Infinitesimal model¶
A quantitative-genetic model treating a trait’s heritable component as the sum of very many individually tiny genetic effects.
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.
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. 2. 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) — more general patterns this builds on
-
Infinitesimal model is a kind of Aggregation Prime
The proposed strict upward parent is
prime:aggregation.
Hierarchy path (1) — routes to 1 parentless root
- Infinitesimal model → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Infinitesimal model sits in a crowded region of the domain-specific corpus (30th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Inheritance, Lineage & Development (17 abstractions)
Nearest neighbors
- Additive genetic effects — 0.95
- Selection limits — 0.93
- General selection model — 0.91
- Genotype–phenotype distinction — 0.90
- Complex segregation analysis — 0.90
Computed from structural-signature embeddings · 2026-09-08