Source
Luque (2016), LIT-205 (Biology & Philosophy 32(1):97–125), read in full in NOTE-101 from the author’s PhilSci-Archive manuscript, probably the accepted text. Page numbers are the manuscript’s.
What was actually shown
The derivation (§3, p. 7). Δz̄ = Cov(w, z) + E(wΔz) follows from a mapping of ancestors i (frequency q_i, character z_i, fitness w_i) to descendants, with the one stated restriction that the population is closed: every entity at t + 1 descends from, or is, an entity at t, so no migration (p. 8). It holds over any time interval. Equivalent partitions follow (Table 1), including Okasha’s Cov(ω, z′) + E(Δz) and a three-term form after Godfrey-Smith for non-additive selection and transmission.
Unification (§4). The diallelic viability-selection result Δp = p(w*_A − w̄)/w̄ is re-derived from the covariance term (pp. 10–11). Robertson’s secondary theorem and the classical reading of Fisher’s fundamental theorem are stated as derivable, with derivations deferred. Tables 2 and 3 collect about 25 derived identities and extensions across selection theory, stochastic evolution, ecology, epidemiology and non-genetic and cultural inheritance.
The schema reading (§6). Kuhn’s generalization-sketch: a law whose symbolic form changes from one application to the next, learned through exemplars. Two cases specialise it: Day & Bonduriansky’s overlapping-generation versions, separating selection, reproductive transmission and survival transmission (§6.1); and Rice’s stochastic Price equation, on which all moments of the fitness distribution contribute to directional evolution (§6.2). Under Sober’s distinction it is a consequence law, not a source law (p. 21).
The critics answered (§7). Dynamic sufficiency belongs to particular models, and van Veelen et al. (2012) concede as much. Sketches are predictively empty by nature, and unification is an explanatory value in its own right (Kitcher).
What could have come out otherwise. The equation could have needed substantive assumptions beyond closure, or failed to yield the classical results. It does not. The schema reading itself is an interpretation, and nothing in the paper could have refuted it.
What this does not say
- That the equation is not a tautology in the critics’ sense. §7.1 argues that mathematical truths are not logical tautologies (Gödel, Putnam). That answers the word. The critics’ point, that the equation follows from notational definitions and adds no empirical content, is conceded in §7.2.
- That the disputes are resolved. The abstract says they “could be diverted”, which the reading accepts; it does not support “resolved”.
- That Price-based modelling outperforms direct modelling. The prescription is asserted. The case-study authors “found previous results” already derivable by other means (p. 27).
- That the invariance is of a kind with physical symmetries. It rests on Frank’s (2012a) information-geometric identity with no derivation, and the analogy is informal (C4, weak).
- That the partition is fixed. The non-uniqueness of Price partitions, and their dependence on how ancestor–descendant maps are drawn, is noted but not treated as a problem for the reading.
- What the biological source laws are. Force in mechanics has source laws (gravitation, Coulomb); the paper does not say what plays that role for selection.
- Anything about Hamilton’s rule. It appears only in fn. 13, through Birch’s two versions.
Connections
- The multilevel Price partition underwrites decomposing selection by level in the units-of-selection material, LIT-160.
- No THEORY in the record states a general equation of this kind. The reusable move, granting that a general identity is predictively empty and locating its value in unification and model-building, is what NOTE-101 names as this paper’s contribution to the record.
Dated note, 2026-10-20
The derivation in this entry’s first clause is now held on its own as THEORY-770 (Active), split off by the promotion audit (batch 058). What remains Proposed here is the reading: that the equation is a generalization-sketch whose value lies in guiding model construction, and that the tautology and predictive-power charges ask of it what only its specialisations can supply. Wave 5 found no change to the premises, the rivals or the promote_when since batch 056.