Читать книгу Ecology - Michael Begon - Страница 147

We proceed, therefore, by examining possible bases for the general trend, and then asking why different species or populations might display their own variations on this common theme. Two broad types of explanation for the trend have been proposed. The first (and for many years the only one) is areal and based on a resource falling on the organisms from above (like light); the second is based on resource allocation in organisms of different sizes. Again, the similarities to the arguments at the heart of a metabolic theory of ecology, discussed in Section 3.9, are clear.

Limiting ourselves for now to plants, the areal argument runs as follows. In a growing cohort, as the mass of the population increases, the leaf area index (L, the leaf area per unit area of land) does not keep on increasing because beyond a certain point the canopy is full and so L remains constant irrespective of plant density (N). It is, in fact, precisely beyond this point that the population follows the dynamic thinning line. We can express this by saying that beyond this point:

(5.26)

where λ is the mean leaf area per surviving plant. However, the leaf area of individual plants increases as they grow, and so too therefore does their mean, λ. We expect λ, because it is an area, to be related to linear measurements of a plant, such as stem diameter, D, by a formula of the following type:

(5.27)

where a is a constant. Similarly, we expect mean plant weight, P, to be related to D by:

(5.28)

where b is also a constant. Putting Equations 5.26–5.28 together, we obtain:

(5.29)

This is structurally equivalent to the −3/2 power relationship in Equation 5.23, with the intercept constant, c, given by b(L/a) ^3/2.

It is apparent, therefore, why thinning lines might generally be expected to have slopes of approximately −3/2. Moreover, if the relationships in Equations 5.27 and 5.28 were roughly the same for all plant species, and if all plants supported roughly the same leaf area per unit area of ground (L), then the constant c would be approximately the same for all species. On the other hand, suppose that L is not quite the same for all species, or that the powers in Equations 5.27 and 5.28 are not exactly 2 or 3, or that the constants in these equations (a and b) either vary between species or are not actually constants at all. Thinning lines will then have slopes that depart from −3/2, and slopes and intercepts that vary from species to species. It is easy to see why, according to the areal argument, there is a broad similarity in the behaviour of different species, but also why, on closer examination, there are likely to be variations between species and no such thing as a single, ‘ideal’ thinning line.

complications of the areal argument

Furthermore, contrary to the simple areal argument, the yield–density relationship in a growing cohort need not depend only on the numbers that die and the way the survivors grow. We have seen (see Section 5.8) that competition is frequently highly asymmetric. If those that die in a cohort are predominantly the very smallest individuals, then density (individuals per unit area) will decline more rapidly as the cohort grows than it would otherwise do. It seems possible, too, to use departures from the assumptions built into Equations 5.26–5.29 to explain at least some of the variations from a ‘general’ −3/2 rule. We see this in a study by Osawa and Allen (1993), who estimated a number of the parameters in these equations from data on the growth of individual plants from two species: mountain beech (Nothofagus solandri) and red pine (Pinus densiflora). They estimated, for instance, that the exponents in Equations 5.27 and 5.28 were not 2 and 3, but 2.08 and 2.19 for mountain beech, and 1.63 and 2.41 for red pine. These suggest thinning slopes of −1.05 in the first case and −1.48 in the second, which compare quite remarkably well with the slopes that they observed: −1.06 and −1.48 (Figure 5.38). The similarities between the estimates and observations for the intercept constants were equally impressive. These results show, therefore, that thinning lines with slopes other than −3/2 can occur, but can be explicable in terms of the detailed biology of the species concerned. They also show that even when slopes of −3/2 do occur, they may do so, as with red pine, for the ‘wrong’ reason (−2.41/1.63 rather than −3/2).

Figure 5.38 The species boundary line for populations of red pine,Pinus densiflora, from northern Japan (slope = −1.48).

Source: After Osawa & Allen (1993).

self‐thinning in sessile animals

Animals must also ‘self‐thin’, insofar as growing individuals within a cohort increasingly compete with one another and reduce their own density. And in the case of some sessile, aquatic animals, we can think of them, like plants, as being reliant on a resource falling from above (typically food particles in the water) and therefore needing to pack ‘volumes’ beneath an approximately constant area. It is striking, therefore, that in studies on rocky‐shore invertebrates, mussels have been found to follow a thinning line with a slope of −1.4, barnacles a line with a slope of −1.6 (Hughes & Griffiths, 1988), and gregarious tunicates a slope of −1.5 (Guiñez & Castilla, 2001). There is, however, nothing linking all animals quite like the shared need for light interception that links all plants.