Chapter 9: ψ-Dynamics of Natural Selection = Environmental Filtering

Natural selection is evolution's editor, filtering the variations that mutation provides. This chapter explores how ψ = ψ(ψ) interfaces with environmental pressures to shape the trajectory of life.

9.1 The Selection Function

Definition 9.1 (Natural Selection): Differential reproductive success: $\Delta\bar{\psi} = \text{Cov}(\psi, w) / \bar{w}$

where $\psi$ is trait value, $w$ is fitness, and $\bar{w}$ is mean fitness.

Selection acts when:

• Variation exists
• Variation affects reproduction
• Variation is heritable

9.2 Fitness Landscapes

Theorem 9.1 (Adaptive Topography): Evolution climbs fitness peaks: $\frac{d\psi}{dt} = \nabla W(\psi)$

where $W(\psi)$ is the fitness surface.

The landscape metaphor reveals:

• Multiple peaks (alternative adaptations)
• Valleys (fitness barriers)
• Ridges (neutral networks)
• Plateaus (drift domains)

Proof: Populations with higher fitness increase in frequency, creating uphill movement in fitness space. ∎

9.3 Types of Selection

Selection takes multiple forms:

Directional: Shifts mean $\psi_{t+1} = \psi_t + h^2 S$

Stabilizing: Reduces variance $\sigma^2_{t+1} < \sigma^2_t$

Disruptive: Increases variance $\sigma^2_{t+1} > \sigma^2_t$

Balancing: Maintains variation $p_{\text{equilibrium}} = \text{stable interior point}$

9.4 The Fundamental Theorem

Definition 9.2 (Fisher's Theorem): Rate of fitness increase equals genetic variance: $\frac{d\bar{w}}{dt} = V_A(w)$

where $V_A(w)$ is additive genetic variance in fitness.

Implications:

• Evolution stops without variation
• Speed proportional to variance
• Selection consumes variation
• Mutation-selection balance

9.5 Sexual Selection

Competition for mates creates unique dynamics:

$w = w_{\text{survival}} \times w_{\text{mating}}$

Male-male competition: Weapons, size, dominance Female choice: Ornaments, displays, songs Fisherian runaway: Preference-trait coevolution Good genes: Indicators of quality

Often opposes natural selection.

9.6 Frequency-Dependent Selection

Theorem 9.2 (Fitness Depends on Context): $w_i = f(p_i, p_j, ..., p_n)$

where fitness depends on frequencies of all types.

Examples:

• Negative: Rare advantage (predator search images)
• Positive: Common advantage (warning coloration)
• Oscillating: Rock-paper-scissors dynamics

Creating complex dynamics.

9.7 Multi-Level Selection

Selection acts at multiple levels:

$\Delta\bar{\psi} = \Delta\bar{\psi}_{\text{within}} + \Delta\bar{\psi}_{\text{between}}$

Levels:

• Genes (selfish elements)
• Cells (cancer evolution)
• Individual organisms
• Groups (social evolution)
• Species (species selection)

Creating hierarchical evolution.

9.8 Environmental Grain

Definition 9.3 (Selection Regimes): Spatial and temporal variation: $w(\psi, x, t) = \text{Fitness function varying in space and time}$

Fine-grained: Individual experiences average Coarse-grained: Populations in different patches Temporal variation: Fluctuating selection

Affecting evolutionary outcomes.

9.9 Constraints on Selection

Selection cannot optimize everything:

Genetic constraints: Pleiotropy, linkage Developmental constraints: Bauplan limitations Physical constraints: Laws of physics Historical constraints: Phylogenetic baggage Trade-offs: Resource allocation

$\psi_{\text{realized}} \neq \psi_{\text{optimal}}$

9.10 Selection in Action

Theorem 9.3 (Response to Selection): Predictable change: $R = h^2 S$

where $R$ is response, $h^2$ is heritability, $S$ is selection differential.

Documented examples:

• Darwin's finches (beak size)
• Peppered moths (melanism)
• Bacterial resistance
• Experimental evolution

Proving selection's power.

9.11 Soft vs Hard Selection

Population regulation matters:

Hard selection: Absolute fitness $N_{t+1} = \sum_i N_i w_i$

Soft selection: Relative fitness $N_{t+1} = K$

Creating different dynamics:

• Hard can cause extinction
• Soft maintains population size
• Reality often intermediate

9.12 The Selection Paradox

Selection seems to eliminate variation, yet diversity persists:

Erosion: Selection reduces variation Maintenance: Yet variation remains high

Resolution: Multiple forces maintain variation against selection's homogenizing tendency. Mutation introduces new variants, gene flow brings external variation, frequency-dependent selection maintains polymorphisms, and environmental heterogeneity creates diverse selective pressures. Selection is not a monolithic force but a complex filter that shapes variation while being shaped by it. Through this recursive interaction, ψ explores fitness landscapes while maintaining the flexibility for future exploration.

The Ninth Echo

Natural selection reveals ψ's method for navigating possibility space—not through foresight but through differential propagation of successful variants. Like a river finding the path of least resistance, life flows toward higher fitness through the simple algorithm of reproducing what works. Yet selection is creative, building complex adaptations from simple beginnings through patient accumulation of improvements. In selection, we see ψ's quality control mechanism, ensuring that each generation carries forward the accumulated wisdom of all previous generations while remaining open to innovation.

Next: Chapter 10 explores Genetic Drift and Collapse Randomization, examining evolution's stochastic component.