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Rob J. Hyndman1, Mohsen B. Mesgaran2 and Roger D. Cousens2

  1. Department of Econometrics & Business Statistics, Monash University, VIC 3800, Australia
  2. Department of Resource Management & Geography, The University of Melbourne, Victoria 3010, Australia

Biological Invasions (2015), 17(12), 3371-3381.

Abstract
Current methods for using herbarium data as time series, for example to estimate the length of the invasion lag phase, often make assumptions that are both statistically and logically inappropriate. We present an alternative statistical approach, estimating the lag phase based on annual rather than cumulative data, a generalized linear model incorporating a log link for overall collection effort, and piecewise linear splines. We demonstrate the method on two species representing good and poor data quality, then apply it to two data sets comprising 448 species/region combinations. Significant lags were detected in only 28 and 40 % of time series, a much lower level than the 95 and 77 % found in previous analyses of the same data. In a case with high quality data, a lag was concluded even though during the “lag” the locations of herbarium collections indicated that it was spreading rapidly at a continental scale. In species with few records, results were sensitive to the way in which zeroes were included. Overall, our method gives very good fit to the data, avoids unrealistic assumptions of other methods and gives more reliable estimates of confidence. However, given the poor representation of herbarium samples in the early stages of invasions and the fact that they do not constitute a structured survey of abundance, we warn against over-reliance on statistical analysis of such data to reach conclusions about the dynamics of invasions.

Working paper

Online paper

R code

  Tag: ecology

33 posts
August 7th, 2015

Statistical issues with using herbarium data for the estimation of invasion lag-phases

By Rob J Hyndman, Mohsen B Mesgaran and Roger D Cousens

November 16th, 2001

Cycles and synchrony in the Collared Lemming (Dicrostonyx groenlandicus) in Arctic North America

Martin Predavec, Charles Kreb,  Kajell Danell and Rob J Hyndman

Oecologia (2001). 126, 216-224.

Abstract: Lemming populations are generally characterised by their cyclic nature, yet empirical data to support this are lacking for most species, largely because of the time and expense necessary to collect long-term population data. In this study we use the relative frequency of yearly willow scarring by lemmings as an index of lemming abundance, allowing us to plot population changes over a 34-year period. Scars were collected from 18 sites in Arctic North America separated by 2-1,647 km to investigate local synchrony among separate populations. Over the period studied, populations at all 18 sites showed large fluctuations but there was no regular periodicity to the patterns of population change. Over all possible combinations of pairs of sites, only sites that were geographically connected and close (<6 km) showed significant synchrony in fluctuations. The populations studied may not even be cyclic, at least for the time period 1960 to 1994, and although fluctuating, randomisation tests could not reject the null hypothesis of random fluctuations. These data have implications for the testing of hypotheses regarding lemming cycles and highlight the need for long-term trapping data to characterise the lemming cycle.