Connectivity of Niches of Adaptation Affects Vegetation Structure and Density in Self-Organized (Dis-Connected) Vegetation Patterns

Soil Moisture Specific Niche

We assume that coexisting species adapt to specific niches of soil moisture within the tiger bush periodic gradient (Ursino & Callegaro, 2016a; Ursino & Callegaro, 2016b). The soil moisture content is an environmental proxy determining environmental variables influencing niche adaptation and competition for resources.

The study is limited to the presence of two species, hereinafter called species 1 and species 2, respectively. The first adapts to the driest part of the soil moisture gradient (niche 1), and the second adapts to the most humid part (niche 2). Niche 1 is bounded on the left by the minimum possible soil moisture content, and on the right by the specific niche upper boundary w₁; niche 2 is bounded on the right by the maximum possible moisture water content, and on the left by the specific niche lower boundary w₂.

Soil Moisture and Biomass Balance Equations

The tiger bush evolution under species differentiation is simulated by 2SM, a model which describes the dynamics of soil moisture and two plant species, with biomass density n₁ and n₂, over a 1D domain. The non-dimensional form of 2SM (Ursino & Callegaro, 2016a) is:

(1a)

(1b)

(1c)

Equation 1a describes the dynamics of soil moisture w. The first term on the right-hand side is the infiltration rate, which is a fraction of effective annual rainfall a, increasing with total local biomass density n = n₁ + n₂, due to the positive feedback between vegetation growth and infiltration. Infiltration increases with n according to a Monod function, with half-velocity constant k_n. When n equals k_n, the infiltration rate is 0 · 5 a; for greater n, the infiltration rate tends to a asymptotically; the infiltration rate vanishes when n tends to 0. The second right-hand term accounts for soil moisture losses due to evaporation and leakage, and is modeled as a linear function of w itself. The transpiration rate has a linear dependence on soil moisture availability w and a quadratic dependence on local biomass density (Klausmeier, 1999) to simulate inter- and intra-specific facilitation (Ursino & Callegaro, 2016a). Water advection with constant and uniform velocity v is taken into account by the last term (Klausmeier, 1999; Ursino, 2005).

Equations 1b and 1c describe the dynamics of two plant species. The growth rate of each species is a function of the local biomass density and of the local soil moisture value, vanishing outside the environmental niche of adaptation of each species. In harsh environments, different species lead to inter- and intra-specific facilitation (Bertness & Callaway, 1994; Malkinson & Tielboerger, 2010), although they compete for resources. In the simulations, each species positively affects the other species growth, leading to intraspecific facilitation. The growth rate functions f₁ and f₂ are (Ursino & Callegaro, 2016a):

(2)

Mortality and dispersal of each species are accounted for by the second and the last right-hand side terms in Equations 1b and 1c.

Parameter values used for the simulations are listed in Table 1. In order to investigate the effect of niche extension and connectivity; parameters quantifying any other hydrological condition (a, k_n, v) or biological function (m, d) are kept unchanged throughout the simulations. Both w₁ and w₂ were set at 12 different values ranging from 0 · 25 to 3 · 0 with a costant increment of 0 · 25, so a total of 144 combinations of w₁ and w₂ were tested.

The initial condition used for the simulations is Klausmeier's model homogeneous steady-state solution for soil moisture (w₀) and biomass (n₀) (Klausmeier, 1999).

Definition of Connectivity Indexes

Niche complementarity index

Complementary adaptation strategies encompass the cases of (i) overlapping (when w₁ > w₂), ); (ii) complementary (when w₁ = w₂); and (iii) separate (when w₁ < w₂) niches of adaptation, as illustrated in the left, central and right part of Figure 1. The expected species organization, according to typical soil moisture patterns, is also shown in Figure 1 (bottom panels).

The degree of complementarity of the two niches is quantified by the niche complementarity index NCP

(3)

which is obtained by dividing the difference between the two extreme niche boundaries w₁ and w₂ by the homogeneous steady-state solution for soil moisture w₀ (see section on Soil Moisture and Biomass Balance Equations).

Overlapping niches lead to negative values of the niche complementarity index, perfectly complementary niches lead to zero values, whereas separate niches lead to positive values. The index module is proportional to the width of the gap or of the overlap. This index does not account for the position of the gap or overlap along the soil moisture gradient, meaning that if species 1 has a narrow niche close to the minimum possible water content and species 2 has a wide niche that covers the entire soil moisture domain, or species 1 has a wide niche and species 2 has a narrow niche close to the maximum possible water content, the value of the niche complementarity index is the same.

In this study, values of w₁ and w₂ are kept constant, and NCP has a fixed value throughout each simulation scenario.

Niche connectivity index

As adaptation with differentiation of traits occurs, the vegetation spatial distribution coevolves with soil moisture patterns toward a new steady configuration.

The niche connectivity index NCN considers the actual presence of a gap or overlap in the post-adaptation spatial distribution of soil moisture.

(4)

In Equation 4, L_overlap is the length of regions of the spatial domain where the local soil moisture w belongs to both adaptation niches concurrently, L_gap is the length of regions of the spatial domain where w does not belong to any niche and L_x is the domain length. Therefore, NCN is a nondimensional index between −1 and +1.

Figure 2 shows how the Niche Connectivity Index NCN varies with niche boundaries (w₁ and w₂) and the post-adaptation soil moisture (w). The output of 2SM is a continuous distribution of soil moisture, either uniform or periodic. The value NCN =  − 1 occurs for separate niches, when the simulated soil moisture does not belong to either of the two niches in every part of the domain. Negative values in −1 < NCN < 0 only occur for separate niches, in particular when the simulated soil moisture values exclusively belong to one of the two niches in some parts of the domain and do not belong to any niche in the remaining parts of the domain. The Niche Connectivity Index (NCN) is zero, both for separate and overlapping niches, if the simulated soil moisture exclusively belongs to one of the two niches; for complementary niches, the Niche Connectivity Index is always zero, independently of the presence of the niches in the resulting soil moisture distribution. Positive values in 0 < NCN <  + 1 only occur for overlapping niches, in particular when the local soil moisture value belongs to both niches in some parts of the domain. The value NCN =  + 1 is reached for overlapping niches, when simulated soil moisture belongs to both niches. In the cases NCN =  − 1, NCN = 0 and NCN =  + 1, the qualitative soil moisture distribution (uniform or periodic) does not affect the value of NCN.

Spatial Correlation between Soil Moisture and Biomass as a Function of Niche Complementarity Index

The correspondence between Niche Complementarity Index NCP and the cross-correlation between n and w, in many post-adaptation scenarios, is evaluated numerically by (i) hypothesizing an adaptation strategy (set w₁ and w₂) and estimating NCP (Equation 3); (ii) solving 2SM (Equations 1a–1c); and (iii) estimating the cross correlation between w and n = n₁ + n₂.

The growth rate function implemented in 2SM is typical of species which completely exploit resources in the near root zone, thus creating zones of accumulation of soil moisture below the bare interband zones (Ursino, 2007).

Figure 3 shows the correlation coefficient between the biomass density and the soil moisture value versus the Niche Complementarity Index (NCP) for different adaptation strategies. Red and blue markers represent monospecies patterns of specie 1 and species 2, respectively, while the black markers represent patterns with coexistence of both species.

Whatever the ecosystem post-adaptation shape, the model predicts a negative correlation, indicating a phase shift between biomass peaks and soil moisture, and that vegetated bands drain up the soil underneath, while a higher water retention occurs under bare interbands. This is especially true for patterns of species 1 only, because species 1 grows and persists in the most arid areas of the domain. The niche of adaptation of species 2 is in the most humid part of the environmental gradient, and thus, the patterns of exclusion of species 2 only cannot be too densely populated. Furthermore, as NCP increases, segregation into separate ecological niches, reduces interspecific facilitation and the environmental conditions become less favorable to the establishment of species 2.

Upscaling Connectivity from Local Niches of Adaptation to Vegetation and Hydrological Patterns

The correspondence between Niche Complementarity Index (NCN) and Niche Connectivity Index (NCP) is evaluated numerically by (i) hypothesizing an adaptation strategy (corresponding to w₁ and w₂) and estimating NCP (Equation 3); (ii) solving 2SM (Equations 1a–1c); and (iii) estimating NCN (Equation 4) in any post-adaptation scenario.

Different spatial structures emerge in typical ranges of NCP and are characterized by typical values of NCN, as shown in Figure 4.

Patterns of coexisting species (black circles) only emerge when the two niches are largely overlapping (NCP <  − 1) and lead to a soil moisture range which is mostly included in the overlapping regions (NCN ≈ 1), as illustrated in Figure 2, g). This result suggests that the two species need to adapt to highly connected niches and facilitate each others' growth in order to coexist in patterns in water scarcity conditions.

Patterns of species 1 only (red circles), with exclusion of species 2, may arise in a wider range of niche differentiation degrees (−3 < NCP <  + 2). In this type of ecosystem structure, soil moisture is modulated in two different ways, depending on the degree of niche differentiation. For separate niches (NCP > 0), the niche connectivity is neutral (NCN ≈ 0), meaning that the soil moisture range is mostly belonging to niche 1, as illustrated in Figure 2, c), upper black bar. For overlapping niches (NCP > 0), the niche connectivity can be from neutral to positive (0 ≤ NCN < 1) meaning that the soil moisture range is mostly belonging to niche 1, Figure 2, e), upper black bar, or partially belonging to niche 1 and the overlapping region, as illustrated in Figure 2 f), lower black bar, or even also partially belonging to niche 2, Figure 2, e), middle black bar. This result suggests that a species demanding low soil water levels may survive, exclude a higher water demanding competitor and self-organize into patterns leading to soil moisture within or outside the adaptation range and nevertheless excluding the competitor.

Patterns of species 2 only (blue circles), with exclusion of species 1, may arise in a scenario where niche differentiation is characterized by complementarity of niches (−1 < NCP <  + 1). In this type of ecosystem structure, soil moisture is modulated in two different ways, depending on the degree of niche differentiation. For separate niches (NCP > 0), the niche connectivity is slightly negative (NCN < 0), meaning that the soil moisture range is partially belonging to niche 2, or partially belonging to niche 1 and the gap region, or partially belonging to niche 1, the gap region and niche 2 as illustrated in Figure 2, b), lower, middle and upper black bar, respectively. For overlapping niches (NCP < 0), the Niche Connectivity Index appears to have a linear negative correlation with the Niche Complementarity Index, and the niche connectivity is positive (NCN > 0), meaning that the soil moisture range is mostly belonging to niche 2, Figure 2, e), lower black bar, or partially belonging to niche 2 and the overlapping region, as illustrated in Figure 2, f), upper black bar, or partially belonging to niche 1, Figure 2, e), middle black bar. This result suggests that a species, adapting to high w, may survive, exclude a less water demanding competitor and self-organize into patterns in a narrow range of niche differentiation scenarios, and the final niche connectivity is highly related to the niche differentiation. Perfectely complementary niches (NCP = 0) lead to monospecies patterns with neutral niche connectivity (Figure 2, d)).

Wide gaps in niche differentiation lead to uniform vegetation distributions or bare soil (white circles). These configurations are characterized by hydrological connectivity of flow and low efficiency in water harvesting.

Interestingly, patterns of coexistence only result in cases with extended niche overlapping (left part of the plot, NCP <  − 1), while in cases of niche gaps, only monospecies patterns are obtained, and still for gaps of limited extensions (NCP < 2, species 1, and NCP < 1, species 2). On the other hand, patterns of species 2 with the exclusion of species 1 do not appear with extended niche overlapping, while patterns of species 1 with the exclusion of species 2 occur frequently in this range.

Figure 4 shows that connectivity of niches of adaptation upscales to connectivity of vegetation patterns. Hydrological disconnectivity of runoff flow, which sustains the self organization of the eco-hydrological system, is commonly ascribed to vegetation pattern connectivity. In contrast, disconnectivity of ecological niches of adaptation results in less efficient water harvesting systems, such as hydrologically connected bare soil or uniform cover. Ecological connectivity is an index of synergisic evolutionary strategy of species acting as ecosystem engineers in arid lands, facilitating each others' growth, breaking the connectivity of overland flow paths, enhancing infiltration and water harvesting below ground.