The meaning and measurement of size hierarchies in plant populations

Abstract

The term "size hierarchy" has been used frequently by plant population biologists but it has not been defined. Positive skewness of the size distribution, which has been used to evaluate size hierarchies, is inappropriate. We suggest that size hierarchy is equivalent to size inequality. Methods developed by economists to evaluate inequalities in wealth and income, the Lorenz curve and Gini Coefficient, provide a useful quantification of inequality and allow us to compare populations. A measure of inequality such as the Gini Coefficient will usually be more appropriate than a measure of skewness for addressing questions concerning plant population structure.

Estrutura populacional de Xylopia aromatica (Lam.) Mart. e de Roupala montana Aubl. em fragmentos de cerrado no Estado de São Paulo

“…As distribuições de estádios ontogenéticos foram comparadas entre os fragmentos e entre as espécies através do teste de Kolmogorov-Smirnov (Zar 1999), com correções de Bonferroni para testes seqüenciais (Rice 1989). As estruturas de tamanho (diâmetro e altura) foram analisada através do coeficiente de Gini (Weiner & Solbrig 1984). Foi feito um teste de bootstrap com 1.000 repetições para verificar diferenças dos coeficientes entre fragmentos e espécies.…”

Variation and Developmental Change in Activity of Gregarious Caterpillars, Hemileuca Lucina (Saturniidae)

“…Therefore, the variation in distance traveled was represented graphically using Lorenz curves and evaluated using the Gini statistic (Weiner and Solbrig, 1984 (Table 3) and therefore we concluded that distance traveled was unrelated to larval size.…”

“…Following the terminology and definitions of Weiner and Solbrig (1984), we believe that the analytical methods used by plant ecologists to evaluate a graded series of sizes of individuals within a population are particularly appropriate for behavioral data such as distance traveled when: 1) the aggregation yields large variation in individual distances, 2) there are relatively few large distances and many small ones, and 3) the few large distances contribute greatly to the observed pattern. Weiner and Solbrig (1984) indicate that standard measurements of skewness are inappropriate because they are designed to be insensitive to the degree of variability and only reflect the second aspect of the three listed above. Specifically in our study, it is inequality among larvae in distance traveled, not asymmetry in the distribution of distances ((2) above), that is of biological interest here.…”

Possible interactions between bacterial diversity, microbial activity and supraglacial hydrology of cryoconite holes in Svalbard

“…G corr was corrected to minimize the bias in estimating the underlying population, as it may result in skewed estimations of G corr (Weiner and Solbrig, 1984;Deltas, 2003)):…”