Temporal Changes in the Inequality of Early Growth of Cunninghamia lanceolata (Lamb.) Hook.: A Novel Application of the Gini Coefficient and Lorenz Asymmetry

Growth within tree populations varies among individuals due to changes in biotic and abiotic factors. The degree of such variation, defined as growth inequality, serves as a useful indicator of the uniformity of growth within a population in response to the prevalent environmental conditions. By application of the Gini coefficient (G), an index for inequality, we characterized the early growth inequality of ninety crosses of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) and their open-pollinated parental lines. Tree cumulative height was measured annually for 8 consecutive years. Both the crosses and parental lines exhibited temporal changes in growth inequality. The inequality of total height among the crosses decreased logarithmically with age by nearly 3-fold after 13 growing seasons, suggesting that tree height became less variable among the crosses as trees grew larger. Interestingly, the Lorenz asymmetry, an index reflecting the shape of the Lorenze curve from which G is derived, revealed that the inequality of annual height increment among the crosses resulted from an alternate contribution of the fast-growing and slow-growing trees. Among parental lines, two provenances with the smallest and the largest overall inequality in total height showed a similar pattern of changes in annual growth inequality, and the provenance differences were consistent over time. Compared to the other provinces, a local provenance exhibited less variation in total height among individual trees as reflected by a smaller value of inequality, and was better adapted to the field conditions. Our results demonstrated the sensitivity and usefulness of the Gini coefficient and Lorenz asymmetry for the analysis of growth inequality in non-natural populations. Growth inequality is a potentially useful evaluation criterion for early selection. Given comparable initial growth, provenances/families with lower growth inequality values would likely outperform those with higher growth inequality, and eventually tree size of the latter would be more variable due to greater variations among individual trees. Assessment of growth inequality at early ages will advance our understanding of variability of tree growth within a population, facilitate forest genetics improvement programs, and enhance the efficiency of tree breeding.