Journal of
Ecology 1998,
86,780-793
Modelling the impact of small-scale heterogeneities on
tree-grass coexistence in semi-arid savannas
F . J E L T S C H * , S . J . M I L T O N f - ,W . R . J . D E A N L N . V A N R O O Y E N S and
K . A . MOLONEYS
*Departnzent of Ecological Moilellil~g,Ce~zti,e,forEn~~irol~n~ental
Research, PO Box 2, 0-04301 Leipzig,
~,
7700, South Afiica; $Botany
Gernlarzy; fFitzPutrick I~?stifute,Uir'icersifj.o f Cape T o I I ,Roildebosch
Departn~eizt,Uni~vrsityof Pretoria, Pretoria 0002, So~ithAfiica; alzd §Departnzelzt o f Botany, 353 Bessej) Hull,
Anzes, I A 5001 1-1020, U S A
Summary
1 Savanna ecosystems show codoininaiice of trees and grasses, and the mechanisms
involved in their coexisteiice remain unresolved. We investigated the possible influence
of small-scale heterogeneities and disturbances in deterniining tree spacing and treegrass coexistence in semi-arid savannas, using a spatially explicit, grid-based siinulation model.
2 We added factors such as seed clumping, locally improved moisture conditions,
vegetation clearing and colnbinatiolls of all three of these variables to a previously
published model. We also exaillined the influence of changing the size and spatiotemporal correlation aillong individual heterogeneities.
3 Increased seed availability in localized clumps, especially in combination with the
other heterogeneity types, had the strongest impact on the long-term tree-grass
coexisteiice in the model. Localized deposition of tree seeds in herbivore dung and
underground seed caches built by seed-collecting rodents may act as a determinant of
the distribution of trees in savannas.
4 Spatially autocorrelated small-scale heterogeneities led to a more stable coexistence
of trees and grasses than uiicorrelated heterogeneities did, and at high levels of
autocorrelation runs with all three variables led to long-term coexistence in up to
60% of the rainfall scenarios tested.
5 The size of individual heterogeneities also played a significant role in determining
whether trees would establish as lone individuals or in clumps. In simulations that
included small-scale heterogeneities, the number of isolated trees scattered throughout
the landscape increased, whereas large heterogeneity patches and high spatiotemporal
autocorrelation tended to promote tree clustering.
6 Simulations based on rainfall data from the southern Kalahari produced a realistic
density and spatial distribution for trees in this semi-arid savanna for a realistic range
of small-scale heterogeneities.
7 Small-scale disturbances and heterogeneities, at least those that furnish better establishment conditions for tree seedlings, therefore act to increase the range of environmental conditions under which trees and grasses can coexist as savanna.
Kej)~>orn's:
coexistence, grid-based silnulation model, Kalahari, savanna, seed clumping, spatial vegetation dynamics, stability, tree spacing
Journal ofEcoloyj) (1998) 86, 780-793
Introduction
ecology CollcerIls the
mechanislns allowi~lgthe long-term coexistence of
trees and grasses (Sarmie~lto1984; Scholes & Walker
1993). Both functional types essentially use the same
resources, i,,, radiant energy, water and nutrients,
and there is little evidence for niche separation i11
Correspondence: F. Jeltscll (fax 49 (341)235 3500; e-mail
flori&oesa.ufz.de).
either the depth of rooti~lgor the season of moisture
uptake (Scholes & Walker 1993). Classical com-
A central question
111 savanna
781
F. Jeltsch et al.
0 1998 British
Ecological Society,
Jollrnnl of Ecology,
86, 780-793
petit~ontheory predicts that when two competitors
use the same resource, one should out-compete the
other. Nevertheless, the large-scale, long-term pattern
in savannas is often one of a relnarkably stable
coexistence of trees and grasses (Scholes & Walker
1993). What is special about the savanna environment
that allows trees and grasses to coexist, as opposed to
the general pattern in other areas of the world where
either one or the other functional type is dominant?
The classical equilibrium view of savanna dynainics
(Walker et rrl. 1981; Walker & Noy-Meir 1982: Eagleson & Segarra 1985) has recently been replaced by a
disequilibrium view that suggests that the coexistence
of trees and grasses is achieved through disturbance
(Skarpe 1992; Scholes & Walker 1993). Disturbances
can potentially act to prevent the savanna system
from developing into either a pure grassland or a
woodland, where tree growth is only limited by competition with other trees. Consequently soine largescale disturbances, such as drought, grass fires and
grazing, are considered to be driving forces in savanna
ecosystem dynamics (Frost & Robertson 1987;
McNaughton 1992; Rebertus & Burns 1997) that also
allow for the long-term coexistence of trees and
grasses (Skarpe 1990, 1992; Scholes & Walker 1993).
Results of a recently developed spatially explicit
model for semi-arid savannas partly support this
hypothesis (Jeltsch et riI. 1996). For example. inodel
simulations suggest that, although fluctuating rainfall
and competition for moisture are not sufficient alone,
a combination of rainfall, fire and grazing may generate and sustain the coexistence of trees and grasses
(Jeltsch et al. 1996). However, the nlodel results also
indicate that the coexistence of savanna trees and
grasses, which is caused by the large-scale disturbances of fire and grazing, is restricted to a vegetation pattern consisting of tree clumps. Such clumped tree patterns are found in soine savannas
(Hochberg et ril. 1994), although in Inany other savannas, such as the Kalahari (Leistiler 1967). trees have
a more scattered distribution. Scattered trees are of
considerable ecological importance in the latter type
of savanna (Leistner 1967; Belsky et 01. 1993; Belsky
1994; Milton & Dean 1995) but this pattern cannot
currently be produced by our simulation model.
The question therefore arises as to whether the
long-term persistence of a scattered tree distribution
is in fact possible in principle (i.e. a scattered tree
distribution might only represent a transitioilal state
in savanna dynamics) or whether factors or processes
other than coinpetition for moisture, herbivory and
fire may be required to facilitate the persistence of this
spatial pattern. An intuitive view is that the isolated
distribution of some of the trees may be predetermined by small-scale heterogeneities in the
environment, causing differential probabilities of tree
establishinent and survival. We hypothesize that such
small-scale heterogeileities and disturbailces are an
important factor in the dynamics of semi-arid sav-
annas that (i) may lead to persistence of a tree distribution with a considerable number of scattered
trees, and (ii) may increase the range of conditions
under which there can be long-term tree-grass coexistence. To test these hypotheses, we introduced various
types of small-scale heterogeneities and disturbances
into a spatially explicit simulation model of semi-arid
savannas (Jeltsch et ul. 1996) and investigated the
impact of varying patch size, patch formation rates
and spatioteinporal correlations among newly produced patches on the dynamics and spatial patterning
of savanna trees.
Biological background of small-scale
heterogeneities and disturbances in semi-arid
savannas
The origin of processes leading to small-scale heterogeneities, and so altering the local probability of
successful tree establishment, can differ among savanna systems (Bews 1917; Scholes & Walker 1993).
In essence, there are three basic mechanisms that,
alone or in combination, can improve the local establish~nelltprobability of tree seedlings: (i) localized
increase in the density of tree seeds; (ii) reduced competition with herbaceous vegetation; and (iii)
improved resource conditions (e.g. moisture or nutrients).
In the Kalahari a localized increase in the density
of tree seeds may be produced by seed caches of some
species of rodents, i.e, gerbils (Desnzodillus auriculaiis), ground squirrels (XEYLIS
ilzauris) and otonlyids
(Pcri.otonzys bralztsii) (Nel 1978; Smithers 1983; Nel et
01. 1984), or result from seed dispersal in the dung of
indigenous antelopes (Leistner 1961; Dean & Milton
1991; compare Fragosa 1997). Local seed densities
may also be increased by seed accumulation at the
edges of dry riverbeds during occasional floods.
Locally reduced competition with the herbaceous vegetation may result from vegetation clearing by colonial rodents (Nel 1978) or other animal-produced
disturbances, e.g. the digging activity of aardvarks
(Orycterop~1~),that also modify soil microtopography. Resource conditions can improve at sites
where a tree has grown for many years (Scholes &
Walker 1993; Belsky 1994; Milton & Dean 1995), or
on termite heaps (Yeaton 1988), or may be produced
by dung middens or by the nest building activities of
fossorial rodents (Chew & Whitford 1992; Hansel1
1993). Patches with improved moisture availability,
through water collecting in depressions, water channelled by topographic features ('washes') or a high
aquifer level, may also improve the local establishment probabilities of tree seedlings (Ward & Breen
1983).
We conducted a preliminary field investigation to
examine the role some of these processes might have
in deter~niningthe distribution of tree seedlings in the
Kalahari Gemsbok National Park (KGNP; situated
782
Small-scale
Izefeiogeneities arzrl
coexistence in
suz:a~~nas
between latitudes 24'1 5's and 26-30's. and longitudes
2OC00'E and 2OC45'E), a well-preserved area, largely
representative of the southern Kalahari (Leistner &
Werger 1973; van Rooyen et 01. 1990). The results
indicated that the patchy distribution of seeds in herbivore dung may be the most influe~ltialfactor leading
to the patchy distribution of tree seedlings (Table 1).
Of all sample sites, 9.4% contained antelope dung
accumulations and, although only 7.6% of these had
tree seedlings growi~lgin them, this represented 30.3%
of all of the seedlings found in the study (Table 1).
01lly sites with high termite activity showed a greater
probability of co~ltainingtree seedlings (16.7%), but
these sites were rare (only 0.5% of all sample patches)
and only contained 3% of the seedlings found in the
study area (Table 1). Depressions made by antelopes
that roll on their back to clear their hair were too rare
(0.2% of the sample patches) to interpret the nonoccurrence of seedli~lgs.No seedlings were found in
sites occupied by active rodent burrows either, probably due to the browsing activities of the rodents.
Consequently, rodent colo~liesmay represent potential establishme~ltsites but only after they are abandoned.
A chi-square test co~ltrasti~lg
the probability of
heterogeneity-forfinding seedlings in sites co~ltaini~lg
ming patches (except active rodent burrows; 'Rode' in
Table 1) vs. sites contai~liilgnone of the heterogeneityformiilg patches (the category 'None' in Table 1)
showed that there is a sigilifica~ltlygreater probability
of finding seedlings in sites affected by one of the
heterogeneity-producing processes compared to
unaffected patches ( ~ ( 1 ) '= 9.3; P < 0.01; the
inclusion of active rodent burrows 'Rode' in the
analysis led to a decrease of the significance:
~ ( 1 ) '= 3.5; P < 0.1). Although these empirical findings provide an initial ullderstalldi~lgof the relative
importa~lceof different heterogeneity types for tree
seedl~ngestablishme~lt,they are restricted to a specific
locatloll and do not allow for the evaluat~onof longterm effects. We therefore analysed the basic het-
erogeneity types in more detail by means of a computer si~nulatio~l
model. 111this way, we hope to derive
more general results and to evaluate the relative
importance of the different heterogeneity-generating
processes in allowing the coexiste~lceof trees and
grasses over long time periods.
The model
The spatially explicit simulation model used in this
study is based on the ecological dyna~nicsoccurri~lg
in the South African part of the southern Kalahari,
includi~lgKGNP. However, rainfall sce~lariosand
other model parameters can be varied over a wide
range of values to allow for more generalized results
concerning vegetation dynamics in savanna ecosystems. Results from an earlier versio~lof the model
have been preseilted elsewhere (Jeltsch et al. 1996).
The lnodel has since been modified to allow for a
systematic exploration of the impact of small-scale
heterogeneities and disturbances which give rise to
them in the modelled e~lvironment.
The earlier version focused 011 the impact of largescale disturba~lces(e.g. precipitatio~l,fire and grazing)
on tree spacing and long-term coexistence of trees and
grasses. We now use a fixed fire and grazing scenario
as a starting point and systematically explore the
impact of various types of small-scale heterogeneities
on long-term vegetation dynamics.
GENERAL MODEL STRUCTURE
The savanna model is a spatially explicit, grid-based
simulation model (Fig. 1). Within the model, an area
of 50 ha is subdivided into 20 000 individual 5 m x 5
111 grid cells. The size of an individual cell is large
enough to accommodate a mature tree canopy. On the
basis of these spatial subunits, the model simulates, in
annual time-steps, those processes that are crucial to
a tree-grass coexiste~lce,i.e. (i) rainfall and moisture
availability, (ii) vegetation dynam~csof the relevant
Table 1 Frequency of tree seedling establisl~ine~~t
in conlbination with small-scale heterogeneities in the K G N P (S. J. Milton,
unpublisl~eddata). Twenty-eight transects of 20 111 width and 50 m length were subdivided iuto 5 In x 5 in patches. The presence
of tree seedlings, adult trees (Adult). and several small-scale heterogeneities, including autelope duug acculllulatiotls (Dung),
rodent burrows (Rode), aninla1 diggings (Dig). depressions made by antelopes that roll o n their backs to clear their hair (Roll),
termite heaps (Ternl) and water channels caused by topographic features (Wash), were recorded at each transect position.
None represents transect positions without heterogeneities
Type of heterogeneity
~c1998 British
Ecological Society,
Jourr~nlof E c o l o g ~ ,
86, 780-793
Relative frequeucp of heterogeneity type ( % of total
area)
Relative frequency of patches with tree seedlings
(% of patches of the specific heterogeneity type)
Relative inlportance of heterogeneity type (% of all
tree seedlings)
Dung
Rode
Dig
Roll
Tern1
Wash
Adult
None
9.4
12.8
3.1
0.2
0.5
4.7
7.3
62.0
7.6
0.0
0.0
0.0
16.7
1.9
7.3
1.9
30.3
0.0
0.0
0.0
3.0
6.0
21.2
39.5
783
F. Jeltsclz et al.
.
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: . :.
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z$ed~otentia~
productivity
determ~nes
Rainfall
. .. . . . . .. . . .
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a
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(c)
heterogeneity pate
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..
,,
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1x1 cell
4x4cells
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8
heterogeneity regio
(correlation)
Fig. 1 (a) Schematic description of the basic features of the spatially explicit si~nulationmodel (100 x 200 grid cells). The
annual rainfall determines the a n ~ o u ~ofi ttopsoil and subsoil moisture (M,. M,) available to plants for the given year. Moisture
levels are locally nlodified by the vegetation and, in turn, influence the vegetation dynanlics of the dominant life forms. The
local moisture combination (M,,M,) also deternlines the potential productivity of shrubs and perennial herbaceous vegetation
in the grid cells. (b) and (c), sample heterogeneity maps showing approxi~nately200 heterogeneity cells (black) distributed in
patches of 1 x 1 cell (b) and 4 x 4 cells (c). I n the u~icorrelatedscenario. the heterogeneity patches are relocated randomly in
each time-step. In the correlated scenario a heterogeneity patch is relocated randomly within a corresponding heterogeneity
region (black frame, c). The probability of the relocation of a heterogeneity region describes the degree of a~~tocorrelation
of
the heterogeneities.
life forms, (ii) grazing, (iv) grass fires, and (v) the
formati011 of small-scale heterogeneities. At the level
of the individual grid cell, the model determines
whether trees, shrubs, perennial grasses and herbs or
an~lualsd ominate the local patch, or whether a mixture of some of these life forms is present. The model
also keeps track of the age of individual trees and
distinguishes between three different levels of potential productivity (classified as high, llloderate or low)
for patches of perennial plants, other than trees.
R A I N F A L L A N D MOISTURE AVAILABILITY
'0
1998 British
Ecological Society,
J
~
~
,
.
86, 780-793
Differing rai~lfallscenarios were simulated by varying
moisture combinations in the topsoil and subsoil layers of the model ecosystem. For both soil layers, we
distinguished among four water availability classes:
(0) none; (1) poor; (2) moderate; and (3) good. Thus,
the moisture status of a grid cell for each time-step of
a model run could be characterized by one of 16
possible combillations of topsoil (M,) and subsoil (M,)
water availability, i.e. (M,, M,) (Fig. la). After choosing the initial moisture co~lditio~ls
for a time-step, the
moisture available to plants was further modified in
each grid cell by other processes operating in the
model, e.g. moisture reduction by plants (see below).
In most of the model rulls presented here. the rainfall scenario was based on a stochastic simulation of
~rainfall
~
~events,
~ ranging
~
E from
~
~low~ to high
~
~levels
~ of~
meall annual precipitation. In addition, we inves-
tigated the impact of a real rainfall scenario based on
data from the Kalahari.
For each model run using a stochastic rai~lfallscenario, one water availability class (M,, M,) was dominant, having a 60% probability of occurring during
each time-step (1 time-step = 1 year). However, there
was also a 40% probability that one of the 15 other
classes would be chosen for a particular time-step,
with a bias towards choosing classes differing only
slightly from the dominant class in the amount of
subsoil and topsoil water available (for details see
Jeltsch et (11. 1996). We systematically explored 16
possible rainfall scenarios by assigning each of the
moisture class conlbinations (M,, M,) the peak probability in different model runs, keeping all other parameters and factors equal. Other types of general
rainfall patterns have been a~lalysedelsewhere (Jeltsch
et 01. 1996).
KGNP inilz sceiztlr.io
We also ran versions of the model using a rainfall
regime based on 32 years of daily rainfall data
obtained from a weather station in the south of the
KGNP. (This rainfall submodel is described in detail
in
Jeltsch et 01. 1997a, 1997b.) For each year of rainfall
,
data, we aggregated daily rainfall amounts into longer
784
Sninll-scale
heferogerzeities and
coesisteizce in
snvnnlzns
rainfall events (E,). The soil moisture availabilities
(M,, M,) for each year of rainfall data were then based
upon the sun1 of the rainfall amounts occurring over
the year. The 32 combinations of topsoil and subsoil
inoisture classes (M,. M,) that resulted were then
applied to simulations by choosing one of the 32 combinations at random for each time-step of a model
run.
VEGETATION DYNAMICS
Shrubs, yerelzr~inlgrasses mid herbs, nlzrl m ~ n ~ ~ o l s
We distinguish ainong three different levels of potential productivity to characterize the condition of a
vegetation patch dominated by shrubs or perennial
grasses and herbs. Transitions between these levels
depend on the moisture available to plants in a grid
cell (Jeltsch e f nl. 1996). Annuals are either present or
absent in a grid cell and are not characterized by
different levels of productivity. Colonization of empty
space (i.e. grid cells) and extinction of the different
types of plants (i.e. grid cells becoilling enlpty of a
certain life form) also depend on available illoisture
in the two soil layers. The herbaceous vegetation is
more dependent on topsoil moisture than on subsoil
moisture, whereas shrubs are illore dependent 011 subsoil moisture, reflecting differences in the rooting
depth (Jeltsch et a/. 1996).
Conlpetition for space occurs via the colonization
of empty grid cells. If an empty grid cell is successfully
colonized by more than one life form. or if tree seedlings establish in an occupied grid cell (see below),
competitioil for nloisture occurs. The moisture available to one life form or to tree seedlings is reduced by
the water uptalce of the other vegetation that is present
in the grid cell (Jeltsch et 01. 1996). Lateral root extension of woody life forms also reduces soil illoisture in
neighbouring grid cells (compare Scholes & Walker
1993; Belslcy 1994). The extinction probability of the
life forms depends on the available water and thus
increases as a result of these reductions in soil moisture.
Trees
1998 British
Ecological Society.
Jotlrr?nl of Ecology,
86, 780-793
Trees (as well as tree seeds and seedlings) are nlodelled
using an individual-based approach (DeAngelis &
Gross 1992). The successful establishilleilt of tree
seedlings in a grid cell depends on the availability of
seeds and moisture. Seed availability in the illode1 is
a function of the distribution of mature trees. Seeds
are distributed away from mature savanna trees using
an exponential decay function with a inaxiillum of 50
germinable seeds beneath the tree canopy (Jeltsch rt
al. 1996; see below for additional nlodes of tree seed
dispersal).
As with the other life forins in the model, establishment probabilities for savanna tree seedlings
increase with increasing moisture availability. Rates
of establishment are therefore based on parameters
characterizing the dependence of establishment on
levels of topsoil and subsoil moisture, up to a maximal
establishment probability of 0.6 under optimal moisture conditions (Jeltsch et nl. 1996). Tree seedling mortality decreases with increasing moisture and age
(Jeltsch et 01. 1996). If at least one tree seedling or
sapling survives the first 10 years after germinating,
one submature tree is modelled as dominating the grid
cell (implicit self-thinning). After a 5-year period of
maturation, a tree starts to produce seeds until it dies.
Extremely dry conditions [(M,,M,) = (O,O)] lead to
drought stress, which causes a reduction in the life
span of trees (Jeltsch e f nl. 1996). This life span is
modelled to be a maxiinunl of 250 years, with a linear
increase in the probability of mortality starting at an
age of 120 years. The tree parameters are all based on
the general life-history attributes of Acacia erioloba.
GRASS FIRE AND GRAZING
Since the probability of the occurrence of a grass fire
increases with availability of grass as a fuel (Frost &
Robertson 1987), the probability of a fire occurring
in the model is directly proportional to the number of
grass-dominated grid cells present in a given year.
Tree- and shrub-dominated grid cells are ignited and
killed only if they are adjacent to a grass-dominated
cell during a fire and then only at low probability
(shrub mortality 5%; tree mortality 10%) (Trollope
1982; Frost & Robertson 1987; N. van Rooyen,
unpublished data)
Grazing, defined to be the consumption of herbaceous bioillass combined with trampling, is modelled as occurring in individual cells and only the
detriillental effects are considered. Grazing in the
nlodel acts to decrease the level of potential productivity of herbaceous vegetation and reduces the
establishment probabilities of all life forms. For all
of the model runs reported here, there was a 10%
probability that any given cell was affected by grazing
during any particular time-step. This represents a
lightly grazed scenario (Jeltsch e f al. 1996).
For the effects of varying the fire and grazing parameters see Jeltsch er nl. (1996).
SMALL-SCALE HETEROGENEITIES
In each time-step, patches of different heterogeneity
types and sizes are distributed in the modelled landscape in variable numbers. They are either distributed
randoinly or with variable degrees of spatiotemporal
correlation (Fig. lb,c).
Given the ecological dynamics of the savanna system,
the following heterogeneity types are modelled to
785
F. Jeltsclz et al.
determine their potential impact on the spatial distributions of savanna trees.
(S) - seed clumping (e.g. seed caches, tree seeds
concentrated in the dung of herbivores, seed accumulations caused by floods): the n~unberof tree seeds
(S,,,,) was increased in selected patches, based on the
actual number of seed-producing tsees (N,) in the 50ha modelled area:
S,,,, = rocrrid(l0 x log (N, + 1))
(M) - iillproved moisture conditions (e.g. local
depressions where water collects. soil disturbances,
patches with higher aquifer levels): topsoil and subsoil
moisture were inlproved by one level in selected patches (i.e. (M,, M,) was changed to (M, 1. M, 1)).
(C,,,) - total vegetation clearing (e.g. rodent activities, animal caused disturbances): all vegetation.
except mature trees, was reinoved from selected patches.
(C,,,.,) - partial vegetation clearing (e.g. rodent
activities, herbivory): all vegetation, except trees in
any life stage, was removed from selected patches.
Because most of these heterogeneity types are
unlikely to occur separately, the followiilg combinations were also explored: (C,,,M), (C,,,.,M),
(Calls),(C,, S), (C,,,MS) and (C,,,,,M S). For example,
the heterogeneity types (C;,,,S) or (C,,,,,S) are likely
to occur in places where animals collect to rest (i.e.
trampling removes the vegetation and seeds accumulate in antelope dung). And, wheil this is in combination with local depressions where water collects.
they are (CaIlMS)or (C,,,,MS).
+
+
+
locations of patches at time-step t 1 depend on the
locations of heterogeneities at time-step t). Since the
patch size (i.e. 5 m x 5 in or 20 nl x 20 in) did not
influence the general results concerning spatioteinporal correlation, we will present results of one
patch size only (20 m x 20 nl or 4 x 4 grid cells,
respectively). Different levels of spatiotemporal autocorrelation were produced in the following way (compare Moloney & Levin 1996): each 4 x 4 cell heterogeneity was randomly positioned within a
heterogeneity region of 20 x 20 cells (Fig. lc). Variations of the size of the heterogeneity regions do not
influence the qualitative results presented below. The
heterogeneity rate for a model run was set by fixing
the number of heterogeneity regions distributed
within the model grid. Heterogeneity regions were
distributed at random within the grid prior to the
first time-step. During subsequent time-steps, each
heterogeneity region either remained in the same
location or was repositioned at random with probability P,,. P,, will be referred to as the heterogeneity
turnover rate. (Individual heterogeneities could only
occur within a heterogeneity region.) We varied P,,
from 0.0 (no repositioning, i.e. high correlation) to
1.0 (repositioning at each time-step, i.e. no correlation). At low values of P,, there was a high probability that a grid cell iinpacted by a heterogeneityproducing process during one time-step would also
be impacted during subsequent time-steps (i.e. high
correlation of heterogeneity patches), due to little
repositioning of heterogeneity regions.
Results
Heterogeneity size
Two different patch sizes were explored in the illode1
simulations: (i) patches of 5 in x 5 111 (I-grid cell) (Fig.
lb) and (ii) patches of 20 n~ x 20 in (4 x 4 grid cells)
(Fig. lc). These patch sizes are in the range of einpirically observed heterogeneities of the types inodelled
(Nel& Rautenbach 1975; Lovegrove &Painting 1957;
Nel 1990).
Rates of'heterogeiieit~~,f'o1~171c1tion
The 'heterogeneity rate' (i.e. the proportioil of the
total area per time-step that is affected by heterogeneity-producing processes) was varied systematically froin low (1 grid cell per time-step) to high
(80% of the total area per time-step). High heterogeneity rates are unrealistic, but were explored to
improve the understailding of the inodelled processes
and system responses.
. .
1998 British
Ecological society,
jouinnl o f ~ c o l o-.
nv,
86, 780-793
- .
In the following, we analyse the impact of both uncorrelated patches (i.e. patches randomly positioned during each time-step) and correlated patches (i.e. the
Earlier studies with the savanna model have shown
that, in the absence of small-scale heterogeneities, the
system is generally driven to a state of either pure
grassland or pure woodland (Jeltsch et nl. 1996). Relatively few scenarios (model runs with different parameter settings) lead to the long-term coexistence of
trees and grasses. However, with the introduction of
small-scale heterogeneities (as defined above), we find
that coexistence call occur under a broader range of
conditions and that the response of the system may
depend on whether or not heterogeneities are correlated in space over time. We first present results
for uncorrelated heterogeneities and then examine the
effects of correlated heterogeneities. We also compare
the distribution pattern of trees predicted by the
model with patterns observed for trees in the southern
Kalahari to provide a preliminary assessment of how
well the inodel depicts spatial relationships in this
system.
UNCORRELATED HETEROGENEITIES
Under low rates of uncorrelated heterogeneities
(< 0.01 % of the cells affected during each time-step),
63% of the rainfall scenarios in the inodel savanna
786
Snzall-scale
heterogeneities and
coexistence in
savannas
system tend towards grassland, 31°/0 towards woodland, and only 6% (one out of the 16 scenarios tested)
towards long-term tree-grass coexisteilce (Fig. 2).
(These three possible outcoines represent long-term
S
100 -
M
100
80 -
60
trends with respect to the tree-grass ratio over the
20 000 year time span of an individual simulation; see
Jeltsch et 01. 1996 for details.)
The iiltroduction of local enrichment in seed avail-
80 60 -
o...oo' 40
40
,
, .* .
. . '0 0 . m a -0 0a..
.,
/
-
D-
D-
20
0
20
-
-
Q . grassland 1x1
+coexistence 1x1
--irr-
0
0.001
0.01
0.1
1
10
100
0
0.001
I
I
I
I
0.01
0.1
1
10
grassland 4x4
t coexistence 4x4
-+ woodland 4x4
woodland 1x1
100
.
-1
0.
. .O 0 . Q 0 0 . O
0 . C'.
.
'Z,
.'part'
n
Q)
CI
V) Q,
0.
. .O 0.CK)O
..;
0
;. F
CI
Heterogeneity rate (% of area time-stepM')
0 1998 British
Ecological Society,
Journal of Ecology,
86,780-793
Fig. 2 Frequency of the different long-tern states (i.e. grassland. woodland, coexistence) for different heterogeneity types, heterogeneity rates and heterogeneity patch sizes in the uncorrelated scenario. The frequency represents the percentage of the 16 tested
rail1 scenarios that lead to the correspondiiig long-tern state. Heterogeneity types: S (tree seed clumping), M (improved ~noisture
conditions), C,;,,, (partial vegetation clearing), C,,,,(total vegetation clea~ing)and various con~binationsof these types.
787
F. Jeltsch et al.
0 1998 British
Ecological Society,
Journal ?f EcologyJ
86,780-793
ability (heterogeneity type S) has a profouild effect
on the predicted long-term state of the savanna systenl
(Fig. 2). For heterogeneity rates above 0.1 %, there is
a transition from grassland to woodland, and for rates
between 0.1% and 1% there is an increase in the
proportion of rainfall scenarios that lead to longterm tree-grass coexisteilce (up to 75% of the rainfall
scenarios for 4 x 4 cell heterogeneities: Fig. 2).
In contrast to the iinpact of enriching local seed
availability, locally improving moisture conditions
(heterogeneity type M) have alillost no influence on
the long-term state of the savanna system (Fig. 2).
Only unrealistically high heterogeneity rates for this
factor lead to a slight increase in woodland. This
result indicates that the suppressing effect from the
competing life forins is too strong to allow for successful establishment of tree seedlings, even if the
moisture status is improved in iildividual cells during
some years.
Partial vegetation clearing (C,,,,,),alone and in combination with inlproved moisture conditions (C,,,,M).
only has an effect at interinediate to high heterogeneity rates (i.e. more than 1 % of the modelled
area per time-step; Fig. 2). In this range, there is a
clear trend towards woodlaild. resulting from reduced
coinpetition with the cleared life forins. We also found
that differences in heterogeneity size and greater
nloisture availability in the heterogeneity patches
have little effect under conditioils of partial vegetation
clearing (Fig. 2).
Of all the heterogeneity types. those \vhich conlbine
partial vegetation clearing with local seed accurnulation, i.e. C ,;,,, S and C ,,,, MS. have the strongest
impact on the long-term state of the modelled
savanna. (C,,,,MS also includes ilnproved moisture
conditions.) Both heterogeneity types cause a transition from grassland towards woodland, via treegrass coexistence, begiilning at heterogeneity rates
below 0.1 %. The additio~lalinoisture available in the
C,,,,MS type of heterogeneity results in a slightly
stronger effect than the C,~,,,Stype. and C ,,,,,,S has a
slightly stronger effect than seed accum~~lation
(S)
alone. In fact. a coinparisoil with the effects of the
individual heterogeneity types M and C,,:,,,shows that
local seed accumulation is the nlost important component of the conlbined heterogeileity types C , , , , S
and C ,,,,,M S (Fig. 2).
Unlike C,,,,, the heterogeneity type C,,,includes the
removal of tree seedlings. C,,, and C,,,M produce no
interesting trends except at high heterogeneity rates,
where there is an increase in the n ~ ~ i n b of
e r rainfall
scenarios that produce savanna grassland (Fig. 2).
This contrasts the trend observed for C ,, and C,,,,,,M.
where the development of woodland is favoured.
Clearly, for C,,, and C,,,M, the positive effects of
additional establishment sites and greater nloisture
availability, which would lead to woodlaild development at high heterogeneity rates, are out\veighed
by the detrinlental effects of clearing away tree seed-
lings. At all but the highest heterogeneity rates, Calls
and C,,,MS produce results similar to those produced
by the related heterogeneities with only partial vegetation clearing.
For the uncorrelated heterogeneities exainiiled
here, long-term tree-grass coexistence occurred
mainly within a range of heterogeneity rates that was
transitional between rates producing pure grassland
and those producing pure woodland. Coexistence was
inore frequent for heterogeneity types incorporating
local seed enrichment (S. CS a i d CMS). However,
under realistic heterogeneity rates (i.e. those below
10% of the total area per time-step), at nlost 30% of
the rainfall sceilarios produced a long-term tree- grass
coexisteilce (Fig. 2).
CORRELATED HETEROGENEITIES
We found that spatioteillporal correlation among heterogeneities can act to expand the range of long-term
tree-grass coexistence in the modelled savanna systein
(Fig. 3). (The heterogeneity type M, as with uncorrelated heterogeneities, has almost no iinpact on the
long-term dyilainics of the modelled savanna system
and is thus excluded froin Fig. 3.) Both types of vegetation clearing (C,,,, and C,,,), when considered
alone, show no clear trend caused by correlation
anlong heterogeneities. However, conlbiiling patch
clearing with improved moisture conditions (C,,,,M
and CaI,M)leads to an increase in the range of rainfall
sceilarios that lead to long-term coexistence, particularly at intermediate heterogeneity rates with high
temporal correlation anlong heterogeneity locations.
This is especially true for partial vegetation clearing,
which has no detriineiltal effect on tree seedlings. In
this case. up to 40% of the tested rainfall scenarios
lead to tree-grass coexistellce under the highest level
of spatiotelnporal autocorrelation.
As with uncorrelated heterogeneities, S, CS and
CMS types caused the greatest increase in the proportion of rainfall scenarios producing long-term
tree-grass coexistence (Fig. 3). With a high degree of
spatiotemporal
autocorrelation
among
heterogeneities (tmnover rates < 0.20). local seed
acc~~nlulation
(S) sigilificantly increases the proportion of rainfall scenarios exhibiting tree-grass
coexistence. particularly for i~ltermediate heterogeneity rates between 0.1% to 1%. If this type of
heterogeneity is colnbined with either type of local
vegetation clearing (C) with or \vithout inlproved
inoisture conditions (M), the level of coexistence is
illcreased even inore at lower heterogeneity rates,
occurring in nlore than half of the tested rainfall scenarios (Fig. 3).
In general, the simulation experinlents with correlated heterogeneities show that the degree of
coexistence decreases rapidly wit11 decreasing correlation anlong heterogeneities. The reason for this
788
Small-scale
heterogeneities and
coexistence in
savannas
--t
turnover rate 0.0
- - v . turnover rate 0.05
--, - turnover rate 0.2
+ turnover rate 1.0
Heterogeneity rate (% of area time-step")
Fig. 3 Frequency of long-term tree-grass coexistence (in percentage of the tested rain scenarios) under the impact of correlated
heterogeneities of various types and heterogeneity rates. Uncorrelated heterogeneities (i.e. turnover rate 1.0) are also shown
for comparison (compare with Fig. 2). Low values of the turnover rate correspond to high spatiotemporal autocorrelation
among heterogeneity patches and vice versa. The heterogeneity patch size is 20 111 x 20 in (a smaller patch size of 5 in x 5 In
gives similar results and is thus not shown here).
0 1998 British
Ecological Society,
Journal of Ecology,
86, 780-793
789
F. Jeltsch et al.
trend becomes obvious when we look at the spatial
distributions of trees.
SPATIAL TREE DISTRIBUTIONS
Small-scale heterogeneities increase the number of
isolated trees occurriilg in scenarios that produce
long-term coexistence (Fig. 4). However, a purely
scattered tree distribution (as opposed to one with
some degree of clumping) only occurs in some of the
rainfall-scenario, heterogeneity-regime co~nbi~latiolls
that lead to long-term coexistence (e.g. Fig. 4b). More
often, a mix of small tree clumps and scattered trees
occurs (Fig. 4c-e). This is especially true in the case
of simulations with the larger heterogeneity patch size
(20 m x 20 nl), where the size of the area occupied by
small tree clusters is similar to the underlying patch
size of the heterogeneities (Fig. 4e). High temporal
autocorrelation in the location of heterogeneity patches leads to coexistence, but this is primarily due
to local patches of woodland scattered within pure
grassland, since the heterogeneity regions are confined
within a limited part of the total landscape for long
time spans (Fig. 4f). In this case, tree clumps are
generally larger than the heterogeneity patch size.
This is caused by two different processes: (i) tree seeds
100' ,;. . , . ......
. .. . ,
. .. .. ... ... . .
.;. .:'. . ':. .
80. ,!.',
:, ;: . .. . .: .. . .. . ..' . . .. .. . " :
. .. . ' . : . . . ' .: " " ' .". '. . . . . . ..,,..,.
60 . . . . . .;,: . . . . . .,.<;.. . . . ." . .:. . . . .,., .' . ..
.*'. : . <'
.'
..
40.. ::. ...,: ... . +. j , : ..........
: . , : .,,::' . .
,
,
'
,
,
,
',
5
5
#
.
I,:
I..
,
'
. . . .. . . . .
.','
' "
I . .
.
.
:,
.
'
.
2 0 . . : . , : . . . ,;.:/ :
. .:...,'.
. :. . .. .. .. ....... ..
: :
!
. : . . . . . . . ......
. . . :.: ' .
.
, ,, '
i
0 1998 British
Ecological Society,
Jo~unalo fEcology,
86, 780-793
,
'
'
,
Fig. 4 Examples of spatial tree distributions in states of long-term tree-grass coexistence under contrasting model scenarios.
(1) Heterogeneity: no small-scale heterogeneity (a) vs C,,,,MS(b through f). (2) Autocorrelation: no autocorrelation among
heterogeneities (turnover rate of 1.0 in b through e) vs. high autocorrelation anlong heterogeneities (turnover rate of 0.0 in f).
(3) Patch size: heterogeneity patch size of 1 cell (b through d) vs. heterogeneity patch size of 4 x 4 cells (e and f). Rainfall
scenarios (M,, M,) and the rate of production of heterogeneity patches also varied ainong the examples, as follows: (a) (M,,
Ms) = (1,2); (b) (M,, M,) = (1, 0), rate = 100 cells time-step-'; (c) (M,, M,) = (3,1), rate = 10 cells time-step-'; (d) (M,,
M,) = (2,2), rate = 100 cells time-step-': (e) (M,. M,) = (2.2). rate = 32 cells time-step-'; and (f) (M,, M,) = (2, O), rate = 48
cells time-step'. For reasons of contrast only tree-dominated cells (black) are shown in (a through f).
acculllulate in the neighbourhood of groups of trees
causing higher local establishment probabilities (cf.
Table 1); and (ii) reduced grass cover in tree-dominated patches (S. J. Milton, unpublished data) reduces
fire-induced tree mortality within these patches
(Jeltsch et crl. 1996; coillpare Rebertus & Burns 1997).
Thus, the random establishment of two or lllore trees
near to each other is sufficient to promote the formation of a tree clump. In contrast, scattered trees
result from establishmeilt in isolated patches with
favourable establishment co~lditioils (i.e. heterogeneity as defined here) or represent single trees
that are remilants of former tree clumps that have
declined in number.
KGNP SCENARIO
The iinportance of accuillulatioils of tree seeds for the
long-term coexistence of trees and grasses in the
model corresponds well with eillpirical findings from
the K G N P (Table 1). We therefore analysed the longterm vegetation dynamics that might be typical for the
southern Kalahari, by applying the K G N P rainfall
scenario (see the Model descriptioi~)to a series of
model runs iilcorporating variable type S heterogeneity rates (all other parameters and processes
reinailled unchanged from the studies utilizing the
16 stochastic rainfall scenarios). Model results were
compared with tree density data and spatial tree distributions froill the area in the southern Kalahari that
supplied the raillfall data.
The results of the southeril Kalahari scenario confirm our previous findiilgs that small-scale heterogeneities of an interillediate frequeilcy are necessary for long-term persistence of trees and grasses (Fig.
5). Without small-scale heterogeneities, the model
predicts that the southern Kalahari would develop
towards a grassland without trees, whereas too high
a heterogeneity rate would cause a contiiluous
increase in woody species (Fig. 5). What is i~loststriking is that tree densities in model runs produciilg longterm tree-grass coexistellce correspoild very well with
tree densities fouild in the K G N P (Fig. 5). The spatial
distribution of trees predicted by model ruils produciilg long-term tree-grass coexistence also correspoilds well with the distributioll of trees observed
ill the southern Kalahari savailila (Fig. 6). A statistical
point pattern analysis of all of these distributioils
shows that all patterns exhibit a trend towards even
spacing at sillall scales, clumpiilg at intermediate
scales, and random spacing at large scales (F. Jeltsch
& K . Moloney, unpublished ailalysis). However, distances between individual trees are slightly closer in
the model runs, which is probably caused by an underestimation of the strength of iilterspecific neighbourhood competition.
'01998 British
Ecological Society,
Jouilinl qf Ecologj~,
86, 780-793
Discussion
We explored the impact of small-scale heterogeneities
on the long-term dyllaillics of a model savanna eco-
system, with a particular emphasis on identifying conditions that allow the long-term coexistence of trees
and grasses. We examined the effects of heterogeneity
type and formation rate (first level), heterogeneity size
(second level), and spatiotemporal organization (i.e.
autocorrelation anlong heterogeneity patches; third
level) (cf. McCoililaughay & Bazzaz 1991; Moloiley
& Levin 1996).
F I R S T LEVEL
Heterogeneity rate and type had the greatest influence
on the long-terin dynamics of the savanna system
model. Intermediate rates of small-scale heterogeneity
formatioil favoured long-term coexistence of trees
and grasses, as would be predicted by the intermediate
disturba~lcehypothesis (Huston 1979). Of all the heterogeneity types examined, increased seed availability
in local patches (e.g. seed accuillulation in herbivore
dung) had the strongest impact on the long-term state
of the illodelled savanna. It also produced a realistic
density and spatial distribution for trees in the semiarid savanna of the southeril Kalahari. Although ecologists have recognized for a long time that seed dispersal by inamn~alsis a critical factor in the developlnellt of 'tree veld' (grassland with scattered trees)
in southern Africa (Bews 1917; Burtt 1929), it has not
been clear what impact this process has on the longterm coexistence of trees and grasses.
SECOND LEVEL
We found that heterogeneity patch size does affect
tree distribution patterns. The model results indicate
that heterogeneity patches larger than the average size
of a mature tree canopy lead to tree clumping on a
small scale. I11 contrast, small patch sizes have a higher
probability of bringing about a scattered tree distribution that persists for long time spans. However,
this result is restricted to low levels of autocorrelatioil
in the regime of heterogeileity formation.
THIRD LEVEL
High levels of autocorrelation among individual heterogeneity patches increased the range of environillelltal conditions that led to long-term coexistellce
of trees and grasses in the model ecosystem. High
levels of autocorrelation are not unrealistic in savanna
ecosystems. Some heterogeneities, such as those produced by rodent colonies (Nel & Rautenbach 1975;
Nel 1978) and the collcentrated activity of herbivores
beneath trees, are likely to show a higher degree of
autocorrelation than ailinla1 diggings or the scattered
distributioll of herbivore dung. It is plausible that
heterogeileities that are closely linked to landscape
elements, such as water holes or water collecting
depressions and salt licks, will also show a high degree
of spatioteinporal autocorrelation.
791
F. Jeltsch et al.
m After 2000 years
0After 3000 years
Heterogeneity rate (% of area time-step-')
Fig. 5 Impact of variable l~eterogeneityrates of type S (seed accumulations) on the long-term dynamics of a simulated Acacia
rriolobn population in the K G N P (southern Kalahari). Turnover rate: 0.2, i.e. in each time-step 20% of the heterogeneity
regions are randomly relocated. The horizontal lines indicate the average tree density (solid line) and the nlaxinlunl tree density
(dashed line), respectively, of seven open savanna regions in the K G N P (Bothma et (11. 1994).
Fig. 6 Real tree distributions (a and b) derived from aerial photographs of two sanlple 50-ha regions in the K G N P (Sout11
African Surveys and Land Inforn~ationBureau, unpublished data) conlpared with two sanlple tree distributions (c and d) in
a state of long-tern~coexistence (model simulations described in Fig. 5; heterogeneity rate 0.5% of total area time-step-'). The
real tree distributions are representative exanlples of several distributions exalnined by the authors (unpublished analysis).
'01998 British
Ecological Society,
Jouinn/
E ~ ~
86, 780-793
The simulatiolls show that states of long-term
coexistence resulting from high levels of correlation
[ among
~ ~ heterogeneities
~ ,
are typically characterized by
tree clumps, with a few trees exhibiting a scattered
distribution. However, it is plausible that tree clumps
could be reduced to the size of a single tree under
conditions of maxilnuln autocorrelatioll anlong heterogeneities (i.e. no relocation of heterogeneity pat-
ches over the course of time) if individual heterogeneities are, on average, snlaller than the size of
an average tree canopy.
SMALL-SCALE HETEROGENEITIES A N D
EQUILIBRIUM STATES
Small-scale heterogeneities in semi-arid savannas may
favour the establishment of tree seedlings either by
reducing competition with grasses (i.e, vegetation
clearing) or by increasing the nuinber of 'opportunities' for establishment (i.e. seeds existing in
clumps). Small-scale heterogeneities thus enable tree
seedlings to establish in the grass layer, which is otherwise inore competitive (Scholes & Walker 1993; Davis
et al., ill press). This result corresponds to Grubb's
(1977) ideas of coexistence through 'regeneration
niches' in plant communities. Model results indicate
that, in semi-arid savannas, these regeneration niches
are of crucial importance under conditiolls of tree
decline: ill periods of low rainfall inter- and intraspecific competition for moisture reduces the probability of tree seedling establishment and additional
establishment patches facilitate the persistence of the
tree population at a low level, despite the unfavourable conditions. Small-scale heterogeneities that favour tree seedli~lgestablishment thus function as an
ecological 'buffer mechanism' that prevents the
extinction of the tree population ill critical situations.
A similar buffering effect may exist in other areas
such as dry river beds, which nlay serve as a place of
survival for trees in periods of drought, when conditions are otherwise unfavourable for establishlnent
(Bews 1917). Results of the current and previous
(Jeltsch et 01. 1996) versions of the model indicate
that, during periods of high rainfall, tree seedling
establishineilt is sufficient to maintail1 the presence of
trees ill the system and does not require additional
establishment patches. Continuously favourable conditions even lead to a continuous increase of savanna
trees that is only controlled by increasing fire
frequency. Long-tern~coexistence of savanna trees
and grasses ill semi-arid savannas thus does not represent a stable equilibrium state, but a transitiollal
state between grassland and woodland that persists
owing to small-scale heterogeneities and disturbances
on various scales (compare Scholes & Walker 1993).
Conclusion
'01998 British
Ecological Society.
Journol of E c o l o g ~ ,
86,780-793
The silnulatioil results support our hypotheses that
small-scale heterogeneities and disturbances in the
landscape, which produce iinproved establishment
conditions for tree seedlings, will act to (i) increase
the range of envirollinental coilditions under which
long-tern~coexistellce of trees and grasses can occur,
and (ii) facilitate a more scattered distribution of savanna trees. The probability of long-term coexistence
and the realized pattern of tree distributions were
influenced by all three of heterogeneity type and formation rate, heterogeneity patch size, and spatiotemporal autocorrelation of individual heterogeneity patches.
The approach applied here explored the impact of
different forms of heterogeneity in a series of model
runs, where only one type of heterogeneity and one
rate of heterogeneity formation were used ill any one
run. This was done to facilitate an evaluation of the
relative importallce of each regime of heterogeneityproducing processes. However, it is evident that, in
nature, several types of heterogeneities occur simultaneously and that the rate with which they occur
fluctuates both in space and time. It is likely that these
local fluctuatiolls have a further stabilizing effect on
a regional scale. Further field studies are necessary to
quantify the frequency of the relevant heterogeneity
types, their spatial arrangement and correlation, as
well as colonization success of tree seedlings in different types of heterogeneity patches. However, it is
encouraging that a first application of the model to
a specific site in the southern Kalahari gives results
coilsistent with the empirical data.
In summary, the simulation experiments presented
here will help to formulate more precise hypotheses
concerniilg the processes operating in savanna ecosystems, and will stimulate new aspects of savanna
research (Scholes & Walker 1993; Jeltsch et al. 1996).
Acknowledgements
The authors are grateful to C. Wissel, V. Grimm, T.
Wiegand, G. Weber and three anonymous referees
for valuable comments on earlier drafts of this paper.
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