8.4 Effect of Density on Populations

Carrying capacity, K, is the largest population size of a species that an environment can sustain over time with its available resources, such as food, water, nesting sites and space. A resource in short supply that limits growth is called a limiting resource. K isn't fixed: a drought can lower it, and a good rainy season can raise it.

When limits apply, growth follows the logistic model: dN/dt = rₘₐₓN × (K − N)/K. The new part, (K − N)/K, is the fraction of carrying capacity still unused.

When N is small, (K − N)/K is close to 1, so growth is nearly exponential. As N approaches K, (K − N)/K shrinks toward 0 and growth slows. At N = K, growth stops (dN/dt = 0). If N goes above K, (K − N)/K is negative and the population declines back toward K. The fastest growth, in individuals added per unit time, happens at N = K/2.

Graphed against time, logistic growth makes an S-shaped (sigmoid) curve: a slow start, a steep middle and a flat top at K. Real populations often overshoot K and then fluctuate around it.

Density-dependent factors have a bigger effect as population density rises. Competition for food and space gets fiercer, predators focus on abundant prey, diseases and parasites spread more easily between crowded individuals, and wastes build up. These factors push birth rates down and death rates up as N rises, which produces logistic growth.

Density-independent factors affect a population regardless of its density. Floods, fires, hurricanes, a sudden freeze or drought can kill the same fraction of a population whether it's sparse or crowded. They can cause sudden crashes that don't depend on how close the population is to K.

Density-dependent factors work like the negative feedback loops in 4.4. When the population rises above K, food runs short, disease spreads and predators gather, so deaths rise and births fall, pulling the population back down. When it drops below K, resources are plentiful, so births rise and the population grows again. The result is a population that hovers around its carrying capacity instead of growing without limit.

Real data rarely trace a perfectly smooth S-curve. A population can overshoot K before the effects of crowding catch up, then crash and rebound. When you read a graph, look for where the curve levels off (that's about K), where it's steepest (around K/2), and any sudden drops that a density-independent event could explain.