Controlling for life-history traits in vertebrates reveals that effective population size does not affect mutation rate or genome size

Why mutation rates (<i>μ</i>) and genome sizes (GS) vary among species remains a central question in evolutionary genetics. Two influential models, the drift-barrier hypothesis (DBH) and the mutational-hazard hypothesis, propose that effective population size (<i>N_e</i>) shapes these traits via the efficiency of selection, predicting higher <i>μ</i> and larger genomes in small populations. A recent comparative analysis of vertebrates reported a significant negative correlation between <i>N_e</i> and <i>μ</i>, interpreted as support for the DBH. Using phylogenetic path analysis, we reanalyze the same dataset of 55 vertebrate species spanning mammals, birds, reptiles, and fishes, in which <i>μ</i> was estimated from high-coverage parent-offspring trios, while explicitly controlling for six life-history traits within a causal framework that tests model-implied conditional independencies. We show that the reported <i>N_e</i>-<i>μ</i> association is entirely mediated by generation time (GT), which independently influences both variables; once this "back-door" path is blocked, <i>N_e</i> has no detectable effect on <i>μ</i>. Once GT is accounted for, mating system shows the largest association with <i>μ</i>. Parallel analyses of GS within the same validated life-history framework reveal that GS is unrelated to <i>N_e</i>, <i>μ</i>, or their interaction and is decoupled from the life-history covariation that strongly structures <i>μ</i>. These results are robust to alternative <i>N_e</i> estimators and causal model formulations. Together, our findings indicate that <i>N_e</i> provides little explanatory power for variation in <i>μ</i> or GS across vertebrates, challenging the presumed universality of drift-limited genome evolution.