamic behavior, unpredictable and low rainfall and complicated interactions between species make it difficult to assess probabilities and time scales of vegetation change.

To gain a better understanding of the main processes and mechanisms involved in vegetation change, we have developed a spatially explicit individual based model that simulates changes in plant communities over long time spans. The model, based on life-history attributes of the five dominant component plant species of a typical Karoo shrub community, follows the fate of each individual plant within the community, the sum of which is community dynamics. The model explores the differential effects of a realistic range of rainfall pattern on the abilities of these species to compete, survive, grow and reproduce.

The specific aim of the model is to identify key processes of vegetation change and to calculate probabilities and timespans for transitions between different vegetation states. Such knowledge is needed for species conservation and sustained animal production.

We show that the time-scale for changes of the dynamic state of the system are long compared with human lifespans. Employing the full range of possible rainfall scenarios showed that short-term community dynamics (years to decades) and species composition depend strongly on the short- term (years) sequence of rainfall events. In all simulation experiments the final vegetation state varied by more than 37% after a 60 year simulation period. Simulating resting of an overgrazed part of the shrub community indicated that little improvement in rangland condition was likely during a period of 60 years. Even such active management, as (simulated) clearing of unpalatable shrubs, resulted in only a 66% probability that degraded shrubland would be in good condition after 60 years resting. Simulated overgrazing of a rangeland in good initial condition only became obvious 40 or 50 years after the initiation of heavy grazing, and after 70 years the mean vegetation state eventually reached that of an overgrazed rangeland.

Introduction

An understanding of the dynamic behavior of arid shrubland plant communities is needed in order to manage them for sustained animal production and species conservation. On all continents, utilization of arid shrubland by domestic livestock has resulted in changes in plant species composition that reduce carrying capacity for these animals (Friedel et al. 1990;

Schlesinger et al. 1990; Dean and Macdonald 1994). Rehabilitation of overgrazed shrubland on extensive sheep ranches in the South African Karoo and comparable Australian and American arid and semiarid shrubland has seldom been achieved by withdrawal of livestock (Westoby et al. 1989; Bahre 1991; Milton et al. 1994). Attempts at increasing densities of natural forage plants by reseeding rarely succeed. Inertia of this kind (Walker 1993) casts doubt on the

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widely used range succession concept (Clements 1916) which envisages that resting restores what grazing has removed. Alternative conceptual models, for example the cup-and-ball (West 1994) and state-and-transition models (Westoby et al. 1989), envisage that vegetation can exist in any one of a number of quasi-stable states (Westoby et al. 1989; George et al. 1992; Milton & Hoffman 1994). Transitions between states may be initiated by either physical (fire, hail) or biotic forces (grazing, clearing, reseeding). Although models of this type are more appropriate for arid shrubland than the range succession model, they can do little more than suggest probable responses of a given state to a transition factor. However, such models draw attention to aspects of arid rangeland dynamics that may explain the failure of some of the rehabilitation attempts, as well as to the lack of more appropriate models (Walker 1993).

Arid rangelands are often characterized by episodic and event-driven changes in species composition (Walker 1993; Wiegand et al. 1995) that occur in response to rare or extreme events. Such events, often a coincidence of several independent events (e.g. a certain yearly rainfall pattern that facilitates seed production, germination and post-germination survival of seedlings and availability of establishment sites (Wie- gand et al. 1995)) may only take place once in 10, 20 or 30 years (Wilson & Hodgkinson 1991). Between such events species composition may remain 'stable' for long periods. Since the occurrence and sequence of (rainfall) events cannot be predicted, vegetation change in arid rangelands may also be unpredictable (Har- rington et al. 1984). Rehabilitation of overgrazed rangelands that are dominated by unpalatable species is frequently hindered by demographic inertia (Westoby et al. 1989) and lag-effects: once an abundant population of unpalatable species has established (e.g. due to a rare establishment event) the resulting cohort per- sists for a long time (Williams & Roe 1975; Crisp 1978; Griffin & Friedel 1985; Austin & Williams 1988). Because of the long time scale and the unpredictability of vegetation change in arid rangeland, the time taken for transformation from one state to anoth- er may exceed the human life-span. But data bases for assessing vegetation trends seldom exceed a few years. Because of the mismatch between time scales for observation and vegetation change (Scholes 1990), little is known about the dynamics of semiarid ecosystems over long temporal scales.

Recent development of computer techniques for simultaneously modeling the spatial and temporal

responses of organisms to their environment (grid- based or individual-based dynamic automata models), offers scope for quantitatively exploring long-term vegetation dynamics (e.g. Wissel 1992; Jeltsch and Wissel 1994; Lavorel et al. 1994; Wiegand et al. 1995; Moloney & Levin 1996). This approach focuses on the processes and mechanisms that drive community dynamics on species or individual level. Although there is little (long-term) field data available on the full dynamics of arid plant communities, life-history attributes such as growth, reproduction, dispersal, nat- ality, survival and interactions between individual species are relatively easy to observe. The basic idea of individual-based, dynamic automata models is to incorporate such (short-term) knowledge in form of simple rules into a computer simulation model. In order to investigate community dynamics, the model simulates the fate and the interactions of individual plants (within the community), the sum of which is community dynamics (Wiegand et al. 1995). In this way the model extrapolates from the behavior of individual plants to long-term community dynamics.

Here we show how a model simulating the dynamics of a Karoo shrubland (Wiegand et al. 1995) can be used to estimate time scales for vegetation change as well as to investigate the effects of the unpredictable rainfall pattern and management (grazing, resting, partial clearing of unpalatable shrubs) on the relative abundances of component plant species. We conduct a series of simulation experiments concentrating on typical or extreme cases and simulate (1) resting of rangeland in a good condition, (2) resting of overgrazed rangeland, (3) resting and removal of unpalatable shrubs of overgrazed rangeland, (4) resting of heavily overgrazed rangeland, and (5) grazing of a rangeland in good (initial) condition. To consider the unpredictability of the rainfall pattern we run for each simulation experiment a subseries of 100 simulations that only differ in the rainfall data used. The rainfall data sets used are a randomization of the original 93 year monthly rainfall data of the Prince Albert area.

Site description

The arid plant community simulated in our model is typical of the southern Karoo, South Africa. Field data were collected at Tierberg Karoo Research Centre (TKRC) 33010 ' S, 22°17 ' E, 800 m above sea level. Rainfall occurs mainly in autumn and spring but varies considerably in timing and amount (mean 167 mm

p.a., range 50-400 mm over 93 years). Folded sedi- mentary strata give rise to rocky outcrops and intervening plains with deep colluvial soils. Vegetation on the plains covers 15-25% of the soil surface and comprises dwarf succulent and non-succulent shrubs (200-600 mm in height and canopy diameter), pre- dominantly Asteraceae, Aizoaceae and Mesembryan- themaceae. The shrubs, which occur at a density of 3-7 plants m -z, are isolated or aggregated in small, mixed- species clumps interspersed with bare ground (Milton et al. 1992). Grasses and forbs are largely restricted to drainage lines.

Five shrub species dominated the plains vegetation at TKRC. These were Brownanthus ciliatus (Mesem- bryanthemaceae), a mat-forming stem-and-leaf succulent, Ruschia spinosa (Mesembryanthemaceae) an evergreen leaf-succulent, and three non-succulent species, namely semi-deciduous Galeniafruticosa (Aizo- aceae), deciduous Osteospermum sinuatum (Aster- aceae), and evergreen Pteronia pallens (Asteraceae). These shrubs differed in their life-history attributes and in acceptability to domestic sheep. Information on longevity, seed production, seed dispersal distance, establishment sites, competitive abilities, rainfall thresholds for seed production, germination and survival and on palatability of these species to livestock at TKRC has recently been published (Esler 1993; Milton 1992, 1994, 1995; Milton & Dean 1990, 1993; Yeaton & Esler 1990). We assumed that 34 less frequent species present at the study site played a relatively minor role in vegetation dynamics. The dominant species do not reproduce vegetatively, B. ciliatus, P. pallens and O. sinuatum have no seedbank, and G. fruticosa and R. spinosa appeared to have a short- lived seedbank (Esler 1993).

Carrying capacity of the vegetation for domestic livestock is low, approximately 6 ha being required to maintain one sheep (Vorster 1985). Selective browsing by sheep reduces the size and seed production of certain shrub species (Milton & Dean 1990; Milton 1992).

The model

Model description

The spatially explicit models we use may be called dynamic automata (Jeltsch & Wissel 1994; Wiegand et al. 95). They are an advanced form of the cellular automata (Wolfram 1986; Hogeweg 1988; Silvertown et al. 1992; Caswell & Etter 1993). The ecological

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state of a cell depends on (1) its present or previous state (or content), (2) external factors (weather, management), and (3) the ecological state of neighboring cells (competition, seed dispersal). Because automata models use rules instead of mathematical equations they are able to use qualitative as well as quantitat- ive knowledge. Thus, they are especially suitable for working out ecological problems.

The five dominant species can be divided into two functional groups. Seedlings of 'colonizer species' (B. ciliatus, G. fruticosa and R. spinosa) need large gaps in open vegetation to establish while seedlings of 'successor species' (P. pallens and O. sinuatum) establish in shaded sites under the canopy of colonizer plants. Plants of the five dominant species reproduce only sexually (via seeds). We divide the space into a grid of cells which represent mature plant sites.

The local dynamics (succession) within a cell is given by the sequences ( 'empty' --+ 'colonizer plant' -+ 'successor plant' --+ 'empty') or ( 'empty' --+ 'colonizer plant' -+ 'empty'). For a given cell, the pathway followed and the duration (in time steps) of each state, is determined (1) by the variables which characterize the state of a cell, and (2) the rule-set which determines how these variables change in the course of time with dependence on the states of neighboring cells and on external factors like rainfall, disturbances or management actions.

Rules were developed for the five dominant species at TKRC. We considered less common species in the model only as occupiers of space, and termed them 'fixed plants'. Their life-histories were not considered, and they remained at fixed densities throughout simulated time, their only function being to prevent colonization of cells by pioneers. The rules for the dominant species are summarized below (for a detailed description of the rules see Wiegand et al. (1995)). To provide 100 different data sets with monthly rainfall data for 60 (or 100) years we employed the rainfall simulation program GENRAIN (Zucchini et al. 1992). This program generates rainfall sequences with the same monthly mean and mean variation as rainfall data from Prince Albert. However, with this procedure we are not able to model possible temporal long-term autocorrelation (Tyson 1986) of the rainfall.

Rule 1. Seed production of adult plants depends on the timing and amount of rainfall. Certain thresholds of rainfall during the growing season (which differ among species) are required to stimulate seed production (Table 1). The number of seeds produced is determined by the amount of rainfall during the grow-

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Table 1. Selected parameters of the model: mean lifespan; rainfall thresholds for seed production (April- September), germination (March-June) and seedling survival (July~October); germination site; minimal gap size for safe sites and time to first flowering (T). * G. fruticosa does not tolerate P. pallens as a near neighbour, • * P. pallens cannot establish in the neighbourhood of more than 4 adult P. pallens plants. ** * Successor seedlings are able to rest up to 9 years

Species M e a n Thresholds (mm) Safe sites Minimal T (years) lifespan Seed Germi- Seedling gap size (years) production nation survival (cells)

B. ciliatus 10 20 20 l0 gap 12 0.5 G. fruticosa 30 50 30 15 gap 4, 8* 1.5 O. sinuatum 50 20 30 20 colonizer - 1-9"** P. pallens 70 20 30 20 colonizer 4** 1-9"** R. spinosa 25 70 30 10 gap 5 2.5

Fixed plants . . . . . .

ing season. Seed production of established plants that have not reached maximum size is proportional to their surface area.

Rule 2. Germination of all species occurs during autumn (March to June). With the exception of G. fruticosa andR. spinosa in which 70% and 11.5% of seeds respectively remain dormant in a soil seedbank, all viable seeds germinate after (monthly) rainfall events during the germination season that exceed a species specific threshold (Table 1).

Rule 3. Seedling survival depends on a minimum amount of rain during the post-germination period (July to October). For seedlings in safe sites, survival is 70% in high rainfall years (>70 mm between July and October), 10% in normal years and 0% in dry years (less than threshold (Table 1)).

Rule 4. Seed dispersal of small-seeded colonizer species (B. ciliatus, R. spinosa, G. fruticosa) is by means of water. The seeds are trapped by soil particles and seldom move more than 2.5 m from the parent plant. Successor species have wind-dispersed tumble seeds that are assumed to moved 10-40 m from the parent plant before being trapped by a mat-forming succulent or plant debris. In the model, we distribute single seeds of each plant. We determine the direction of the seed-movement randomly and choose the dispersal distance (within limits of the maximum dispersal distance) in accordance with a weighted random distribution based on field experience (see Wiegand et al. 1995). Seeds of colonizer species are only trapped if they are dispersed to open cells, otherwise they become deleted. Tumbleseeds of successor plants are trapped by established colonizer plants.

Rule 5. Safe sites for colonizers are those free of competition from other plants. The minimum size of a safe site (gap) differs among with colonizer species (Table 1). Additionally seedlings of G. fruticosa cannot establish in the neighbourhood of established P. pallens plants. Successor species can establish in cells that contain colonizers, but P. pallens cannot establish in the neighbourhood of more than four adult P. pallens plants.

Rule 6. Competitive interactions are modeled by assuming that only one of many seedlings that germinate in a given cell can survive. If seedlings germinating within a cell are different species, survival will be determined by competitive ability, defined in our model as growth rate. The competitive ranks are (B. ciliatus > G. fruticosa > R. spinosa) and (0. sinuatum > P. pallens). In this way, the rule implicitly takes self-thinning into account.

Rule 7. Establishment is attainment of reproductive maturity and the time taken for establishment is considered to be species-specific (Table 1). Seedlings of P. pallens and O. sinuatum are able to survive without growing for up to 9 years. When their host plant becomes senescent, they establish and eventually replace it.

Rule 8. Growth of a shrub canopy is modeled for each annual timestep as its responses to age and rainfall during the growing season (see Wiegand et al. 1995).

Rule 9. Mortality occurs mainly during the seedling stage. Mortality factors for established plants include occasional damage by hail or drought and excavation by foraging mammals. Therefore we consider in the model a low (age independent) mortality of established plants until they attain 80% of their expected lifespans.

Thereafter, the probability of mortality increases expo- nentially.

Although the output for the spatial and temporal simulations is in annual time-steps, processes such as seed production, germination and survival depend on rainfall seasonality. For this purpose we developed a submodel 'SEED' that internally calculates on a monthly basis, the total number of seeds produced and dispersed, germinating and surviving (using Rules 1 to 4), and sums these values for one year. The cell dynamics for a single iteration (one year) then proceeds by determining effects of neighboring plants (Rule 5) and competition (Rule 6) on seedling survival, and delet- ing all dispersed, non-surviving seeds other than those in the seed bank. The annual iteration is concluded once time, weather and disturbance effects on plant size, reproductive maturity and survival (Rules 7 and 8) have been considered. The cycle for one year is thus complete and the simulation of the next year begins.

Dynamic properties of the model

Starting with a species composition typical for rangeland in good condition (Milton & Dean 1990) and using a parameter set for ungrazed vegetation (Wie- gand et al. 1995) we simulated the spatial and temporal dynamics of the shrubland community and found that all five species could co-exist for a simulation period of some centuries (Wiegand et al. 1995). However, relative densities of component species did not reach a state of equilibrium. Instead, we a found episodic, event-driven behavior, with quasi-stable periods inter- rupted by sudden, discontinuous changes in species composition (Wiegand et al. 1995). Sudden increases in density of colonizer species occur when rains suitable for germination and recruitment follow long periods with rainfall not favorable for recruitment. Failure of plant populations to replace natural mortality during these prolonged periods leads to a decrease in the density of established plants, and consequently, to an increase in the size and abundance of gaps that serve as safe establishment sites for colonizers. Large recruitment events occur only if timing and amount of rainfall over the year facilitates seed production, seed germination and post-germination survival of seedlings, and secondly if safe sites are available to the dispersing seeds. The coincidence of rainfall conditions suitable for reproduction and availability of safe recruitment sites is such a rare event that large recruitment events are likely to occur only 2- 5 times per century in these arid shrublands.

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Validation (),['the model

We varied and tested all rules and parameters imple- mented into the model within their probable ranges to find out if all essential processes were captured and how sensitive the model output depended on vari- ations of rules and parameters. Generally, the model output was insensitive among most parameters and rules. Only seed production (Wiegand et al. in press), the rainfall pattern (Wiegand et al. 1995) and disturbances (T. Wiegand, unpublished analysis) could alter the event-driven dynamics of the model qualitatively. Using the Prince Albert rainfall data we found a broad range in the (seed production) parameter space where all five species could coexist over long timespans within the episodic and event-driven dynamic state (Wie- gand et al. in press). To calibrate the parameter values for seed production we first assumed that seed production parameter should facilitate coexistence of all five species over long timespans. Next we conducted a series of simulations with varying seed production parameters starting with a rangeland in good condition and using the original rainfall data from Prince Albert. We then compared the simulation output of the years 1987 to 1993 with plant density data available from the study site for this period (Table 3) and chose the set of seed production parameters that most closely reproduced the data.

Quanto~,ing the vegetation state

To be able to categorize and compare the vegetation state we introduce a grazing potential index P. This index sums up the densities of all species weighted with their sheep utilization index s (Milton & Dean 1993):

P = s]Di + s2D2 + s3D3 q- s4D4 Jr- ssDs. (1)

The Di are the densities of plants of species i in the simulation grid (= abundance of plants divided by the total number of cells). Table 2 shows the sheep utilization index (Milton & Dean 1993) for the five dominant species.

Although some of the plants only roughly included in the model as 'fixed plants' are palatable (Milton & Dean 1993) we assume them to be unpalatable because fixed plants have no attributes in the model other than occupation of space (see Model, Model description). The value 0 of the grazing potential index indicates a species composition without any palatable plants while a value of 1 indicates the extreme situation of each cell

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Table 2. The sheep utilization index for the five dominant species at the study site and the grazing factor that describes the reduction of seed production due to heavy grazing

Species Sheep utilization index Grazing factor

B. ciliatus 0.063 1 G. fruticosa 0.588 0.51 O. sinuatum 1.000 0.25 P. pallens 0.000 1 R. spinosa O. 185 0.29 Fixed 0.000

Table 3. Initial abundances of the five dominant species and abundance of fixed plants on the 4081 cell grid for good, overgrazed and heavily overgrazed range conditions. The values in brackets are data from Milton & Dean (1990) from the study site (good condition) and from the adjacent farm Argentina (overgrazed condition) scaled to the simulation grid size

G o o d Overgrazed Heavily Overgrazed

B. ciliatus 49 (56) 115 (242) 12 G. fruticosa 284 (259) 75 (65) 7 O. sinuatum 260 (280) 97 (108) 19 P. pallens 161 (130) 367 (294) 277 R. spinosa 251 (267) 37 (4) 8 Fixed plants 504 (517) 504 (492) 504 Total plants 1509 (1508) l 195 (1205) 827 Grazing potential 0.117 0.058 0.006

occupied by a 100% palatable species. We found that during simulations of the ungrazed plant community (Simulation experiment 1) plant cover usually ranged between 0.3 and 0.5 plants per cell (roughly 3 to 5 plants m-2). At the study site shrub density ranged between 3 and 7 plants m -2 (Milton et al. 1992). The sparse plant cover restricts the biological range of the grazing potential index to values between 0 and 0.5. But even a plant community in good condition (e.g. initial vegetation state of simulation experiment 1) reaches a value of only about 0.12. This is because the sheep utilization index is not 1 for all plants. Table 3 shows the three initial conditions employed in the different simulation experiments (good [ 1, 5], overgrazed [2, 3], severely overgrazed [4]), and the corresponding values for the grazing potential index.

Results

Simulation experiment 1

Variability of the short-term dynamics

The stochastic and unreliable rainfall results in unpredictable driving events (see Dynamic properties o f the

model). For this reason the future development of the plant community in the next, say 60, years can be described only probabilistically. To deal with this problem we conducted, for each simulation experiment, a subseries of 100 (60 year) simulation runs using a different sequence of Prince Albert rainfall data (see Model description) for each run. This allowed us to cover the full range of statistically possible rainfall sequences that are constrained by the characteristics of the original rainfall data from Prince Albert.

We began all 100 simulatioff runs with an initial plant distribution that corresponded to a rangeland in good condition (see Table 3). To obtain a realistic initial spatial pattern of the plants as well as realistically age- structured initial plant populations, we used the plant distribution that resulted from simulating the temporal and spatial dynamics of the ungrazed plant community for 93 years using the original rainfall data from Prince Albert.

We found that the short-term dynamics (decades) and the development of the grazing potential index P were sensitive to the rainfall pattern. Figure 1 shows three typical time-series selected of the hundred 60 year simulations runs. Depending on the occurrence - or absence - of driving events, the pathway that the plant community follows can vary considerably between simulation runs.

We define the change of the grazing potential index P after 60 years as

P(60) (76o - - - (2) P(l) '

where P(1) is the grazing potential index of the initial plant distribution (year 1), and P(60) is the grazing potential index of year 60. To quantify the stochastic variability of the grazing potential index P we cat- egorized the change 6'6o for the 100 simulation runs in 0.2 wide classes. Figure 2 shows the probability that the grazing potential index has changed after 60 years towards a certain class. The change of the grazing potential index after 60 years ranged between 0.3 and 2.5. with a mean of 1.27 and a mean variation of 0.47 (Figure 2). Figure 3a shows the temporal development of the mean grazing potential P and its mean variation.

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Figure 1. Three typical time series from simulation experiment 1. Solid white: B. ciliatus, solid gray: G.fruticosa, dashed gray: P. pallens, dotted gray: O. sinuatum, dashed white: R. spinosa. The solid black line indicates the grazing potential of the 4081 cell simulation grid (= 4081P).

~ 0.15

0.1 o

0.05

Table 4. The probability that the state of the rangeland in good condition will have changed to a given condition after 10, 30 and 6(I years resting

Grazing After After After

potential index P 10 years 30 years 60 years

Worse (<(I.8) 0% 5% ! 3%

Stable (>0.8, <1.5) 100% 71% 44%

Better (> 1.5, <2) 0% 24% 32%

Better (>2, <2.5) 0% 0% 11%

0.2 0.6 1 1.4 1.8 2.2 2.6 3

Change of grazing potential index

Figure 2. Good initial range condition. Change (76o of the grazing potential index P after 60 years of resting.

We see that the mean condition of the ungrazed rangeland does not improve much within the 60 years resting period. The mean grazing potential index P increases in the 60-year period only from 0.117 to 0.148 4- 0.055.

Table 4 summarizes the results of simulation experiment 1. The vegetation state does not change much on the short-term (10 years), but on the longer term (30 to 60 years) there is a high probability that the condition of the vegetation will change, either for better or w o r s e .


Resting of an overgrazed rangeland In this simulation experiment we investigate the question of whether overgrazed parts of the plant community are able to recuperate without any management action, only by resting. This question is of great practical interest for species conservation as well as for rehabilitation because large areas of the Karoo and other semiarid parts of the world are already overgrazed and resources (money) for rehabilitation and management are scarce or not available.

We start all simulation runs with a plant distribu- • tion typical for an overgrazed rangeland where plants of unpalatable species are abundant while plants of palatable species are rare (see Table 3). The initial plant distribution was generated by simulating the temporal and spatial dynamics of the grazed plant community using the 93 years original rainfall data from Prince Albert. The densities of the species obtained by this

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~0.2 O

t~

r~

(a)

0 15 30 45

Years resting

60

~0.2 0

0

(b)

0 15 30 45

Years resting

60

~0.2 0

• F,,,,I

N

~ 0 0

(c)

15 30 45 60

~0.2 0

N

~ 0

(d)

0 15 30 45 60

Years resting Years resting

Figure 3. The temporal development of the mean grazing potential index P and its mean variation for the first four simulation experiments. (a) simulation experiment 1, (b) simulation experiment 2, (c) simulation experiment 4, (d) simulation experiment 3.

procedure are in good agreement (see Table 3) with plant densities recorded at the overgrazed farm Argen- tina (Milton & Dean 1990) which is adjacent to the study site.

Figure 3b shows the outcome of the simulation experiment. Resting of the overgrazed plant community does not improve the grazing potential to a good condition (P = 0.12) within 60 years. During this period the grazing potential increases to a value of only P --= 0.055 4- 0.027, which is 1.5 times the initial grazing potential, but still less than one half of that of a range in good condition. Table 5 summarizes the results of simulation experiment 2. After 60 years there is a 54% probability that the overgrazed rangeland will remain in an overgrazed condition or even deteriorate, and only a 7% probability that there will be a substantial improvement in its condition (3 times the initial grazing potential).


Resting combined with removal of unpalatable shrubs from overgrazed rangeland Recovery of grazing potential may possibly be accel- erated by partial clearing of long-lived, unpalatable shrubs. To test the impact of this management action we repeated the simulations of experiment 2, but in each simulation run we removed some unpalatable, long-lived plants. More precisely, we cut at random a fixed number of unpalatable P. pallens plants (= 40% of the initial density) in the simulation years 0, 10, 20, 30, 40, 50. After cutting an established plant in the model, we designated that 50% of the sites (cells) would be open and the remainder occupied by dead plants. Leaving a fraction of dead plants in situ is a common management action to prevent soil erosion. The dead plants remain in situ for the next 10 years and trap large tumbleseeds. The probability of trapping was 80% for a newly created dead plant and declined expo- nentially with the decay of the dead plant (S. J. Milton,

pers. obs.). A dead plant provides shaded sites for the establishment of seedlings of the successor species.

Figure 3d shows the results of this simulation experiment. We found that removal of the unpalatable species P. pallens indeed improves the grazing potential of the overgrazed rangeland. The mean grazing potential index P increases linearly between simulation years 10 and 60. The mean grazing potential index P after 60 years (= 0.145 4- 0.066) is almost the same as the mean grazing potential index P (= 0.149 :t: 0.055) of the rangeland in good conditions after 60 years resting (see Figure 3a). Table 5 summarizes the results of this simulation experiment. On the short term (10 years) the rangeland does not improve much, but has a 21% probability of returning to a good condition after 30 years with shrub removal (0% without shrub removal). After 60 years, there is a 66% probability that the selectively cleared rangeland will be in a good condition, but only a 7% probability without shrub removal. In contrast to simulation experiment 2, where overgrazed rangeland was managed by resting alone, a decline in range condition was unlikely.

Simulating experiment 4

Resting of heavily overgrazed rangeland To cover the full range of possible initial range conditions we now turn to a heavily overgrazed initial vegetation composition (see Table 3). For example such a heavily overgrazed vegetation composition can be found in the region of Belair Damm (33o42 ' S, 20o36 ' E) in the south western Karoo (S. J. Milton, R. I. Yeaton, unquantified observations). The results of this simulation experiment (Figure 3c) confirm the tend- encies that we already found in the other simulation experiments. Time scales for rehabilitation are very long compared with human lifespan. After 60 years resting the mean grazing potential index P of the heavily overgrazed rangeland increased from 0.006 to a value of 0.026 + 0.018. This is less than the grazing potential index of the overgrazed rangeland (see simulation experiment 2). Figure 4 shows the change 6'6o of the grazing potential after 60 years resting. Even the maximal change of 12 yields only a grazing potential index of 0.07, which is only little more than the grazing potential index of the overgrazed rangeland (0.058).

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0.1

o.os

1 2 3 4 5 6 7 8 9 101112 Change of grazing potential index

Figure 4. Heavily overgrazed initial condition. Change C60 of the grazing potential index P after 60 year of resting.


Overgrazing of a rangeland in good condition Besides investigating time-scales of vegetation change of ungrazed rangeland for purposes of rehabilitation and species conservation the assessment of time-scales for vegetation change due to overgrazing are of great practical value. To investigate this question we conduct a subseries of simulation experiments where we first rest a rangeland in good conditions (see Table 3) for 20 years (to obtain a certain variability in the initial condition) and proceed in the following 80 years with the simulation of heavy, continuous grazing. We simulate continuous grazing by reducing the seed production of palatable species by a certain factor. This grazing factor summarizes the impact of heavy grazing (sheep eat flowers and reduce the size of the shrubs) on seed production. Table 2 shows the values of the grazing factor for the five dominant species.

The results of this simulation experiment (Figure 5) are unexpected. For 20 years after the initiation of heavy grazing the rangeland remains (on the mean) in good condition. Thereafter the mean grazing potential index declines almost linearly and after 50 years the probable range of the grazing potential varies from degraded to good. After 70 years of this treatment, the mean grazing potential index has declined to that of an 9vergrazed rangeland.

Discussion

Within the last 10 years it has been increasingly recog- nized (Harrington et al. 1984; Smith 1988; Walk-

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Table 5. The probability that the state of overgrazed rangeland will change to a given condition after 10, 30 and 60 years of resting and removal of unpalatable shrubs. Left columns: only resting, right columns: resting and removal of unpalatable shrubs

Grazing potential After 10 years After 30 years After 60 years

index

Worse (<0.8) 0% 0% 3% 1% 10% 0%

Stable (>0.8, <1.5) 91% 78% 62% 23% 44% 9%

Better (> 1.5, <2) 9% 17% 26% 18% 20% 4%

Better (>2, <3) 0% 5% 9% 37% 19% 21%

Good (>3) 0% 0% 0% 21% 7% 66%

0.2 * ~

. oas

o ~" 0.1

"~0,05

-20

f

0 20 40 60 80 Years of grazing

Figure 5. The temporal development of the mean grazing potential index and its mean variation for a rangeland in good condition under heavy, continuous grazing. The rangeland was rested the first 20 years (years - 2 0 to 0), and heavy continuous grazing started at year 0. The upper horizontal line gives the value of the grazing potential index of a rangeland in good condition (P = 0.117), the lower line corresponds with an overgrazed rangeland (P = 0.038).

er 1988; Westoby et al. 1989; Friedel 1991; Walker 1993; Milton & Hoffman 1994) that arid- and semiarid plant communities often exhibit complex nonequi- librium dynamics where complicated nonlinear processes (Westoby et al. 1989) and stochastic event- driven behavior (Walker 1993) are involved. Veget- ation changes generally occur unpredictably on short time scales (years) and episodically on long time-scales (several decades) in response to rare events (Eldridge and Westoby 1991; Milton et al. 1995), or due to grazing pressure (Skarpe 1991; O'Connor 1991), climatic change (Le Houerou 1989), changed disturbance regimes (Perkins and Thomas 1993; Schofield & Bucher 1986; Bahre 1991), or a combination of these factors (Danckwerts & Stuart-Hill 1988; Hoffman et al. 1990). The complex dynamics of arid- and semiarid plant communities and the mismatch between observa-

tion times (years) and time scales of vegetation change (centuries) make it difficult to assess the full properties of community dynamics. But even the availability of long-term records of the dynamics of a semiarid plant community would have limited predictive value much because of the high inherent stochasticity of these sys- tems.

One way of dealing with these problems while obtaining an estimation of time scales for vegetation change and a better understanding of the mechanisms involved, is to use advanced modeling techniques that are able to extrapolate from (available) short-term knowledge to long term community dynamics. In this paper we have presented a model that is based on detailed (short-term) knowledge about the life history of five dominant shrub species at a typical semiarid Karoo plant community. A detailed bookkeeping (Wie- gand et al. 1995) of all processes that are relevant for the temporal and spatial dynamics of this plant community and the individual-based modeling technique forced us to structure the available knowledge into a logical framework. However, because every model is an abstraction, we have to make sure that the essential processes have been captured and that the parameter estimation was good enough. We found that all five species could coexist over long periods (Wiegand et al. 1995) showing typical event-driven dynamics with episodic mortality and recruitment events with intervening quasi-stable periods. Simulated densities of the five species were in good accordance with data collected at the study site (Wiegand et al. 1995). However, changing parameters of the submodel SEED (e.g. seed production) in a way that the reproductive output of selected species decreased, resulted in oscillatory or degraded dynamics where one or more species became rare or locally extinct (Wiegand & Milton, in press).

Using a computer simulation model enabled us to perform a series of (simulation) experiments that are

impossible to perform in the field. Firstly, we were able to simulate the spatial and temporal dynamics of the plant community over long time spans. Secondly, we could start our simulations using different initial plant distributions to cover all possible states of the vegetation, ranging from heavily overgrazed to good condition. Thirdly, the model easily allows us to perform management actions such as grazing, resting or removal of unpalatable shrubs. And lastly, we were able to tackle the problem of stochastic and unpredictable rainfall by repeating each simulation experiment several times using the full range of rainfall scenarios that are constrained by the characteristics of the original rainfall data of the region. This enabled us to calculate probabilities for vegetation change.

What we have learned

Stochasticity. We found that the stochastic and unpredictable sequence of rainfall events strongly influences the short-term dynamics of the plant community (Fig- ure 1). For example, just the occurrence of one big establishment event after a sequence of dry years can drive the dynamics of the plant community towards a completely different (desired or undesired) direction. Because of the long lifespans of component species and the rare occurrence of big establishment events a single such event can determine the vegetation state of the plant community for many years. Consequently, we found in all simulation experiments that the grazing potential index, a measure for the vegetation state, varies greatly between simulation runs. The mean variation of the grazing potential index after 60 years ranged between 37% (resting ofrangeland in good condition) and 67% (resting of heavily overgrazed rangeland). A direct consequence of this high stochasticity is that the condition of even a good, ungrazed rangeland has a high probability of deteriorating (e.g. 13% after 60 years rest in simulation experiment 1). Figure 1 (center) shows an example of a simulation from this simulation experiment without any big establishment events. After 60 years the vegetation composition is similar to that of an overgrazed rangeland. Therefore, a period of exceptional dry years can have a similar effect on vegetation dynamics as overgrazing. Field studies of the impact of drought on the species composition and potential carrying capacity of arid southern African shrublands support these simulation findings (Hoffman et al. 1990; Milton et al. 1995).

To test the effect of overgrazing on the vegetation state we simulated heavy grazing (simulation experi-

179

ment 5). We started our simulation with vegetation in good condition (P = 0.117). In this case we also found a high stochasticity in the grazing potential index. After 50 years of heavy grazing, the probable range of the vegetation condition (P = 0.084+0.032) was between good (P = 0.116) and overgrazed (P = 0.052), but the mean grazing potential index declined almost linearly. Thus, a favorable rainfall sequence may conceal (potential) overgrazing, but good management cannot compensate for unfavorable weather. Both in the model and in the field (Danckwerts & Stuart-Hill 1988), bad management is found to exacerbate the effects of drought by accelerating negative changes in the condition of rangeland vegetation.

We found that both 'bad periods' and 'good periods' are innate to the system, because of the high stochasticity and unpredictability in the driving (rainfall) events. 'Bad periods' and 'good periods' are evenly distributed over centuries, but not over the short term (decades) which is the economic time scale of the farmer. Even resting of rangeland does not guarantee an improvement in carrying capacity. Thus, we conclude that managing semiarid rangelands always involves a considerable risk.

Demographic inertia. The comparison of the two simulation experiments 2 and 3 (with and without removal of unpalatable shrubs) demonstrated clearly how strong demographic inertia determines the dynamics and the vegetation composition of arid or semiarid rangelands where plants are long-lived. Once a long- lived species has established an abundant population it will persist for a long time and occupy sites that otherwise could serve as establishment sites for competing species. On the other hand demographic inertia can also obscure the evidence of overgrazing. Once an abundant population of a palatable, long lived species (e.g. O. sinuatum) has established, a change of the vegetation state (increasing overgrazing) will be obvious only once mortality of old plants of this species is no longer compensated for by recruitment. This process may take several decades. Our simulation indicated that even after 50 years of heavy, continuous grazing, the probable state of the vegetation ranged between good and overgrazed. However, once overgrazing becomes obvious, rehabilitation is almost impossible (Simula- tion experiment 2). One possible management tool to detect undesired vegetation changes (early enough) is to monitor the age distribution and recruitment of the dominant species.

Long time-scale of vegetation change. We found that time scales of vegetation change in the Karoo plant

180

community are generally much longer than human lifespans. Demographic inertia and the rare occurrence of establishment opportunities are responsible for this property. We found that overgrazing of a rangeland in good condition takes (on average) at least 70 years to become evident, and that during the first 20 years no significant changes are likely to occur. Rehabilita- tion after withdrawal of sheep may take much longer than degradation. This result is supported by air photographs of the study site and the adjacent farms Argen- tina and Tierberg taken in 1939, 1962, 1974 and 1991. The farm Argentina was heavily grazed between 1913 and 1960, the Farm Tierberg was moderately grazed for the past 35 to 40 years (Milton et al. 1992). No contrast in vegetation texture between the two farms was visible on the 1939 air photograph after 25 years of differing management. But contrasts in vegetation texture across the farm boundaries become increasingly marked on subsequent photographs. The effects of reduced stocking rates over the past 30 years on Argentina are not yet evident on air photographs.

Rehabilitation. We can attribute the rehabilitation of the rangeland after removal of unpalatable shrubs to the fact that (1) cutting creates new establishment sites for the palatable successor species O. sinuatum (dead plants) that otherwise are not available (P. pallens is a long-lived species with a lifespan of 70 years) and that (2) cutting reduces the resource exploiting ability of P. pallens relative to that of its competit- or O. sinuatum. Removal of P. pallens has an effect comparable to reducing the mean seed production of P. pallens. In both cases P. pallens is not able to maintain a viable population and almost disappears within a few decades. As consequence of the disappearance of P. pallens the dynamic state of the plant community changes. Instead of the episodic event-driven behavior the dynamics become more oscillatory.

The comparison of the two simulation experiments 2 and 3 demonstrates to what extent dynamic inertia can determine the future pathway of the rangeland. Once an abundant population of a long-lived (unpalatable) species has established (e.g. due to overgrazing), it will remain there for a long time, selfstabilizing. This is because its high density guarantees a high seed availability (higher resource exploiting potential) and because there are not enough safe sites available for it's potential competitor (O. sinuatum) to establish an abundant population.

Clearly, the removal of palatable shrubs can only lead to rehabilitation where there is an adequate source of seeds of palatable species. Moreover, the positive

effect that the removal of unpalatable shrubs had in the model is limited by the negative effect that an exposure of too much open ground may have on subsequent soil erosion. Soil degradation was not considered in the model, however, leaving the dead plants in situ is one possible management action to reduce the exposure and erosion of soil. More detailed investigations are needed in order to assess the point at which soil degradation starts, and to find a selective clearing strategy (e.g. cutting interval, cutting intensity, cutting technique) that achieves a compromise between ecological and economic costs and benefits of this management action.

Limitations of the model and ().]"available data

A gradual increase in the less palatable perennial component of vegetation has been recorded in arid and semi-arid shrubland (Westoby et ill. 1989) and savanna rangelands (Bahre 1991; Skarpe 1991 ; Schofield & Bucher 1986) throughout the world. It has also widely been reported that the process cannot be reversed in the medium term (decades) merely by withdrawal of livestock (reviewed by Milton et al. 1994). The model thus simulates the pattern and time-scale for grazing- induced vegetation changes realistically. On the other hand, there is little empirical evidence that degraded rangelands can be rehabilitated, either by resting or partial clearing. Experimental removal of selected com- ponents of the vegetation, by mechanical or chemic- al means, can lead to re-colonization by ephemerals or pioneer grasses within a few years (Moore 1989), but clearing that restored both diversity and structure has yet to be reported. We suggest that the reasons for lack of empirical data to support the model findings are two-fold. Firstly, few experimental clearing experiments have run for a long enough duration in the absence of utilization by domestic livestock to produce comparable results. Secondly, prolonged overgrazing may cause changes in processes including soil structure and chemistry, runoff, decomposition rates (Schlesing- er et al. 1990; Seastedt et al. 1988), density-dependent feedbacks on pollination (Bond 1994) that are not considered in our simulation model.

Our model therefore not only supports the proverbi- al view that the next two generations will bear the high opportunity of rangeland overexploitation, but presents a moderately optimistic view that, in the long-term, recovery is possible. The addition of information on effects of degradation on processes may modify this view, and it is clear that further empirical data will improve the model.

Comparison with other rangelands and applications of the model

The Karoo plant community analyzed in this paper shares several features (rainfall characteristics and year-to-year variability of precipitation, local dynamics, similarity in life-forms, etc.) with other arid or semiarid communities throughout the world. An application of our modeling technique and perhaps of some of our results would therefore be reasonable and fruitful. Clearly, the rules of our model base on local dynamics observed at the Tierberg study site, but a similar rule-set could be build for species or functional groups showing local dynamics different from that in the Karoo.

Rainfall characteristic and vegetation. Rainfall in arid or semiarid areas can be divided roughly into three groups: (1) summer rainfall areas such as the Kalahari desert in Southern Africa and the Chihuahuan desert of Mexico; (2) winter rainfall areas such as the Suc- culent Karoo in South Africa and the Mojave desert of California; and (3) mixed-rainfall areas such as the central and southern Nama Karoo, South Africa and the Sonoran desert of Arizona. The vegetation of the mixed-rainfall areas of the southern Nama Karoo and the Sonoran desert is more physiognomically diverse and species rich than adjacent summer and winter- rainfall deserts (Louw & Seely 1982; Cowling et al. 1994), and comprises a mixture of grasses, succulent and non-succulent shrubs (MacMahon & Wagner 1985; Cowling et al. 1994). The shrubs include both long-lived species such as Larrea tridentata: Zygo- phyllacec (Sonoran) and Pteronia: Asteraceae (Karoo), and short-lived shrubs such as Ambrosia: Asteraceae (Sonoran) and Brownanthus: Mesembryanthemaceae (Karoo). However, succulents are more abundant in the winter and mixed rainfall Karoo than in any other arid or semiarid region of the world (Cowling et al. 1994; Milton et al. 1992).

Similar local dynamics. In the Sonoran desert there is good evidence for episodic mortality and episodic recruitment with intervening quasi-stable periods (Turner 1990). Moreover, the local dynamics of a species-rich Arizona upland plant community, described by McAuliffe (1988), has states similar to that in the Karoo: (1) open space, (2) a 'colonizer' species Ambrosia dumosa and three groups of 'successors' that follow this colonizer: (3) a Saguaro Cacti Carnegiae gigantea, (4) a tree Cercidium microphyl- lum, (5) various perennials and transitions from open (1) to colonizer (2) to open (1); or from open (1) to

181

colonizer (2) to successor (3), (4) or (5) to open (1); or, additionally, transition between successors from tree (4) to cactus (3). However, the role of life-forms in the local dynamics are different in the Sonoran dessert and the Karoo. Whereas the water-dispersed leaf succulent shrubs (Mesembryanthemaceae) are colonizers of open space in the Karoo (Yeaton & Esler 1990), the stem succulents of the Sonoran desert are late successional, being dispersed to shaded sites in shrubs or trees by wind- tumbled fruits (Cody 1993) or fungi- vorous birds (McAuliff 1988). Colonizer plants in the American deserts are short-lived, non succulent shrubs (Asteraceae, Fabaceae), or grasses, dispersed by wind, water or present in long-lived seed bank (McAuliff 1988, Montafia 1992).

Limitations. On important ingredient of our modeling technique is the individual-based approach which is appropriate if single individual can be easily identified and if the size of different functional groups does not differ too much. However, this approach is not suitable to model a mixture of shrubs and grasses or trees and grasses (savannas). In this cases non individual-based or partly individual-based models, such as the recent savanna model from Jeltsch et al. (in press), gap models (e.g. Coffin & Lauenroth 1990) or an grid-based model for serpentine grasslands by Moloney & Levin (1996) may be more suitable. Moreover, our approach requires a good knowledge about the life-history attributes of the species or functional groups involved in dependence on monthly or seasonal rainfall.

Acknowledgements

Field studies by S. J. Milton were supported by the Foundation for Research Development and the Depart- ment of Environmental Affairs and Tourism, South Africa, the Southern African Nature Foundation and the FitzPatrick Institute, University of Cape Town. Funding provided by the UFZ-Centre for Environ- mental Research, Leipzig enabled all authors to travel between Germany and South Africa for co-operative work. The authors thank C. Wissel, W. R. J. Dean, W. Bond, M. T. Hoffman, E Jeltsch, J. Overton, T. Stephan and one anonymous referee for assistance during the development of ideas or for comments on drafts of this manuscript.

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