Biology · Introductory biology · Worked example
Build a life table and read a survivorship curve
A cohort of 1,000 newly hatched frogs has 400, 200, 120, 80 and 0 alive at ages 1, 2, 3, 4 and 5 years. Build the life table, describe the survivorship curve, and find the life expectancy at hatching and at age 1.
Compute survivorship and deaths
lₓ is each count divided by 1,000, and dₓ is the drop to the next age.
| Age x (years) | nₓ | lₓ | dₓ | qₓ |
|---|---|---|---|---|
| 0 | 1000 | 1 | 600 | 0.6 |
| 1 | 400 | 0.4 | 200 | 0.5 |
| 2 | 200 | 0.2 | 80 | 0.4 |
| 3 | 120 | 0.12 | 40 | 0.33 |
| 4 | 80 | 0.08 | 80 | 1 |
| 5 | 0 | 0 | — | — |
Find the death rate in each year
qₓ = dₓ/nₓ. Sixty percent die in the first year, and the yearly death rate then falls.
Read the curve
Heavy loss in the first year followed by falling death rates is early loss: a Type III curve. On a log scale, log₁₀ nₓ falls from 3 to about 2.6 in the first year, then by smaller steps each year.
Life expectancy at hatching
Average each year’s starting and ending counts to get the frog-years lived in it: 700, 300, 160, 100 and 40. From hatching they add to 1,300 frog-years for 1,000 frogs.
Life expectancy at age 1
A one-year-old has the frog-years from age 1 onward, shared among 400 frogs. It can expect to live longer than a hatchling, a mark of Type III survivorship.
Result
qₓ falls from 0.6 to 0.33 after heavy first-year loss: a Type III curve. Life expectancy is 1.3 years at hatching but 1.5 years at age 1.
Your turn
A cohort of 500 animals has 490, 475, 450, 300 and 0 alive at ages 1, 2, 3, 4 and 5 years. Find q₃ and describe the curve.
Show the answer and explanation
q₃ = 150/450 ≈ 0.33, up from 0.02 in the first year: deaths come late, a Type I curve.
q₀ = 10/500 = 0.02, q₁ = 15/490 ≈ 0.03, q₂ = 25/475 ≈ 0.05, q₃ = 150/450 ≈ 0.33 and q₄ = 1. The death rate climbs with age.
Keep exploring
The survivorship tool opens with this cohort, builds the full life table and describes the curve as Type III.
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