Dynamic thinning lines

The patterns that emerge in growing, crowded cohorts of individuals were originally the focus of particular attention in plant populations. For example, perennial rye grass (Lolium perenne) was sown at a range of densities, and samples from each density were harvested after 14, 35, 76, 104 and 146 days (Figure 5.31a). Figure 5.31a has the same logarithmic axes - density and mean plant weight - as Figure 5.14. It is most important to appreciate the difference between the two. In Figure 5.14, each line represented a separate yield-density relationship at different ages of a cohort. Successive points along a line represent different initial sowing densities. In Figure 5.31, each line itself represents a different sowing density, and successive points along a line represent populations of this initial sowing density at different ages. The lines are therefore trajectories that follow a cohort through time. This is indicated by arrows, pointing from many small, young individuals (bottom right) to fewer, larger, older individuals (top left).

Mean plant weight (at a given age) was always greatest in the lowest density populations (Figure 5.31a). It is also clear that the highest density populations were the first to suffer substantial mortality. What is most noticeable, however, is that eventually, in all cohorts, density declined and mean plant weight increased in unison: populations progressed along roughly the same straight

Figure 5.30 (a) A coastal area in the Netherlands providing both nesting and feeding territories for oystercatchers. In 'resident' territories (dark shading), nesting and feeding areas are adjacent and chicks can be taken from one to the other at an early age. 'Leapfrogs', however, have separate nesting and feeding territories (light shading) and food has to be flown in until the chicks fledge. (b) Residents (•) fledge more chicks than leapfrogs (•). (c) Residents (•) deliver more food per tide (grams of ash-free dry weight (g AFDW), with standard deviations) than leapfrogs (•). The latter deliver more, the more effort (in flying) they expend, but still cannot match the residents. (After Ens et al., 1992.)

line. The populations are said to have experienced self-thinning (i.e. a progressive decline in density in a population of growing individuals), and the line that they approached and then followed is known as a dynamic thinning line (Weller, 1990).

The lower the sowing density, the later was the onset of self-thinning. In all cases, though, the populations initially followed a trajectory that was almost vertical, i.e. there was little mortality. Then, as they neared the thinning line, the populations suffered increasing amounts of mortality, so that the slopes of all the self-thinning trajectories gradually approached the dynamic thinning line and then progressed along it. Note also that Figure 5.31 has been drawn, following convention, with log density on the x-axis and log mean weight on the y-axis. This is not meant to imply that density is the independent variable on which mean weight depends. Indeed, it can be argued that mean weight increases naturally during plant growth, and this determines the decrease in density. The most satisfactory view is that density and mean weight are wholly interdependent.

Plant populations (if sown at sufficiently high densities) have repeatedly the -3/2 power law been found to approach and then follow a dynamic thinning line. For many years, all such lines were widely perceived as having a slope of roughly -3/2, and the relationship was often referred to as the '-3/2 power law' (Yoda et al., 1963; Hutchings, 1983), since density (N) was seen as related to mean weight (P) by the equation:

Figure 5.31 Self-thinning in Lolium perenne sown at five densities: 1000 (•), 5000 (•), 10,000 (■), 50,000 (■) and 100,000 (a) 'seeds' m-2, in: (a) 0% shade and (b) 83% shade. The lines join populations of the five sowing densities harvested on five successive occasions. They therefore indicate the trajectories, over time, that these populations would have followed. The arrows indicate the directions of the trajectories, i.e. the direction of self-thinning. For further discussion, see text. (After Lonsdale & Watkinson, 1983.)

Figure 5.31 Self-thinning in Lolium perenne sown at five densities: 1000 (•), 5000 (•), 10,000 (■), 50,000 (■) and 100,000 (a) 'seeds' m-2, in: (a) 0% shade and (b) 83% shade. The lines join populations of the five sowing densities harvested on five successive occasions. They therefore indicate the trajectories, over time, that these populations would have followed. The arrows indicate the directions of the trajectories, i.e. the direction of self-thinning. For further discussion, see text. (After Lonsdale & Watkinson, 1983.)

Density of survivors (m 2)

Density of survivors (m 2)

where c is constant.

Note, however, that there are statistical problems in using Equations 5.22 and 5.23 to estimate the slope of the relationship (Weller, 1987). In particular, since P is usually estimated as B/N, where B is the total biomass per unit area, P and N are inevitably correlated, and any relationship between them is, to a degree, spurious. It is therefore preferable to use the equivalent relationships, lacking autocorrelation:

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