Effect of vegetation–water table feedbacks on the stability and resilience of plant ecosystems

Authors


Abstract

[1] The interaction of vegetation with the groundwater is one of the key mechanisms affecting the dynamics of wetland plant ecosystems. The main feature of these interactions is the feedback between the downward shift of the water table caused by riparian vegetation and the emergence of soil aeration conditions favorable to plant establishment, growth, and survival. We develop a conceptual framework to explain how vegetation–water table feedbacks may lead to the emergence of multiple stable states in the dynamics of wetland forests and riparian ecosystems. This framework is used to investigate the sensitivity of these ecosystems to vegetation disturbances and changes in water table depth. As a result of these feedbacks, such ecosystems are prone to catastrophic shifts to an unvegetated state. Because of their competitive advantage, water-tolerant and shallow-rooted species can replace the original vegetation, contributing to the occurrence of vegetation succession in riparian zones and to the existence of alternative vegetation states between areas with shallow and deep water tables.

1. Introduction

[2] Riparian and wetland ecosystems are known for their environmental and economical value, as they are among the most productive terrestrial ecosystems [Naiman and Decamps, 1997], provide habitat to a diverse animal population [Le Maitre et al., 1999], and offer important resources for logging [e.g., Dubé et al., 1995; Roy et al., 2000] and livestock grazing [Wright and Chambers, 2002]. Understanding the response of riparian and wetland forests to anthropogenic and natural disturbances (e.g., wood harvesting, fires, and changes in water table depth) is of foremost importance to the management and restoration of these ecosystems [Wright and Chambers, 2002]. In what follows, we will denote “wetland ecosystems” plant ecosystems in areas with shallow water tables, and consider riparian forests as a particular case of these ecosystems.

[3] The two-way interaction between vegetation and groundwater is one of the key mechanisms affecting the dynamics of wetland vegetation. There is broad experimental evidence that phreatophyte vegetation, i.e., plants relying on water from the phreatic aquifer, affects the average depth and the diurnal fluctuations of the local water table, as suggested by significant increases in water table elevation (or “watering up” [Dubé et al., 1995]) subsequent to the removal of riparian vegetation [e.g., Wilde et al., 1953; Peck and Williamson, 1987; Borg et al., 1988; Riekerk, 1989] and by the opposite effect observed after planting vegetation in areas with relatively shallow water tables [Wilde et al., 1953; Chang, 2002]. Vegetation–water table interactions occur also in forested wetlands [Dubé et al., 1995; Roy et al., 2000], and salt marshes [Dacey and Howes, 1984; Ursino et al., 2004]. The water table drop caused by the presence of vegetation is generally attributed to lower recharge rates due to rainfall interception and plant transpiration [e.g., Wilde et al., 1953; Borg et al., 1988; Riekerk, 1989; Dubé et al., 1995], and to uptake by “taproots” extracting water directly from the (unconfined) aquifer [e.g., Le Maitre et al., 1999].

[4] Waterlogging conditions resulting from post-clear-cut water table rise may, in turn, inhibit seedling establishment and growth [Wilde et al., 1953], thereby preventing the regeneration of forest stands (Figure 1). In fact, the anaerobic conditions existing in saturated soils are detrimental to the root system and reduce both the productivity and the rate of survival of new seedlings [Roy et al., 2000, and references therein; Chang, 2002]. As a result, the clear-cut of riparian and other wetland vegetation may lead to ecosystem conversion, i.e., to the encroachment (Figure 1) of water-tolerant or of shallow-rooted invasive species [Chambers and Linnerooth, 2001; Wright and Chambers, 2002; Roy et al., 2000].

Figure 1.

Scheme of the processes resulting from vegetation–water table interactions in wetland ecosystems.

[5] These experimental results suggest that, by increasing the depth of the water table, phreatophytes are able to maintain sufficient aeration of the root zone, thereby providing favorable conditions for their own survival. Thus, in some riparian and wetland environments a positive feedback exists between vegetation establishment (or removal) and the occurrence (or disappearance) of water table depths tolerable by vegetation [Wilde et al., 1953; Chang, 2002] (Figure 1). This type of feedback mechanism can be associated with the possible emergence of multiple stable states in vegetation dynamics [e.g., Walker et al., 1981; Scheffer et al., 2001].

[6] A conceptual model is here developed to explain the possible existence of two preferential states in the dynamics of some wetland ecosystems [e.g., Roy et al., 2000; Chambers and Linnerooth, 2001; Wright and Chambers, 2002; Schroder et al., 2005]. This framework is here used to investigate the susceptibility of wetland vegetation to catastrophic shifts [Scheffer et al., 2001] to the other stable state, and to provide qualitative indications on the possible response of riparian environments to management strategies and restoration projects.

2. Modeling Framework

[7] We propose a model for vegetation–water table interactions, which accounts for the demographic dynamics of only one dominant species. The model mechanistically relates plant–water table feedbacks to the emergence of multiple stable states in vegetation density. Because no other species is included in the system, the model does not account for the likely occurrence of ecological succession in response to the loss of the original vegetation. It will be shown that both complete vegetation cover and unvegetated conditions can turn out to be stable states of the system. However, the unvegetated state is seldom observed in riparian areas or wetlands because water-tolerant species are commonly found to replace the original vegetation, leading to ecosystem conversion in response to water table rise. Thus, in what follows the occurrence of “unvegetated states” does not imply that the system will ultimately remain with no vegetation. Rather, the loss of the original vegetation suggests the occurrence of conditions favorable to ecosystem conversion, leading to a new stable vegetated state.

[8] Changes in riparian vegetation can be modeled through a growth-death process in which the net growth rate is expressed by the logistic curve [e.g., Noy-Meir, 1975; Tsoularis and Wallance, 2002], i.e., is taken proportional to the existing biomass, V, and to the available resources, VccV, with Vcc being the ecosystem carrying capacity. Vcc is the maximum amount of vegetation sustainable with the available resources (e.g., water, light, etc.) and the existing disturbance regime, including the occurrence of waterlogging conditions. Thus vegetation dynamics are expressed as

display math

where α regulates the temporal response of the system.

[9] To account for the vegetation–water table feedback we express the depth, d, of the water table as a (linear) function of V (see inset of Figure 2), d = d0 + βV, with d0 representing the water depth in the absence of vegetation and β the sensitivity of the water table to the presence of vegetation. The change in water table depth between vegetated (V = Vcc) and unvegetated (V = 0) conditions may range between 20 and 50 cm [e.g., Riekerk, 1989; Dubé et al., 1995; Roy et al., 2000], and more than a meter [Wilde et al., 1953; Peck and Williamson, 1987]. The parameter d0 depends on hydrologic conditions dictated by “external” factors (i.e., not inherent to vegetation dynamics), such as the stage in an adjacent river or lake, or the sea level. Here we consider d0 as a (constant) deterministic variable, though in some cases it could be treated as a random variable to account for hydrologic fluctuations.

Figure 2.

Dependence (Vcc = f(d) for ddlim), between ecosystem carrying capacity and water table depth: line a, the case of mesophyte vegetation extracting water from the vadose zone (f(d) = (1 − exp[−a1(ddlim)]); line b, the case of phreatophyte vegetation relying on water uptake from the groundwater (f(d) = a2(ddlim) (dlim + hlimd) H(dlim + hlimd), with H( ) being the Heaviside's function); line c, the case of vegetation partly relying on uptake by roots reaching the water table (f(d) = a4(ddlim) exp[−a3 (ddlim)]). Inset shows dependence of water table depth, d, on vegetation biomass, V.

[10] The effect of the water table on vegetation dynamics is complex and difficult to quantify. Experimental evidence suggests that the emergence of waterlogging conditions increases the mortality rate and decreases the rate of seedling establishment, thereby reducing the ecosystem productivity [e.g., Roy et al., 2000]. These effects translate into a reduction in ecosystem carrying capacity, Vcc (equation (1)). To investigate the qualitative properties of vegetation dynamics emerging from these interactions with the water table we express Vcc as a function of d

display math

with dlim representing the threshold of vegetation tolerance to shallow water tables and to the consequent insufficient aeration of the root zone. In these conditions the ecosystem carrying capacity can be assumed to be zero. We stress that while d0 depends on the hydrologic conditions, dlim is a function of plant physiology, in that it expresses vegetation tolerance to waterlogging. The function f(d) in equation (2) accounts for the dependence of Vcc on the water table depth. Three different types of relations are here considered depending on the type of vegetation (Figure 2).

[11] 1. Vegetation adapted to moderate levels of soil moisture (mesophytes) extracts water from the unsaturated zone without requiring uptake from the water table. Mesophytes grow on well-aerated soils and with adequate supply of moisture. In this case, f(d) increases with d to account for the decrease in productivity and ecosystem carrying capacity associated with waterlogging conditions (i.e., with shallow water table), while it remains constant for high values of d, as shown in Figure 2 (line a).

[12] 2. Plants with tap roots rely on water from the saturated zone (phreatophytes). These plants are stressed both when the water table is too shallow (waterlogging) and when it is relatively deep (i.e., out of the reach of taproots). In this case Vcc depends on d as qualitatively shown by line b in Figure 2.

[13] 3. Intermediate conditions are represented by vegetation types that partly rely on water from the underlying aquifer (line c in Figure 2).

[14] The overall net growth of vegetation (equation (1)) tends to a maximum value of biomass (Vcc) allowed by the available resources and the water table conditions. There is a two-way interaction of vegetation with the groundwater, in that plants affect the water table depth, which, in turn, determines the ecosystem carrying capacity. Equation (2) combined with the dependence of d on V provides a relation, Vcc = Vcc(V), between vegetation biomass, V, and its upper bound, Vcc. Because vegetation biomass increases with time for V < Vcc and decreases for V > Vcc (equation (1)) the dependence of Vcc on V provides useful indications on some general properties of the dynamics. In particular, three different behaviors (Figures 3a, 3b, and 3c) can be observed, depending on the sign of d0dlim and the number of equilibrium states, i.e., of states in which dV/dt = 0. Because V = V0 = 0 is always an equilibrium state of the system (see equation (1)), the existence of multiple equilibrium states depends on the existence of real, nonnull roots of the equation Vcc = V, with Vcc being a function of V given by equation (2) with d depending on V as shown in the inset of Figure 2. In what follows we discuss the possible equilibrium states and their stability through the analysis of the intersections of the curve Vcc(V) with the line Vcc = V. The following cases can occur:

Figure 3.

Stable and unstable states of vegetation dynamics resulting from interactions with the water table. Figures 3a–3c give graphical solutions of Vcc(V) = V shown as intersections between the curve Vcc(V) (equation (2); see Figure 2) and the line Vcc = V. In Figures 3a and 3d, because d0 > dlim, the system has only one stable state, V1, and an unstable state V0 = 0 (not shown). V always tends to V1, regardless of its initial value (Figure 3d). In Figures 3b and 3e, d0 < dlim, and there are three solutions of Vcc(V) = V (i.e., equation (1) has three equilibrium states). The system has two stable states (i.e., attractors), V0 and V1, and an unstable state Vu. Depending on whether the initial value of V is larger or smaller than Vu the system tends to V1 or V0, respectively (Figure 3e). In Figures 3c and 3f, because there are no solutions of Vcc(V) = V,equation (1) is zero only for V = V0, which is the only stable state. Regardless of the initial condition, the system always tends to the unvegetated state, V0 (Figure 3f).

2.1. Case A

[15] If d0 > dlim, the water table is always deeper than the minimum depth required for plant establishment and survival. In these conditions the system has only one equilibrium state (V = V1 in Figure 3a), which is stable. In fact, vegetation biomass decreases (i.e., dV/dt < 0, see equation (1)) when V exceeds V1. Conversely, V increases when V < V1 as shown in Figure 3d.

2.2. Case B

[16] If d0 < dlim the water table prevents vegetation encroachment starting from unvegetated initial conditions. However, in this case vegetation, if present, is able to keep the water table below the maximum elevation tolerable by plants. Thus the system has three equilibrium states, shown as intersections in Figure 3b. Two of these states are stable, i.e., V = V0 and V = V1, while the third one (V = Vu) is unstable. The unstable state marks the transition between the domains of attraction of V0 and V1, corresponding to bare ground and vegetated conditions, respectively. As V drops below (grows above) Vu, V evolves toward V0 (V1) (Figure 3e).

2.3. Case C

[17] If d0 < dlim and plants are not sufficiently effective at decreasing the water table elevation to a point that is suitable for the stable occurrence of vegetated conditions, the only stable state corresponds to unvegetated conditions (i.e., V = V0 = 0) as shown in Figures 3c and 3f. As mentioned before, the loss of the original vegetation is likely followed by the growth of water-tolerant species.

3. Discussion and Conclusions

[18] The roots of the right-hand side of equation (1) represent equilibrium states of the system. One of them is always V = V0 = 0; this state may turn out to be stable or unstable depending on the values of d0, dlim and the shape of the Vcc(V) curve. For a given vegetation type (i.e., dlim and Vcc(V)) d0 is the only environmental variable determining the stable states of the system. For d0 > dlim the system has one stable vegetated state (Figure 4), while bare soil conditions are unstable. Thus, if disturbed, the dynamics evolve always toward this stable state. As d0 decreases below dlim the unvegetated state V = V0 becomes stable. In these conditions the system has two stable states. One of them (i.e., V = V1) is associated with the existence of vegetation, while the other (i.e., V = V0) corresponds to bare soil conditions. As d0 decreases below a critical value, dc, the stable vegetated state disappears (i.e., there are no intersections of Vcc = V with Vcc(V) other than V0). In this case the only equilibrium state, V = V0 is stable.

Figure 4.

Stable (solid line) and unstable (dashed line) states of the system as a function of the undisturbed depth, d0, of the water table.

[19] Ecosystems with multiple stable states are often analyzed using the concept of resilience. Ecosystem resilience is usually defined [Holling, 1973] as the minimum magnitude of disturbances able to cause phase transitions to the other stable state. For example, the resilience of the equilibrium state, V1, can be measured by the distance between V1 and Vu (i.e., ∣V1Vu∣): when V1 is close to Vu the vegetated state has low resilience, in that a relatively small disturbance is able to shift the ecosystem to the alternative stable state V = V0. Thus the resilience of V = V1 is zero when do = dc (Figure 4). Conversely, a small resilience of the unvegetated state suggests that vegetation restoration may be feasible.

[20] The emergence of multiple stable states is of great importance to our understanding of wetland ecosystems, in that the disturbance of the stable vegetated state may lead the system away from its initial conditions and change the vegetation in riparian zones. In fact, if V is reduced below Vu vegetation dynamics evolve toward the unvegetated state (V = V0) and remain locked therein. This suggests that because of the vegetation–water table feedback, the system would not revert back to its stable vegetated state unless a change in the hydrologic conditions controlling the water table depth destabilizes the unvegetated state by increasing d0 above dlim. Indeed, soil drainage is a relatively frequent management practice to restore wetland vegetation in boreal regions (e.g., Finland) where forested wetlands are intensively used for wood harvesting [Dubé et al., 1995].

[21] Thus wetland ecosystems are vulnerable to disturbances and may respond to biomass losses with highly irreversible catastrophic shifts to unvegetated conditions. Recovery from this stable state with no change in the externally driven hydrologic controls (i.e., of d0) is not likely to occur. However, water-tolerant and shallow-rooted species (i.e., with different Vcc(V) curves and values of dlim) can colonize the systems thanks to their competitive advantage in waterlogged soils. Interesting dynamics may arise from the interaction of these water-tolerant species with the water table: if the water table depth increases sufficiently to favor the reestablishment of the original vegetation, the ecosystem reverts back to its initial state; otherwise the system undergoes a permanent conversion to a different vegetated state. Thus the catastrophic shift to the unvegetated state is likely followed by important changes in the composition and structure of vegetation. On the basis of this reasoning we interpret the frequent occurrence of vegetation succession in riparian environments [Chambers and Linnerooth, 2001; Wright and Chambers, 2002] as a possible sign of alternative stable states (e.g., shallow-rooted grasses in shallow-water table sites and shrubs in deep water table areas [Chambers and Linnerooth, 2001]), resulting from water table–vegetation feedbacks.

[22] The understanding of these dynamics of disturbance, response, and succession is relevant to the correct management of wetland ecosystems, in that it may provide useful indications on the possible occurrence of abrupt and irreversible changes in vegetation and on the feasibility of vegetation restoration projects in wetland environments. In addition to disturbance-induced vegetation losses, wetland ecosystem may experience the transition to (stable) unvegetated conditions as a result of water table rise due to changes in groundwater resources management. In fact, as d decreases below dc (Figure 4) the equilibrium state V = V1 disappears and the system catastrophically shifts to the stable state, V = 0. Similar changes could occur in salt marsh vegetation [e.g., Dacey and Howes, 1984; Ursino et al., 2004], under the long-term effect of a sea level rise, though other processes not included in our simplified framework (e.g., sediment deposition, marsh erosion, vegetation burial) are known for adding more complexity to the dynamics of marsh ecosystems [e.g., Allen, 1997; van de Koppel et al., 2005].

Acknowledgments

[23] This research was funded by the Fondazione CRT, Cassa di Risparmio di Torino.

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