This function uses models from Foote (1996) to calculate the probability of sampling a descendant of a morphotaxon in the fossil record, given the sampling probability and estimates of origination and extinction rates.
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Instantaneous rate of speciation (lambda). If the underlying model assumed is
anagenetic (e.g. taxonomic change within a single lineage, 'phyletic evolution')
with no branching of lineages, then
Instantaneous rate of extinction (mu)
Per-interval probability of sampling a taxon at least once.
Mode of morphotaxon differentiation, based on definitions in Foote, 1996. Can be
pure cladogenetic budding (
The type of analysis to be performed, either the probability of sampling direct
The maximum number of direct descendants (M) to sum over in the function, which
is ideally meant to be a sum from zero to infinity, like
Number of repetitions to run in functions which are meant to sum over infinity. Default is arbitrarily high.
These values are always calculated assuming infinite time for the potential ancestor to produce daughter taxa (assuming it lives that long) and under homogenous birth, death and sampling rates/probabilities, which is a situation that may be overly ideal relative to many real fossil records.
These probabilities can be calculated for either direct descendants, i.e. the probability
of sampling any morphotaxa that arise immediately from the particular
morphotaxon that could be an ancestor, or indirect descendants, i.e. the
probability for any morphotaxon that has the morphotaxon of question as an
ancestor, no matter how distant. See the argument
details. Mode of differentiation can also be varied
for three different models, see the argument
The probability of sampling a taxon's ancestor
is calculated while accounting for the probability that extinction might
occur before any descendants are produced. Thus, if
p = q, the probability of
a taxon going extinct before it produces any descendants will be 0.5, which
means that even when sampling is perfect (
R = 1, meaning completeness of
can be no higher than 0.5. See Foote (1996) for a graphic depiction of this
non-intuitive ceiling. For reasons (probably?) having to do with finite
approximations of infinite summations, values close to perfect sampling
may have values slightly higher than this ceiling, which is also apparent
visually in the figures in Foote (1996). Thus, values higher than 0.5 when p = q
should be discounted, and in general when sampling rate is high, results should
be treated cautiously as overestimates.
Foote, M. 1996 On the Probability of Ancestors in the Fossil Record. Paleobiology 22(2):141–151.
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# examples, run at very low nrep for sake of speed (examples need to be fast) # default options # probability of sampling a direct descendant probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "budding", analysis = "directDesc", nrep = 100) # other modes probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "bifurcating", analysis = "directDesc", nrep = 100) probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "anagenesis", analysis = "directDesc", nrep = 100) # probability of having sampled indirect descendants of a taxon # first, the default probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "budding", analysis = "indirectDesc", nrep = 100) probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "bifurcating", analysis = "indirectDesc", nrep = 100) probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "anagenesis", analysis = "indirectDesc", nrep = 100)
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