Theory of marine communities: the intermediate disturbance hypothesis

Ecology, June, 1998 by Roman Dial, Jonathan Roughgarden

INTRODUCTION

The intermediate disturbance hypothesis states that intermediate levels of disturbance maximize species diversity because competitively dominant species exclude subordinate species at low disturbance, but too much disturbance leads to local extinctions. The hypothesis enjoys such widespread application as an explanation for patterns of local and regional biodiversity, particularly for sessile organisms (e.g., Harper 1969, Connell 1978, Huston 1979), that it is sometimes elevated from the status of hypothesis to principle. However, experimental detection of the effect of disturbance is often sensitive to recruitment (Dayton 1971, Underwood et al. 1983, Gaines and Roughgarden 1985). This sensitivity motivates the modeling effort presented here, where disturbance affects benthic adults, and pelagic processes determine larval settlement.

Many prior theoretical treatments of disturbance and competition used habitat patch models (e.g., Hutchinson 1951, Levins and Culver 1971, Horn and MacArthur 1972, Armstrong 1976, Yodzis 1978, Hastings 1980, Sebens 1987, Nee and May 1992, Tilman 1994). Most studies found that subordinate species must be better patch colonizers for disturbance-mediated coexistence. How much better sets the lower level of disturbance generating coexistence, while the dominant species' tolerance for disturbance sets the upper level for coexistence (Armstrong 1976, Hastings 1980, Sebens 1987). These earlier models typically applied Lotka-Volterra competition dynamics to hypothetical organisms with simple life cycles. Yet many examples of the intermediate disturbance principle - like barnacles, bivalves, bryozoans, corals, algae, even seed plants - usually involve species with complex life cycles, long-lived propagules, and space-limited adults (e.g., Harper 1969, Dayton 1971, 1975, Porter 1974, Connell 1978, Menge 1983). Thus a theory of disturbance should explicitly couple adult and propagule dynamics (Gaines and Roughgarden 1985, Menge and Sutherland 1987, Roughgarden et al. 1988).

A theoretical framework specifically developed for marine organisms with complex life cycles as typified by barnacles (Roughgarden et al. 1985, Roughgarden and Iwasa 1986, Roughgarden et al. 1988, Possingham and Roughgarden 1990) provides the foundation for the communities considered here. The idea behind this modeling approach is that larvae exist in a fundamentally different environment than do adults and so are subject to different forces. While benthic disturbance increases adult mortality, it leaves larval mortality unaffected. Similarly, settlement forces increase recruitment of new adults from the larval pool but with no effect on per capita births. With this view on disturbance and settlement we derive conditions for invasion, coexistence, and extinction in a two-species competitive hierarchy and find they depend on both the relative pelagic and benthic abilities of the two species.

THE MODEL

We build on the modeling approach of Roughgarden and Iwasa (1986) for species with space-limited adults and pelagic larvae in an environment of essentially closed populations. Using a system of two coupled differential equations for each of two species constrained by habitat area, we construct the simplest model of hierarchical competition under the influence of disturbance and settlement that their approach allows.

Two species, 1 and 2, have adults with body size [a.sub.i] and numerical abundance [N.sub.i](t) within a habitat of size A. Free space is open to settlement and consists of habitat unoccupied by adults:

F(t) = A - [a.sub.1][N.sub.1](t) - [a.sub.2]N(t).

Each species produces larvae with abundance [L.sub.i](t) at a per capita rate [m.sub.i]. Larvae recruit onto the substrate as new adults at a rate that depends on both the number of larvae in the water and the free space available: [c.sub.i]F(t)[L.sub.i](t). We interpret [c.sub.i], the per capita larval settlement rate with units of number per area per time, as a parameter of larval transport. Larvae die at a density-independent rate [v.sub.i] and adults suffer density-independent mortality at rate [[Mu].sub.i].

We consider a strongly asymmetric, hierarchical competition community where a dominant species (subscripted by 1) can always settle upon and kill individuals of the subordinate species (subscripted by 2). We assume that the subordinate settles only on substrate empty of either species, F(t) = A - [a.sub.1][N.sub.1](t) [a.sub.2][N.sub.2](t), but the dominant settles on free space plus habitat occupied by the subordinate species: F(t) [a.sub.2][N.sub.2](t). Dominant larvae settle on subordinate adults at rate [c.sub.1][L.sub.1](t)[a.sub.2][N.sub.2](t).

Finally, we assume that increasing disturbance increases adult mortality, while increasing settlement increases larval recruitment to adults. To investigate these forces we introduce tuning parameters, [Alpha] [greater than or equal to] 1 and [Beta] [greater than or equal to] 1, which increase adult mortality and recruitment in density-independent ways.