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under‐ and overcompensating density dependence

The likely effect of intraspecific competition on any individual is greater the more competitors there are. The effects of intraspecific competition are thus said to be density dependent. We see this in more detail in Figure 5.3a, which shows the pattern of mortality in the barnacle, Semibalanus balanoides, on a rocky shore in north Wales, UK, between their recruitment as settling larvae and their survival as established adults two years later. The same data have been expressed in two ways. From the upper panel it is clear that initially, as the number of recruits increased, this led to a corresponding increase in the number of surviving adults. But the number of survivors peaked at a recruit density of around 30 per cm² and thereafter declined. We can therefore say that at densities beyond this peak, the mortality rate showed overcompensating density dependence in that increases in initial numbers led to decreases in final numbers. By contrast, before the peak, the density dependence was undercompensating in that final numbers continued to rise as the number of recruits increased.

Figure 5.3 Density‐dependent mortality. (a) Upper panel: the density of surviving adults of the barnacle, Semibalanus balanoides, in the UK as a function of the density of recruits two years earlier. Lower panel: the same data expressed as the relationship between the daily mortality rate and the density of recruits. (b) The density of surviving seedlings recruited to a population of the yellow star thistle, Centaurea solstitialis, in California as a function of the number of seeds present in the previous year.

Source: (a) After Jenkins et al. (2008). (b) After Swope & Parker (2010).

The lower panel plots the mortality rate against the initial number of recruits (mortality rate being calculated as –ln(S/R), where S and R are the number of survivors and recruits, respectively, divided by 730 (two years) to give a daily rate – similar to the intrinsic rate of natural increase, r, calculated in Section 4.7.1). We can see that at the very lowest abundances of recruits, the relationship was flat. That is, the mortality rate stayed the same and was thus density independent. There was no evidence of intraspecific competition when initial abundances were low. As those abundances increased, the slope of the relationship became positive – there was density dependence and thus evidence of competition – and that slope became steeper as the density dependence moved from under‐ to overcompensation.

exactly compensating density dependence

A similar relationship is shown in Figure 5.3b, but this time for a plant, the yellow star thistle, Centaurea solstitialis, in California, USA, relating the density of seedlings to the initial number of seeds in the soil. This time, though, at the highest seed densities, the number of surviving seedlings levelled off. The density dependence was exactly compensating: as initial density increased the mortality rate rose to counteract it.

intraspecific competition and fecundity

The patterns of density‐dependent fecundity that result from intraspecific competition are, in a sense, a mirror‐image of those for mortality (Figure 5.4). Here, though, the per capita birth rate falls as intraspecific competition intensifies. At low enough densities, the birth rate may be density independent (Figure 5.4a, lower densities). But as density increases, and the effects of intraspecific competition become apparent, birth rate initially shows undercompensating density dependence (Figure 5.4a, higher densities), and may then show exactly compensating density dependence (Figure 5.4b, throughout; Figure 5.4c, lower densities) or overcompensating density dependence (Figure 5.4c, higher densities).

Figure 5.4 Density‐dependent fecundity. (a) The fecundity (seeds per plant) of the annual dune plant Vulpia fasciculata is constant at the lowest densities (density independence, left). However, at higher densities, fecundity declines but in an undercompensating fashion, such that the total number of seeds continues to rise (right). (b) Fecundity in the southern pine beetle, Dendroctonus frontalis, in East Texas, USA (the number of eggs laid each time a beetle ‘attacks’ a tree) declines with increasing density of these attacks in a way that compensates more or less exactly for the density increases: the total number of eggs produced (eggs per attack × attack density) was roughly 100 per 100 cm², irrespective of attack density over the range observed (, 1992; , 1993). (c) When the planktonic crustacean Daphnia magna was infected with varying numbers of spores of the bacterium Pasteuria ramosa, the total number of spores produced per host in the next generation was independent of density (exactly compensating) at the lower densities, but declined with increasing density (overcompensating) at the higher densities. Standard errors are shown.

Source: (a) After Watkinson & Harper (1978). (b) After Reeve et al. (1998). (c) After Ebert et al. (2000).