Spatial distribution and sampling of Corythucha ciliata (Hemiptera: Tingidae) in London plane trees

Taylor’s power law and Iwao’s patchiness regression were used to describe the dispersion patterns for overwintering and wandering stages of Corythucha ciliata on the London plane trees, Platanus x acerifolia (Ait.) Willd. Both Taylor’s and Iwao’s tests fit the distribution data for the overwintering stage. The overwintering adults were spatially aggregated. In the wandering stage, Taylor’s power law consistently fit the data, whereas the fit of Iwao’s patchiness regression was erratic. Both Iwao’s and Taylor’s indices indicated a clumped distribution pattern for eggs, nymphs, and wandering adults. Trunk was identified as the best sampling target for the overwintering stage whereas twig was the best for the wandering stage. In order to determine the sample size for evaluating whether the population has reached the control threshold, the sampling of 35 and 7 trunks for the overwintering stage and 32 and 8 twigs per tree for the wandering stage would provide 0.5- and 0.25-precision levels, respectively.

Taylor's power law in the Wenchuan earthquake sequence with fluctuation scaling

Taylor's power law (TPL) describes the scaling relationship between the temporal or spatial variance and mean of population densities by a simple power law. TPL has been widely testified across space and time in biomedical sciences, botany, ecology, economics, epidemiology, and other fields. In this paper, TPL is analytically reconfirmed by testifying the variance as a function of the mean of the released energy of earthquakes with different magnitudes on varying timescales during the Wenchuan earthquake sequence. Estimates of the exponent of TPL are approximately 2, showing that there is mutual attraction among the events in the sequence. On the other hand, the spatio-temporal distribution of the Wenchuan aftershocks tends to be nonrandom but approximately definite and deterministic, which highly indicates a stable spatio-temporally dependent energy release caused by regional stress adjustment and redistribution during the fault revolution after the mainshock. The effect of different divisions on estimation of the intercept of TPL straight line has been checked, while the exponent is kept to be 2. The result shows that the intercept acts as a logarithm function of the time division. It implies that the mean–variance relationship of the energy release from the earthquakes can be predicted, although we cannot accurately know the occurrence time and locations of imminent events.