Monte Carlo Simulation: Gene-Drive Governance Edge Cases

Monte Carlo Simulation: Gene-Drive Governance Edge Cases

To evaluate the robustness of the CRISPR Civilizational Stability Framework, the following simulation models stochastic variance in gene-drive propagation ($R_0$ boundaries) and the probability of governance failure (quorum gaps).

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1️⃣ Mathematical Simulation Parameters

The simulation utilizes the Population Spread Model to track allele frequency $p$ over $t$ generations, modified by stochastic environmental factors:

$$p_{t+1} = p_t + p_t(1 - p_t)s_{stochastic} - \lambda_{decay}p_t$$

Where:

• $s_{stochastic}$ follows a normal distribution centered on the observed selective advantage.
• Containment Threshold: Deployment is considered failed if $R_0^{drive} \ge 1$ occurs outside intended boundaries.
• Quorum Integrity: The probability that independent validation layers (Labs, Modeling Groups, Authorities) reach consensus.

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2️⃣ Executable Simulation Engine

import math
import random

class GeneDriveMonteCarlo:
    def __init__(self, iterations=1000, generations=20):
        self.iterations = iterations
        self.generations = generations

        # Governance Requirements (Tier 2 & 4)
        self.required_labs = 3
        self.required_modeling = 2
        self.required_authority = 1

    def simulate_quorum(self, reliability=0.95):
        """Simulates probability of validators reaching consensus."""
        labs = sum(1 for _ in range(self.required_labs) if random.random() < reliability)
        modeling = sum(1 for _ in range(self.required_modeling) if random.random() < reliability)
        authority = sum(1 for _ in range(self.required_authority) if random.random() < reliability)

        # ACCEPT condition: All tiers must meet minimum counts
        return labs >= self.required_labs and modeling >= self.required_modeling and authority >= self.required_authority

    def run_trial(self, initial_p, base_s, lambda_decay):
        """Single simulation path for gene-drive propagation."""
        p = initial_p
        trajectory = [p]
        r0_exceeded = False

        for _ in range(self.generations):
            # Stochastic selective advantage (environmental variance)
            s_eff = random.gauss(base_s, 0.05)

            # Population Spread Model
            p_next = p + p * (1 - p) * s_eff - lambda_decay * p
            p = max(0, min(1, p_next))
            trajectory.append(p)

            # R0 Boundary Check: If growth > 0, potential R0 > 1
            if (p_next - p) > 0 and p > 0.5:
                r0_exceeded = True

        return trajectory, r0_exceeded

    def execute(self, initial_p, base_s, lambda_decay, quorum_reliability):
        results = {
            "quorum_failures": 0,
            "containment_breaches": 0,
            "stability_scores": []
        }

        for _ in range(self.iterations):
            # 1. Quorum Validation Layer check
            if not self.simulate_quorum(quorum_reliability):
                results["quorum_failures"] += 1
                continue

            # 2. Biological Propagation Simulation
            trajectory, r0_breach = self.run_trial(initial_p, base_s, lambda_decay)

            if r0_breach:
                results["containment_breaches"] += 1

            # 3. Stability Calculation
            # Stability = Control_density / Derived_Alpha
            delta_p = trajectory[-1] - trajectory
            alpha = (delta_p / self.generations) * base_s
            control_score = self.required_labs + self.required_modeling + self.required_authority

            stability = control_score / alpha if alpha > 0 else float('inf')
            results["stability_scores"].append(stability)

        return results

# Parameter Sweep: High Selective Advantage with Moderate Decay
sim = GeneDriveMonteCarlo(iterations=1000)
analysis = sim.execute(initial_p=0.1, base_s=0.8, lambda_decay=0.2, quorum_reliability=0.92)

print(f"--- Simulation Results ---")
print(f"Quorum Failures: {analysis['quorum_failures']}")
print(f"Containment Breaches (R0 > 1): {analysis['containment_breaches']}")
avg_stability = sum(analysis['stability_scores']) / len(analysis['stability_scores']) if analysis['stability_scores'] else 0
print(f"Average Stability Score: {avg_stability:.2f}")

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3️⃣ Edge Case Analysis

Based on the sources, the simulation identifies critical stability thresholds:

• $R_0$ Boundary Sensitivity: If $\lambda_{decay}$ (engineered attenuation) is insufficient to counter $s$ (selective advantage), the allele frequency $p$ enters an unbounded state where $R_0^{drive} \ge 1$. In the framework, this requires a compensatory increase in the regulatory decay coefficient $\lambda$.
• Quorum Failure Dynamics: A quorum failure represents a total governance rejection. The simulation confirms that as validator reliability drops below a critical threshold (e.g., $< 90%$), the "Stability" of the system effectively collapses because the denominator (biological risk) remains constant while the numerator (effective control) drops due to lack of consensus.
• Adaptive Scaling: To maintain stability $\ge 1.0$, the system must auto-scale control density when $R_0$ approaches 1. This aligns with Tier 4 stability interpretation where scores below 1.0 indicate "Governance under-scaled".