The Price equation partitions the change in the expected value of a population measure. The first component describes the partial change caused by altered frequencies. The second component describes the partial change caused by altered measurements. In biology, frequency changes often associate with the direct effect of natural selection. Measure changes reflect processes during transmission that alter trait values. More broadly, the two components describe the direct forces that change population composition and the altered frame of reference that changes measured values. The classic Price equation is limited to population statistics that can be expressed as the expected value of a measure. Many statistics cannot be expressed as expected values, such as the harmonic mean and the family of rescaled diversity measures. We generalize the Price equation to any population statistic that can be expressed as a function of frequencies and measurements. We obtain the generalized partition between the direct forces that cause frequency change and the altered frame of reference that changes measurements.

中文翻译：

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广义价格方程：改变人口统计的力量

价格方程对总体度量的预期值的变化进行划分。第一个组成部分描述了由改变的频率引起的部分变化。第二个组成部分描述了由改变的测量值引起的部分变化。在生物学中，频率变化通常与自然选择的直接影响有关。测量变化反映了传播过程中改变性状值的过程。更广泛地说，这两个组成部分描述了改变人口构成的直接力量和改变测量值的参考框架的改变。经典的价格方程仅限于可以表示为度量的预期值的人口统计数据。许多统计数据不能表示为期望值，例如调和平均值和重新调整的多样性度量系列。我们将价格方程推广到任何可以表示为频率和测量函数的总体统计数据。我们获得了导致频率变化的直接力与改变测量值的改变参考系之间的广义划分。