Resource pulses, species interactions, and diversity maintenance in arid and semi-arid environments

Abstract

Arid environments are characterized by limited and variable rainfall that supplies resources in pulses. Resource pulsing is a special form of environmental variation, and the general theory of coexistence in variable environments suggests specific mechanisms by which rainfall variability might contribute to the maintenance of high species diversity in arid ecosystems. In this review, we discuss physiological, morphological, and life-history traits that facilitate plant survival and growth in strongly water-limited variable environments, outlining how species differences in these traits may promote diversity. Our analysis emphasizes that the variability of pulsed environments does not reduce the importance of species interactions in structuring communities, but instead provides axes of ecological differentiation between species that facilitate their coexistence. Pulses of rainfall also influence higher trophic levels and entire food webs. Better understanding of how rainfall affects the diversity, species composition, and dynamics of arid environments can contribute to solving environmental problems stemming from land use and global climate change.

Appendix: the simulation models

The simulations depicted in this article are particular illustrations of general principles developed elsewhere (Chesson 1994, 2000a; Chesson et al. 2001). The illustrative simulations are all for annual plant communities in which some fraction of the seed bank of a species germinates when a pulse occurs, and the fraction not germinating in any particular year experiences a survival rate s _i (for species i) over a year. However, in the case of relative nonlinearity, the equations have been reinterpreted in the figures for perennials with a bud bank or simply dormant biomass taking the place of the seed bank. Such reinterpretation is possible in other cases too, at least qualitatively.

The biomass arising from the germination of one seed is the unit of biomass, which grows according the differential equation

$$ {{{dB_{i} }}\over {{dt}}} = {\left[ {c_{i} f_{i} {\left( R \right)} - m_{i} } \right]}B_{i} $$

(1)

between germination and flowering. Here R is resource availability (soil water content), f _i (R) is the rate of resource uptake per unit biomass as a function of resource availability, c _i is conversion of uptake into new biomass, and reflects water use efficiency, and m _i is the per unit loss rate of biomass due to respiration, tissue death, and herbivory. The resource uptake rate, f _i (R), is given by the equation

$$f_{i} {\left( R \right)}={{{a_{i} R^{{\theta _{i} }} }} \over{{1 + a_{i} d_{i} R^{{\theta _{i} }} }}}$$

(2)

where a _i controls the rate at which uptake increases as the resource increases, d _i controls the rate at which uptake saturates (1/d _i is the maximum uptake rate) and θ _i controls the shape of the uptake curve, as illustrated in Fig. 1B. The total biomass of a species remaining at flowering was converted to new seed and added to the seedbank at the beginning of the next year at the rate φ _i per unit biomass.

In order to produce easily understood graphs, only one pulse of rain arriving at a point in time was allowed each year. In general, this restriction is highly conservative with respect to the mechanisms illustrated here because multiple pulses, and broad pulses that arrive continuously over an interval of time, simply increase the opportunities for partitioning. The timing of the rain pulse in a year was determined by a random draw from the beta distribution with parameters p and q (Johnson et al. 1995), and the amount of rain was a random draw from the log-normal distribution with parameters μ and σ ² for the mean and variance, respectively, of the natural log of the amount of rain. After the beginning of a pulse, soil water content declines due to uptake and evaporation according the equation

$$ \frac{{dR}} {{dt}} = - {\sum\limits_{i = 1}^n {f_{i} {\left( R \right)}B_{i} - \varepsilon R} } $$

(3)

with no carry-over of soil water permitted from one year to the next.

In simulations in which germination depends on the time of year when the pulse occurs, germination occurs at the beginning of the pulse with a fraction of the seed bank germinating given by the Gaussian curve

$$G_{i} e^{{ - h{\left( {t_{p} - \tau _{i} } \right)}^{2} }} ,$$

(4)

where G _i defines the maximum possible germination, t _p is the time of the pulse, τ _i is the time giving maximum germination of species i, and h controls the rate at which germination declines as the pulse time deviates from the optimum for the species. These curves are depicted in Fig. 1A. For germination timing relative to the beginning of the pulse, germination at the rate G _i was assumed to occur at time τ _i after the arrival of the pulse.

In all simulations depicted here, a species-specific difference in resource use was chosen according to the mechanism to be illustrated (timing independent of the pulse, timing relative to the beginning of the pulse, differently shaped uptake curves). Water use efficiency was adjusted, if necessary, to reduce average fitness differences between species until stable coexistence was found. The particular parameters chosen for these simulations were simply the first we happened upon that gave clear illustrations. Broad parameter ranges in fact give stable coexistence according the general principles discussed in Chesson (2000a). For each specific difference in timing of resource use, and for values of the parameters allowing the qualitative mechanistic features described in this article, there is always a range of average fitness differences between species supporting stable coexistence provided each species is capable of persisting in the modeled environment in monoculture.

For the simulations depicted here, the specific parameters used were G ₁=G ₂=0.5, s ₁=s ₂=0.8, φ ₁=φ ₂=0.05, a ₁=a ₂=20, d ₁=d ₂=1, θ ₁=θ ₂=1, c ₁=c ₂=12, m ₁=m ₂=0.05, ε=1, τ ₁=0.35, τ ₂=0.4, h=100, μ=ln(2), σ=0.2, p=q=2 (Fig. 2). For Fig. 3, some of these parameters changed as follows:

G ₁=G ₂=0.25, φ ₁=φ ₂=0.12, a ₁=a ₂=20, d ₁=d ₂=0.5, c ₁=7, c ₂=10.7, τ ₁=0, τ ₂=0.05. The relative nonlinearity figure, Fig. 5, differed from Fig. 2 in having a ₁=40, a ₂=5, d ₁=1, d ₂=0.05, θ ₁=1, θ ₂=4, c ₁=c ₂=0.5, τ ₁=τ ₂=0.35, μ=ln(1.5), σ=1, p=4, q=8.

All simulations were performed using Gauss 6.0 (Aptech Systems), with the simulation module Simgauss.