Survivorship Curves Calculator
Calculate and classify survivorship curves (Type I, II, III) from life table data. Find age-specific survival rates, life expectancy, and mortality rates from cohort census data.
🌳 Ecology📐 lx = Nx / N0🧬 Biology
Initial cohort size N0
Age class survivors (comma-separated)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Survivorship Curves Calculator | — | lx = Nx / N0 | proportion surviving |
Step-by-Step Examples
Example 1
Type I (human-like)
N0=1000. Survivors: 990,970,940,800,500,100,10.
- lx = 0.990,0.970,0.940,0.800,0.500,0.100,0.010
- Most die late in life: Type I
- Life expectancy at birth ≈ high proportion of lifespan
✓ Type I: most deaths in old age (humans, elephants)
Example 2
Type II (constant mortality)
N0=100. Survivors: 72,52,37,27,20,14,10.
- lx ≈ e^(-0.33×x): constant per-capita mortality
- All age classes equally likely to die
- Birds, many lizards show Type II
✓ Type II: constant death rate (slope constant on log scale)
Example 3
Type III (high juvenile mortality)
N0=1000. Survivors: 100,60,40,30,25,22,20.
- Most die young; survivors live long
- Fish, oysters, most insects, many plants
- Low parental care, many offspring, few survive
✓ Type III: massive early mortality (fish, invertebrates)
Real-World Applications
Life History Theory
Survivorship curve shape reflects reproductive strategy: Type I = K-selected, Type III = r-selected.
Demography
Human survivorship tables used for life insurance, pension planning, public health assessment.
Wildlife Management
Age-specific survival rates guide population viability analysis for endangered species.
Evolutionary Biology
Predation patterns shape survivorship curves. High predation on juveniles → Type III. On elderly → Type I.
Common Mistakes to Avoid
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lx0 = 1.0 by convention
All cohort members are alive at start (age 0). lx decreases or stays the same as age increases — it can never increase.
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Log scale reveals curve type
Plot ln(lx) vs age. Straight line = Type II. Concave up = Type I. Concave down = Type III.
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Distinguish age-specific from period mortality
Cohort analysis follows one group. Period life table uses current age-specific rates. They differ when conditions change over time.
Frequently Asked Questions
What are the three types of survivorship curves? ▾
Type I: most individuals survive until old age, then die rapidly (humans, elephants). Type II: constant mortality throughout life (many birds). Type III: heavy early mortality, long-lived survivors (fish, trees, marine invertebrates).
What is age-specific mortality rate qx? ▾
qx = 1 - lx+1/lx. Probability of dying in age interval x to x+1 given survival to age x. qx is the age-specific mortality rate.
What is life expectancy? ▾
ex = Tx/lx where Tx = Σlx over remaining life. Expected additional years of life from age x. e0 = life expectancy at birth.
How do predators affect survivorship curves? ▾
Predators targeting juveniles → shift toward Type III. Predators targeting old/sick → shift toward Type I for survivors. Herding behavior modifies which ages are targeted.
What is the Leslie matrix? ▾
Age-structured population matrix model. Uses age-specific survival (lx) and fecundity (mx) data to project population size and structure over time. More detailed than R0 calculation.