1. Density-dependent population growth The concept of an upper limit –K denotes ‘carrying capacity’

2. Density-dependent population growth The concept of an upper limit –K denotes ‘carrying capacity’ A simple equation: what does it mean?

3. Density-dependent population growth The concept of an upper limit –K denotes ‘carrying capacity’ A simple equation: what does it mean? In words: “the rate of change of the population equals the exponential growth rate discounted by how close the population is to carrying capacity.”

4. Density-dependent population growth You can also calculate the population size at any time, using the integral of this equation:

5. Density-dependence: some examples How fast is this population growing (or, what is dN/dt)? This population is growing exponentially

6. Density-dependence: some examples The population growth rate (dN/dt) increases linearly (at a constant rate) with population size. Note that the x-axis is N, not t. This population is growing exponentially

7. Density-dependence: some examples By contrast, this population is growing logistically (exhibiting density-dependence). Note that although the equation is written as dN/dt, we plotted N vs. t. Why? How fast is this population growing (or, what is dN/dt)?

8. Density-dependence: some examples Remember, this population is growing logistically (exhibiting density-dependence) The population growth rate (dN/dt) increases and then decreases with population size. Why?

9. A brief assignment What do you think the carrying capacity is for your home town, your home country, and the planet? Be prepared to defend your estimates. Based on your estimates of K, and the data you found last weekend for r, plot population growth curves for your home town, your home country, and the planet.