Introduction

Climate change studies predict an increase in precipitation variability at intra-annual, interannual, and decadal time scales (Easterling and others 2000; Fischer and others 2013; IPCC 2013). Such changes could result from a variety of mechanisms, including an increase of water-holding capacity in a warmer atmosphere (Kharin and others 2007; Liu and others 2013) and changes in atmospheric circulation (for example, intensification of El Niño Southern Oscillation) (Easterling and others 2000; Levis and others 2011). Increasing evidence indicates that precipitation variability is an important driver of ecological processes, including plant growth, interspecies interactions and community composition, primary productivity, and carbon and water fluxes (Knapp and others 2008; Reichstein and others 2013; Holmgren and others 2013; Zeppel and others 2014).

Previous studies have investigated the effects of intra-annual rainfall variability on plant and ecosystem processes (D’Odorico and others 2003; Knapp and others 2008; Kulmatiski and Beard 2013a; Zeppel and others 2014). Studies on the effect of interannual rainfall variability on soil moisture dynamics and plant water stress have also attracted some attention (Ridolfi and others 2000; D’Odorico and others 2000), but the impacts of interannual rainfall fluctuations on species composition and ecosystem productivity remain less investigated. Indeed, research in this field is strongly limited by the availability of long-term field observational data and technical capability to measure all relevant variables (Fatichi and Ivanov 2014). Long-term field campaigns have seldom addressed the impacts of interannual rainfall variability on ecosystem dynamics (Munson and others 2012; Collins and Xia 2015; but see Knapp and others 2002). Indeed, in field experiments with no rainfall manipulations, changes in rainfall variability may often be associated with changes in mean rainfall, thus making it difficult to differentiate the effects of changes in rainfall variability from those of changes in mean rainfall (Hsu and others 2012; Reyer and others 2013). To overcome these limitations, process-based models—possibly integrated with field or satellite data—could offer alternative approaches to gain a mechanistic understanding of the ecological impacts of trends in rainfall variability (Reyer and others 2013; Fatichi and Ivanov 2014).

Some studies have shown that interannual rainfall variability could affect the interannual fluctuations of vegetation productivity (Knapp and others 2002; Fatichi and Ivanov 2014; Hsu and Adler 2014). It has been argued that a nonlinear (“concave down”) relationship between mean annual precipitation and net primary productivity (ANPP) (also known as Jensen’s inequality) could lead to a negative response of mean ANPP in grasslands to increasing interannual rainfall variability (Hsu and others 2012). Using satellite data, Holmgren and others (2013) have reported a consistent positive response of tree cover to increasing rainfall variability in the dry tropics, but mixed responses of tree cover to interannual rainfall variability in the wet tropics (that is, neutral in Africa, positive in South America, or negative in Australia). Expanding an earlier spatially explicit savanna model, some studies have reported either a positive or an insignificant response of shrub cover (that is, G. flava) to increasing interannual rainfall fluctuations in southern Kalahari savannas (mean annual rainfall, 200 mm < MAP < 700 mm), a response that could depend also on seed availability (Tews and others 2004, 2006). Liedloff and Cook (2007) used a model of tree population dynamics to show a negative response of tree cover to increasing interannual rainfall variability in North Australian savannas (MAP ≈ 1000 mm). These studies shed light on the response of tree or grass alone to increasing interannual rainfall variability, whereas the effect on species composition remains poorly understood.

How a functional group (that is, trees) responds to an increase in interannual rainfall variability depends on the trade-off between wet and dry years (Holmgren and others 2013) as well as on its competitive relationship with other functional groups (grasses) and associated disturbance regime (that is, fires) (Williams and Albertson 2006; Reyer and others 2013; Zeppel and others 2014). A dynamic soil moisture model has been used to show the effect of grass dynamics on tree response to increasing interannual rainfall variability (Scanlon and Albertson 2003). Fernandez-Illescas and Rodriguez-Iturbe (2003) developed a hierarchical competition–colonization model in which dynamic water stress affects the tree–grass competition–colonization relationship; these authors used this model to investigate the impact of interannual rainfall fluctuations on tree–grass associations. Both of these models, however, ignored the roles of fires. Indeed, grasses typically have relatively high growth rates especially in wet environments (Teuling and others 2010; Collins and others 2012; Xu and others 2015) and thus may more quickly take up soil water or other resources, thereby more effectively competing with trees in wet years. The competitive advantage of grasses in wet years could enhance fire occurrences, thereby increasing tree mortality (Bond 2008; Ratajczak and others 2014); as a result, the increase in interannual rainfall variability is expected to favor grasses at the expenses of trees.

To our knowledge, only few studies have modeled the impact of interannual rainfall fluctuations in savannas accounting for both water competition and fires (Williams and Albertson 2006). Key to the understanding of vegetation response to changes in rainfall variability in water-limited ecosystems is an adequate representation of the soil water balance (Porporato and others 2002). In fact, the increase in rainfall intensity (with the total rainfall amount remaining constant) has been found to lead to shrub encroachment because of increased drainage into the deeper soil layer where trees with deeper roots can have exclusive access to soil water (Kulmatiski and Beard 2013a). Recent studies suggest that the increase in interannual rainfall variability may also increase soil water availability in the deep soil, thereby favoring deep-rooted over shallow-rooted species (Sala and others 2015; Gherardi and Sala 2015a, b). It remains unclear how the trait-based trade-off (that is, higher growth rate but shallower roots in grasses than trees) affects the response of tree–grass associations to increasing interannual rainfall variability along a rainfall gradient.

This study uses satellite data and develops a new mechanistic model to investigate the response of tree–grass associations to increasing interannual rainfall variability. We apply this model to the Kalahari Transect in Southern Africa, a region that exhibits relatively homogenous soils (sand) along a rainfall gradient, and therefore provides a good setting to investigate changes in plant community composition associated with different rainfall regimes without confounding effects associated with soil heterogeneity (Koch and others 1995; Wang and others 2007). This model couples a soil water balance with vegetation dynamics and accounts for fire-induced disturbance and competition between trees and grasses in access to soil water. We particularly investigate the following: (1) how trees or grasses alone and tree–grass associations respond to increasing interannual rainfall variability along the rainfall gradient; (2) the mechanisms underlying the response of these plant functional groups to increasing interannual rainfall fluctuations.

Methods

We develop a model to investigate the response of trees or grasses alone and tree–grass associations to increasing interannual rainfall variability along a rainfall gradient. For simplicity, the term “tree” is used here to include all forms of woody plants (that is, trees and shrubs). The model simulates soil moisture dynamics in two soil layers and accounts for flows between them due to drainage. The model simulates the biomass dynamics of trees and grasses as a logistic growth coupled with the soil water balance and accounts for biomass loss from senescence, litter fall, and disturbance (fires). Trees are assumed to have roots in both layers, while grasses are assumed to have roots only in the shallow soil layer (van Wijk and Rodriguez-Iturbe 2002; Van Langevelde and others 2003; Kulmatiski and Beard 2013b; Yu and D’Odorico 2015a, b). Thus, trees and grasses are assumed to compete for soil water resources in the shallow soil layer, whereas trees can exclusively access the soil water resources in the deep soil layer. Although in some savannas grasses could have roots as deep as trees (Sankaran and others 2004; Beckage and others 2009), here we consider the case in which tree roots span a much deeper soil column than grasses (Walter 1971; Kulmatiski and Beard 2013a, b; Holdo and Nippert 2015). An increase in interannual rainfall variability changes the soil moisture profile in the root zone and thus is expected to affect the interactions between trees and grasses. Rainfall and soil moisture dynamics are represented as stochastic processes, as explained below (Rodriguez-Iturbe and others 1999); interannual rainfall fluctuations are accounted for by a two-parameter gamma distribution (D’Odorico and others 2000; Porporato and others 2006). Deterministic laws are used to express the interactions and dynamics of trees and grasses, without accounting for the randomness of demographic growth in trees (Higgins and others 2000; Gardner 2006), and the stochastic nature of fire (D’Odorico and others 2006). The model does not explicitly represent the spatial interactions among trees and grasses (Jeltsch and others 1996; van Wijk and Rodriguez-Iturbe 2002) and thus uses a lumped approach to simulate dynamics of trees and grasses.

Water Balance

Soil moisture dynamics in the two soil layers are modeled at the landscape scale by two coupled equations:

$$ nZ_{1} \frac{{{\text{d}}S_{1} }}{{{\text{d}}t}} = P - {\text{ET}}_{1} - D_{1} , $$
(1)

and

$$ nZ_{2} \frac{{{\text{d}}S_{2} }}{{{\text{d}}t}} = D_{1} - T_{2} - D_{2} , $$
(2)

where the subscripts 1 and 2 refer to the shallow and deep soil layer, respectively; n is the soil porosity, Z 1 and Z 2 the soil layer thickness (mm), S 1 and S 2 the relative soil moisture (0 < S 1, S 2 ≤ 1), P the rate of rainfall infiltration into the top soil layer (mm d−1), ET1 and T 2 the soil moisture losses from each soil layer due to evapotranspiration (mm d−1), and D 1 and D 2 are the drainage rates (mm d−1). Runoff occurs when the surface layer is saturated (that is, S 1 = 1). Calculations of ET1, T 2, D 1, and D 2 are presented in Online Appendix. The soil water balance is interpreted at the daily time scale because no diurnal fluctuations in ET are accounted for; the equations, however, are solved numerically using a smaller (hourly) time step because rainfall and soil water resources are pulsed in time.

Landscape Dynamics of Trees and Grasses

The dynamics of grass biomass (V g, kg m−2) and tree biomass (W l, kg m−2) at the landscape scale are expressed as a logistic growth:

$$ \frac{{{\text{d}}V_{\text{g}} }}{{{\text{d}}t}} = g_{\text{g}} V_{\text{g}} \left( {V_{1} - V_{\text{g}} - \gamma W_{\text{l}} } \right) - m_{\text{G}} V_{\text{g}} , $$
(3)
$$ \frac{{{\text{d}}W_{\text{l}} }}{{{\text{d}}t}} = g_{\text{w}} W_{\text{l}} \left[ {\left( {V_{1} - V_{\text{g}} - \gamma W_{\text{l}} } \right) + V_{2} - \left( {1 - \gamma } \right)W_{\text{l}} } \right] - m_{\text{W}} W_{\text{l}} - k\eta W_{\text{l}} , $$
(4)

where the \( m_{\text{G}} V_{\text{g}} \) and m W W l mortality terms account for biomass loss from senescence and litter fall by grasses and trees, respectively; kηW l is a mortality term accounting for fire, and g g and g w are the growth coefficients for grasses and trees, respectively; V 1 and V 2 are the vegetation carrying capacities contributed by soil moisture in the shallow and deep soil layer (kg m−2), and γ is the fraction of woody plant biomass relying on the shallow soil layer. Thus, γ is a term expressing the belowground competition of trees on grasses for soil water in the shallow soil layer. Observations in several savanna ecosystems indicate that grasses rapidly recover after fires (Russell-Smith and others 2001); therefore, no fire-induced mortality is included in the grass dynamics equation. Plant biomass loss from senescence and litter fall is modeled as a process that removes a proportion of biomass every year at the end of the growing season (Yu and D’Odorico 2015a). In agreement with other studies (Walker and Noy-Meir 1982; van Langevelde and others 2003), fires are modeled as a process that continuously removes the biomass of woody plants; the fire frequency (η) depends on grass biomass (van Wilgen and others 2000) (Table 1). Satellite data report the values of tree cover (%); for data-model inter-comparisons, tree biomass simulated in this study is converted to tree cover (F c) following the framework by Caylor and others (2006) and Yu and D’Odorico (2015a). This approach represents the landscape as a mosaic of “canopy” and “between canopy” areas resulting from a two-dimensional Poisson distribution of individual woody plants (with circular footprint). In this case, F c is a function of the number of woody plant individuals per unit area (i w, individuals, m−2) and the average canopy radius of an individual woody plant (u c, m), expressed as

$$ F_{\text{c}} = 1 - \exp^{{ - \pi i_{\text{w}} u_{\text{c}}^{2} }} . $$
(5)

The biomass of woody plants at the landscape scale (kg m−2) can be expressed as

$$ W_{\text{l}} = W_{\text{p}} \times i_{\text{w}} , $$
(6)

where W p is the biomass of an individual woody plant canopy (kg per individual). Rearranging Eqs. (5) and (6), we obtain

$$ F_{\text{c}} = 1 - 1/\exp \, (\pi W_{\text{l}} u_{\text{c}}^{2} /W_{\text{p}} ). $$
(7)

Details for calculating F c are provided in Caylor and others (2006) and Yu and D’Odorico (2015a). Table 1 presents symbols, descriptions, and values of all the variables used in this study. The dynamics of grass and tree biomass are solved on a daily time scale.

Table 1 Variables, Parameters, and Reference Sources Used in the Study
Full size table

Different from the study by Williams and Albertson (2006), V 1 and V 2 are here expressed as a function of soil moisture and soil layer thickness (Yu and D’Odorico 2015a):

$$ V_{1} = C_{0} Z_{1} S_{1} , $$
(8)
$$ V_{2} = C_{0} Z_{2} S_{2} , $$
(9)

where C 0 (kg m−2 mm−1) is a coefficient converting the soil water resources into vegetation carrying capacity. In contrast to other studies which related vegetation carrying capacity to annual rainfall (for example, Williams and Albertson 2006), this approach relates carrying capacity to soil moisture availability, which depends on soil texture, rainfall variability, rainfall gradient, and interspecies interactions (Knapp and others 2008; Reyer and others 2013; Zeppel and others 2014); thus, this framework allows us to explicitly investigate the impacts of increasing interannual rainfall variability with a detailed process-based approach. Growth rate is an important parameter in affecting tree–grass dynamics under interannual rainfall fluctuations. Previous studies imposed a constant growth rate in trees and grasses (Walker and Noy-Meir 1982; Anderies and others 2002) or expressed the growth rate as a function of annual rainfall (Williams and Albertson 2006). However, rainfall and soil water resources are pulsed in time, particularly in arid environments (Schwinning and Sala 2004; Knapp and others 2008; Collins and others 2014); thus, an appropriate temporal resolution needs to be used to capture pulsed rainfall fluctuations (Reyer and others 2013). Here we express g g and g w as a function of the fraction of time during the growing season in which grasses and trees are not water stressed (that is, with soil moisture exceeding the vegetation-specific value of soil moisture above which plants experience unstressed transpiration and photosynthesis):

$$ g_{\text{g}} = t_{\text{g}} /Tg_{{{\text{gmax}} }} , $$
(10)
$$ g_{\text{w}} = t_{\text{w}} /Tg_{\text{wmax}} , $$
(11)

where t g and t w are the number of hours grasses and trees do not experience water stress, respectively; T is the duration of the growing season (in h), and g gmax and g wmax are the maximum growth rates of grasses and trees when they remain unstressed during the whole growing season. Soil moisture (and the occurrence of water stress) evolves as a function of the accumulated biomass and therefore cannot be determined a priori before having simulated vegetation dynamics during the growing season. Thus, in this model t g/T and t w/T refer to the previous growing season. This approach allows us to capture the widely documented legacy effect of trees and grasses in the response to rainfall fluctuations (Sherry and others 2008; Sala and others 2012; Anderegg and others 2015). We note that growth rate was not determined by instantaneous soil moisture. In fact, the ability of plants to photosynthesize and grow (that is, the growth rate) also depends on traits such as specific leaf area and leaf phenology (Tomlinson and others 2013); plants with a low specific leaf area and/or senescent leaves could have a low photosynthetic rate and thus have a low growth rate even when soil moisture is high as a result of a rainfall pulse. Investment in these key traits for plant photosynthesis has energetic cost (DeWitt and others 1998; Kishida and Nishimura 2006). The energetic costs associated with developing these traits require carbon capture (and therefore soil moisture availability) over longer time scales (that is, one growing season).

Numerical Simulations

Three sets of numerical simulations were conducted, each addressing a specific objective. The first set of numerical simulations is to investigate the response of trees alone to increasing interannual rainfall variability along a rainfall gradient. For this purpose, Eqs. (1), (2), (4), (7), (8), (9), and (11) were used; grass biomass (G l) and the fire frequency (η) in Eq. (4) are taken to be zero because in this case there is no grass and thus no fire occurrence. The second set of numerical simulations is to investigate the response of grass alone to increase in interannual rainfall variability along a rainfall gradient. To this end, Eqs. (1), (3), (8), and (10) were used; tree biomass (W l) in Eq. (3) is taken to be zero since there are no trees in this case. For the response of tree–grass associations in the third set of numerical simulations, Eqs. (1)–(11) were used.

Precipitation (R) is modeled as a sequence of intermittent rainfall events using a marked Poisson process of storm occurrences with average rainfall frequency, λ (events per day). Each storm is modeled as an exponentially distributed random depth with mean, h (mm per event) (Rodriguez-Iturbe and others 1999). This stochastic rainfall model fits observed daily rainfall data during growing seasons quite well, but underestimates the interannual rainfall variability when applied to all years combined (Porporato and others 2006). To account for interannual rainfall fluctuations, we follow the approach by D’Odorico and others (2000) and Porporato and others (2006), in which interannual fluctuations in the average rainfall frequency (λ) and the average rainfall depth (h) can be assumed to be independent; interannual rainfall fluctuations can be represented by a two-parameter gamma distribution. Because the model is parameterized along the Kalahari Transect in Southern Africa where h is relatively uniform (Porporato and others 2003; Caylor and others 2005; Bhattachan and others 2012) (see section “Study site: the Kalahari Transect in Southern Africa” for details), the two-parameter gamma distribution is used to determine the interannual fluctuations only in λ, while h is kept constant. In this case, we have a two-parameter gamma distribution (\( g_{\lambda } \left( \lambda \right) \)):

$$ g_{\lambda } \left( \lambda \right) = b_{\lambda }^{{a_{\lambda } }} \lambda^{{a_{\lambda } - 1}} {\text{e}}^{{ - b_{\lambda } \lambda }} / \Gamma \left( {a_{\lambda } } \right), $$
(12)

where b λ is the scale parameter, and a λ is the shape parameter of this distribution; both parameters can be expressed as a function of the mean and standard deviation of λ. This approach reasonably represents the interannual rainfall fluctuations along Kalahari Transect in Southern Africa and elsewhere (D’Odorico and others 2000; Porporato and others 2006). Soil moisture in the shallow (S 1) and deep (S 2) soil layers is then quantified using Eqs. (1)–(2), which drives the dynamics of grasses and trees according to Eqs. (3)–(4). Each of the three sets of numerical simulations was run for 200 years and was repeated 100 times. Then the response of tree or grass alone and tree–grass associations to interannual rainfall fluctuations is averaged over simulation years and averaged across ensemble simulations.

Study Site: The Kalahari Transect in Southern Africa

The Kalahari Transect in Southern Africa is one of the International Geosphere-Biosphere Programme (IGBP) transects. It spans a north–south mean annual rainfall gradient from Angola and Zambia, through Botswana, into South Africa. Various studies based on field campaigns and model simulations have investigated various aspects of the ecology, ecohydrology, and biogeochemistry of savanna ecosystems along this transect (Porporato and others 2003; Caylor and others 2005; Bhattachan and others 2012). It remains unclear, however, how an increase in interannual rainfall variability would affect plant community composition in this region.

The duration of the rainy/growing season varies along the transect but it lasts roughly 210 days from October to May and accounts for about 95% of mean annual rainfall (MAP) (Bhattachan and others 2012). Across the Kalahari rainfall gradient, the average rainfall frequency (λ) typically spans from 0.1 to 0.5 d−1, whereas mean rainfall depth (h) is relatively uniform, h = 10 mm per event (Porporato and others 2003; Caylor and others 2005; Bhattachan and others 2012). Thus, numerical experiments in this study are mainly parameterized with two rainfall regimes corresponding to dry (λ = 0.2 d−1 and h = 10 mm per event) and wet (λ = 0.4 d−1 and h = 10 mm per event) environments. As noted above, the two-parameter gamma distribution [Eq. (12)] is used to account for interannual fluctuations in λ. Note that the average total precipitation over the growing season remains constant with changes in interannual fluctuations in λ and thus allows us to differentiate the effects of interannual rainfall fluctuations from those of changes in mean precipitation.

Because experimental measurement of the growth coefficients, g gmax and g wmax, are not available, their values are estimated, relying on other studies (Anderies and others 2002; Williams and Albertson 2006) and verifying that model simulations are in good agreement—in terms of vegetation composition (that is, relative/absolute magnitude of tree and grass biomass)—with experimental observations (Sankaran and others 2005; Bhattachan and others 2012) and satellite data (see below for details). Values of other parameters are from previous studies and are summarized in Table 1. The sensitivity of this model is investigated with respect to changes in g gmax, g wmax, and plant sensitivity to fire (Online Appendix). To investigate the generality of these results, the response of tree–grass composition to increased interannual rainfall variability is also investigated in less sandy soil (sandy loam).

Satellite Data

Daily Tropical Rainfall Measuring Mission (TRMM) rainfall data (3B42_daily product) were used to characterize interannual variability in rainfall over the period 1998-2014 (Huffman and others 2007). These data provide daily estimates of rainfall rates at 0.25° × 0.25° resolution. To avoid potential issues with tallying rainfall over the calendar year, we defined annual rainfall as cumulative rainfall from August 1 to July 31 each year, corresponding to the dry season over the study area. For each pixel, we calculated mean annual precipitation (MAP) and the standard deviation of annual precipitation (σAP) as the average and standard deviation of yearly rainfall, respectively.

Woody plant cover was characterized using the tree cover product Moderate Resolution Imaging Spectroradiometer (MODIS) MOD44 collection 5 version 1 vegetation continuous field product (Hansen and others 2003). The MODIS tree cover algorithm estimating tree cover with regression trees is available globally at 250 m resolution on a yearly basis. We resampled tree cover to the native 0.25° × 0.25° native TRMM resolution by averaging the value of MODIS pixels whose centroid was within each larger TRMM pixel, omitting missing data and pixels over water bodies. We then averaged tree cover across all available years of data (2000–2013).

Grasses favor fires and therefore the presence of grass cover increases the average proportion of burned areas (Bond 2008; Ratajczak and others 2014). Therefore, we use the burned area as a proxy for grass biomass and investigate grass (that is, burned area) response to changes in interannual rainfall variability. The MODIS MOD45A1 collection 5 version 1 burned area product was acquired for all months (Roy and others 2008). This product estimates whether each 250 m pixel has burned in a given month and estimates the day that the burn occurred if a fire was sensed. We resampled burned area to the 0.25° × 0.25° by calculating the percentage of MODIS pixels within each TRMM pixel that had burned in a given year. We then averaged the annual percent burned across 14 full years of available data starting in April 2000 to achieve a long-term of proportion burned in each pixel.

Results

Impacts of Interannual Rainfall Variability on Tree–Grass Associations: Satellite Data

Satellite data show a positive response of tree cover to increasing interannual rainfall variability in dry environments (that is, mean annual precipitation, MAP < 900–1000 mm) but a negative response of tree cover in wet environments (MAP > 900–1000 mm) (Figure 1A). The average proportion of burned areas (that is, grass biomass) increases with increasing interannual rainfall variability in wet environments (that is, MAP > 1000–1100 mm), in contrast to what happens in dry environments (that is, MAP < 1000–1100 mm) (Figure 1B).

Figure 1
figure 1

(A, B) MODIS-derived tree cover (A) and annual percentage burned (B) as a function of the standard deviation of annual precipitation (σ AP, mm) and mean annual rainfall (MAP, mm). MAP is binned into 150-mm bins and simple linear regression is used to highlight σ AP-related trends within these bins.

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Modeling Impacts of Interannual Rainfall Variability on Tree or Grass Alone

The modeling results show that tree cover/biomass alone has a positive response, but grass biomass alone has a negative response to increasing interannual rainfall variability in dry environments (that is, λ  = 0.2 event d−1, h = 10 mm per event) (Figure 2A); this pattern is explained by the increase in drainage (D 1) beneath the root zone of grasses on wet years (Figure 3A). D 1 increases and thus soil evaporation decreases, while drainage (D 2) beneath the root zone of trees remains negligible (Figure 3B), thereby leading to a positive response of trees. Conversely, in wet environments (that is, λ  = 0.4 event d−1, h = 10 mm per event), both grass and tree biomass alone have a negative response to the increase in interannual rainfall variability (Figure 2B) because of the increase in drainage beneath the root zones of both grasses (D 1) and trees (D 2) (Figure 3A, B). Changes in runoff are negligible because of the coarse texture of Kalahari sands.

Figure 2
figure 2

The modeled average grass biomass (V g) and tree cover (F c) alone or in associations for the case of sandy soil as affected by interannual rainfall variability (standard deviation of λ, δ) in dry (A λ  = 0.2 event d−1, h = 10 mm per event) and wet (B   λ = 0.4 event d−1, h = 10 mm per event) environments.

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Figure 3
figure 3

A Drainage (D1) from the shallow soil layer to the deep soil layer for the case of grass alone as affected by soil texture (sand and sandy loam) and interannual rainfall variability (standard deviation of λ, δ) in dry (λ = 0.2 event d−1, h = 10 mm per event) and wet environments (λ = 0.4 event d−1, h = 10 mm per event). (B) D1 and drainage (D2) from the deep soil layer (that is, from beneath the root zone of trees) for the case of trees alone in sandy soil as affected by interannual rainfall variability (standard deviation of λ,) in dry and wet environments.

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Modeling Impacts of Interannual Rainfall Variability on Tree–Grass Associations

The modeling results show that in dry environments (that is,   λ = 0.2 event d−1, h = 10 mm per event) tree–grass associations exhibit a substantial increase in tree biomass and cover, and a decrease in grass biomass with increasing interannual rainfall variability (Figure 2A), in agreement with our results based on satellite data (Figure 1). Grasses in tree–grass associations substantially decrease with increasing interannual rainfall variability because of increased competition from trees (Eq. 3; Figure S1). In wet environments (that is,   λ = 0.4 event d−1, h = 10 mm per event), grass biomass in tree–grass associations increases, while tree cover in tree–grass associations decreases (Figure 2B), in agreement with satellite data (Figure 1B). This pattern of grass in tree–grass associations, which is opposite to the results obtained in the case of grasses alone (Figure 2B), could be explained by the high growth rate of grasses (Figure S2) and their ability to take advantage of increased pulses in shallow soil moisture with increasing interannual rainfall variability (Eq. 3; Figure S3). The increase in grass biomass enhances the fire regime, thereby increasing fire-induced tree mortality (Eq. 4) and thus reducing competition from trees (Eq. 3). Sensitivity tests indicate that the increase in grass growth rate and/or fire-induced tree mortality increase the competitive advantage of grasses (Figures S4, S5). Overall, the increase in interannual rainfall variability increases the total biomass in tree–grass associations in dry environments, whereas it decreases the total biomass in wet environments (Figure S6).

Generality and Synthesis of These Results

Model simulations show that the results shown above for tree–grass associations in sandy soil along the Kalahari Transect in Southern Africa are consistent with those obtained in the case of sandy loam. In fact, tree cover (grass biomass) in tree–grass associations increases (decreases) with increase in interannual rainfall fluctuations in dry environments (Figure 4A), whereas the opposite pattern is found in the case of wet environments (Figure 4B). Moreover, with a lower soil hydraulic conductivity and thus a lower drainage (D 2) beneath the root zone of trees (Figure 3A), the results obtained for sandy loam exhibit a higher rate of increase in tree cover and decrease in grass biomass with increasing interannual rainfall fluctuations in dry environments (Figure 4A). With an increased proportion of wet years, increase in interannual variation in precipitation provides windows of opportunity in soil moisture enrichment in the shallow and deep soil in wet years (Figure 5A); the response of tree–grass composition to increased interannual variation in precipitation would depend on their key traits in taking advantage of these windows of opportunity. Grasses typically have shallow roots that cannot take advantage of the water stored in the deep soil; however, grasses with a high growth rate could greatly benefit from soil moisture enhancement in the shallow soil, increase their biomass, and consequently generate fires and kill trees; trees typically have deep roots and can take advantage of deep soil moisture, while they typically have a low growth rate and thus are less competitive than grasses in getting access to shallow soil moisture. Thus, as synthesized in Figure 5B, the response of vegetation composition in savannas to an increase in interannual rainfall variability depends on the relative magnitude of the growth rates and root depths of grasses and trees. A higher ratio of grass to tree growth rate and a lower ratio of tree to grass root depth favors grasses in the response to increasing interannual rainfall variability, while the opposite pattern of growth rates and root depths favors trees.

Figure 4
figure 4

The modeled average grass biomass (V g) and tree cover (F c) alone or in associations for the case of sandy loam as affected by interannual rainfall variability (standard deviation of λ) in dry (A   λ = 0.2 event d−1, h = 10 mm per event) and wet (B  λ = 0.4 event d−1, h = 10 mm per event) environments.

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Figure 5
figure 5

A A conceptual diagram showing that increased interannual rainfall fluctuations provide windows of opportunity in resource enrichment in the shallow and deep soil in wet years. The solid black line represents the case of normal rainfall, whereas the dash black line represents the case of increased interannual rainfall fluctuations. The red line represents the threshold of windows of opportunity in resource enrichment below which the growth rate of grasses is low and fires are rare and thus grasses would be outcompeted by trees. B A conceptual framework of the contingent responses of tree–grass composition to alterations in soil water dynamics resulting from increased interannual rainfall variability (Color figure online).

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Discussion

Climate change studies predict an increase both in intra-annual and interannual rainfall variability (Easterling and others 2000; Fischer and others 2013; IPCC 2013). Although previous studies have investigated the ecological impacts of changes in intra-annual rainfall variability (Knapp and others 2008; Kulmatiski and Beard 2013a; Zeppel and others 2014), the effects of interannual rainfall variability on vegetation composition and ecosystem processes is not well understood, mostly because of limitations in long-term observational data (Fatichi and Ivanov 2014). This study uses satellite data and develops a new mechanistic model to investigate the response of tree/grass composition to increasing interannual rainfall variability along the Kalahari Transect in Southern Africa.

Satellite data show that increasing interannual rainfall variability favors trees over grasses in dry environments (that is, mean annual precipitation, MAP < 900–1000 mm) and disfavors trees over grasses in wet environments (that is, MAP > 900–1000 mm) (Figures 1B, 2B). In contrast to this study, Holmgren and others (2013) used the satellite data to show a neutral response of tree cover to increasing rainfall variability in wet tropics in Africa, possibly because of soil texture effects and disturbance (that is, grazing). Most of the other studies on this subject have used models as diagnostic tools to gain mechanistic understanding of ecosystem dynamics in response to increasing interannual rainfall fluctuations (Fernandez-Illescas and Rodriguez-Iturbe 2003; Tews and others 2004, 2006; Williams and Albertson 2006; Liedloff and Cook 2007). This study develops a new mechanistic model to clarify the role of tree–grass competition for soil water resources and fire-induced disturbance as determinants of savanna response to changes in interannual rainfall variability.

Previous studies have stressed the role of competition in the response of vegetation composition to increasing interannual rainfall variability (Scanlon and Albertson 2003; Fernandez-Illescas and Rodriguez-Iturbe 2003), whereas the effect of fires has been ignored (but see Williams and Albertson 2006). This new mechanistic model shows that in dry environments an increase in interannual rainfall variability leads to a reduction in grass competition and fire or an increase in competition from trees (Figure S3) that cause a higher rate of reduction in grass biomass and a higher rate of increase in tree cover than in the case of tree or grass alone (Figure 2A). The competitive advantage of trees results from deeper root systems than grasses, which allow trees to have exclusive access to increased deep soil water (on wet years) with increasing interannual rainfall variability. Extensive field studies in Africa have found deeper root systems in trees than grasses (Kulmatiski and Beard 2013a, b; Holdo and Nippert 2015), although in some savannas grasses could have roots as deep as trees (Sankaran and others 2004; Beckage and others 2009). Consistent with this study, Gherardi and Sala (2015a, b) show that in a 6-year field experiment an increase in interannual rainfall variability shifts species composition in favor of deep-rooted (that is, trees) over shallow-rooted (that is, grasses) species.

Interestingly, our study shows that increases in interannual rainfall variability in wet environments shift species composition favoring grasses over trees (Figures 1, 2). This is a novel finding because other studies in grasslands (Hsu and others 2012) have shown that grasses alone have a negative response to increasing interannual rainfall variability in wet environments (Figure 2). Grasses typically have a high growth rate especially in wet environments (Teuling and others 2010; Collins and others 2012; Xu and others 2015), consistent with the concept of the world-wide ‘fast–slow’ plant economics spectrum (Reich 2014); thus, grasses could quickly take advantage of the window of opportunity existing in years with above average precipitation. The high growth rate in grasses increases fire frequency and fire-induced tree mortality (Bond 2008; Ratajczak and others 2014), thereby leading to a reduction in tree competition with grasses for soil water, which further favors grass biomass. These results are in agreement with a general theory of invisibility in plant communities under fluctuating resources (Davis and others 2000). Based on field studies (Davis and Pelsor 2001; Corbin and D’Antonio 2004), this theory holds that fluctuations in resource availability provide windows of opportunity in resource enrichment, whereby species with a high growth rate could quickly take up resources, change the disturbance regime, and then invade or dominate the landscape. Consistent with these studies, our study shows that the way tree–grass composition responds to increased interannual variation in precipitation would depend on key traits of trees and grasses (that is, growth rate and root depth) that determine their ability to take advantage of the windows of opportunity offered by periods with higher soil moisture.

The encroachment of woody plants into grasslands has been widely documented in arid and semiarid environments in many regions of the world including southern Africa (Moleele and others 2002). The mechanisms typically invoked to explain this phenomenon involve exogenic drivers including overgrazing, fire suppression, increase in CO2 concentration, and long-term global changes in rainfall or temperature and endogenic positive feedbacks (D’Odorico and others 2012; Yu and D’Odorico 2014). This study shows that the increase in tree dominance in dry environments may also result from an increase in interannual rainfall variability.

A number of studies have invoked fire–vegetation feedbacks to explain the existence of savannas in a wide range of rainfall conditions in southern Africa (Staver and others 2011a, b). The increase in grass biomass and thus fire frequency in wet environments found in this study indicates that interannual rainfall fluctuations may expand the range of environmental conditions in which savannas are stable. This idea is in agreement with the emerging view that the interplay between tree/grass growth rate and fires regimes governs savanna–forest transitions (Hoffmann and others 2012; Murphy and Bowman 2012).

The model developed in this study expressed vegetation capacity as a function of instantaneous soil moisture and thus allows for a process-based analysis of impacts of increasing interannual rainfall variability and/or soil texture on tree–grass composition. We also noted that an alternative modeling approach relating vegetation capacity to mean growing seasonal rainfall and root depth by trees and grasses did not change the general pattern found in this study (Figure S7). Moreover, we notice that this model does not account for other factors, including rainfall seasonality (Vico and others 2015) and plant life histories (that is, annuals or perennials; evergreen or deciduous) (Kos and others 2012), which play an important role in determining plant community composition in savannas. In fact, an increase in winter rainfall increases deep soil water and thus favors trees (deep-rooted plants) over grasses (shallow-rooted plants) (Brown and others 1997; Germino and Reinhardt 2014). The high interannual variability of rainy season duration favors deciduous trees over evergreen trees, which may affect the competition with grasses (Vico and others 2015). The legacy effect of trees and grasses attributed to water and/or carbohydrate storage, available seeds/meristems, and/or nutrient availability from litter decomposition in response to rainfall fluctuations are also expected to be affected by plant life histories (Sherry and others 2008; Sala and others 2012; Anderegg and others 2015).

Conclusions

This study uses satellite data and develops a new mechanistic model to assess the effects of increasing interannual rainfall variability on tree/grass composition along the Kalahari Transect in Southern Africa. Both satellite data and model results show that increasing interannual rainfall fluctuations favor deep-rooted trees over shallow-rooted grasses in drier environments (that is, mean annual rainfall, MAP < 900–1000 mm), whereas in wetter environments it favors grasses over trees (that is, MAP > 900–1000 mm). The relative magnitude of the growth rates and root depths of grasses and trees greatly affects the response of tree–grass composition in response to increasing interannual rainfall variability. When interpreting the response of each functional group (that is, trees or grasses), it is crucial to account for the direct effects of interannual rainfall variability on soil water availability and also the indirect effects mediated by tree–grass interactions.