EUROPEAN JOURNAL OF ENTOMOLOGY

Eur. J. Entomol. 91 (2): 145-161, 1994

Measuring variation in abundance, the problem with zeros

WOLDA H., MAREK J.

N/A

Using time series of estimates of population abundances of moths from a light-trap in Brno, Czech Republic, the usefulness of a number of variability measures was examined. There are two problems that may occur. One is that time series data of population counts usually do not constitute a series of independent data, another is the occurrence of zeros when logarithms need to be taken. It is assumed here that the observed zeros no not represent extinction. All but one of the measures used suffered from the problem with interdependent abundances, making these measures difficult to use in statistical testing. The exception, ln{var(ln[R_i])}, on the other hand, generally, though not always, deals with mutually independent R_i (= y_i/y_(i-1)) and can then be used in statistical tests. This measure, however, measures variability of change rather than overall variability as the other statistics do. Moreover, when series with zeros are included, the arbitrariness of dealing with these zeros detracts also from the usefulness of this measure. Avoiding one of the problems usually forces one to accept the other, except when there are no zeros in the data. It being impossible for us to properly deal with this dilemma, we explored its consequences, especially those of dealing with zeros in one way or another. Any conclusions are purely ad hoc. When, in the literature, zeros presented a problem, they were either replaced by some positive number, the zero replacement value (ZRV), or one used the ln(y_i + z) transformation, with various values of z. We tried both in the present paper. Time series with a mean abundance smaller than 5 were found unreliable and should be omitted from analyses. The ln(y_i + z) transformation should be avoided for series without zeros and does not perform better than the ln(y_i) transformation for series with zeros. No statistically robust solution for the problem with zero values seems to exist, but for both mean and variability of abundance, a ZRV of 0.5 provided the most acceptable log transformation. For correlation between abundance and time the value of ZRV used was unimportant. One can avoid having to take the logarithms of zero by selecting only time series without zeros, but this implies a strong selection against the more variable species. Alternatively one can use ln[CV], or Lloyd's index, although one still has to deal with the interdependence of the data.

Keywords: Population variability, variation in abundance, variation in change in abundance, variability measurement, range, variance, coefficient of variation, Lloyd's index, log transformation

Accepted: November 19, 1993; Published: May 15, 1994  Show citation