Infinitesimal model¶

A quantitative-genetic model treating a trait’s heritable component as the sum of very many individually tiny genetic effects.

Version: v2 · 2026-09-19 · History
Domain-specific #: 5029
Domain group: Natural Sciences
Origin domain: Biology & Ecology
Subdomain: Quantitative Genetics → Biology & Ecology
Aliases: Polygenic model

Core Idea¶

The model concerns aggregate segregation and need not assert literally infinite loci or a normally distributed phenotype; linkage, selection, assortative mating and finite-effect loci create departures. Many Mendelian loci contribute small additive increments, random inheritance makes their aggregate approximately continuous and family resemblance is summarized through additive genetic variance and relatedness. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

How would you explain it like I'm…

Lots of Tiny Gene Pieces

Things like how tall you grow come from lots and lots of tiny pieces you got from your mom and dad. Each piece adds just a little bit. Because there are so many little pieces mixed in a random way, kids in a family end up kind of like each other and their parents, but not exactly the same.

Many Small Genes Add Up

Some traits, like height, don't come in just a few types. They come in a smooth range. The Infinitesimal model explains this by imagining many genes, each adding a small amount to the trait. Which genes you get from each parent is random, so all those little pieces add up to a smooth spread of results. The model also lets scientists predict how much relatives will resemble each other. The name says "infinitesimal," but it doesn't claim there are truly infinite genes. It's a handy picture that works best when no single gene matters a lot.

Many-Small-Genes Inheritance Model

The Infinitesimal model is a quantitative-genetics model for continuous traits. It treats a trait as the sum of small additive contributions from many Mendelian genes, plus environmental effects. Because each gene is inherited randomly, the combined genetic value of offspring varies smoothly. Resemblance between relatives can then be summarized by the additive genetic variance and how closely related the individuals are. Despite the name, the model doesn't require literally infinite genes, nor that the trait follows a normal distribution. Real-world factors like genes inherited together (linkage), selection, people choosing similar mates, and genes with large effects all cause departures. Using the model properly means stating its assumptions clearly for a given population and trait.

The infinitesimal model posits that a quantitative trait is built from many Mendelian loci, each contributing a small additive increment. Random Mendelian segregation makes the aggregate genetic value approximately continuous, and family resemblance is captured by the additive genetic variance scaled by relatedness. The model concerns aggregate segregation behaviour. It need not assert literally infinite loci or a normally distributed phenotype. Linkage, selection, assortative mating and loci of finite effect all produce departures. A rigorous application makes its assumptions explicit: the population and trait, the genotype-to-phenotype decomposition, the number and distribution of locus effects, additivity versus dominance, recombination, environmental contribution, the mating and selection regime, and the predicted covariance between relatives. Keeping separate what the model asserts, what evidence supports a given use, and what predictions it licenses guards against applying it beyond its assumptions.

Scope of Application¶

Infinitesimal model belongs to quantitative genetics and is useful where the analyst can specify the typed quantitative genetics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance are explicit. The scope is broad within that domain but bounded by the need for the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance are explicit.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Infinitesimal model. Infinitesimal model compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed quantitative genetics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem.
Lock the constitutive rule. Express the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of quantitative genetics because they reuse the typed quantitative genetics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Many Mendelian loci contribute small additive increments, random inheritance makes their aggregate approximately continuous and family resemblance is summarized through additive genetic variance and relatedness., and type the carrier, state every parameter and convention in the definition, test that the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Infinitesimal model Domain-specific

Parents (1) — outgoing typed relations

Infinitesimal model is a kind of Aggregation Prime

It remains its own entry because its identity is fixed by the population and trait, genotype-to-phenotype decomposition, number and distribution of locus effects, additivity and dominance assumptions, linkage and recombination, environmental contribution, mating and selection regime, additive variance and predicted relative covariance.

Hierarchy path (1) — routes to 1 parentless root

Infinitesimal model → is a kind of Aggregation → is a kind of Transformation → is a kind of, typical Function (Mapping)

Neighborhood in Abstraction Space¶

Infinitesimal model sits in a crowded region of the domain-specific corpus (17^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Population Genetics & Evolutionary Dynamics (30 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25