Fitness Landscapes

Topic: fitness landscapes, static versus dynamic, and the metaphor critique

Status: Supporting concept — formed Session 4 Connected to: NK model, Echo model, stigmergy, niche construction, computational irreducibility

The Concept

A fitness landscape (Wright, 1932) maps genotypes (or phenotypes) to fitness values, with a notion of distance (mutation graph) between genotypes. The landscape metaphor: genotypes are points on a terrain, fitness is elevation, evolution climbs uphill.

Key assumptions:

  1. Fixed mapping: genotype → fitness is a pre-defined function
  2. Local search: evolution proceeds via mutations to adjacent genotypes (adaptive walk)
  3. Peak climbing: selection drives populations toward local fitness peaks
  4. Static landscape: the landscape doesn't change during evolution

The Problem: Static vs. Dynamic Landscapes

Static landscapes (traditional view)

The fitness landscape is fixed. Agents adapt TO the landscape. This is the NK model, the Echo model (partially), and most optimization algorithms.

Dynamic landscapes (niche construction / stigmergy view)

Agents MODIFY the landscape as they adapt to it. The landscape changes as a function of agent behavior. This is:

  • Niche construction (Laland, Odling-Smee): organisms modify selection pressures
  • Stigmergy (Session 3): agents leave traces that constrain future behavior
  • Downward causation (Hofstadter): emergent patterns reshape lower-level dynamics

The fitness function becomes: F(genotype, environment_state), where environment_state is a function of the history of agent actions.

Why this matters for multi-scale composition

A dynamic landscape is the mechanism for cross-scale interaction:

  • Agents at scale S1 modify their environment (stigmergic traces)
  • These modifications change the fitness landscape for agents at scale S1
  • When accumulated traces become self-maintaining (autopoietic), they become a new actor at scale S2
  • The new actor at S2 has its own fitness landscape, which it in turn modifies
  • This creates a cascade of dynamic landscapes across scales

The Fitness Landscape Metaphor Criticism

Kaplan (2008, 126 citations) — "The end of the adaptive landscape metaphor?"

  • The metaphor is "deeply problematic" because genotype space is high-dimensional
  • The 2D/3D visualization is misleading
  • "Peak climbing" ignores drift, recombination, non-adaptive processes
  • Argues for abandoning the metaphor in favor of rigorous mathematical models

Petkov (2015) — "The Fitness Landscape Metaphor: Dead but Not Gone"

  • The metaphor persists despite criticisms
  • Its primary function is as a "general unifying conceptual framework"
  • It reconciles heterogeneous evolutionary phenomena
  • Should not be abandoned even when specific models built on it fail
  • The metaphor is a linguistic-theoretical tool, not a falsifiable model

Gavrilets (2004) — "Fitness Landscapes and the Origin of Species"

  • Proposes "holey landscapes" — landscapes where high-fitness genotypes form connected networks
  • Alternative to the "rugged landscape" view
  • Speciation occurs along these high-fitness ridges, not by climbing peaks

Relevance to Our Project

1. Static landscapes cannot produce multi-scale composition

If the landscape is fixed, agents can only climb to local optima. They cannot reshape the landscape to create new scales. This is why Echo fails — even with endogenous fitness, the landscape is effectively static within a run.

2. Dynamic landscapes are necessary but not sufficient

Making the landscape dynamic (agents modify it) is necessary for multi-scale composition, but not sufficient. The modifications must:

  • Persist (stigmergic traces with appropriate decay rate)
  • Accumulate (build up over time)
  • Become self-maintaining (autopoietic crossing — H7)
  • Constrain agents at the original scale (downward causation)

3. The metaphor problem applies to ALife

ALife simulations implicitly use fitness landscapes. Even "emergent" ALife (Lenia, EvoLoop) has implicit landscapes defined by the rules. The criticism applies: if we think in terms of "fitness peaks," we'll design simulations that converge to peaks. We need to think in terms of dynamic, multi-scale landscape cascades.

Empirical Evidence

Wright (1932) — original metaphor

Visual representation of genotype frequency space. Not a mathematical model.

Gavrilets (2004) — holey landscapes

Mathematical framework for high-fitness networks. Alternative to rugged landscape view. Supported by speciation models.

Wiser, Ribeck & Lenski (2013) — long-term E. coli

50,000+ generations show power-law (not exponential) fitness growth. Consistent with hard (rugged) landscape dynamics.

No empirical studies on dynamic multi-scale landscapes

No study tests whether dynamic, multi-scale fitness landscapes produce open-ended evolution. This is our novel contribution territory.

Cross-References

  • [[concepts/nk-model]] — The formal mathematical framework for rugged landscapes
  • [[concepts/echo-model]] — Echo's endogenous fitness is a step toward dynamic landscapes
  • [[concepts/stigmergy]] — Stigmergy makes landscapes dynamic (agents reshape the landscape)
  • [[concepts/multi-scale-composition]] — Multi-scale dynamic landscapes are the unaddressed problem
  • Wright (1932) — original metaphor
  • Kaplan (2008) — "end of the metaphor" criticism
  • Petkov (2015) — "dead but not gone" defense
  • Gavrilets (2004) — holey landscapes alternative