Multifractal-Driven Optimization of Read Length and Depth in Metagenomic Sequencing: A Utility-Based Framework

Background: Metagenomic sequencing has become a cornerstone of microbial ecology, yet the trade-off between read length and sequencing depth remains a critical challenge for cost-effective experimental design. Methods: We introduce a novel framework—fractal economics—that leverages multifractal analysis to quantify information recovery from metagenomic data. By simulating 20 × 20 parameter combinations (read length 100–2000 bp, depth 1–20 M reads, 100 replicates each) and computing the deviation of the multifractal dimension from an ideal asymptotic value, we define a utility function U(N, L) = − ln(dev) and derive elasticities (EL, EN) and marginal rates of substitution (EN,L). Results: Our results reveal a steep information gain when read length increases from 100 bp to 200 bp—particularly pronounced in shallow sequencing—followed by diminishing marginal returns beyond 500 bp and 10Mreads, with utility saturating near 1800 bp. We also observe near 1:1 substitution between read length and depth in the range 5–10 M reads and 500–1000 bp. A subsequent cost-benefit analysis, grounded on real Illumina NovaSeq SP platform specifications (maximum read length 600 bp, data-proportional pricing), reveals that the optimal parameters depend strongly on the number of multiplexed samples and total budget. For a typical large cohort (192 samples) with a moderate budget (5000 USD), the constrained optimum is N = 3 M reads and L = 600 bp, achieving utility U = 5.25 at a per-sample cost of 20.36 USD. Conclusion: This framework provides a theoretically grounded, data-driven roadmap for balancing information yield and cost in metagenomic experimental design.