When a species is introduced into an environment in which food and space are abundant, the population increases exponentially at the intrinsic rate of increase, r, characteristic of the species under the particular environmental conditions of temperature, moisture, food quality, etc. (See Figure 1). If conditions remain favourable for long enough, resources become limiting at high densities. Population growth then slows through density-dependent intra-specific competition as the carrying capacity of the environment, K, under the particular environmental conditions is approached or exceeded (See Figure 1). The population may stabilise at, or fluctuate about, the carrying capacity (See Figure 1).

Change in population density of an organism after introduction into an environment with a mean carrying capacity of K.

The discussion of r and K assumed stable environmental conditions, but major seasonal changes in conditions and shorter term weather influences may also be significant. As abiotic components of the environment become less favourable they limit development of all individuals in the population, and thus reduce r, whether the density is high or low (i.e. density-independent limitation). The population may decrease until favourable conditions return and the population again increases. Seasonal changes and weather influences may also affect biotic components of the environment, such as food, parasites and predators, so altering the carrying capacity of the environment (K) and inducing density-dependent limitation. Populations increase and decrease through time because of environmental changes. Both density-dependent and density-independent regulation affect most populations, but they may act at different times and in different places.

If biological control of weeds is to be successful, the biological control agent must build up to densities that significantly affect the host, and the herbivore and the host then become locked into a mutual density-dependent relationship (See Figure 2). If the host density increases, the herbivore population will rapidly increase in the presence of excess food to eventually reduce the density of its host. When the host density is low, the herbivore experiences local food shortage resulting in a decrease in population growth rate, and most dispersing individuals will die without finding another host plant. Considering the relationship from the other point of view, if the herbivore density is low, the host plant population will increase. If herbivore density is high, the host plant density will decrease through attack by the herbivore. This alternate cycling of herbivore and host densities usually occurs at different times in different places across the distribution of the plant resulting in an overall density of the host plant much less than would exist if the herbivore was not present.

Change in population density of a weed (solid line) after introduction to a new environment, and a successful biological control agent (dashed line) after its release.

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