Table 2 Notation and definitions of key concepts used in the text.

X

The set of "potential" cell (lineage)/tissue fates.

K

The set of all non-empty finite subsets of X.

L = {L₁, ..., L _n }

The set of cell lineages.

R _i

Lineage profile: propensities of cell lineage i on X.

(R₁, ..., R _n )

n-tuple of propensities, also referred to as a "profile".

R

Tissue profile: ranking of propensities over tissue fates - the consequence of a cross-level principle, which is determined by a lineage-tissue mapping.

A ∈ K

A possible set of "actual" fates - considered in a particular context in which a lineage-tissue mapping is used to aggregate lineage profiles into one tissue profile.

X\A

The set of potential-but-not-actually-considered fates.

F

Lineage-tissue mapping: a map from K × D into K such that for all A ∈ K and all (R₁, ..., R _n ) ∈ D: F(A,(R₁, ..., R _n )) ⊆ A.

Ξ

Universal set of sets of alternatives (alternative fates) such that X ∈ Ξ is one set of potential alternative fates.

Ψ

Universal set of lineages such that L ∈ Ψ is some possible set of cell lineages.

Ω

A function that defines for a given set X the set K of non-empty finite subsets of X; For all X ∈ Ξ: Ω(X) = K.

Φ

For all X ∈ Ξ, all L ∈ Ψ: Φ(X, V) = D is the set of all logically possible profiles when the set of alternatives is X and the set of cell lineages is L.

Γ

Cross-level principle: a map Γ defined on Ξ × Ψ such that for all X and L, Γ defines a lineage-tissue mapping the domain of which is Ω(X) × Φ(X, L), where Ω(X) = K and Φ(X, L) = D such that for any A ∈ K and any (R₁, ..., R _n ) ∈ D, F(A, (R₁, ..., R _n )) gives a ranking of propensities for tissue fates (a tissue profile).

iff

short for "if and only if".

h, e, d

short for "homeostasis", "expansion" and "depletion". For the tissue level these correspond to "tissue homeostasis", "aberrant tissue" (e.g. dysplasia), and "aging tissue" as a consequence of niche depletion. At the cell level they stand for the lineages' capacity to contribution towards homeostasis, clonal expansion and a reduction of stem cells.