Evolution

Evolution is the change in heritable trait distributions across generations of a replicating population. Under the formal conditions identified by Richard Lewontin, evolution by natural selection is deductively entailed whenever three premises hold simultaneously in a population:

1. Variation. Individuals differ in traits.
2. Heredity. Offspring resemble parents with respect to those traits.
3. Differential fitness. Trait variants differ in expected reproductive success.

These conditions are jointly sufficient. Given (1)–(3), the distribution of traits in generation n+1 is not independent of the distribution in generation n, and the expected direction of change is toward variants of higher fitness. No further assumption — not organic chemistry, not DNA, not even biology — is required. Evolution is therefore best understood as a property of replicator dynamics, not a fact about Life specifically.

Minimal formalism

Let p_i denote the frequency of trait variant i and w_i its fitness. The Price Equation expresses the change in mean trait value as a covariance between fitness and trait, plus a transmission term:

Δz̄ = Cov(w, z) / w̄ + E(w · Δz)

The first term is selection; the second captures biased transmission (e.g. Mutation, drift, recombination). When the transmission term vanishes, selection alone determines the trajectory. Fisher's fundamental theorem is the special case in which trait = fitness: Δw̄ = Var(w) / w̄, so mean fitness is non-decreasing whenever additive genetic variance is positive.

Substrate independence

Because the Lewontin conditions make no reference to chemistry, any system exhibiting replication with heritable variation and differential success is governed by the same formal dynamics. This includes genetic populations, cultural traits (Memetics), and algorithmic processes such as Genetic Algorithms. The distinction between "biological" and "non-biological" evolution is therefore not a dichotomy but a question of which substrate carries the replicators.

This substrate-independence connects evolution to the broader study of Emergence: selection is one of the few well-formalised mechanisms by which simple local rules reliably generate cumulative, non-random structure at a higher level of description.

What evolution is not

Three conflations deserve explicit rejection:

• Evolution is not progress. The covariance term is directional only with respect to current fitness, which is itself a function of the environment. An environmental shift can invert it.
• Evolution is not optimisation. Selection operates on available variants, not on the space of possible designs; the outcomes are local, path-dependent equilibria.
• Evolution is not gradualism. The formalism is silent on rate. Punctuated trajectories are fully consistent with the premises.

See also

• Emergence
• Epistemology — evolutionary epistemology extends these dynamics to the growth of knowledge.
• Price Equation
• Replicator Dynamics
• Natural Selection