Divide before you compare. Per capita rates and survivorship types are about fractions, not head counts.
Population ecology runs on per capita rates. Growth equals rate times number, so a steady rate on a growing population adds more and more. Read every table in proportions, not head counts.
Key terms
- Per capita rate of increase (r) — births minus deaths, divided by population size. It lets you compare populations of any size.
- Exponential growth — a constant per capita rate acting on a growing population. The graph curves upward in a J shape.
- Carrying capacity (K) — the largest population a habitat can sustain. The resource that runs short first, the limiting factor, sets it.
- Survivorship curve — a plot of how many in a cohort (a group born together) are still alive at each age.
How it works
- A population changes by births minus deaths, plus immigrants minus emigrants. With no migration, dN/dt = B − D.
- Divide the change by N to get r. If 200 mice have 30 births and 10 deaths in a month, r = 20 ÷ 200 = 0.10 per month.
- With plenty of resources, r stays at its maximum, r_max, so dN/dt = r_max N. The same rate acting on more individuals adds more each month: exponential growth.
- Exponential growth can't last. As the limiting factor runs short, growth slows and the population levels off near K.
- To study mortality, follow a cohort from birth, count survivors at each age, and plot the counts on a log scale.
- Type I drops late: few young, lots of care. Type II is a straight line: the same fraction dies each interval. Type III plunges early: many young, little care.
Why it matters
Expect a table. You'll calculate r, name a survivorship type from cohort counts, or explain why growth sped up while the per capita rate held steady. Every one of those turns on proportions. Next comes what happens as resources run short: growth slows toward K along the logistic curve.
Exam traps
| Trap | Actually |
|---|
| A steady per capita rate means the same number is added each month. | The same rate acting on more individuals adds more each month. Only a constant number added plots as a straight line. |
| Type II means the same number of individuals dies each year. | Type II means the same fraction dies. Fifty deaths a year from a shrinking pool means a growing share dies each year. |
| Carrying capacity is a fixed number for each species. | K depends on the habitat. Add more of the limiting resource and K rises until something else runs short. |
| A population with a high birth rate must be growing fast. | r is a net figure. High births with high deaths can match the r of low births with low deaths. |
Worked example
Two deer herds are surveyed for one year, with no migration. Herd A starts at 2,000 deer and has 500 births and 400 deaths. Herd B starts at 250 deer and has 90 births and 40 deaths. Which herd has the higher per capita rate of increase?
- Find each net change. Herd A: 500 − 400 = 100 deer. Herd B: 90 − 40 = 50 deer.
- Divide by the starting size. Herd A: 100 ÷ 2,000 = 0.05 per year. Herd B: 50 ÷ 250 = 0.20 per year.
- Compare the rates, not the gains. Herd B's rate is four times herd A's.
Herd B, at 0.20 per year versus 0.05 per year for herd A.
The per capita rate removes the effect of size, so it's the fair comparison. The near miss is herd A, because it added 100 deer to herd B's 50. A big herd with a low rate can still add more animals than a small herd with a high one. Herd A's 500 births look impressive too, but 400 deaths cancel most of them.