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To determine how mutation order and selection jointly govern clonal architecture, the authors formulate a multitype branching-process model tracking two-hit malignant transformation pathways. Under successive exponential approximations, they derive point-process limits and a closed-form expression for the limiting expected Simpson's index, decomposing intratumor heterogeneity into upstream pathway weights and intermediate-to-malignant growth ratios. They reveal that acquiring a strong driver early promotes polyclonal expansion by seeding multiple founders, whereas acquiring it late accelerates clonal monopoly, yielding a non-monotone relationship between selection strength and clonal concentration.
The exact sequence in which driver mutations occur dictates whether a tumor diversifies or consolidates, showing that identical selective fitness advantages can drive either extreme polyclonality or rapid clonal dominance based purely on mutation order.
Cancer progression often requires multiple driver mutations, but the same drivers may be acquired in different orders. How these pathways jointly shape tumor clonal structure remains unclear. We develop a multitype branching-process model in which malignant transformation requires two driver mutations, distinguishing malignant cells by mutation order and the independent transformation event that founded their clone. Under a successive exponential approximation, we establish point-process limits for pathway-specific clone sizes and derive a closed-form expression for the limiting expected Simpson's index of the combined malignant population. When both mutation orders yield malignant cells with the same net growth rate, the index decomposes into effective pathway weights, determined by mutation rates and birth-death dynamics at preceding stages, and within-pathway concentration terms, determined by intermediate-to-malignant growth-rate ratios. A driver's effect on heterogeneity thus depends critically on when it is acquired. A strong driver acquired early expands the intermediate lineage and increases the supply of independent malignant founders, whereas the same driver acquired last strengthens the growth and age advantage of early-founded malignant clones. Under additive fitness effects, these opposing mechanisms can produce a non-monotone relationship between selective advantage and clonal concentration. Threshold-like non-additive fitness effects can generate highly concentrated malignant populations, while order-dependent terminal fitness causes the faster-growing pathway to dominate asymptotically. These results show how mutation order, mutational accessibility, selection, and epistasis jointly determine lineage-level intratumor heterogeneity.