calibration lognormal priors

[Fabia]

Dear Beast-users,

I am new to Beast and I am trying to figure out how to calculate the
lognormal priors for a calibration point.
The type of analysis that I want to run is one that uses a calibration
point defined by a minimum (or maximum) boundary only so that, for
example, node A can be younger than 2.7 but not older. The lognormal
tree prior seems the one suitable for this type of analysis but I do
not know how to calculate a prior for the mean and stdev (the zero-
offest would be 2.7 in my previous example) since I have only one
value (precisely 2.7) to base my calibration on. The default values
for these parameters seem to be stdev=1 and mean=0 but there is no
indication in the manual if these can be used with most zero-offsets
and how much they impact the time estimation.

Any suggestion would be appreciated.
Thanks,
Fabia

[Fabia]

[Simon Ho]

Dear Fabia,

The mean and standard deviation for lognormal calibration priors are
not easy to choose, especially when you have very limited
palaeontological information. In most cases there is no objective
means for determining these two values, because several of the factors
contributing to uncertainty in calibration points are not readily
quantifiable (e.g., uncertainty over the taxonomic affinity of
fossils). Divergence dating methods, including penalized likelihood
and the Bayesian autocorrelated relaxed-clock implemented in
multidivtime, cannot really estimate dates with only a single minimum
age constraint.

The mean and standard deviation essentially reflect how close you
think the fossil lies to the calibration node. This will generally be
judged on the number and degree of apomorphic features that can be
seen in the fossil. If most of the fossil's features are plesiomorphic
then it is likely to lie quite close to the calibration node.
Additionally, if the fossil record for a taxonomic group is very
incomplete, then we might suspect that the actual divergence
substantially predates the first appearance of fossils from either of
the descendent lineages.

One way to choose values for the parameters is to think of some 'soft'
maximum, beyond which it is unlikely that the divergence actually
occurred. In your example, you might believe that the divergence is
unlikely to have occurred before, say, 3.5 Myr. The mean and standard
deviation of the prior distribution can be chosen so that 95% of the
distribution lies between 2.7 and 3.5 Myr, but there is still no
convincing method for choosing the mean by itself.

An alternative would be to use an exponential prior, which requires
the specification of only the offset and mean. Then the mean can be
chosen such that 95% of the distribution lies between 2.7 and 3.5 Myr.

Generally speaking, choosing prior calibration distributions is a
difficult exercise, and it needs to be tackled on a case-by-case basis
because the fossil record relating to each divergence event will vary
in quality. You might find the following papers about probabilistic
calibrations useful:
- Hedges and Kumar (2004) in Trends in Genetics
- Yang and Rannala (2006) in Molecular Biology and Evolution
- Benton and Donoghue (2006) in Molecular Biology and Evolution
- Ho (2007) in Journal of Avian Biology
- Donoghue and Benton (2007) in Trends in Ecology and Evolution

Simon

[Fabia Ursula Battistuzzi]

Thanks for the clear explanation. I found the link to your avian paper and found it very interesting and following the suggestion you give I'm using now an exponential distribution. 

I do have another question, though. Is it possible to have an exponential distribution that is skewed towards younger times, instead of older ones? In other words, can I use the 2.7 calibration as a maximum boundary so that the node can be younger than 2.7 but not older? There is a brief mention in the Beast manual about a translated lognormal distribution but I am not able to figure out how to apply it to either a lognormal or an exponential distribution.

Thanks again,

Fabia