An Example

The 'community approach' can be fruitfully applied to populations displaying nonlinear growth rates to illustrate how perturbations can bring about both alternative stable states and hysteresis. When there are depensatory responses in population growth rates such as may arise through Allee effects, for example, two population equilibria may be possible (Figure 4). In this case, the familiar S-curve is generated by having low growth rates at both high and low population densities. When populations are small, an Allee effect can result in low growth rates because of the increased difficulty experienced by individuals in finding mates. At high population sizes, a leveling off the birth rate occurs as resource limitation sets in. Such a nonlinear birth rate curve, combined with a linearly increasing death rate as population size increases, leads to two intersection points and thus two population equilibria where populations are at constant density (death rate = birth rate). Unfortunately, such alternative equilibrium points are often revealed through catastrophic losses of harvested populations of economically important species, such as many marine fish stocks.

Although the basins of attraction are fixed in this case, there is an asymmetry in the likelihood of the perturbation required to shift between states. Given that birth rates are lower than death rates when such populations are small, supplemental aid to populations 'trapped' in a low-density equilibrium will be necessary if these populations are to revert back to a state where birth rates are higher than natural death, and the population to recover to the high-density state (Figure 4). Hysteresis arises in such situations because population density perturbation through overfishing of large populations is not simply reversed by cessation of population harvesting. Instead,

. Death rate Birth rate

Population size

Figure 4 The relationship between population death and birth rates that allow for alternative stable states in population size for harvested fish. Intersections of the lines represent possible states with the circles representing stable ones and the X representing the unstable state. Reproduced with permission from Beisner BE, Haydon D, and Cuddington KL (2003) Alternative stable states in ecology. Frontiers in Ecology and the Environment 1: 376-382, © Ecological Society of America.

Population size

Figure 4 The relationship between population death and birth rates that allow for alternative stable states in population size for harvested fish. Intersections of the lines represent possible states with the circles representing stable ones and the X representing the unstable state. Reproduced with permission from Beisner BE, Haydon D, and Cuddington KL (2003) Alternative stable states in ecology. Frontiers in Ecology and the Environment 1: 376-382, © Ecological Society of America.

for such over-harvested populations a stronger reverse perturbation will be required, such as adding fish grown in hatcheries to aid recovery.

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