Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- A population is all the individuals of one species in one area at one time. Members interact (competing, mating, spreading disease) and interact with their environment.
- In a closed population, size changes only through births and deaths. Growth depends on birth rate, death rate and population size.
- Births and deaths depend on energy and matter. Adaptations for obtaining and using food (feeding structures, energy budgets, breeding when food peaks, dormancy) change B and D.
- With no constraints on reproduction, the per capita growth rate stays at its maximum, rₘₐₓ, and growth is exponential. It cannot last: resources eventually run short.
Key relationships
| Equation | Meaning and units |
|---|---|
| dN/dt = B − D | B, D = births and deaths per unit time in the whole population; dN/dt in individuals per unit time |
| b = B ÷ N, d = D ÷ N | per capita birth and death rates (per individual per unit time) |
| r = (B − D) ÷ N, so dN/dt = rN | per capita growth rate; compares populations of different sizes |
| dN/dt = rₘₐₓN | exponential growth; rₘₐₓ = maximum per capita growth rate |
| Feature of exponential growth | What stays the same | What increases |
|---|---|---|
| shape | per capita rate, doubling time | dN/dt, N |
| graph | straight line on a log y-axis | steeper and steeper J on a linear axis |
Graphing population data
Line graph of N (or density) against time; time on the x-axis; labels and units on both axes; even scale; plot means with error bars for replicates; log y-axis for exponential data; trend line through the general pattern.
Assumptions behind the numbers
- dN/dt = B − D assumes no immigration or emigration.
- Exponential growth assumes unlimited resources and a constant rₘₐₓ.
- Month-by-month (step) projections are estimates of a continuous process.
Mistakes to avoid
- Treating B and D as per capita rates, or forgetting to divide by N when comparing populations.
- Saying the growth rate is constant in exponential growth (only the per capita rate is).
- Reporting N after one step when asked for dN/dt.
- Using a bar chart for a time series, or leaving out units.
- Calling a group of several species a population.
Quick self-check
- N = 500, B = 60 per year, D = 35 per year. dN/dt and r? (25 per year; 25 ÷ 500 = 0.05 per year)
- rₘₐₓ = 0.3 per day, N = 1,000. dN/dt? (0.3 × 1,000 = 300 per day)
- Why does a straight line on a log graph show exponential growth? (Equal steps on a log axis are equal ratios, so a constant slope means the same multiplication in each time interval.)
Next: practice questions.