vultures were sighted during a subsequent, ‘settling’ stage (1995–2001).
Source: After Hirzel et al. (2004).
5.9 Self‐thinning
We have seen throughout this chapter that intraspecific competition can influence the number of deaths, the number of births and the amount of growth within a population. We have illustrated this largely by looking at the end results of competition. But in practice the effects are often progressive. As a cohort ages, the individuals grow in size, their requirements increase, and they therefore compete at a greater and greater intensity. This in turn tends to increase their risk of dying. But if some individuals die, then the density is decreased as is the intensity of competition – which affects growth, which affects competition, which affects survival, which affects density, and so on.
In trying to understand these interconnected processes it is important to distinguish three types of study: (i) those in which the ‘final’ performance of competitors is monitored over a range of densities and hence over a range of intensities of competition; (ii) those in which density and performance are monitored together over time as groups of competitors grow and undergo density‐dependent mortality; and (iii) those which seek relationships between density and performance in sets of populations, each observed just once (Weiner & Freckleton, 2010). Each type of study involves density and the performance of either individual competitors or the whole population, but the three tend to be aimed at addressing rather different questions. We examined the first in Section 5.2.2 when we discussed constant final yield. We turn here to the second and third.
5.9.1 Dynamic thinning lines
Starting with the second, 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 5.36a). Figure 5.36a has the same logarithmic axes – density and mean plant weight – as Figure 5.7: what we referred to previously as a type (i) study. In Figure 5.7, each line represented a separate yield–density relationship at different ages of a cohort, and the points along a line represented different initial sowing densities. In Figure 5.36, on the other hand, each line itself represents a different initial density and successive points along a line represent populations at different ages. Each line is therefore a trajectory that follows a cohort through time, as indicated by the arrows in Figure 5.36, pointing from many small, young individuals (bottom right) to fewer, larger, older individuals (top left).
Figure 5.36 Crowded plant populations typically approach and then track self‐thinning lines. Self‐thinning in Lolium perenne sown at five densities: 1000 (
Source: After Lonsdale & Watkinson (1983).
We can see that mean plant weight at a given age was always greatest in the lowest density populations (illustrated, for example, after 35 days (circled points) in Figure 5.36a). It is also clear that the highest density populations were the first to suffer substantial mortality. What is most noticeable, though, is that eventually, in all cohorts, density declined and mean plant weight increased in unison: populations progressed along roughly the same straight 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, reflecting the fact that 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 5.36 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 the truth is the reverse of this: 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.
’the –3/2 power law’
Plant populations (if sown at sufficiently high densities) have repeatedly 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
or:
where c is constant. (In fact, as we shall see, this is even further from being a universal law than the ‘law’ of constant final yield, discussed previously.)
Note, however, that there are statistical problems in using Equations 5.22 and 5.23 to estimate the slope of the relationship
