Diversity and rates

This module computes curves for diversity (species richness), origination and extinction from a presence-absence (binary) matrix with the oldest sample or interval in the last (lowest) row, and the youngest in the first row.

The many options reflect the considerable literature on such curves – for a short overview see Hammer and Harper (2024, pp. 192-196).

Richness

Species richness is estimated simply by counting the number of presences in each row. The Range-through option will fill in any absences between the first and last appearance of each species. The Endpoint adjust option will count any species beginning or ending in the row as 0.5 unit, while species confined to the row (singletons) will count 1/3 unit. This option should be used if rows represent time intervals instead of point samples (Foote 2000; Hammer & Harper 2024).

Origination and extinction – method “Simple”

Counts metric: The simple number of first appearances in the row (originations) and the number of last appearances (extinctions). These numbers are calculated with or without range-through, as selected by the Range-through option.

Ratios metric: Simple origination/extinction counts divided by the number of presences in the row.

Rates metric: Calculated according to Foote (2000) as follows.

Origination rate: R_o = ln ( ( N_bt + N_t ) / N_bt ) where N_t is the number of taxa present both in the focus row and the row above, and N_bt is the number of taxa present both in the focus row and in the rows below and above.

Extinction rate: R_e = ln ( ( N_bt + N_b ) / N_bt ) where N_b is the number of taxa present both in the focus row and the row below.

Origination and extinction, method “Three-timer”

The data are not subjected to range-through.

Counts metric: Not available

Ratios metric: Calculated according to Alroy (2008), see also the Past manual for details.

Rates metric: Logarithms of the ratios.

Origination and extinction, method “Gap-filler”

Counts metric: Not available

Ratios metric: Calculated according to Alroy (2014), see also the Past manual for details.

Rates metric: Logarithms of the ratios.

References

Alroy, J. 2008. Dynamics of origination and extinction in the marine fossil record. Proceedings of the National Academy of Sciences USA 105:11,536–11,542.

Alroy, J. 2014. Accurate and precise estimates of origination and extinction rates. Paleobiology 40: 374–397.

Foote, M. 2000. Origination and extinction components of taxonomic diversity: general problems. Paleobiology 26:74–102.

Hammer, Ø. & Harper, D.A.T. 2024. Paleontological Data Analysis, 2^nd ed. Elsevier.