chemart / jain-krishna

hub:
  repo_type: generator
  builtin: jain-krishna
  tags:
  - banzhaf-yamamoto
chemistries:
- id: jain-krishna
  name: Jain-Krishna autocatalytic set model
  intuition: 'The life cycle of an autocatalytic set, stripped to a graph. Nodes are species and a directed
    edge means one catalyses another''s production; concentrations follow from the graph and the least-populated
    node is periodically replaced at random. Nothing happens for a while - then the first small autocatalytic
    cycle appears and the population organises around it and grows fast. Later a new cycle can undercut
    the incumbent, causing a crash and a reorganisation of the core. Innovation, dominance and collapse
    from one rule.

    '
  origin: Jain & Krishna, 1998-2002
  book: 15.2.2, 15.2.3
  refs:
  - '[425]'
  - '[426]'
  - '[427]'
  - '[428]'
  family: evolutionary-dynamics
  kind: generator
  constructive: true
  S:
    repr: m nodes of a directed graph; only the CATALYTIC action is represented, not the underlying reactions
    definition: explicit
  R:
    definition: explicit
    arity: 1
    scheme: 'c_ij = 1 means X_j catalyses the production of X_i: X_j -> X_j + X_i ; x_i'' = sum_j c_ij
      x_j - x_i sum_kj c_kj x_j'
  A:
    reactor: ode
    dilution: normalisation sum_i x_i = 1
    notes: 'Two timescales. Fast: integrate to the fixed point. Slow: remove a species with the smallest
      concentration, replace it with a fresh node whose in/out edges are redrawn with probability p, reset,
      repeat.

      '
  params:
  - name: m
    type: int
    default: 100
    min: 2
    max: 300
    role: structural
    meaning: number of nodes (the state-space dimension stays constant)
  - name: p
    type: float
    default: 0.0025
    min: 0
    max: 1
    role: structural
    meaning: link probability, both initially and on rewiring; the phase parameter
  - name: graph_updates
    type: int
    default: 0
    min: 0
    max: 20000
    range: the book's run finds the first autocatalytic set at update 2854 (m = 100, p = 0.0025)
    role: population
    meaning: slow-timescale steps (least-fit node replaced) applied before the network is returned; 0
      returns the initial random graph
  - name: self_loops
    type: bool
    default: false
    role: structural
    meaning: allow c_ii = 1 (direct self-replicators); the model sets c_ii = 0
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - flow
  - initial-state
  fidelity: book+decisions
  decisions:
  - 'The book''s prose says c_ij is ''a catalytic function of species i on species j'', but eq. 15.7 (x_i''
    = sum_j c_ij x_j ...) needs j to catalyse i. The equation is followed: c_ij = 1 becomes X_j -> X_j
    + X_i with rate 1, under constant-total dilution.'
  - The fast attractor is the Perron-Frobenius eigenvector of C, recorded as the initial state. When there
    is no autocatalytic set (eigenvalue 0), (C + I)^m is iterated instead, which concentrates on the ends
    of the longest chains. Ties for the least-populated node are broken at random.
  - After a replacement the book perturbs the remaining concentrations. That has no effect when the next
    attractor is computed exactly, so it is not modelled. extras.analysis records the eigenvalue and the
    attractor's support.
  - x0, the concentration given to a new node, only matters for numerical integration, so it is not a
    parameter.
  phenomena:
  - random phase -> growth phase (once the first small ACS appears) -> organising phase
  - crashes and core shifts when a stronger ACS out-competes the incumbent
  - attractor = eigenvector of the Perron-Frobenius eigenvalue lambda_1 of C
  notes: 'Comes with a published TAXONOMY OF INNOVATIONS worth encoding as an analysis output: Type A
    short-lived (blip, incremental); Type B long-term - independent organisation (core-shift / birth of
    an organisation / dormant) and modification of an existing organisation (core-enhancing / neutral).

    '