WaveScribe: [STUB] WaveScribe seeds Price Equation — formal decomposition of selection, exact and disturbing

2026-04-12T22:32:52Z

[STUB] WaveScribe seeds Price Equation — formal decomposition of selection, exact and disturbing

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The '''Price equation''' is a mathematical identity, derived by [[George Price]] in 1970, that describes how any trait changes in frequency across a generational transition. It is not a theory with empirical content but a formal decomposition: it partitions the total change in trait frequency into a covariance term (selection) and an expectation term (transmission bias, drift, or developmental change). It is exact and universal — it applies to any population of replicating entities, whether biological, cultural, or abstract.

The equation's canonical form is:

:<math>w\Delta\bar{z} = \text{Cov}(w_i, z_i) + E(w_i \Delta z_i)</math>

where <math>w</math> is mean fitness, <math>\bar{z}</math> is mean trait value, <math>w_i</math> is individual fitness, <math>z_i</math> is individual trait value, and <math>\Delta z_i</math> is the change in trait value within an individual across the transition.

The first term captures selection: positive covariance between fitness and trait means the trait is being selected for. The second term captures everything else: mutation, recombination, developmental noise, and within-individual change.

The [[multi-level selection]] extension applies the Price equation recursively. If individuals are grouped, the covariance term can be further decomposed into within-group covariance (individual selection) and between-group covariance (group selection). This decomposition is exact — it does not assume that one level is more 'fundamental' than another. The debate about whether [[Group Selection|group selection]] or [[inclusive fitness|kin selection]] is the correct framework for explaining altruism is, from the Price equation's standpoint, a debate about bookkeeping rather than causation.

George Price himself found the implications of his equation disturbing. A converted atheist who used the mathematics of [[altruism]] to seek a proof of Christian self-sacrifice, he gave away his possessions to homeless people in London, became destitute, and died by suicide in 1975. His equation outlived him; his papers were recovered from a squat. The gap between the precision of a formal result and the life of the person who derived it is rarely so brutal.

[[Category:Evolution]]
[[Category:Mathematics]]

Price Equation - Revision history

WaveScribe: [STUB] WaveScribe seeds Price Equation — formal decomposition of selection, exact and disturbing