Survivorship Calculators

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A survivorship curve is a graphical representation of the proportion of individuals in a cohort that survive to each age. First formalized by Raymond Pearl, survivorship curves are fundamental tools in demography and population ecology — they reveal when mortality is concentrated in a life history, allowing ecologists and wildlife managers to identify vulnerable life stages and design targeted conservation interventions. Three idealized types (Types I, II, and III) capture the major patterns seen in nature, from long-lived mammals to marine invertebrates.

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What Is a Survivorship Curve?

A survivorship curve plots the number (or proportion) of individuals from a starting cohort that are still alive at each age, on a logarithmic y-axis. The x-axis represents age (often standardized as a fraction of maximum lifespan), and the y-axis shows lx — the proportion surviving to age x — on a log₁₀ scale. The shape of the curve reveals the age pattern of mortality.

The Three Types of Survivorship Curves

Type I — Late Loss

Most individuals survive through most of their potential lifespan, with mortality concentrated in old age. The curve is convex — nearly flat for most of life, then dropping sharply at the end. Characteristic of humans, elephants, and other large mammals with extensive parental care and low juvenile mortality.

Type II — Constant Loss

Mortality rate is roughly constant across all age classes — a fixed proportion of survivors dies in each time interval. The survivorship curve is approximately a straight diagonal line on a log scale. Characteristic of many birds, reptiles, and some rodents.

Type III — Early Loss

Extremely high mortality early in life, with survivors having a high probability of reaching old age. The curve drops steeply at first, then flattens. Characteristic of species that produce many offspring with little or no parental care — marine invertebrates, most fish, insects, many plants, and annual plants.

Life Tables

A life table systematically calculates age-specific survival and reproduction. Key columns:

  • x: Age class
  • nx: Number alive at start of age x
  • lx: Proportion surviving to age x (lx = nx / n₀)
  • dx: Number dying during age interval x
  • qx: Age-specific mortality rate (qx = dx / nx) — the probability of dying during age x given survival to that age
  • mx: Age-specific fecundity (offspring per female per age class)

Net Reproductive Rate (R₀)

R₀ = Σ(lx × mx)

R₀ is the average number of offspring produced per individual over a lifetime. R₀ > 1 means the population grows; R₀ < 1 means it declines; R₀ = 1 means stable population.

Glossary

Survivorship Curve
A graph of the proportion of a cohort surviving to each age, plotted on a log scale. Three idealized shapes (Types I, II, III) describe late-loss, constant-loss, and early-loss mortality patterns in different species.
Life Table
A table summarizing age-specific survival (lx), mortality (qx), and fecundity (mx) for a cohort. Used to calculate net reproductive rate (R₀) and intrinsic rate of increase (r) in population ecology.
Net Reproductive Rate (R₀)
The average number of offspring produced per individual over a lifetime, calculated as R₀ = Σ(lx × mx). R₀ > 1 means population growth; R₀ = 1 means replacement; R₀ < 1 means decline.

Frequently Asked Questions

Type I (late loss): most individuals survive to old age; mortality concentrated near maximum lifespan. Examples: humans, elephants. Type II (constant loss): constant mortality rate throughout life; straight line on log scale. Examples: many birds, some reptiles. Type III (early loss): extremely high mortality early in life; survivors likely to reach old age. Examples: fish, insects, marine invertebrates, plants.

lx is the survivorship function — the proportion of the original cohort (l₀ = 1.0) that survives to the beginning of age class x. It is calculated as nx / n₀, where nx is the number alive at age x and n₀ is the starting cohort size. lx decreases monotonically from 1.0 to near 0 as age increases.

R₀ = Σ(lx × mx) is the average number of offspring produced per individual over their lifetime, accounting for age-specific survival and fecundity. R₀ > 1 indicates a growing population; R₀ = 1 indicates a stable population at replacement level; R₀ < 1 indicates a declining population. It is a generation-level measure of population growth, unlike the instantaneous rate r.

Type III curves indicate a high-fecundity, low-parental-care strategy — producing many offspring and accepting that most will die before reproducing. This r-selected strategy is characteristic of species that exploit variable, unpredictable environments. The few survivors benefit from reduced competition and full resource access. It is a successful strategy despite (or because of) the high early mortality.