Fitness Model F(g)

Rotifer uses a multiplicative fitness model — fundamentally different from the weighted averages used by most ranking systems.

The Formula

$$F(g) = S_r \cdot \log_2(1 + C_{util}) \cdot \frac{1 + R_{rob}}{2} \cdot L_{score} \cdot Cost_{score}$$ $$L_{score} = \frac{1}{1 + L / L_{ref}} \qquad Cost_{score} = \frac{1}{1 + Cost / Cost_{ref}}$$

Symbol	Meaning
S_r	Success rate (0–1)
C_util	Coverage utilization (0–1)
R_rob	Robustness — resilience to edge cases and adversarial input
L_score	Latency score: 1/2 at the reference latency L_ref, nearer 1 when faster, toward 0 as latency grows
Cost_score	Resource-cost score, the same shape against Cost_ref
L_ref, Cost_ref	Season median of genes in the same domain and fidelity; fixed constants when too few of them have measured runs

The efficiency scores multiply; they are not divided into the score. Each of the five factors lies in [0, 1], so F(g) does too: a perfect score is 1, and every shortfall takes its share off.

Why Multiplicative?

In a weighted average (e.g., 0.4×speed + 0.3×quality + 0.3×reliability), a gene with 0% reliability can still score 40% if it’s fast. The weak dimension is masked.

In a multiplicative model, any single zero-valued factor drives the entire score to zero:

• 0% success rate → F(g) = 0, regardless of speed
• Infinite latency → F(g) = 0, regardless of correctness
• Zero robustness halves the score instead of zeroing it: (1 + R_rob)/2 never drops below 1/2

This creates genuine selection pressure: genes cannot specialize in one dimension while ignoring others.

F(g) vs R(g): Two Different Metrics

The website’s creator page displays a Gene Reputation Score:

$$R(g) = W_{\text{arena}} \times \text{Arena} + W_{\text{usage}} \times \text{Usage} + W_{\text{stability}} \times \text{Stability}$$

Weights vary by ecosystem phase: W0 cold-start (0.70/0.05/0.25), W1 normal (0.60/0.20/0.20), W2 mature (0.50/0.30/0.20).

These are different metrics at different layers:

	F(g) Fitness	R(g) Reputation
Purpose	”How good is this gene right now?"	"How trusted is this gene over time?”
Model	Multiplicative (zero-intolerant)	Weighted average (balanced)
Layer	L3 Arena (protocol-level)	Product-level (website ranking)
Temporal	Per-evaluation snapshot	Rolling historical average

F(g) determines Arena survival. R(g) determines creator-facing visibility.

URAA Layer Assignment

F(g) lives at L3 Competition & Exchange. It is a protocol-level metric, not a product feature. Any binding that implements the Rotifer protocol must use the multiplicative model — this is not configurable.

Further Reading

• Protocol Specification: Overview — formal fitness function definition
• Arena Commands — how to submit genes and view fitness scores