## Quantifying intraspecific competition

Every population is unique. Nevertheless, we have already seen that there are general patterns in the action of intraspecific competition. In this section we take such generalizations a stage further. A method will be described, utilizing k values (see Chapter 4) to summarize the effects of intraspecific competition on mortality, fecundity and growth. Mortality will be dealt with first. The method will then be extended for use with fecundity and growth.

A k value was defined by the use of k values formula:

k = log (initial density) — log (final density), or, equivalently:

k = log (initial density/final density).

For present purposes, 'initial density' may be denoted by B, standing for 'numbers before the action of intraspecific competition', whilst 'final density' may be denoted by A, standing for 'numbers after the action of intraspecific competition'. Thus:

Note that k increases as mortality rate increases.

Some examples of the effects of intraspecific competition on mortality plots of k against log are shown in Figure 5.16, in which k is density plotted against log B. In several cases, k is constant at the lowest densities. This is an indication of density independence: the proportion surviving is not correlated with initial density. At higher densities, k increases with initial density; this indicates density dependence. Most importantly,

Figure 5.13 The relationship between yield per pot and sowing density in carrots (Dacaus carrota) at four harvests ((a) 29 days after sowing, (b) 62 days, (c) 76 days, and (d) 90 days) and at three nutrient levels (low, medium and high: L, M and H), given to pots weekly after the first harvest. Points are means of three replicates, with the exception of the lowest density (9) and the first harvest (9). □, root weight, •, shoot weight, o, total weight. The curves were fitted in line with theoretical yield-density relationships, the details of which are unimportant in this context. (After Li et al., 1996.)

however, the way in which k varies with the logarithm of density indicates the precise nature of the density dependence. For example, Figure 5.16a and b describes, respectively, situations in which there is under- and exact compensation at higher densities. The exact compensation in Figure 5.16b is indicated by the slope of the curve (denoted by b) taking a constant value of 1 (the mathematically inclined will see that this follows from the fact that with exact compensation A is constant). The undercompensation that preceded this at lower densities, and which is seen in Figure 5.16a even at higher densities, is indicated by the fact that b is less than 1.

Exact compensation (b = 1) is often referred to as pure contest competition, because there are a constant number of winners (survivors) in the competitive process. The term was initially proposed by Nicholson (1954), who contrasted it with what he called pure scramble competition. Pure scramble is the most extreme form of overcompensating density dependence, in which all competing individuals are so adversely affected that none of them survive, i.e. A = 0. This would be indicated in Figure 5.16 by a b value of infinity (a vertical line), and Figure 5.16c is an example in which this is the case. More common, however, are examples in which competition is scramble-like, i.e. there is considerable but not total overcompensation (b > 1). This is shown, for instance, in Figure 5.16d.

Plotting k against log B is thus an informative way of depicting the effects of intraspecific competition on mortality. Variations in the slope of the curve (b) give a clear indication scramble and contest

Figure 5.14 The 'constant final yield' of plants illustrated by a line of slope —1 when log mean weight is plotted against log density in the dune annual, Vulpia fasciculata. On January 18, particularly at low densities, growth and hence mean dry weight were roughly independent of density. But by June 27, density-dependent reductions in growth compensated exactly for variations in density, leading to a constant yield. (After Watkinson, 1984.)

Figure 5.15 Intraspecific competition in plants often regulates the number of modules. When populations of rye grass (Lolium perenne) were sown at a range of densities, the range of final tiller (i.e. module) densities was far narrower than that of genets. (After Kays & Harper, 1974.)

Figure 5.14 The 'constant final yield' of plants illustrated by a line of slope —1 when log mean weight is plotted against log density in the dune annual, Vulpia fasciculata. On January 18, particularly at low densities, growth and hence mean dry weight were roughly independent of density. But by June 27, density-dependent reductions in growth compensated exactly for variations in density, leading to a constant yield. (After Watkinson, 1984.)

Figure 5.15 Intraspecific competition in plants often regulates the number of modules. When populations of rye grass (Lolium perenne) were sown at a range of densities, the range of final tiller (i.e. module) densities was far narrower than that of genets. (After Kays & Harper, 1974.)

Figure 5.16 The use of k values for describing patterns of density-dependent mortality. (a) Seedling mortality in the dune annual, Androsace septentrionalis, in Poland. (After Symonides, 1979.) (b) Egg mortality and larval competition in the almond moth, Ephestia cautella. (After Benson, 1973a.) (c) Larval competition in the fruit-fly, Drosophila melanogaster. (After Bakker, 1961.) (d) Larval mortality in the moth, Plodia interpunctella. (After Snyman, 1949.)

Figure 5.16 The use of k values for describing patterns of density-dependent mortality. (a) Seedling mortality in the dune annual, Androsace septentrionalis, in Poland. (After Symonides, 1979.) (b) Egg mortality and larval competition in the almond moth, Ephestia cautella. (After Benson, 1973a.) (c) Larval competition in the fruit-fly, Drosophila melanogaster. (After Bakker, 1961.) (d) Larval mortality in the moth, Plodia interpunctella. (After Snyman, 1949.)

Figure 5.17 The use of k values for describing density-dependent reductions in fecundity and growth. (a) Fecundity in the limpet Patella cochlear in South Africa. (After Branch, 1975.) (b) Fecundity in the cabbage root fly, Eriosichia brassicae. (After Benson, 1973b.) (c) Growth in the shepherd's purse plant, Capsella bursa-pastoris. (After Palmblad, 1968.)

Figure 5.17 The use of k values for describing density-dependent reductions in fecundity and growth. (a) Fecundity in the limpet Patella cochlear in South Africa. (After Branch, 1975.) (b) Fecundity in the cabbage root fly, Eriosichia brassicae. (After Benson, 1973b.) (c) Growth in the shepherd's purse plant, Capsella bursa-pastoris. (After Palmblad, 1968.)

of the manner in which density dependence changes with density. The method can also be extended to fecundity and growth.

For fecundity, it is necessary to think of B as the 'total number of offspring that would have been produced had there been no intraspecific competition', i.e. if each reproducing individual had produced as many offspring as it would have done in a competition-free environment. A is then the total number of offspring actually produced. (In practice, B is usually estimated from the population experiencing the least competition - not necessarily competition-free.) For growth, B must be thought of as the total biomass, or total number of modules, that would have been produced had all individuals grown as if they were in a competition-free situation. A is then the total biomass or total number of modules actually produced.

Figure 5.17 provides examples in which k values are used to describe the effects of intraspecific competition on fecundity and growth. The patterns are essentially similar to those in Figure 5.16. Each falls somewhere on the continuum ranging between density independence and pure scramble, and their position along that continuum is immediately apparent. Using k values, all examples of intraspecific competition can be quantified in the same terms. With fecundity and growth, however, the terms 'scramble' and especially 'contest' are less appropriate. It is better simply to talk in terms of exact, over- and undercompensation.

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