Mechanisms for stable coexistence of plant species based on the niche concept contain several ingredients including:7'61-64 (a) differentiation of species in niche space (different species occupy different volumes), (b) landscape diversity giving rise to spatial heterogeneity, and (c) tradeoffs in t If the species has no competitors or enemies the niche is often called the "fundamental niche".
i The micro-habitats in the physical space are sometimes referred to as the "realized niches"48 although originally the realized niche has been defined as a volume in niche space that takes into account species competition effects.49
species traits (none of the species is a superior competitor with respect to all niche axes). With these ingredients different species may stably coexist in different physical locations. Moreover, a strong positive correlation is expected between landscape diversity and species richness.
In the context of the model landscape diversity is determined by the diversity of pattern solutions which dictate the instantaneous spatial distributions of the ecosystem engineer's biomass and of the soil-water resource. A high diversity of pattern solutions can be realized in parameter regimes giving rise to irregular solutions. One possible mechanism leading to irregular solutions is spatial chaos. So far, however, we have not identified chaotic solutions and therefore we will not address here this possibility. Irregular patterns can also result from coexistence of stable states (e.g. bistability), where spatial mixtures of the coexisting states form stationary or long lived patterns. We demonstrate two aspects of these patterns; the first pertains to the dominant roles arbitrary initial conditions have in shaping the asymptotic patterns, and the second to the irregular soil-water distributions that can result from these patterns. Fig. 3.10 shows the time evolution of two identical initial conditions (leftmost frames), one in a parameter range where spots are the only stable state (upper frames) and the other in a coexistence range of spots and bare soil (lower frames). In the former case the system evolves towards a spot pattern and the initial pattern has little effect. In the latter case the initial pattern has a strong imprint on the asymptotic pattern; the system becomes sensible to random factors and the asymptotic patterns will generally show high landscape diversity. Fig. 3.11A,B show biomass and soil-water distributions in a coexistence range of stripes and gaps. As the one-dimensional cut in Fig. 3.11C shows the soil-water distribution is pretty irregular, creating a diversity of micro-habitats as compared with uniform or regular periodic patterns.
Climatic or human induced environmental changes, such as alternation in rainfall regime or biomass harvesting, may affect the patterns formed by the ecosystem engineer and consequently the micro-habitats they create for other organisms. The most significant pattern changes are those involving transitions between different biomass pattern states (catastrophic shifts).
We illustrate this mechanism of micro-habitat change as a result of an environmental change with a transition from a banded ecosystem engineer t=0
Fig. 3.10. Bistability as a mechanism for pattern diversity. Snapshots of the time evolution of the same initial state (leftmost frames) when spotted patterns are the only stable state (upper frames, P = 300 mm/yr), and when spotted patterns stably coexist with bare soil (lower frames, P =75 mm/yr). In the former case the asymptotic state is independent of the initial state; any initial state will converge to a spotted pattern as this is the only stable state of the system. In the latter case the asymptotic state is highly sensitive to the initial one; although the spot size changes the pattern remains invariant. The domain size is 7.5 X 7.5 m2, and the parameters are as Table 1. Time is dimensionless (divide by factor of 4 to obtain time in units of years).
pattern to a spotted pattern on a uniform slope as precipitation decreases. Snapshots of the pattern transition and the associated soil-water distributions are shown in Fig. 3.12. Surprisingly, the transition involves the appearance of spot patches with higher soil-water densities, despite the lower precipitation value. This counter-intuitive result can be explained as follows. The spot pattern self-organizes to form an hexagonal pattern. As a result each spot "experiences" a bare area uphill which is twice as large as the bare area between successive bands, and therefore absorbs more runoff.
A transition from bands to spots involving soil-water gain can also be induced by a local disturbance (e.g. clear-cutting) at a given precipitation value corresponding to a coexistence range of stable bands and stable spots, as shown in Fig. 3.6.
We have already discussed, in the context of a single patch, the ability
Fig. 3.11. Biomass (A) and soil-water distributions (B,C) of an asymptotic pattern in a coexistence range of stripes and gaps. Frame C shows the soil-water profile along the transect denoted by the dashed line in B. The soil-water distribution is pretty irregular as is evident by the variable grey shades in frame B and by the profile in frame C. Such irregular distributions create a diversity of micro-habitats as compared with uniform or regular periodic patterns. The domain size is 7.5 X 7.5 m2 and the parameters are as Table 1 with P = 950 mm/yr.
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