By limiting the efficacy of selection on mutations of small effects, random drift is expected to play a major role in the evolution of genomes. Formalizing this idea, the nearly-neutral theory predicts that the proportion of non-synonymous mutations that are effectively neutral depends negatively on the effective population size (Ne). As a result, the ratio of non-synonymous over synonymous polymorphism ({pi}N /{pi}S) within populations, and divergence (dN /dS) between species, should both correlate negatively with Ne. Some of these predictions have previously been tested in mammals. However, most studies have either focused on dN /dS or on{pi} N /{pi}S and have not addressed the problem globally across evolutionary scales. Here we propose to test the nearly-neutral prediction in an integrative manner using the genomes of 150 mammals species and around 6000 orthologous genes. Our investigation spans the macro and the micro-evolutionary scale, using for the latter a measure of heterozygosity in the annotated orthologous coding sequences of the assembled diploid genomes. We confirm the positive correlation between dN /dS and life history traits. We also observe, for the first time in mammalian nuclear genomes, a relationship between{pi} N /{pi}S and{pi} S. Across time scales, the correlation patterns between micro and macro-evolutionnary quantities are in agreement with the nearly-neutral predictions, although the correlation between{pi} S and life-history traits is weaker and less robust than all other correlations. Together, these ob-served correlations are globally consistent with the nearly-neutral expectations and can be explained by invoking that all variables are in fact correlated with a single hidden variable: Ne.