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peak recruitment occurs at intermediate densities

An alternative general view of intraspecific competition is shown in Figure 5.13a, which deals with numbers rather than rates. The difference there between the births curve and the deaths curve is ‘net recruitment’, the net number of additions expected in the population during the appropriate stage or over one interval of time. Because of the shapes of the curves, the net number of additions is small at the lowest densities, increases as density rises, declines again as the carrying capacity is approached and is then negative (deaths exceed births) when the initial density exceeds K (Figure 5.13b). Thus, total recruitment into a population is small when there are few individuals available to give birth, and small when intraspecific competition is intense. It reaches a peak, i.e. the population increases in size most rapidly, at some intermediate density.

Figure 5.13 Intraspecific competition typically generates n‐shaped net recruitment curves and S‐shaped growth curves. (a) Density‐dependent effects on the numbers dying and the number of births in a population: net recruitment is ‘births minus deaths’. Hence, as shown in (b), the density‐dependent effect of intraspecific competition on net recruitment is a domed or ‘n’‐shaped curve. (c) A population increasing in size under the influence of the relationships in (a) and (b). Each arrow represents the change in size of the population over one interval of time. Change (i.e. net recruitment) is small when density is low (i.e. at small population sizes: A to B, B to C) and is small close to the carrying capacity (I to J, J to K), but is large at intermediate densities (E to F). The result is an ‘S’‐shaped or sigmoidal pattern of population increase, approaching the carrying capacity.

The precise nature of the relationship between a population’s net rate of recruitment and its density varies with the detailed biology of the species concerned (e.g. the trout, wildebeest and clover plants in Figure 5.14a–c). Moreover, because recruitment is affected by a whole multiplicity of factors, the data points rarely fall exactly on any single curve. Yet, in each case in Figure 5.14, a domed curve is apparent. This reflects the general nature of density‐dependent birth and death whenever there is intraspecific competition. Note also that one of these (Figure 5.14c) is modular: it describes the relationship between the leaf area index (LAI) of a plant population (the total leaf area being borne per unit area of ground) and the population’s growth rate (modular birth minus modular death). The growth rate is low when there are few leaves, peaks at an intermediate LAI, and is then low again at a high LAI, where there is much mutual shading and competition and many leaves may be consuming more in respiration than they contribute through photosynthesis. We return to these net recruitment curves in Section 15.3 when we look in detail at how natural populations (fisheries, forests) may be exploited – pushed from right to left along their net recruitment curves – in order to optimise the sustainable harvest we can take from them.

Figure 5.14 Some dome‐shaped net‐recruitment curves. (a) Six‐month old brown trout, Salmo trutta, in Black Brows Beck, UK, between 1967 and 1989. (b) Wildebeest, Connochaetes taurinus, in the Serengeti, Tanzania 1959–95. (c) The relationship between crop growth rate of subterranean clover, Trifolium subterraneum, and population size (leaf area index) at various intensities of radiation (0.4–3 kJ cm⁻² day⁻¹).

Source: (a) After Myers (2001), following Elliott (1994). (b) After Mduma et al. (1999). (c) After Black (1963).

back to an integral projection model of Soay sheep

Finally here, we return to Figure 4.17, where integral projection models were used to combine density‐dependent patterns of growth, survival and fecundity for Soay sheep in Scotland in order to estimate how a population’s net reproductive rate will itself vary with abundance. We saw, as we have now come to expect, that as abundance increased the net reproductive rate, R, declined (Figure 4.17e). What is also apparent now is that ln R (= r) was equal to zero (R = 1) at a population size of around 455 sheep, which is therefore the predicted carrying capacity of the population, and an equilibrium, with positive values of ln R at population sizes smaller than this, but negative values at population sizes larger.