A more precise speciation and extinction rate estimator

Abstract

A new turnover rate metric is introduced that combines simplicity and precision. Like the related three-timer and gap-filler equations, it involves first identifying a cohort of taxa sampled in the time interval preceding the one of interest (call the intervalsi0andi1). Taxa sampled ini0andi1are two-timers (t2); those sampled ini0andi2but noti1are part-timers (p); and taxa sampled only in eitheri1,i2, ori3are newly notated here as eithers1,s2, ors3. The gap-filler extinction proportion can be reformulated as (s1−s3)/(t2+p). The method proposed here is to substitutes3with the second-highest of the three counts when the expected orderings1≥s2≥s3is violated. In simulation, this new estimator yields values that are highly correlated with those produced by the gap-filler equation but more precise. In particular, it rarely produces highly negative values even when sample sizes are quite small. It is mildly upwards biased when sampling is extremely poor and turnover rates are extremely low, but it is otherwise highly accurate. Examples of Phanerozoic extinction rates for four major marine invertebrate groups are given to illustrate the method’s improved precision. Based on the results, the procedure is recommended for general use.

Five palaeobiological laws needed to understand the evolution of the living biota

“…Nonetheless, the palaeontological insights encapsulated by the laws described above have not yet become part of the foundational thinking in evolutionary biology. We need better molecular phylogenetic tools, more comprehensive testing of these tools on groups with good fossil records, better methods for integrating palaeonto logical and neontological data [1][2][3] , as well as better methods for using the fossil record to estimate origination and extinction rates [54][55][56][57] if we are to understand the evolutionary dynamics of the living biota. For groups without a fossil record, we need to learn what statements can and cannot be made from the living species alone.…”

Improved estimation of macroevolutionary rates from fossil data using a Bayesian framework

“…Indeed, treating origination, extinction and preservation rates in predefined time bins as independent parameters (i.e. without explicitly model-testing) is common practice in paleobiological studies of macroevolution (Foote, 2003; Liow and Finarelli, 2014; Alroy, 2015), and analogous models are available in PyRate as well (Silvestro et al, 2015b). However, this practice may generate spurious results if the amount of data is insufficient to confidently estimate all the parameters (Smiley, 2018), which is a general problem with overparameterization (Burnham and Anderson, 2002).…”

The R package divDyn for quantifying diversity dynamics using fossil sampling data

“…Foote, 1999(Alroy, 1996 ext3t, ori3t three-timer extinction and origination rates This is a provisional file, it has not been peer-reviewed. (Foote 1999), C3t = corrected three-timer rates (Alroy 2008), GF = gap-filler rates (Alroy, 2014) and 2f3 = second-for-third-substitution rates (Alroy, 2015…”

“…We computed diversity dynamics at both stratigraphic resolutions (stages and 10 myr), with three different treatments of the data (raw, CR and SQS). Four different rate metrics were applied: per capita rates (Foote 1999, used most frequently in studies), corrected three-timer rates (Alroy 2008), gap-filler equations (Alroy 2014), and second-for-third substitution rates of Alroy (2015). This resulted in 24 different sets (2 timescales × 3 data treatments × 4 rate metrics) of richness, origination and extinction rate series, each affected in a different way by the distorting effects of incomplete, heterogeneous sampling This is a provisional file, it has not been peer-reviewed.…”