Figure 5.12 Density‐dependent birth and mortality rates lead to the regulation of population size. When both are density dependent (a), or when either of them is (b, c), their two curves cross. The density at which they do so is called the carrying capacity (K). Below this the population increases, above it the population decreases: K is a stable equilibrium. However, these figures are caricatures. The situation is closer to that shown in (d), where mortality rate broadly increases, and birth rate broadly decreases, with density. It is possible, therefore, for the two rates to balance not at just one density, but over a broad range of densities, and it is towards this broad range that other densities tend to move.

      5.4.1 Carrying capacities

      Figures 5.12a–c reiterate the fact that as density increases, the per capita birth rate eventually falls and the per capita death rate eventually rises. There must, therefore, be a density at which these curves cross. At densities below this point, the birth rate exceeds the death rate and the population increases in size. At densities above the crossover point, the death rate exceeds the birth rate and the population declines. At the crossover density itself, the two rates are equal and there is no net change in population size. This density therefore represents a stable equilibrium, in that all other densities will tend to approach it. In other words, intraspecific competition, by acting on birth rates and death rates, can regulate populations at a stable density at which the birth rate equals the death rate. This density is known as the carrying capacity of the population and is usually denoted by K (Figure 5.12). It is called a carrying capacity because it represents the population size that the resources of the environment can just maintain (‘carry’) without a tendency to either increase or decrease.

      real populations lack simple carrying capacities

However, while hypothetical populations caricatured by line drawings like Figures 5.12a–c can be characterised by a simple carrying capacity, this is not true of any natural population. There are unpredictable environmental fluctuations, individuals are affected by a whole wealth of factors of which intraspecific competition is only one, and resources not only affect density but respond to density as well. Hence, the situation is likely to be closer to that depicted in Figure 5.12d. Intraspecific competition does not hold natural populations to a predictable and unchanging level (the carrying capacity), but it may act upon a very wide range of starting densities and bring them to a much narrower range of final densities, and it therefore tends to keep density within certain limits. It is in this sense that intraspecific competition may be said typically to be capable of regulating population size.

      In fact, the concept of a population settling at a stable carrying capacity, even in caricatured populations, is relevant only to situations in which density dependence is not strongly overcompensating. Where there is overcompensation, cycles or even chaotic changes in population size may be the result. We return to this point later (see Section 5.6.5).

      5.4.2 Net recruitment curves

      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.