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Copyright ? 2007 by the Genetics Society of America

DOI: 10.1534/genetics.107.078931

Letter to the Editor

Estimation of the Population Scaled Mutation Rate

From Microsatellite Data

Peter Beerli1

School of Computational Science and Department of Biological Science, Florida State University, Tallahassee, Florida 32306

Manuscript received July 17, 2007

Accepted for publication September 4, 2007

I

timating the population scaled mutation rate u from

microsatellite data; u is equivalent to four times the

effective population size times the mutation rate per

generation and can also be viewed as the scaled popu-

lation size. Their approximation delivered impressively

accurate results with little bias. They compared their

results with several other commonly available programs.

Their study is a good example of how comparisons with

other programs should be presented; but I was not

impressed by the bias and median absolute error re-

ported for my own program MIGRATE (Beerli and

Felsenstein 2001). RoyChoudhury and Stephens

(2007) used the defaults of MIGRATE and wondered,

given the large observed biases, how more difficult pop-

ulation models would fare when MIGRATE 1.7.3 has

difficulties estimating a single parameter. On my re-

quest, A. RoyChoudhury sent me their data sets, so

that I could check whether the current version of

MIGRATE (2.3; http:/ /popgen.scs.fsu.edu) suffers from

the same problem as the tested version. The data sets,

which contained 50 unlinked microsatellite loci for sample

sizes of 10, 20, 40, and 80 gene copies from a single

population of size uTof 2, 8, and 32, were simu-

lated using the coalescent simulator of Paul Fearnhead

(RoyChoudhury and Stephens 2007). I ran these data

sets through MIGRATE 2.3 using default settings with

the stepwise mutation model and the Brownian motion

approximation. A comparison of my Figure 1 with Figure

1 in their article shows clearly that the current version

of MIGRATE is much less biased. In fact, the results are

verysimilartotheapproximatemethodofRoyChoudhury

and Stephens. My Figure 1 includes their results for

uT¼ 32 as a reference. The Brownian motion approx-

imation in MIGRATE, already available in version 1.7.3,

N a recent issue of Genetics, RoyChoudhury and

Stephens (2007) showcased a new method for es-

delivers similar results much faster; the runtime for the

largest single locus data set was ?30 sec on a 2 Ghz

Figure 1.—Bias and absolute error for MIGRATE version

2.3. Each point is the median scaled mutation rate u, bias,

or error of 50 data sets per sample size and scaled population

size uT. (Left) Using the stepwise mutation model; (right)

using the Brownian motion approximation. Data sets, scale

and calculations of bias, and absolute error are the same

as in Figure 1 of RoyChoudhury and Stephens (2007); for

reference, the bias and absolute error of their estimator for

uT¼ 32, taken from their Figure 1, is shaded.

1Address for correspondence: 150-T Dirac Science Library, Box 4120,

Florida State University, Tallahassee, FL 32306.

E-mail: beerli@scs.fsu.edu

Genetics 177: 1967–1968 (November 2007)

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Opteron CPU. The microsatellite implementation in

1.7.3 seems, retrospectively, inefficient and extremely

slow. The large biases were most likely a result of an

aggressive default setting for a tuning parameter gov-

erning the conditional likelihood calculation and an

inefficient calculation of the actual probability to make

k mutational steps in time t. The effect of this tuning

parameter is most pronounced with highly variable data

associatedwithhighu values.Asaresultofthesefindings,

I have changed the default for this tuning parameter.

Additionally, I removed inefficiencies in the conditional

likelihood calculation: this improved the runtime for

the stepwise mutation model from ?40 min on 3 Ghz

machines as reported by RoyChoudhury and Stephens

(2007) to ?5 min on 2 Ghz Opteron machines.

I thank Arindam RoyChoudhury and Matthew Stephens for

supplyingtheirsimulateddataandtheirexplanationsoftheirstatistics

and also an anonymous reviewer for helpful comments. This work was

supported by the joint National Science Foundation/National In-

stitute of General Medical Sciences mathematical biology program

under National Institutes of Health grant R01 GM 078985.

LITERATURE CITED

Beerli, P., and J. Felsenstein, 2001

tion of a migration matrix and effective population sizes in n sub-

populations by using a coalescent approach. Proc. Natl. Acad.

Sci. USA 98: 4563–4568.

RoyChoudhury, A., and Stephens, M., 2007

timation of the population-scaled mutation rate, u, from micro-

satellite genotype data. Genetics 176: 1363–1366.

Maximum likelihood estima-

Fast and accurate es-

Communicating editor: M. K. Uyenoyama

1968P. Beerli