On Defining Assembly Space: A Reply to Grover and LawtonAuthor(s): James A. Drake, Terry Flum and Gary R. HuxelSource: Journal of Animal Ecology, Vol. 63, No. 2 (Apr., 1994), pp. 488-489Published by: British Ecological SocietyStable URL: http://www.jstor.org/stable/5566 .

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Journal of Animal Ecology 1994, 63, 488-489

COMMENT

On defining assembly space: a reply to Grover and Lawton

JAMES A. DRAKE, TERRY FLUM and GARY R. HUXEL Department of Zoology and Graduate Program in Ecology, University of Tennessee, Knoxville, TN 37996, USA

We appreciate the concerns raised by Grover & Law- ton (p. 484) regarding our recent work. The central issue raised by Grover & Lawton is the primacy of stability as a property which maintains the status quo-an issue with which ecologists and evolutionary biologists have grappled for a very long time. There is little doubt that thought about the nature of stability strongly influences the design and interpretation of ecological experiments, as well as the form of pre- vailing paradigms. As a result, investigations explor- ing different realms of a system's behaviour often expose dynamics and behaviour which cannot be re- conciled within the framework of current ecological thought. Rather than being at odds with Grover & Lawton, we find our respective approaches comple- mentary if not integral to the development of a broader framework of community phenomenology, particularly given the emerging characterization of the community assembly state space (Drake 1990, 1991; Drake et al. 1993; Luh & Pimm 1993).

To address Grover & Lawton's concerns, we begin by defining an assembly map as a convoluted mesh of variously crossing, and sometimes intersecting, tra- jectories. Trajectories are defined by a given set of species and associated environmental effects moving through space and time. Hence, a trajectory is one of many sequences of community states or configur- ations which exist and move through time (cf. assembly, succession). The form any trajectory can take is initially limited by environmental and geo- logical vagaries. Subsequently, however, the direction a community assembly trajectory can take is richly varied. Factors such as the sequence and timing of species invasion and reinvasion, and the evolutionary and real-time dynamical interactions which occur therein, are all capable of directing a system along different, though equally plausible, trajectories.

The assembly map as described above has several specific geometric properties which tie together studies such as ours. First, there are unreachable portions of the assembly map (e.g. Diamond 1975; Sugihara 1985); these regions represent community con- figurations which simply cannot exist. Secondly, the map of trajectories contains alternative pathways (some shorter than others) between distant commun- ity states. The system can reach state C by travers- ing states A-B-D in sequence, but the sequence A-

D-C might also exist containing very different mech- anisms responsible for the organization of state C. Some trajectories have the same solution, while others traverse very different portions of the assembly space despite identical initial conditions. Disturbance can reset a trajectory onto another or simply back up the current trajectory. So defined, we have a map which is woven together into a mesh of trajectories or per- missible states.

Viewed in this manner we believe that our respective approaches simply focus on different portions of the assembly space-an essential difference if we are to develop a more general framework of community organization. It appears as though Grover & Lawton believe that some aspects of the assembly space offer more information than others. If this were a general rule nature should have relatively few assembly trajec- tories with which to define community organization. In the laboratory and in nature we often find a wide range of trajectories producing both transitory and persistent species ensembles-even within the confines of very similar environments. We also wish to reiterate that the trajectories we observed were the results of invasion timing, dynamics, and the interplay between the two.

On a more technical side, our experimental design involved a relatively rapid sequence of invasions with- out maintenance of constant nutrient levels. However, Grover & Lawton suggest that the slowest meaningful invasion schedule, invasion only at successive equi- libria (implicitly maintaining nutrient levels) is pref- erable. One feature of natural freshwater systems, par- ticularly those in temperate regions, is quite rapid seasonal variation. This feature was a major concern in the design of our experiment because maintaining relatively constant conditions for an extended period would surely reduce environmental variation from our assembly trajectories. We chose to focus on the historical assembly processes which are capable of altering the expression of the mechanisms (e.g. predation, competition) often posited as the causal agent.

To suggest, as Grover & Lawton do, that only certain time intervals are interesting is simply not jus- tifiable by any scientific evidence we are aware of. Rather than 'rapid' invasions being extreme we feel that such a schedule is more likely to be the norm than 488

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489 J.A. Drake T. Flum & G.R. Huxel

the exception. This is particularly true if invasions are the means by which local species extirpations are overcome to maintain high species diversity, as sug- gested in metapopulation and landscape models (e.g. DeAngelis & Waterhouse 1987). It is more likely, in fact, that the type of scaling called for by Grover & Lawton masks the very dynamics capable of main- taining local and regional species diversity.

In addition to the timing of successive invasions, Grover & Lawton take issue with the means by which the transfers were made, particularly with respect to the animals in the systems. Once again, the possible range in the number of organisms that can be trans- ferred between two systems is nearly always variable in nature. We chose to base our transfer rate between systems on a proportion of the total volume of the system. This approach does favour species that repro- duce rapidly, as Grover & Lawton point out. However, it is well known that rapidly reproducing species are often good dispersers, so our transfer pro- tocol simply maintained those ecological strategies. Again, we find the suggestion made by Grover & Lawton that all species invade at the same density to be much more extreme in terms of the range of possibilities than our design.

Even in our nutrient-rich systems competition is severe, to the point where normally superior com- petitors are unable to invade. We have found that most of the nutrients are quickly (within 10 days) removed from the water column and become incor- porated into the biomass (G. Huxel, J. Drake, T.E. Flum & C. LaRue, unpublished). Competition is undoubtedly one of several mechanisms, including allelopathy, complex nutrient-pH interactions and associated indirect effects, which produce alternative persistent states within our landscape. Because the trajectories which produced some of these states never cross there is no possibility that with time the systems will converge to some common composition. In many cases one simply cannot get there from here.

In short, we argue that there is no ecological 'traffic cop' regulating the timing and density of invasions by species among communities. Instead, that traffic cop operates within the internal working of the com- munity, where dynamics are often far from equili-

brium. Offered constancy the system may tend toward one of several, not a single state (see Drake 1991). The approach offered by Grover & Lawton refuses to admit the existence of dynamics beyond those which produce a single steady-state. Unfortunately, this is such a serious constraint that the possibility of non- equilibrium dynamics and alternative states largely vanishes.

History and chance rule the world of ecology; yet, embedded within the historical context which struc- ture a system, there are many alternative suites of ecological interactions and processes. Clearly, biology is not strictly limited by history and chance; indeed, we have shown that community and landscape dynamics can feed back to mechanisms which previously served a regulatory function (Drake 1991; Drake et al. 1993). Progress can only be made when studies spanning different areas of the state space are integrated into a formal phenomenological framework. Let's begin.

References

DeAngelis, D.L. & Waterhouse, J.C. (1987) Equilibrium and nonequilibrium concepts in ecological models. Ecological Monographs, 57, 1-21.

Diamond, J.M. (1975) Assembly of species communities. Ecology and Evolution of Communities (eds M.L. Cody & J.M. Diamond). Harvard University Press.

Drake, J.A. (1990) The mechanics of community assembly and succession. Journal of Theoretical Biology, 147, 213- 233.

Drake, J.A. (1991) Community assembly mechanics and the structure of an experimental species ensemble. American Naturalist, 137, 1-26.

Drake, J.A. et al. (1993) The construction and assembly of an ecological landscape. Journal of Animal Ecology, 62, 117-130.

Luh, H. & Pimm, S.L. (1993) The assembly of ecological communities: a minimalist approach. Journal of Animal Ecology, 62, 749-765.

Sugihara, G. (1985) Graph theory, homology and food webs. Proceedings of the Symposium on Applied Mathematics, 30, 83-101.

Wilson, D.A. (1992) Complex interactions in meta- communities with implications for biodiversity and higher levels of selection. Ecology, 73, 1984-2000.

Received 7 September 1993

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