Of one thing I am certain: count data should be integers (or half integers if partial individuals are counted as one half). The chironomid data from Lake Żabińskie are remarkable in many respects; surely they meet this most basic expectation.

#load the data
library(readxl)
fname <- "zabinskie2015cit.xls"
excel_sheets(fname)
fos_counts <- read_excel(fname, sheet = "Chironomids Zabinskie counts")
chron <- fos_counts[, 1]
fos_counts <- fos_counts[, -c(1, ncol(fos_counts))]

Let’s look at the top left corner of the data matrix

knitr::kable(fos_counts[1:3, 1:3])

4.9980 |
0.000 |
4.998 |

2.9760 |
2.976 |
0.000 |

5.0055 |
0.000 |
0.000 |

Non-integer values!

In the fossil data set, 2.5% have non-integer (or half integer) values. These non-integer counts have a probabilty of occuring of exactly zero. Cromwell’s rule is over.

After Oliver Cromwell’s death, the monarchy was restored and Cromwell was posthumously executed. Other regicides were even less fortunate.

We can be absolutely certain that the archived data are not the original counts. Most likely, they are back-transformed from percent data that had been rounded. Why would anybody do that? Perhaps the authors lost the original counts. That would be unfortunate.

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## About richard telford

Ecologist with interests in quantitative methods and palaeoenvironments

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