Lognormal distribution of water permeability and organic solute mobility in plant cuticles

Abstract

It is shown that water permeabilities and organic solute mobilities in plant cuticles have a lognormal distribution. Seven-hundred and fifty values for rate constants of desorption (^mobility) of 2,4-D from isolated Citrus aurantium L. cuticles from a population of leaves were pooled and analysed. A histogram of the rate constants of individual cuticles showed a skew distribution with a strong tail to higher values. Cuticular membranes with high values did not differ from others in visual appearance and were not leaky. After log-transformation of original data an almost perfect normal distribution was obtained. Statistical tests showed that a normal distribution of original values is not acceptable. Inspection of older data for water permeability in the same species and experiments using large samples of cuticles from leaves of Pyrus communis L. and Stephanotis floribunda Brongn. and from fruits of Capsicum annuum L. showed a similar distribution, as did inspection of data for experiments with organic solutes. A lognormal distribution was found for cuticles of plants from growth chambers, glasshouses and outdoors as well as for water permeability of intact leaves of Hedera helix L. For small samples the overestimation from using the arithmetic mean of original data can be high, but use of the geometric mean or the median leads to smaller deviations. Removing cuticular waxes from cuticles produced normally distributed samples. A normal distribution was also obtained when organic compounds which increase solute mobility were sorbed into cuticles.

Diffusion in plant cuticles as affected by temperature and size of organic solutes: similarity and diversity among species

“…(Batter, Batiie & Slater 1958;Btandt 1959;Vieth 1991;Schlotter & Furlati 1992). Mobilities of a giveti cotnpoimd in cuticles of the .same platit often differ by more thati 1 order of magtiitude atid follow a logtiomial distribution (Baur 1997). Our data sugge.st that differences in activation energies of diffusion among CM cause this lognotmal disttibution of solute tnobilities.…”

“…Rate constants as affected by temperature were studied for each CM individually by using one CM for all consecutive temperaUires. This method of paired observations eliminated variability between individual CM, which can be very large with coefficients of variation for rate constants above 50% (Baur 1997). Arithmetic means and 95% confidence intervals for estimates were calculated from logtransformed values (Baur 1997) and graphs were prepared using the Multigraf (G-Logic, Heidelberg, Gennany) software.…”

“…This method of paired observations eliminated variability between individual CM, which can be very large with coefficients of variation for rate constants above 50% (Baur 1997). Arithmetic means and 95% confidence intervals for estimates were calculated from logtransformed values (Baur 1997) and graphs were prepared using the Multigraf (G-Logic, Heidelberg, Gennany) software. In all experiments, the desorbed amount exceeded the impurity of theradiochemicals (< 2%) at least 10-fold.…”

Wax Layers onCosmos bipinnatusPetals Contribute Unequally to Total Petal Water Resistance

“…Dividing the water flux by the change in water vapor concentration at 25°C yielded the permeance. Permeances are reported as geometric means in accordance with Baur (1997).…”

<strong>Shannon&rsquo;s entropy usage as statistic</strong>

“…Lognormal distribution is known to fit skewed distribution [69] but did it is not always the best model for such data [70]. Lognormal distribution is mainly seen in biological or life science experiments [71,72,73], but also in environmental sciences [74,75], material science [76], or economics [77,78]. Furthermore, lognormal distribution found its usefulness in new derived research fields such as scientometry where Breuer and Bowen proposed a formula based on log-normal distribution to predict the expected number of citations [79].…”