Will small population sizes warn us of impending extinctions?

Several models are used to show that population sizes are often relatively insensitive to deteriorating environmental conditions over most of the range of environments that allow population persistence. As conditions continue to worsen in these cases, equilibrium population sizes ultimately decline rapidly toward extinction from sizes similar to or larger than those before environmental decline began. Consumer-resource models predict that equilibrium or average population size can increase with deteriorating environmental conditions over a large part of the range of the environmental parameter that allows persistence. The initial insensitivity or increase in the population of the focal species occurs because changes in the populations of other components of the food web compensate for the decline in one or more fitness components of the focal population. However, the compensatory processes are generally nonlinear and often approach their limits abruptly rather than gradually. When there is steady directional change in the environment, populations lag behind the equilibrium population size specified by current environmental conditions. The environmental variable can then decline below the level required for population persistence while the population size is still close to or greater than its original value. Efficient consumers and self-reproducing resources are especially likely to produce this outcome. More complex models with adaptive behavior, additional consumers, or additional resources often exhibit similar trajectories of population size under environmental deterioration.