Lognormality in ecological time series

Among ecologists, it is often believed that population abundance is lognormally distributed. To test this hypothesis, we analysed and compared 544 annual time-series of population abundance longer than 30 years (n greater than or equal to 30). Using Khamis' modified KS test we found one-half of the long-term datasets were lognormally distributed (p-value = 0.05). Among those deviating from lognormality, the most consistent feature was that the skewness was less than that expected under the lognormal hypothesis, implying a shorter upper tail (i.e, fewer extremely high values) than expected. There was little evidence of systematic extreme heavy-tail behaviour characteristic of the Levy-stable distributions in long (n greater than or equal to 50 years) time series. Both the standard KS test and the Akaike information criterion (AIC) were used to compare a number of alternative distributions for goodness of fit. Distributions. symmetric in logarithmic scale (lognormal and log-sech) were found to fit the data best according to the KS test. However, by the AIC the gamma distribution was most often the best model. Numbers of significant departures from lognormality varied among taxa, with insects having the highest departure from lognormality. There were also trophic, differences with herbivores deviating from lognormality more than carnivores. We found no habitat or geographic dependencies in the incidence of lognormality. The poor fit of the lognormal to real data means that it is not a good substitute for specific population dynamic and distributional information. However, being a superior "universal" descriptor of population abundance than other two-parameter models, it may be useful in applications where such detailed information is unavailable.