How frequency and intensity shape diversity-disturbance relationships

Abstract

Understanding the relationship between disturbance regimes and species diversity has been of central interest to ecologists for decades. For example, the intermediate disturbance hypothesis proposes that diversity will be highest at intermediate levels of disturbance. Although peaked (hump-shaped) diversity-disturbance relationships (DDRs) have been documented in nature, many other DDRs have been reported as well. Here, we begin to theoretically unify these diverse empirical findings by showing how a single simple model can generate several different DDRs, depending on the aspect of disturbance that is considered. Additionally, we elucidate the competition-mediated mechanism underlying our results. Our findings have the potential to reconcile apparently conflicting empirical results on the effects of disturbance on diversity.

Fig. 1.

Coexistence region in the frequency-intensity plane. (A) Growth rate for each species as a surface. Surfaces are shaded gray where both species have positive growth rates, which leads to stable coexistence. (B) Projection of coexistence region where for each species. Vertical lines indicate how different frequency DDRs [peaked on left (line A) and U-shaped on right (line B)] result from changing disturbance intensity. Horizontal arrows mark different intensity DDRs [peaked on top (C) and increasing on bottom (D)] that result from changing disturbance frequency. For clarity, we present a pair of species with symmetric life-history traits, which generate a symmetric coexistence region. Life-history parameters for (dominant, inferior) species: seed yield Y = (0.9,1.1), seedbank survival s = (0.4,0.6), germination rate G = (0.6,0.4), competition α = (1.1,0.9).

Fig. 2.

Coexistence regions shaded by rate (R) of disturbance, R = F·I; i.e., percent individuals destroyed per year. Coexistence occurs across a range of rates, but rate alone does not determine coexistence. This illustrates the interactive properties of frequency and intensity. (A) On a linear scale, isoclines of constant rate are hyperbolic segments. (B) On a log–log scale, rate isoclines are straight lines. Arrows demarcate rate gradients of equal range. The top left arrow A corresponds to an increasing DDR, and the bottom right arrow B corresponds to a decreasing DDR. In this example, the arrows could not be distinguished if only rate were recorded. This highlights the need to measure multiple aspects of disturbance. Life-history parameters for (dominant, inferior) species: seed yield Y = (0.9,1.1), seedbank survival s = (0.4,0.6), germination rate G = (0.6,0.4), competition α = (1.1,0.9).

Fig. 3.

Long-term low-density growth rates () as sum of relative nonlinearity (ΔN) and fluctuation-independent term (). (Left) Mechanisms for a fixed intensity I = 0.61, corresponding to Fig. 1B line A. Coexistence occurs where is positive for both species, indicated by shaded regions. At intermediate frequencies, relative nonlinearity ΔN has the largest magnitude. (Right) At higher intensity (I = 0.66, corresponding to Fig. 1B line B), relative nonlinearity increases in magnitude, which disadvantages the competitive dominant at intermediate frequencies. Note the coexistence region (shaded rectangles) is split into disconnected components, and represents a U-shaped DDR. Life-history parameters for (dominant, inferior) species: seed yield Y = (0.9,1.1), seedbank survival s = (0.4,0.6), germination rate G = (0.6,0.4), competition α = (1.1,0.9).

Fig. 4.

Density plots for a range of frequency and intensity parameters (F,I). (Left) (corresponding to line A in Fig. 1B) Coexistence occurs at all three frequencies. Note that species 2 has higher mean density at extremal frequencies. (Right) (corresponding to line B in Fig. 1B) Species 1 is forced to extinction (slowly) at intermediate frequencies, because the stronger negative effect of relative nonlinearity forces a negative growth rate (), as shown in Top Right of Fig. 3. Life-history parameters for (dominant, inferior) species: seed yield Y = (0.9,1.1), seedbank survival s = (0.4,0.6), germination rate G = (0.6,0.4), competition α = (1.1,0.9).