Theil's Inequality Index Applied to Quantify Population Variation of Plants With Regard to Dry Matter Allocation

Andel, J. van; Nelissen, H. J. M.; Wattel, E.; Valen, T. A. Van; Wassenaar, A. T.

doi:10.1111/j.1438-8677.1984.tb01795.x

Cited by 17 publications

(6 citation statements)

References 40 publications

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“…Later, when competition for light develops, dominance and suppression occur. The results of Andel et al (1984) on Urtica dioica are illuminating in this context. They compared inequality in individually grown and competing individuals at five harvest dates.…”

Section: Density and Size Inequalitymentioning

confidence: 95%

Size Variability and Competition in Plant Monocultures

Weiner¹,

Thomas²

1986

Oikos

668

483

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Section: Density and Size Inequalitymentioning

confidence: 95%

Size Variability and Competition in Plant Monocultures

Weiner¹,

Thomas²

1986

Oikos

668

483

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“…4). Schmitt et al (1987b) also found less inequality late as compared to early in the season in thinned plots of Impatiens capensis, though in this instance greater mortality among smaller plants may have contributed to the decline (see also Hara 1984b for Helianthus annuus, van Andel et al 1984 for Urtica dioica under non-competitive conditions). It follows then that size inequality will not increase indefinitely but instead will level off or even decline in mature stands (Weiner and Thomas 1986), barring strong competition.…”

Section: Plant Development Size-specific Growth Rates and Size Ineqmentioning

confidence: 98%

“…This was true of control and low-density plantings of P. arenastrum. Schmitt et al (1987b) also found less inequality late as compared to early in the season in thinned plots of Impatiens capensis, though in this instance greater mortality among smaller plants may have contributed to the decline (see also Hara 1984b for Helianthus annuus, van Andel et al 1984 for Urtica dioica under non-competitive conditions). In effect, size differences that are built up during periods of accelerated growth disappear as plants "catch up to each other," unless other factors such as competition intervene to limit the ability of smaller plants to grow to a larger size.…”

Section: Planting Densitymentioning

confidence: 98%

Interplay of Morphology and Development on Size Inequality: A Polygonum Greenhouse Study

Geber¹

1989

Ecological Monographs

120

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Increases in size inequalities with time in cohorts of plants have been attributed to two causes: (1) variation in the exponential relative growth rates (RGR) of plants and (2) asymmetry of competitive interactions, whereby large plants can more readily suppress the growth of smaller neighbors than vice versa. It follows, then, that species with a longer exponential growth phase should develop greater size inequality over time. And since asymmetry is thought to be greater when competition is for light than when it is for below-ground resources, competitive interactions should be more asymmetric and size inequality should increase more in response to competition in species whose morphology results in greater between-plant shading. I tested these two hypotheses in greenhouse studies of two annual species, Polygonum arenastrum and P. douglassii, which differ in the duration of exponential growth and the likelihood of between-plant shading as a result of differences in development and morphology. Polygonum arenastrum has a shorter exponential phase of growth because it switches from vegetative growth to reproduction earlier than P. douglassii. It also has a prostrate growth form, more diffuse branching, and smaller leaves than P. douglassii. There should therefore be less shading of one plant by another in P. arenastrum than in P. douglassii.Seedlings from wild-collected seeds were planted in monoculture arrays at four different densities. The plants were harvested at five dates up to 10 wks; growth and branching pattern were measured at each harvest. As expected, in populations of P. douglassii, the species with the longer exponential growth phase, greater size inequality developed over time. In the absence of intraspecific competition, RGR was independent of plant size and size hierarchies were quire permanent. In contrast, P. arenastrum exhibited a period of decelerating growth which resulted in a negative correlation between RGR and plant size, frequent reversals in the size rankings of individuals over time, and declining size inequality through time under noncompetitive conditions. At high densities the morphology and RGRs of plants were size dependent in both species. Large individuals were more branched, had longer branches, and had higher RGRs than small individuals, and these shape and growth-rate differences became more pronounced as competition intensified. Furthermore, the size-dependence of shape and RGR was stronger in P. douglassii at all densities, and became relatively more pronounced as density increased, compared with P. arenastrum. These results are consistent with the expectation of greater competitive asymmetry in the species whose morphology should have led to greater between-plant shading. Size inequality increased with competition in both species. However, contrary to expectation, it did not increase more as density increased in P. douglassii. Reasons for the discrepancy between the morphological, RGR, and sizeinequality responses of the two species to density are discussed. The link between...

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“…In some cases, it will not matter which framework one uses for looking at inequality. For example, all measures of inequality, such as the Gini coefficient, the coefficient of variation, Theil's measure of entropy (van Andel et al 1984), or the standard deviation of the logtransformed distribution, will tend to be correlated. If one is just asking if a specific factor or treatment will increase or decrease inequality, then the interpretation of the data will probably not be affected by which framework the researcher takes.…”

Section: Discussionmentioning

confidence: 99%

Describing Inequality in Plant Size or Fecundity

Damgaard¹,

Weiner

2000

Ecology

108

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Lorenz curves have been used to describe inequality in plant size and fecundity, where the total inequality is summarized by the Gini coefficient. Here we propose a second and complementary statistic, the Lorenz asymmetry coefficient, which characterizes an important aspect of the shape of a Lorenz curve. The statistic tells us which size classes contribute most to the population's total inequality. This may be useful when interpreting the ecological significance of plant size or reproductive inequality.

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Theil's Inequality Index Applied to Quantify Population Variation of Plants With Regard to Dry Matter Allocation

Cited by 17 publications

References 40 publications

Size Variability and Competition in Plant Monocultures

Size Variability and Competition in Plant Monocultures

Interplay of Morphology and Development on Size Inequality: A Polygonum Greenhouse Study

Describing Inequality in Plant Size or Fecundity

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