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Ecological Modelling 337 (2016) 253–261

Contents lists available at ScienceDirect

Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

oil seed bank dynamics under the influence of grazing as alternativexplanation for herbaceous vegetation transitions in semi-aridangelands

rank van Langevelde a, Zewdu K. Tessema b,∗, Willem F. de Boer a, Herbert H.T. Prins a

Resource Ecology Group, Wageningen University, Droevendaalsesteeg 3a, NL-6708 PB Wageningen, The NetherlandsSchool of Animal and Range Sciences, College of Agriculture and Environmental Sciences, Haramaya University, PO Box 138, Dire Dawa, Ethiopia

r t i c l e i n f o

rticle history:eceived 26 December 2015eceived in revised form 12 July 2016ccepted 18 July 2016

eywords:nnual grassare soilerminationrazingeed longevityerennial grass

a b s t r a c t

Ecological studies have frequently stressed that the availability of seeds in the soil is important for therecovery of semi-arid rangelands. However, the crucial role of soil seed banks has not been incorporatedinto rangeland models to understand vegetation states and transitions in semi-arid rangelands. We devel-oped and evaluated a novel model to show that the availability of seeds in the soil seed banks as a functionof plant cover can trigger transitions from perennial to annual grasses and from annual grasses to baresoil with increasing grazing pressure. The model indicates that when grazing pressure is low, a high coverof perennial grasses and a large soil seed bank of these grasses may be present, whereas annual grasseswith their seeds in the soil appear with increasing grazing. When grazing pressure further increases,vegetation cover and the soil seed bank size decline. We found that the positive feedback between plantcover and the size of the soil seed bank depends on seed traits, i.e., longevity and germination rate. Thispositive feedback is an alternative explanation for a sudden vegetation changes in rangelands, which are

tate-and-transition models often explained by the positive feedback between plant cover and the infiltration rate of rain into thesoil. In contrast to this latter positive feedback, our model can explain shifts in vegetation from perenni-als to annuals and vice versa on different soil types, which are often seen in semi-arid rangelands. Ourmodel contributes therefore to the understanding of vegetation dynamics for the proper managementand possible restoration of degraded semi-arid rangelands.

© 2016 Elsevier B.V. All rights reserved.

. Introduction

Semi-arid rangelands have been described as ecosystems withore than one state and transitions from one state to another,

ften occurring under influence of disturbances such as grazingr fire (Rietkerk et al., 1996; Van Langevelde et al., 2003). Semi-rid rangelands can therefore be described by state-and-transitionodels (Noy-Meir, 1975; Westoby et al., 1989; Rietkerk et al., 1996;

estelmeyer et al., 2003; Briske et al., 2005). A bush encroachedtate of these rangelands, dominated by shrubs and trees with aow cover of grasses, has been reported frequently and is consid-red as a serious threat for livestock and biodiversity (Roques et al.,

001; Ward, 2005). In the herbaceous layer, two states have beenocumented: a state with ample herbaceous cover, mainly peren-ial grasses, and scattered trees (Scholes and Archer, 1997; Simioni

∗ Corresponding author.E-mail address: tessemaz@yahoo.com (Z.K. Tessema).

ttp://dx.doi.org/10.1016/j.ecolmodel.2016.07.013304-3800/© 2016 Elsevier B.V. All rights reserved.

et al., 2003), and a state with a cover of annual grasses, absence ofperennial grasses, and bare soil (Westoby et al., 1989). Tessemaet al., (2011, 2012) studied these two states and the transitionsbetween them under the influence of grazing for semi-arid range-lands in Ethiopia: the state with perennial grass cover was foundin sites with low grazing pressure, whereas the state with annualgrasses and bare ground was found in sites with heavy grazing.

In semi-arid African rangelands, it has been found that inten-sive grazing has indeed resulted in a rapid species turn-over,reducing forage availability and forage quality to livestock (Kumaret al., 2002; Abule et al., 2005; Augustine and McNaughton, 2006;Tessema et al., 2011). Previous models showed the transitionsof semi-arid rangelands due to grazing by using the relationshipbetween water infiltration in the soil and plant cover (Rietkerkand Van de Koppel, 1997; Rietkerk et al., 2002). A reduction ofaboveground biomass due to heavy grazing leads to a reduction of

infiltration of rain into the soil that results in locally lower soil wateravailability, and consequently in reduced plant growth. However,these models do not explain the co-occurrence of annual grasses

254 F. van Langevelde et al. / Ecological Modelling 337 (2016) 253–261

Table 1List of the used parameters and variables, their interpretation, units, estimated values and literature sources.

Interpretation Units Values Sources

P Cover of perennial grass – 0–1A Cover of annual grass – 0–1Sp Availability of seeds of

perennial grass in the soilm−2 0–2200 O’Connor and Pickett

(1992), Tessema (2011),Vogler and Bahnisch (2006)

Sa Availability of seeds ofannual grass in the soil

m−2 0–5000 Veenendaal (1991),Veenendaal et al. (1996a)

R Water availability in thesoil

mm t−1 0–500

cp Rate of increase inperennial grass cover dueto seed germination

m2 0.01

cam Maximal rate of increase inannual grass cover due toseed germination whenlight is not limiting

m2 0.001

gp ga Germination rate of theseeds of grass in the soilbank per unit of wateravailability

mm−1 gp = 0.4/500andga = 0.2/500

Tessema (2011) at 500 mmrainfall per year

lp la Decrease of grass cover, forexample due to death

t−1 lp = 0.6 andla = 0.7

bpba Decrease of grass cover dueto herbivory

m2 g−1 t−1 bp = 0.6 andba = 0.1

Prins (1988): perennialgrass is more palatablethan annual grass

h Herbivore density g m−2 0–15spmsam Maximum amount of seeds

produced when plant coveris maximal

m−2 t−1 spm = 2200 andsam = 30,000

Veenendaal (1991),Veenendaal et al. (1996a),Vogler and Bahnisch (2006)

sp0 sa0 Fraction of amount of themaximum amount of seedsin the seed bank due todispersal

– sp0 = 0.2 andsa0 = 0.4

kp ka Plant cover where the rateof seed production is halfof its maximum

– kp = ka = 0.1

lsp lsa Specific loss rate of seeds t−1 lsp = 0.7 andlsa = 0.4

Tessema (2011) foundlongevity of seed fromperennial grass to be 28%and 62% for annual grass

kl Plant cover where the lightavailability for annual

– 0.2

aotctbnaas1s

teidteagtMq

grasses is half of cam

nd perennial grasses with bare soil as they only recognize theccurrence of a vegetated state alternating with bare areas. Infil-ration of rain into the soil is indeed found to increase with theover of perennials, whereas annual grasses hardly increase infil-ration into the soil (Rietkerk et al., 2000). Hence, the relationshipetween plant cover and infiltration may be not a good mecha-ism to explain the transitions from perennials to annuals and fromnnuals to bare soil. Moreover, the feedback between plant covernd infiltration is assumed to be present on clay soils where exces-ive rainfall can cause crust formation (Rietkerk and Van de Koppel,997), whereas shifts from perennials to annuals are also found onandy soils (Tessema et al., 2011, 2012).

A number of models of grazing lands, from savanna, grasslandso pastures, have been developed (Oomen et al., 2016). The mod-ls so far developed for semi-arid grazing systems do not explicitlynclude the source of recovery of grasses after they have (locally)isappeared. However, ecological studies have frequently stressedhat the availability of seeds in the soil is important for the recov-ry of semi-arid rangelands, since the soil seed banks can serve as

buffer mechanism (Leck et al., 1989), as for example, perennial

rasses after their disappearance can re-establish bare areas fromheir seeds in the soil (De Villers et al., 2003; Scott et al., 2010).

oreover, the importance of soil seed banks has also been fre-uently discussed in restoration efforts (Suding et al., 2004; Van

den Berg and Kellner, 2005), but identifying the presence of annualand perennial grass seeds in the soil seed banks becomes criti-cal in semi-arid rangelands (Müller et al., 2007; Cipriotti et al.,2012). Besides differences in seed production, seed traits like seedlongevity and germination rates may determine the transition fromone state to another in semi-arid rangelands (O’Connor, 1991; Pons,1991; Sternberg et al., 2003).

Annual grass species have generally a lower germination ratethan perennials (McIvor and Howden, 2000; Tessema, 2011). Mostperennial grasses germinate rapidly after initial seed dispersalat the first rains early in the year (Rathcke and Lacey, 1985;Veenendaal et al., 1996a; Tessema, 2011). The recovery of degradedsemi-arid rangelands and the transition from one state to anotherare therefore thought to be determined by the intensity of grazing(Noy-Meir, 1975; Westoby et al., 1989; Stafford Smith et al., 2007)and the availability of seeds in the soil (Leck et al., 1989; De Villerset al., 2003). The crucial role of the soil seed bank for system shiftsis known by rangeland ecologists but has not been incorporatedinto rangeland models. Therefore, we developed a model indicat-ing that the availability of seeds in the soil seed bank as a function of

plant cover can trigger transitions between three vegetation statessuch as from perennial to annual grasses and from annual grassesto bare soil with increasing grazing pressure, which is determined

F. van Langevelde et al. / Ecological M

Fig. 1. The zero-isoclines for the cover of perennial grass (P) (solid line, dP/dt = 0)and the soil seed bank of perennial grass (Sp) (broken line, dSp/dt = 0) drawn in aphase plane for fixed values of herbivore density. The vectors (arrows) indicate thedirection of change. Solid circles indicate a stable equilibrium, and open circles indi-cate an unstable equilibrium. The two domains with different attracting equilibriain panel (b) are separated by a separatrix (broken grey line). (a) no herbivores h = 0,(k

bt

2

2

tr

sp

b) h = 4, and (c) h = 10. Parameter values are: R = 500, cp = 0.01, cam = 0.001, lp = 0.6,p = 0.1, sp0 = 0.2, spm = 2200, ba = 0.4, kl = 1, gp = 0.8 × 10−3, lsp = 0.7.

y seed traits like longevity and germination rate of grass seeds, ashe main mechanisms.

. Model development

.1. Modelling interaction between seed bank size and plant cover

First, we model the relationship between the soil seed bank ofufted perennial grasses and the plant cover of these grasses. Theate of change of plant cover (P as fraction, in m2 m−2) is determined

odelling 337 (2016) 253–261 255

by the recruitment of the plants, the natural losses and the lossesdue to herbivory:

dPdt

= recruitP − lossP − grazingP (1)

The perennial grasses are recruited from seeds in the soil (num-ber of seeds per unit of area Sp, in m−2), which is dependent uponthe availability of resources (R, assuming here rainfall in mm t−1).The seeds determine the recovery of tufted perennial grasses,which are commonly found in semi-arid rangelands (O’Connor andPickett, 1992), so that we did not include vegetative recruitment inour models. As plant available moisture is limited, we assume a lin-ear relationship between water availability and plant recruitment.We define plant recruitment (in fraction area per unit of time, t−1)therefore as:

recruitP = R cp gp Sp P (1 − P) (2)

where cp is the rate of increase of plant cover due to germinationof the seeds in the soil (in area, m2) and gp is the germination rateof the seeds per unit of available water (in mm−1). The natural lossrate (in fraction area per unit of time, t−1) is defined as:

lossP = lp P (3)

where lp is the decrease of plant cover, for example due to death(in fraction area per unit of time, t−1). The effect of herbivory byremoving plant material and trampling (in fraction area per unit oftime, t−1) is modelled as:

grazingP = bp h P (4)

where bp is the decrease of plant cover due to herbivory (inm2 g−1 t−1) and h the herbivore density (in g m−2).

The rate of change of the soil seed bank size(number of seeds perunit of area and per unit of time, in m−2 t−1) is determined by theincrease of the number of seeds in the soil, the losses of the seedsand the germination of seeds, described as:

dSpdt

= increaseSp − lossSp − germSp (5)

The increase of seeds in the soil seed bank is determined bythe plant cover, and we assume that there is always a certain smallamount of seeds in the soil seed bank due to dispersal from externalsources (sp0 as fraction of the maximum number of seeds pro-duced), regardless of the present plant cover. Several studies founda relatively small seed bank in the soil when plant cover was lowor even absent (Dreber, 2011; Bertiller and Carrera, 2015). The pro-duction of seeds saturates with increasing plant cover (Veenendaalet al., 1996b). We modelled this production (number of seeds perunit of area and per unit of time, in m−2 t−1) as:

increaseSp = spmP + kp sp0

P + kp(6)

where spm is the maximum number of seeds produced when plantcover is maximal (number of seeds per unit of area and per unit oftime, in m−2 t−1), and kp is the plant cover where the seed produc-tion is half of its maximum (half saturation constant, as fraction).For reasons of simplicity, we ignore the number of seeds that dis-perse to other locations. The loss rate of seeds in the soil (numberof seeds per unit of area and per unit of time, in m−2 t−1) is definedas:

lossSp = lsp Sp (7)

where lsp is the specific loss rate of seeds (in t−1). This loss ratedetermines the longevity of the seeds: low values of l mean high

longevity. The rate of seed germination (number of seeds per unitof area and per unit of time, in m−2 t−1) is:

germSp = gp R Sp (8)

256 F. van Langevelde et al. / Ecological Modelling 337 (2016) 253–261

Fig. 2. Effects of (a) herbivore density(h), (b) germination rate of the seeds in the soil bank (gp), and (c) seed mortality (lsp) on the cover of perennial grass (P) and the size oft ashedt , lp = 0l

saagiga

c

wiaa

bi

he soil seed bank of perennial grass (Sp). Solid lines give the stable equilibria, and dhe state variables. Parameter values (see Table 1) are: R = 500, cp = 0.01, cam = 0.001sp = 0.7, and (c) h = 0.5, gp = 0.8 × 10−3.

Similar formulations can be used for annual grasses (A) and theeeds from annual grasses (SA). We only added a competition term:nnuals and perennials compete for water in semi-arid rangelands,nd we assume that this competition is asymmetric as perennialrasses can out-compete annual grasses by reducing light availabil-ty (Veenendaal et al., 1996b). Then the rate of increase of annualrass cover decreases when the cover of perennial grasses increasess:

a = cam klP + kl

(9)

here cam is the maximal increase in annual grass cover when lights not limiting (in area, m2) and kl is the plant cover where the lightvailability for annual grasses is half of cam (half saturation constant,

s fraction).

Due to the smaller impact of herbivory on annual grasses,ecause of their lower palatability, and their seed bank dynam-

cs, i.e. more seeds produced and lower seed germination rate

lines give the unstable equilibria. Arrows indicate the direction of development of.6, kp = 0.1, sp0 = 0.2, spm = 2200, ba = 0.4, kl = 1, (a) gp = 0.8 × 10−3, lsp = 0.7, (b) h = 0.5,

than perennial grasses (O’Connor and Pickett, 1992; Veenendaalet al., 1996b), annual grasses can occur at herbivore densities whereperennial grasses are grazed down. The model of perennial plantcover, annual plant cover, seeds of perennial plants in the soil andseeds of annual plants in the soil then becomes:

dPdt

= P(R cp gp Sp (1 − P) − lp − bp h

)(10)

dAdt

= A(Rcam klP + kl

ga Sa (1 − P − A) − la − ba h)

(11)

dSpdt

= spmP + kp sp0

P + kp− lsp Sp − gp R Sp (12)

dSadt

= samA + ka sa0

A + ka− lsa Sa − ga R Sa (13)

We analysed the model by first focusing on the effect of her-bivory (grazing), the germination rate of the seed and the seed

F. van Langevelde et al. / Ecological Modelling 337 (2016) 253–261 257

Fig. 3. Parameter planes of the water availability in the soil (R), herbivory density (h), germination rate of the seeds in the soil bank (gp), seed mortality (lsp), increase in thes duces meterl , R = 5

mptcTa

3

3

dtpjgWbipg

gatSiatt

oil seed bank due to dispersing seeds (Sp0), and the maximum number of seeds prooil and alternate stable states with either cover of perennial grass or bare soil. Parasp = 0.7, sp0 = 0.2, spm = 2200, (b) gp = 0.8 × 10−3, lsp = 0.7, R = 500, spm = 2200, (c) h = 0.5

ortality on the cover of perennial grass and the seed bank oferennial grasses. We then included the cover of annual grass andhe seed bank of annual grasses. We model the change of plantover and seed availability in the soil with time scales of one year.he used symbols, their units, interpretation, values and sourcesre given in Table 1.

. Results

.1. Perennial grass cover and their seed bank size

One way of analysing the dynamics of the cover – soil seed bankynamics of perennial grasses is by plotting the zero-isoclines ofhe perennial grass cover and the size of the soil seed bank in ahase plane (Fig. 1). The soil seed bank zero-isocline is the line

oining combinations of soil seed bank size and cover of perennialrasses where there is no change in soil seed bank size (dSp/dt = 0).

ith increasing cover of perennial grasses, the size of the soil seedank increases. The zero-isocline of the cover of perennial grasses

s the line showing combinations of soil seed bank size and cover oferennial grasses where there is no change in the cover of perennialrasses (dP/dt = 0).

When herbivory is absent (Fig. 1a), a high cover of perennialrasses and a large seed bank in the soil is present. This covernd soil seed bank size decreases with increasing herbivory. Whenhe point where the zero-isocline of the soil seed bank meets thep-axis (Fig. 1b) is at the left hand side of the point where the zero-

socline of the grass cover meets this axis, a different state occurs:

small soil seed bank in the absence of perennial grasses. Underhis herbivore density, there are two states: one with both a rela-ively large soil seed bank and a certain cover of perennial grasses,

d when plant cover is maximal (Spm) for three states: cover of perennial grass, bare values are (see Table 1): cp = 0.01, lp = 0.6, kp = 0.1, bp = 0.6, kl = 1, (a) gp = 0.8 × 10−3,00, sp0 = 0.2, spm = 2200, and (d) h = 0.5, gp = 0.8 × 10−3, lsp = 0.7, sp0 = 0.2.

and one with only a small seed bank and no perennial grasses. Thestate with both a soil seed bank and a cover of perennial grassesdisappears when herbivore density increases (Fig. 1c). This figuresuggests that there is a threshold in herbivore density below whichthere is a state with a sufficiently large soil seed bank and coverof perennial grasses, and above which there is a state with only asmall seed bank. When both perennial grasses and a soil seed bankcan be found, apparently sufficient seeds are produced to maintainthe cover of perennial grasses, whereas a low cover of perennialgrasses under high herbivore density might not be able to producesufficient seeds to maintain the grass cover. Consequently, peren-nial grasses disappear and the soil seed bank is only supplied bydispersing seeds (sp0) from external sources.

The cover of perennial grasses and the size of the soil seed bankdecreases with increasing herbivore density (Fig. 2a), with decreas-ing germination rate (Fig. 2b) and with increasing seed mortality(Fig. 2c). The solid lines give the stable equilibria for the cover andthe seed bank of perennial grasses, whereas the dashed lines referto the unstable equilibria. Perennial grass cover and soil seed banksize are related: decreasing cover of perennial grasses lowers theseed production, whereas a small soil seed bank can only support alow perennial cover. This figure shows that discontinuous changesin the cover and the soil seed bank of perennial grasses occur atdistinct levels of herbivore density, germination rate and seed mor-tality. Discontinuous changes in the cover and the soil seed bank ofperennial grasses due to changes in for example herbivory may beirreversible to a certain extent. Events such as droughts may carry

the grass cover below a break point value leading to a collapse ofthe perennial grasses and a subsequent decrease in the size of thesoil seed bank. Under certain values for herbivore density, there aretwo states: one with both a seed bank and perennial grass cover,

258 F. van Langevelde et al. / Ecological Modelling 337 (2016) 253–261

F eed bab the ug .4, lsp =

aanlsgi

smiwtcaconebtt(inaf

ig. 4. Effect of herbivory(h) on the cover of perennial grass (P), the size of the soil sank of annual grass (Sa). Solid lines give the stable equilibria, and dashed lines givep = 0.8 × 10−3, ga = 0.4 10−3, lp = 0.6, la = 0.8, ka = 0.1, kp = 0.1, sa0 = 0.4, sp0 = 0.2, lsa = 0

nd one with only a small seed bank without perennial grasses (seelso Fig. 1). These discontinuous changes imply that when peren-ial grasses collapse, a gradual decrease in herbivore density could

ead to the recovery of perennial grasses. However, herbivore den-ity should be brought back to very low levels to allow perennialrasses to invade the area again, using the seeds that already occurn the seed bank due to dispersal.

The effects of water availability in the soil (R), herbivory den-ity (h), germination rate of the seeds in the soil bank (gp), seedortality (lsp), increase in the soil seed bank due to dispers-

ng seeds (sp0), and the maximum number of seeds producedhen plant cover is maximal (spm) on the transitions between

he states are shown in Fig. 3. These diagrams show under whatonditions perennial grasses and bare soil can be found. Theylso give the parameter space where the alternate stable statesan be expected: either perennial grasses or bare soil. Becausef an increase in water availability, the regions for which peren-ial grass and alternate stable states are predicted increase at thexpense of the region without perennial grass. An increase in her-ivore density increases the parameter range where bare soil andhe alternate stable states can be found. The seed characteris-ics point in the same direction: an increase in amount of seedincreasing germination rate, decreasing seed mortality, increas-ng amount of influx of dispersing seeds, and increasing maximum

umber of seeds) leads to an increase in perennial grass covernd an increase in the region where alternate stable states can beound.

nk of perennial grass (Sp), the cover of annual grass (A), and the size of the soil seednstable equilibria. Parameter values are (see Table 1): R = 500, cp = 0.01, cam = 0.001,

0.7, sam = 30000, spm = 2200, ba = 0.4, bp = 0.6, kl = 1.

3.2. Perennial and annual grass cover and their soil seed banksizes

We can now analyse the model with the dynamics of both peren-nial and annual grass cover and their soil seed bank sizes. Thecover of perennial and annual grasses and the size of both soil seedbanks decrease with increasing herbivore density (Fig. 4). Regard-ing the cover of annual grasses, a partly similar pattern is foundas for the cover of perennial grasses, but annual grasses are absentat low herbivore density as they are outcompeted by the peren-nial grasses. Due to suppression of perennial grasses by herbivores,annual grasses can occur at higher levels of herbivore density, andthese grasses then also contribute their seeds to the soil seed bank.Also for annual grasses, a region of alternate states exists whereeither a state with annual grasses or a state with bare soil canoccur. Again there is a threshold in annual grasses below which theannual grasses disappear, and above which annual grasses occur.In between there might be a region where only annual grasses canoccur, but where perennial grasses disappear due to grazing (inFig. 4 around h = 7–8).

We can again derive a parameter plane for the model with bothperennial and annual grasses and their soil seed bank size as func-tion of herbivore density (h) and germination rate of the seeds inthe soil (gp) (Fig. 5). For the perennial grass cover, a similar pat-

tern is found in relation to herbivore density and the germinationrate of the seeds of the perennial grasses compared with the modelwithout annual grasses. Annual grasses are affected by both thepresence of perennial grasses and herbivore density. At low herbi-

F. van Langevelde et al. / Ecological M

Fig. 5. Parameter plane of herbivory density (h) and germination rate of the seeds ofthe perennial grasses in the soil bank (gp) for the different states. Parameter valuesa −3

kk

vgfgbtmahsadoansh

4

ceeaaa12u

re (see Table 1): R = 500, cp = 0.01, cam = 0.001, ga = 0.4 × 10 , lp = 0.6, la = 0.8, ka = 0.1,p = 0.1, sa0 = 0.4, sp0 = 0.2, lsa = 0.4, lsp = 0.7, sam = 30000, spm = 2200, ba = 0.4, bp = 0.6,l = 1.

ore density and high germination rate of the seeds of perennialrasses, annual grasses disappear. Also alternate states can occuror the annual grasses: when perennial grasses are present, annualrasses disappear, and when perennial grasses and their soil seedank cannot be maintained (they passed the threshold below whichhe supply of seeds in the soil seed bank is not sufficient anymore to

aintain a perennial grass cover) then annual grasses appear (seelso Fig. 4). When herbivore density increases further to maximally

= 8, especially under conditions that the germination rate of theeeds of the perennial grasses is low, perennial grasses disappearnd annual grasses can be found. With further increase of herbivoreensity (h > 8), the dynamics of the annual grasses is independentf the germination rate of the seeds of the perennial grasses (therere no perennial grasses anymore) and the second region of alter-ate stable states occur (either a state with annual grasses or atate with bare soil). Finally, annual grasses also disappear whenerbivore density further increases.

. Discussion

Knowledge of vegetation dynamics plays an important role inonservation, management and restoration of rangelands (Brisket al., 2005; Stafford Smith et al., 2007). Modelling is essential forxplaining and predicting changes in rangeland at large temporalnd spatial scales (Oomen et al., 2016). For this reason, theoreticalnd empirical models have been developed to show the existence of

lternate vegetation states in semi-arid grazing systems (Noy-Meir,975; Westoby et al., 1989; Rietkerk et al., 1996; Bestelmeyer et al.,003; Van Langevelde et al., 2003). These studies provide differentnderlying mechanisms behind alternate states and transitions in

odelling 337 (2016) 253–261 259

rangelands. For example, some studies reported that water avail-ability under the influence of grazing is the key mechanism thatdetermines transitions in plant communities in semi-arid grazingsystems (Rietkerk and Van de Koppel, 1997). The positive feed-back between plant cover and infiltration of rain into the soil isthought to trigger these transitions. Other studies argue that therelation between grass biomass and fire intensity can explain shiftsin rangelands from tree-dominated to grass-dominated systems(Van Langevelde et al., 2003). Grass biomass under the influenceof herbivory determines fuel load for ground fires that can damagewoody vegetation depending on the intensity of the fire.

In this paper, we consider the impact of grazing on above andbelowground (soil seed bank) vegetation dynamics, and we showthat the availability of seeds in the soil seed bank as function ofplant cover can trigger transitions between three vegetation states:from perennial to annual grasses and from annual grasses to baresoil with increasing grazing pressure. Actually, increased losses dueto low amounts of rainfall in our model give the same results aslosses due to herbivory (results not shown). When grazing pres-sure is absent or low, a high cover of perennial grasses and a largesoil seed bank is present, whereas with increasing herbivore den-sity, the perennial grass cover and the size of the soil seed bank ofperennial grasses decline. This leads to a situation in which the sizeof the soil seed bank can become a limiting factor for the existenceof perennial grasses in semi-arid grazing systems (O’Connor, 1994;Sternberg et al., 2003).The negative effects of grazing on the soilseed bank were also found in other studies (Kinloch and Friedel,2005; Solomon et al., 2006).

In our model study, we found that the positive feedback betweenplant cover and the size of the soil seed bank depends on seed traitslike seed germination rate and longevity (Pons, 1991; Tessema et al.,2012). It has indeed been observed that rapid seed germinationand low seed longevity in perennial grasses allow the transition ofherbaceous vegetation from perennial grasses to annuals (Baskinand Baskin, 2004; Tessema, 2011). There is evidence that seeds ofperennial grasses do not remain viable in the soil for many years(Mott, 1978; McIvor and Howden, 2000), whereas seeds of annualsare persistent in the soil and have long longevity (O’Connor andPickett, 1992). Our model study suggests that the system can berestored if grass cover or the size of the soil seed bank reachesa critical threshold. This means that grasses may re-colonize thearea through seeds imported by wind, water or animals, but therecovery process may take decades (Rietkerk et al., 1996). Onceperennial grasses establish, their rapid growth at the onset of thefirst rain gives them an advantage over annual species in semi-aridgrazing systems (Veenendaal et al., 1996b) and can dominate theherbaceous vegetation under low grazing pressure.

Previous studies reported the existence of alternative states andtransitions in semi-arid grazing systems, with the loss rate due toherbivores or low rainfall as the main driving forces behind thesetransitions from vegetated to non-vegetated states (Westoby et al.,1989; Rietkerk et al., 1996). The main explanation for these suddenchanges in semi-arid grazing systems so far is the positive feedbackbetween plant cover and infiltration of rain into the soil (Rietkerket al., 1996, 2002; Rietkerk and Van de Koppel, 1997). This mecha-nism for sudden changes in the vegetation has been put forward asthe explanation for desertification. The positive feedback betweenplant cover and size of the seed bank is an alternative explanationfor sudden vegetation changes in rangelands, other than the pos-itive relationship between plant cover and infiltration of rain intothe soil. In contrast to the latter positive feedback, our model canalso explain changes in vegetation from perennials to annuals and

vice versa. We kept our model as simple as possible to analyse thepositive feedback between plant cover and size of the seed bank,and we therefore omitted other processes that can occur in reality,such as the increase of perennial grasses with a decrease in rainfall.

2 gical M

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ield studies should test the predictions of the model to validateur assumptions.

Another limitation of the model is that it lacks the spatial dimen-ion, for example patches of bare soil can differ in size. It is likelyhat the soil seed bank in the absence of plants is determined byhe size of the bare soil patches: the centre of large patches of bareoil may contain relatively less seeds per unit area, as the influx ofispersing seeds may decrease with distance from the boundary.

ndeed, restoration of large patches of degraded rangeland takesore time than small patches (Tessema, 2011). We acknowledge

hat including space would give more accurate predictions. How-ver, the pattern of recovery and degradation would not change byncluding the spatial dimension.

. Conclusions

In this paper, we show that our model can explain alternateerbaceous vegetation states and transitions in semi-arid range-

ands as result of soil seeds bank dynamics under the influencef grazing. Our model provides an alternative for the infiltrationechanism to explain these shifts. It needs to be tested underhich conditions the different mechanisms are valid. For exam-

le, the model with the plant cover − infiltration feedback predictshat the risk for herbaceous vegetation shifts is higher on clayeyoils as described in Rietkerk and Van de Koppel (1997), whereasur model does not include any effect of soil type on these shifts.ence, the differences in vegetation shifts on different soil types canelp us to better understand whether infiltration feedbacks or soileed bank dynamics are important. For example, the predictionsf our model are supported by the occurrence of herbaceous veg-tation shifts on sandy soils where also annual grasses are presents described in Tessema et al., (2011, 2012) and Tessema (2011).

ith these predictions, our model contributes to understanding ofhe vegetation dynamics of semi-arid rangelands, and has impor-ant implications for proper management and restoration of theseegraded ecosystems.

cknowledgments

We would like to thank Nuffic, The Netherlands for the financialupport of this research and the Haramaya University of Ethiopiaor providing transport and greenhouse facilities during the imple-

entation of the field research.

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