A resourceallocation basis for thinning boundaries

The increasing recognition that a variety of slope values might be expected, even on the geometric argument, along with the statistical difficulties of estimating slopes, has left the way open for alternative explanations for the underlying trend itself. Enquist et al. (1998) made use of the much more general model of West et al. (1997), which considered the most effective architectural designs of organisms (not just plants) for distributing acquired resources throughout those organisms. This suggested that the rate of resource use per individual, u, should be related to mean plant weight, P, according to the equation:

where a is a constant. Indeed, Enquist et al. (1998) were also able to find empirical support for this relationship.

They then argued that plants -4/3 or -3/2? have evolved to make full use of the resources available, and so if S is the rate of resource supply per unit area and Nmax the maximum allowable density of plants, then:

or, from Equation 5.30:

But when the plants have arrived at an equilibrium with the rate of resource supply, S should itself be constant. Hence:

where b is another constant. In short, the expected slope of a population boundary on this argument is -4/3 rather than -3/2.

Enquist and colleagues themselves considered the available data to be more supportive of their prediction of a slope of -4/3 than the more conventional -3/2. This has not, however, been the conclusion drawn either from previous data surveys or from the analysis of subsequent experiments (e.g. Figure 5.33a; Stoll et al., 2002). In part, the discrepancy may have arisen because the geometric argument is focused on light acquisition, and the data collected to test it have likewise been focused on above-ground plant parts (photosynthetic or support tissue); whereas Enquist et al.'s is a much more general resource-acquisition argument, and at least some of their data were based on overall plant weights (leaves, shoots and roots). Related to this, Enquist et al.'s data sets were focused on maximum densities of large numbers of species, whereas other analyses have focused on the self-thinning process, which occurs largely before the overall resource-determined limit has been reached. Again, therefore, there may be no contradiction between the two approaches.

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