Survivorship Curves

A survivorship curve is a graph of the number of individuals from an initial cohort (often standardized to 1,000, written $l_x = 1000$ at age $x=0$) that are still alive at each subsequent age class, $x$. It is built directly from the survivorship column, $l_x$, of a life table, which itself is derived from either a cohort (dynamic) life table — following one group of same-aged individuals through life — or a static (time-specific) life table, which infers age-specific mortality from a cross-sectional census. Plotting $l_x$ against age $x$, usually with $l_x$ on a logarithmic y-axis, produces a curve whose shape, not just its endpoint, carries biological information: a species with 1% of its cohort surviving to old age can get there by a slow, steady bleed or by an early massacre followed by near-invulnerability, and these are visually distinct. Ecologists sort survivorship patterns into three idealized types, first systematized for a general audience by Edward Deevey in 1947, though the underlying logic traces to the actuarial curves used by human demographers decades earlier. Type I curves are convex: survivorship stays high through infancy, juvenility, and early adulthood, then drops steeply as senescence sets in near the maximum lifespan. Type II curves are (on a semi-log plot) straight lines: the probability of dying in any given age interval is roughly constant, so $l_x$ declines geometrically. Type III curves are concave: survivorship crashes almost immediately after birth or hatching, and the few survivors then experience much lower, more constant risk for the remainder of life. No real species matches an idealized type perfectly — most populations are composites, e.g., Type III early in life followed by Type II or Type I later — but the framework organizes an enormous amount of comparative demography into three interpretable archetypes. Crucially, the axis convention matters: because raw survivor numbers can range over several orders of magnitude (from 1,000 newly settled barnacle larvae down to 2 survivors at metamorphosis), ecologists plot $\log_{10}(l_x)$ rather than $l_x$ itself. This logarithmic transform is what makes a constant mortality rate appear as a straight line (Type II) rather than a curve, and it is what allows Type I, II, and III to be visually distinguished on a common scale despite wildly different absolute numbers.

Step 1 — Build the cohort. Start with $N_0$ individuals born (or, for modular organisms, initiated as seeds/eggs) at the same time. Follow them at fixed age intervals, recording the number still alive, $n_x$. Convert to a standardized survivorship value $l_x = 1000 \times (n_x/n_0)$, so all species and cohorts are comparable on the same starting scale regardless of actual clutch or litter size.

Step 2 — Compute age-specific mortality. From $l_x$, derive $q_x$, the probability that an individual alive at the start of age interval $x$ dies before reaching $x+1$:

This is the mechanistic engine underneath the curve: $l_x$ is just the cumulative product of surviving each interval's $q_x$ in turn. A Type I curve arises mechanically because $q_x$ stays low for most ages and only rises sharply near the end of the physiological lifespan (senescence dominates). A Type II curve arises because $q_x$ is roughly constant across ages — an individual's risk of dying this year is the same whether it is 1 year old or 10, typically because mortality is dominated by unpredictable extrinsic hazards (predation, accident, disease) rather than by internal decay. A Type III curve arises because $q_x$ is enormous in the earliest age classes (a newly hatched fish larva might have a daily mortality risk of tens of percent) and then drops to a low, roughly constant background rate once a size/age refuge from predation and starvation is reached.

Step 3 — Link $q_x$ to underlying biology. The age-schedule of $q_x$ is not arbitrary — it is shaped by real, identifiable hazards:

• Extrinsic, size-independent hazards (accidents, unpredictable predation, disease outbreaks) tend to produce constant $q_x$ → Type II.
• Developmental vulnerability — small body size, no defenses, no parental shielding, being a dispersing propagule exposed to a huge and indiscriminate array of predators/competitors — produces very high $q_x$ concentrated in early life stages → Type III.
• Senescence — the physiological decline in tissue repair, immune function, and homeostatic capacity that accumulates with age (compounded in species with intense parental investment and reduced extrinsic hazard for the young) — produces $q_x$ that stays low through most of life then rises steeply → Type I.

Step 4 — Parental investment and clutch size as the evolutionary lever. The number and size of offspring a species produces is mechanistically coupled to where its curve sits. A species that produces millions of tiny, unprovisioned eggs (many marine invertebrates, fish, insects, most plants) cannot possibly guard each one; natural selection instead favors sheer numerical output to statistically guarantee that some survive, yielding Type III. A species that produces one or a few large, well-provisioned offspring with extended parental care (elephants, primates, humans, albatrosses) shifts mortality risk away from early life and toward senescence, yielding Type I. Species with intermediate investment and relatively exposed but mobile young — many birds, small mammals, lizards — often show the constant-hazard Type II pattern.

Step 5 — Log transform reveals rate, not just count. Because $l_{x+1} = l_x (1-q_x)$, a constant $q_x$ means $l_x$ declines geometrically, i.e., exponentially in continuous time. Taking $\log_{10}(l_x)$ converts this exponential decay into a straight line with slope proportional to $-q_x$ (roughly, for small $q_x$, slope $\approx -q_x/\ln(10)$). This is exactly why the log-linear plot is the diagnostic device: a straight-line segment on this plot is the visual signature of "no age-dependence in mortality" over that segment, regardless of whether the population is a bird, a lizard, or a rodent.

The survivorship curve typology was not invented at a desk — it emerged from painstaking cohort-tracking across very different organisms, then was synthesized into a comparative framework.

Raymond Pearl's Drosophila and human cohorts (1920s). Raymond Pearl, working at Johns Hopkins, built some of the first rigorous laboratory cohort life tables using Drosophila melanogaster reared in bottles under controlled food and temperature. By counting exactly how many flies from an initial cohort remained alive each day, Pearl produced a strongly convex (Type I-like) survivorship curve for flies held at low density with abundant food — mortality stayed low until an age-related crash. Pearl also compared this to human actuarial life-table data (from insurance company records) and proposed that a "rectangular" survivorship curve — most individuals living out nearly the full physiological lifespan — represented an ideal limit approached under benign, low-hazard conditions. This was an important early demonstration that the same species can shift its survivorship shape depending on environmental hazard (crowding and food shortage in flies pushed mortality earlier and flattened the curve toward Type II).

Edward Deevey's 1947 synthesis, "Life Tables for Natural Populations of Animals." Deevey's landmark paper in the Quarterly Review of Biology compiled cohort and static life-table data across a taxonomically broad set of species — including Dall mountain sheep (Ovis dalli) data collected by Adolph Murie in Denali (then Mount McKinley National Park), the herring gull, the American Robin, and several invertebrates and hydra — and for the first time plotted them together on a common log-survivorship axis. This side-by-side comparison is what crystallized the three-type classification (Deevey used the labels Type I, II, and III explicitly). Murie's Dall sheep data, obtained by aging skulls found in the field (using horn growth annuli, an age-at-death method rather than a true cohort follow-up, so technically a static/time-specific approximation), showed low mortality through prime adulthood with a steep rise in old age — a clear Type I signature in a wild large mammal, corroborating what had been assumed but not quantitatively demonstrated for free-ranging populations.

Long-term cohort studies establishing Type III empirically. Studies of intertidal invertebrates and fish populations — for example, tracking barnacle or oyster cohorts from larval settlement, or salmon from egg deposition to adult return — repeatedly show that of the many thousands of eggs or larvae produced, often more than 99% die within the first days to weeks (predation on planktonic larvae, failure to find suitable settlement substrate, starvation), while the small surviving fraction that reaches a size refuge experiences comparatively low and roughly constant mortality thereafter. These field counts (recruitment vs. initial egg production) are what pin Type III to real, measured numbers rather than to theoretical expectation alone.

What this collectively proved. Taken together, these studies demonstrated three things that remain foundational: (1) survivorship shape is measurable directly from field or lab cohort data, not merely inferred; (2) the same broad shape recurs independently across unrelated lineages sharing similar life histories (convergent Type I in large, K-selected mammals; convergent Type III in broadcast-spawning marine invertebrates and small-seeded plants), implicating common selective pressures rather than phylogenetic coincidence; and (3) survivorship shape is plastic within a species under different environmental conditions (Pearl's crowded vs. uncrowded flies), showing that the curve records ecological hazard, not a fixed genetic destiny.

Example 1 — Building and classifying a curve from raw cohort data. Suppose a marine biologist follows a cohort of 5,000 newly settled barnacle larvae (age class 0) at a rocky shore site and censuses survivors at six time points:

Computing $q_x$ column by column: $q_0 = (1000-30)/1000 = 0.970$ — a staggering 97% of the cohort dies in the first week alone, almost entirely to predation on newly settled, undefended spat. By contrast $q_x$ between week 26 and week 52 is only 0.091 (9.1%), a roughly ten-fold drop in risk. Plotted on $\log_{10}(l_x)$, this cohort shows a near-vertical initial plunge (1000 → 30 in one week) followed by a much shallower, nearly flat tail — the textbook concave signature of a Type III curve. Biologically, this matches expectation: barnacle cyprid larvae settle in vast numbers with no parental protection, and the handful that cement successfully and grow past a size refuge from most predators face a much gentler, roughly constant subsequent hazard.

Example 2 — Comparing two human-relevant curves and computing life expectancy shift. Consider two hypothetical human cohort life tables of 1,000 births each, one representing a pre-industrial population with high infant mortality and one representing a modern industrialized population.

In the pre-industrial table, $q_0$ (birth to age 1) is $(1000-720)/1000 = 0.28$ — 28% of babies die in year one, a Type III-like early spike superimposed on what is otherwise a Type I mammal curve. In the modern table, $q_0 = (1000-994)/1000 = 0.006$, a 47-fold reduction in infant mortality risk. Because so many more individuals in the modern cohort survive to old age intact, the modern curve is far more strongly rectangular (steep late drop, flat plateau through most of life) — a purer expression of the Type I shape that public-health improvements (sanitation, vaccination, neonatal care) reveal by removing the early-life risk that historically blurred human curves toward a mixed Type I/III pattern. This illustrates a key general point: Type I is the pattern expected once extrinsic early-life hazards are minimized, letting intrinsic senescence become the dominant determinant of the mortality schedule — exactly the shift Pearl anticipated when he called the fully rectangular curve a limiting ideal.

Survivorship analysis is far from a historical curiosity — it underpins active work across biology and applied science. In conservation biology, comparing observed survivorship curves for endangered populations (e.g., sea turtles, which are strongly Type III as hatchlings but shift toward Type I/II as adults) against expected curves helps managers identify exactly which life stage is the demographic bottleneck, directing intervention (nest protection versus adult bycatch reduction) to where it will most change population growth rate. In fisheries management, age-specific mortality schedules derived from catch data are essentially survivorship curves in disguise, used to set sustainable harvest quotas by estimating how much additional (fishing) mortality a stock's natural $q_x$ schedule can absorb before recruitment collapses. In epidemiology and public health, human survivorship curves are tracked over historical time as a direct, visual metric of societal health progress — the compression of mortality toward old age (a more rectangular Type I shape) is one of the clearest signatures of successful sanitation, vaccination, and neonatal care programs, and comparisons between countries or socioeconomic strata reveal persistent early-life mortality gaps. In agriculture and pest management, survivorship curves for insect pests identify vulnerable early life stages (egg or larval Type III mortality) as the most efficient targets for biological or chemical control, since interventions during naturally high-mortality windows require less added pressure to suppress a population. Finally, survivorship curves feed directly into the population-genetic and demographic modeling connecting mortality schedules to selection on reproductive timing — the conceptual bridge to life-history theory, where the shape of survivorship becomes one of the key inputs determining whether selection favors early, prolific reproduction or delayed, high-investment reproduction.

Ask the tutor: How would a survivorship curve change if I plotted it for males and females of the same species separately — what biological differences would that reveal?