Читать книгу Ecology - Michael Begon - Страница 148

This need to include all types of organisms in considerations of self‐thinning is reflected in studies seeking alternative explanations for the underlying trend itself. Most notably, Enquist et al. (1998) made use of the much more general model of West et al. (1997) that we discussed in Chapter 3, which considered the most effective architectural designs of organisms. We saw there that the rate of resource use per individual, u, or more simply their metabolic rate, should be related to mean organism body mass, M, according to the equation:

(5.30)

where a is a constant and the value ¾ is the ‘allometric exponent’.

−4/3 or −3/2?

They then argued that we can expect organisms to have evolved to make full use of the resources available, and so if S is the rate of resource supply per unit area and N_max the maximum density of organisms possible at this supply rate, then:

(5.31)

or, from Equation 5.30:

(5.32)

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

(5.33)

where c is another constant. In short, the expected slope of a population boundary on this argument is −4/3 rather than −3/2. Similarly, the figure in biomass–density relationships (equations 5.24 and 5.25) would be −1/3 rather than −1/2.

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, though this had not been the conclusion drawn from previous data surveys. Indeed, as we saw in Chapter 3, the idea of ¾ being a consistent or universal allometric exponent, and a slope of −4/3 therefore being expected, has itself been called increasingly into question (e.g. Glazier, 2005). Nonetheless, Begon et al. (1986) had found a mean value of −1.29 (close to a value of −4/3) for self‐thinning in experimental cohorts of grasshoppers, and Elliott (1993) a value of −1.35 for a population of sea trout, Salmo trutta, in the English Lake District. On the other hand, studies on house crickets, Acheta domesticus, have shown that the allometric exponent in in their case is not ¾ but 0.9 (Jonsson, 2017), and the estimated slope of their self‐thinning line −1.11 (the exact reciprocal of the allometric exponent; Figure 5.39a).

Figure 5.39 Self‐thinning lines vary in their support for the metabolic theory. (a) Self‐thinning in house crickets, Acheta domesticus, plotting mean weight against density on log scales. Replicate populations were established with between five and 80 newly hatched nymphs and followed until all survivors had hatched into adults. Lines join points from the same replicate, with the exception of the regression line fitted to self‐thinning populations from the three highest densities only (slope ± 95% CI, −1.11 ± 0.05). (b) Self‐thinning in common buckwheat, Fagopyrum esculentum, plotting log biomass against log density. Three initial densities, 8000 (green), 24 000 (blue) and 48 000 (red) individuals m^–2 were harvested after 22, 32, 42, 54 and 64 days. The dashed line is fitted to all data combined (slope, 95% CI: −0.38 (−0.30 to −0.47)), and the solid lines are fitted to the individual initial densities (slopes, 95% CIs: −0.45 (−0.36 to −0.55), −0.47 (−0.40 to −0.55) and −0.50 (−0.43 to −0.59) for 8000, 24 000 and 48 000, respectively).

Source: (a) After Jonsson (2017). (b) After Li et al. (2013).

Moreover, when experimental populations of common buckwheat, Fagopyrum esculentum, were grown at a range of densities, the best estimate for the slope of the biomass–density relationship overall was −0.38 (Figure 5.39b), very similar to the value of −0.33 predicted by the metabolic theory (and significantly different from −0.5, predicted by the areal argument). But if separate lines were fitted for each of the three initial densities, the slopes were −0.45, −0.47 and 0.50, all consistent with the areal argument and significantly different from −0.33 (Figure 5.39b). The different intercepts of the three lines (plants sown at higher initial densities had greater biomass) seemed to reflect an effect of initial density on growth form and perhaps on the degree of asymmetry in the competitive process (Li et al., 2013). This suggests, in turn, that light interception may drive patterns in individual populations while metabolic constraints set limits in a species overall.

What seems clear is that we have moved further from, not closer to, anything that could be called a self‐thinning ‘law’. But this represents progress in the important sense of acknowledging the range of forces acting on growing, competing cohorts of individuals, and recognising, too, that the details of a species’ morphology or physiology may influence the way in which those forces act and the slopes of the resulting relationships. The patterns we observe are likely to be the combined effect of a range of forces, even if in some cases one of those forces may dominate – metabolic constraints in mobile animals, light interception in many plants; light interception in individual populations, metabolic constraints in a species overall. Universal rules have their attractions but Nature is not so easily seduced.