Probability of being a sampled ancestor of another sampled taxon
Description
Uses models from Foote (1996) to calculate the probability
Usage
1 2 
Arguments
p 
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 p will be used as the rate of anagenetic differentiation. 
q 
Instantaneous rate of extinction (mu) 
R 
Perinterval probability of sampling a taxon at least once 
mode 
Mode of morphotaxon differentiation, based on definitions in Foote, 1996. Can be pure cladogenetic budding ("budding"), pure cladogenetic bifurcating ("bifurcating") or pure anagenetic withinlineage change ("anagenesis"; i.e. Foote's 'phyletic change'). Default mode is "budding". 
analysis 
The type of analysis to be performed, either the probability of sampling direct
descendants ( 
Mmax 
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 nrep. Unfortunately,

nrep 
Number of repetitions to run in functions which are meant to sum over infinity. Default is arbitrarily high. 
Details
probAnc obtains the probability of sampling a descendant of a morphotaxon in the fossil record, given the sampling probability and estimates of origination and extinction rates. 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.
This 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 analysis
for
details. Mode of differentiation can also be varied
for three different models, see the argument mode
.
This probability is calculated including 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
100
can be no higher than 0.5. See Foote (1996) for a graphic depiction of this
nonintuitive 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.
References
Foote, M. 1996 On the Probability of Ancestors in the Fossil Record. Paleobiology 22(2):141–151.
See Also
SamplingConv
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13  #examples, run at very low nrep for sake of speed (examples need to be fast)
#default: 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
probAnc(p = 0.1, q = 0.1, R = 0.5, mode = "budding", analysis="indirectDesc",nrep=100) #default
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)
