Vol. 22 no. 6 2006, pages 768–770
BIOINFORMATICS APPLICATIONS NOTE
Genetics and population analysis
LAMARC 2.0: maximum likelihood and Bayesian estimation of
Mary K. Kuhner1
1Department of Genome Sciences, Box 357730, University of Washington, Seattle, WA 98195-7730, USA
Received on November 15, 2005; revised and accepted on January 9, 2006
Advance Access publication January 12, 2006
Associate Editor: Frank Dudbridge
Summary: We present a Markov chain Monte Carlo coalescent
genealogy sampler, LAMARC 2.0, which estimates population genetic
parameters from genetic data. LAMARC can co-estimate subpopula-
tion Q ¼ 4Nem, immigration rates, subpopulation exponential growth
rates and overall recombination rate, or a user-specified subset
of these parameters. It can perform either maximum-likelihood or
Bayesian analysis, and accomodates nucleotide sequence, SNP,
microsatellite or elecrophoretic data, with resolved or unresolved hap-
lotypes. It is available as portable source code and executables for
all three major platforms.
Availability: LAMARC 2.0 is freely available at http://evolution.gs.
Inference of population parameters (such as effective population
size, growth rate or immigration rate) from sequence data is often
done using summary statistics in order to avoid dealing with the
unknown genealogy relating the sampled sequences. Such genea-
logies are difficult to infer accurately, and nearly impossible in
cases with recombination.
The Lamarc package addresses this difficulty by approximate
integration over the space of possible genealogies using Markov
chain Monte Carlo (MCMC) sampling. This avoids both the loss
of power from using summary statistics and the difficulty of infer-
ring the true genealogy. Previous programs in the package include
COALESCE (Kuhner et al., 1995), estimating Q ¼ 4Nem and
several programs co-estimating Q and one additional type of para-
meter: FLUCTUATE (exponential growth rate) (Kuhner et al.,
1998), MIGRATE (immigration rates) (Beerli and Felsenstein,
1999), (Beerli and Felsenstein, 2001) and RECOMBINE (recomb-
ination rate) (Kuhner and Felsenstein, 2000; Kuhner et al., 2000a).
When multiple evolutionary forces act on a population, analyzing
them one at a time may lead to bias and loss of power. We have
developed an integrated program, LAMARC 2.0, which can infer
multiple forces simultaneously for greater accuracy.
Previous Lamarc package programs have performed maximum-
likelihood analysis, using the sampled genealogies to construct a
likelihood surface for the parameters of interest. LAMARC 2.0
retains this capability, but can also perform a Bayesian analysis
in which the sampler searches among parameter values as well
LAMARC’s maximum-likelihood estimation uses a set of driving
values, working values of the population parameters, to construct
an importance sampling function which will guide the search
among genealogies. This procedure can be inefficient for finding
the maximum-likelihood estimates (MLEs) of the parameter values
unless the driving values are close to the unknown true parameters,
so the search is iterated using the previous estimates as new driving
Bayesian estimation searches simultaneously among genealogies
(guided by the current working values of the population para-
meters) and among values of the population parameters (guided
by the current genealogy). Most probable estimates (MPEs) and
credibility intervals are produced by recording the parameter
values visited by the search and doing one-dimensional curve-
smoothing to obtain the posterior probability curve for each
For both forms of analysis, LAMARC estimates parameters for
each unlinked genomic region separately, as well as a joint estimate
over all regions.
LAMARC estimates Q ¼ 4Nem, where Neis the effective diploid
population size and m is the neutral mutation rate per site per
generation. (The estimated Q can also be interpreted in a haploid,
mitochondrial or alternative ploidy context.) It can co-estimate the
exponential growth rate g. In subdivided populations it estimates Q
and optionally g for each subpopulation, and immigration rate into
each subpopulation from each of the others. Finally, it can option-
ally estimate the overall recombination rate r ¼ c/m, where c is the
recombination chance per site per generation. Customized models
where specific rates are omitted, held constant or forced to be equal
to one another are possible for all parameters.
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3.1 Search strategy
LAMARC 2.0 provides several mechanisms to improve its search
efficiency. Metropolis-Coupled MCMC or ‘heating’ allows auxil-
liary searches with more permissive acceptance criteria to act as
‘scouts’ for the main analysis (Geyer, 1991a). For likelihood
analyses, multiple replicated searches can be combined using
reverse logistic regression (Geyer, 1991b). For Bayesian analyses,
the Bayesian priors and the ratio of parameter change steps to
genealogy change steps can be set by the user.
3.2 Mutational models
LAMARC 2.0 offers the Felsenstein 84 (F84) and General Time-
Reversible (GTR) models for DNA or RNA data, and for SNP data
when information about the total sequence length surveyed is
available. The SNP model used is correct only if all variable
sites in the data have been captured; there will be an ascertainment
bias if SNPs were surveyed based on their presence in an external
panel. Multiple substitution rate categories (including an invariant
category) and potential autocorrelation between rates at adjacent
sites are accomodated using a hidden Markov model (Felsenstein
and Churchill, 1996).
For microsatellites, four models are available: a stepwise muta-
tion model (Ohta and Kimura, 1973); a Brownian-motion approx-
imation to the stepwise model (Beerli and Felsenstein, 2001) which
is much faster, but may be inaccurate when polymorphism is low;
a K-allele model and a mixture model of the stepwise and K-allele
models, with the mixture parameter potentially optimized based on
the data. The K-allele model is also suitable for analyzing elecro-
Separate genetic regions with different forms of data (e.g. a DNA
locus and an unlinked microsatellite locus) may be combined in a
single analysis. The user must provide information on the expe-
cted relative m and/or Neof the various regions if they differ. For
example, mitochondrial and nuclear DNA may be combined in one
analysis, but the program must be informed of the expected 4·
difference in Ne.
3.3 Haplotype uncertainty
Phase-unknown data may be used, although they are less powerful
than phase-known data. The genealogy search is extended to search
among haplotype resolutions as well, so that the estimate takes into
account haplotype uncertainty as well as genealogy uncertainty
(Kuhner and Felsenstein, 2000; Kuhner et al., 2000b).
LAMARC 2.0 is freely distributed as portable C++ source code and
as executables for Windows, Mac OSX and Linux. It provides a
utility to convert PHYLIP, RECOMBINE and MIGRATE input
files. The file converter’s graphical user interface uses a multi-
platform windowing system which works on all three major plat-
forms, but a pure text file converter is also available. The major
requirements for the use of LAMARC are availability of memory
and time. For example, estimation of recombination rate using
60 16 kb mtDNA sequences required 2 GB of memory and
3–4 weeks of workstation time. Smaller analyses will often take
4.1 Model assumptions
LAMARC 2.0 assumes that individuals are drawn from panmictic
subpopulations and that the subpopulation structure has been con-
stant throughout the lifespan of the underlying coalescent tree. It
is not suitable for populations which have recently diverged from
a common ancestor. It assumes that the rate at which a lineage
immigrates into a population is independent of the size of both
source and recipient populations. It also assumes that exponential
growth rates and immigration rates have been constant throughout
the lifespan of the coalescent tree and that recombination rate
does not vary by position, subpopulation or with time. Finally, it
assumes that the variation being observed is neutral, though puri-
fying selection removing harmful mutations does not disrupt the
Violation of these assumptions will potentially result in biased
estimates and inaccurate confidence intervals.
4.2 Bayesian versus likelihood analysis
In most cases examined so far (Kuhner and Smith, manuscript
submitted) LAMARC’s Bayesian and likelihood methods produce
similar point estimates and confidence intervals. The Bayesian
method is vulnerable to a poor choice of priors, but with good
priors it may search among genealogies more efficiently, especially
in cases where one or more parameters are close to zero. Our current
curve-smoothing method does not allow the Bayesian algorithm
to assess correlation among parameters, whereas the likelihood
algorithm can. Speed requirements of the two methods are similar;
the Bayesian sampler must perform more search steps, but its
curve-smoothing is faster than likelihood maximization.
4.3 Data requirements.
LAMARC 2.0 assumes that individuals are sampled randomly
within each subpopulation, but it does not require equal sample
sizes among subpopulations.
If some subpopulations are not genetically differentiated (4Nem
much greater than one) results will be unsatisfactory. Such sub-
populations are best pooled into a single subpopulation.
A sample of 20 individuals per subpopulation is fully adequate
and results are often satisfactory with as few as eight, especially if
multiple loci are available. For estimation of any parameter except
recombination rate, adding unlinked loci will improve the estimate
more than adding individuals or lengthening sequences. For estim-
ating recombination rate, lengthening sequences or adding linked
loci are preferable.
LAMARC 1.0 was released in 2001. LAMARC 2.0 corrects several
deficiencies in the previous versions, particularly errors in likeli-
hood maximization and handling of multi-locus data. LAMARC 2.0
adds Bayesian analysis, the ability to constrain parameters and
new mutational models.
The author thanks the Lamarc team, including Peter Beerli,
Joseph Felsenstein, Eric Rynes, Lucian Smith, Elizabeth Walkup,
Jon Yamato and Wang Yi. Development of this program was sup-
ported by NIH grant 5R01GM51929-11 to M.K. Funding to pay the
Open Access publication charges was provided by the National
Institutes of health grant 5R01CM51929-11 to M.K.
Conflict of Interest: none declared.
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