Siler Mortality Model
Also known as: Siler Model, Siler Competing-Risk Model, Five-Parameter Siler Hazard
The Siler model is a parametric description of the entire age pattern of mortality, from birth to extreme old age, built as the sum of three competing hazards: a high but rapidly declining risk in early life, a roughly constant background risk through the prime adult years, and an exponentially rising risk of senescence. With just five parameters it reproduces the characteristic U-shaped (or bathtub) mortality curve seen across humans and many animal species. Introduced by William Siler in 1979 for animal mortality, it has become a standard tool in paleodemography, anthropological demography, and comparative life-history studies where a smooth full-lifespan mortality law is needed.
Key highlights
- Captures the complete U-shaped mortality curve from infancy to old age, including the juvenile decline that Gompertz models miss.
- Decomposes mortality into three biologically interpretable hazards: immaturity, constant background, and senescence.
- Parsimonious at five parameters, making it well suited to sparse data and cross-species comparison.
- Widely adopted in paleodemography and animal demography, providing a comparable standard across studies.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use the Siler model when you need a smooth, parametric description of mortality across the entire lifespan — including infant and juvenile mortality, which Gompertz and Gompertz-Makeham omit — and when comparing mortality patterns across species or sparse populations through a few interpretable parameters. It is the standard choice in paleodemography and animal-demography, where data are limited and a full-lifespan law is required. Assumptions: mortality decomposes into the three additive hazards, the population is reasonably homogeneous, and there is enough data across ages to identify the five parameters. Do NOT use it when mortality has features the three components cannot capture (such as the young-adult accident hump, for which the Heligman-Pollard model adds a term), when only adult mortality matters (the simpler Gompertz or Gompertz-Makeham law suffices), or when the data are too sparse to estimate five parameters stably.
Strengths & limitations
- Captures the complete U-shaped mortality curve from infancy to old age, including the juvenile decline that Gompertz models miss.
- Decomposes mortality into three biologically interpretable hazards: immaturity, constant background, and senescence.
- Parsimonious at five parameters, making it well suited to sparse data and cross-species comparison.
- Widely adopted in paleodemography and animal demography, providing a comparable standard across studies.
- Lacks a term for the young-adult mortality hump caused by accidents and risk-taking, which the Heligman-Pollard model includes.
- Assumes a homogeneous population, so unmodeled frailty heterogeneity can bias the senescence parameters.
- Five parameters can be weakly identified or correlated when data are sparse or cover a limited age range.
- The additive-hazard decomposition is a convenient idealization, not a literal mechanistic account of cause-specific mortality.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
How does the Siler model differ from the Gompertz-Makeham law?
Gompertz-Makeham models adult mortality as a constant hazard plus an exponentially rising senescence term, but it does not represent the high, declining mortality of infancy and childhood. The Siler model adds a third, exponentially declining juvenile component, extending the law to the full lifespan and recovering the complete bathtub-shaped mortality curve.
Why is the Siler model popular in paleodemography?
Skeletal samples yield sparse, age-aggregated mortality data spanning all ages, and researchers need a smooth full-lifespan mortality law with few parameters to fit such data. The Siler model's five interpretable parameters span infancy to old age and can be estimated from limited data, making it well suited to reconstructing mortality in past populations.
What does the Siler model leave out compared with Heligman-Pollard?
The Heligman-Pollard model adds a hump term capturing the rise in mortality during young adulthood from accidents and risk-taking behavior, which the three-component Siler model does not include. Where that young-adult hump is important, Heligman-Pollard (with more parameters) fits better; where parsimony and full-lifespan coverage matter more, the Siler model is preferred.
Sources
- 1.Siler, W. (1979). A competing-risk model for animal mortality. Ecology, 60(4), 750–757.
- 2.Gage, T. B., & Dyke, B. (1986). Parameterizing abridged mortality tables: the Siler three-component hazard model. Human Biology, 58(2), 275–291.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 22). Siler Mortality Model. ScholarGate. https://scholargate.app/demography/siler-mortality-model