Whitlock, M.C. and D.E. McCauley. 1999. Indirect measures of gene flow and migration: FST p 1/(4Nm + 1). Heredity 82: 117-125.

(Amy Pedersen)

This paper discusses the real deviations from the artificial assumptions of Wright’s Island model, as well as other indirect measures of gene flow, and the reasons that these assumptions undermine the reliability of these models. Reference is also made to the statistical uncertainty of these models.

Whitlock and McCauley address the following unrealistic assumptions of the Fantasy island model:

* No selection: Selection can either increase or decrease FST. Background selection and inbreeding depression are two common examples.
* No mutation: If mutation rate is large relative to the migration rate, then there is potential for a bias in the estimate of FST. Special attention should be paid to DNA-level markers, such as microsatellites or mDNA, which sometimes have high mutation rates relative to migration rates.
* Equally created populations, with constant population size and equal contribution to migrant pool: If the migration rate is high, FST depends on Nm (as opposed to N and m), which often varies among demes. Differences of N and m between populations will cause Nm to vary, so FST measurements from metapopulations would be biased. Distance-dependent dispersal and local extinction/colonization would also affect FST of the metapopulations.
* No spatial structure and migration is completely random: When comparing species, the spatial scale at which samples were taken would have to be identical. Correlation among demes drops with increasing distance. Geographic obstacles can also alter dispersal, and therefore FST.
* Everything is at equilibrium, nothing is changing: Recent range expansion and gene flow among species will give biased results because it takes a long time before equilibrium is reached.

The authors address the differences between dispersal and gene flow. In order for a migrant to have an effect on gene flow, it must be reproductively successful in its new population. Reproductively unsuccessful migrants can, however, significantly affect the ecology of the new deme (i.e., disease). Nm is usually NEm, and NE will be much less than N, so the actual number of migrants may be 10-fold higher than that estimated by FST. Dispersal of individuals is usually more relevant than gene flow alone.

FST is a non-linear function of Nm, so any error in estimating FST is amplified when estimating Nm. Whitlock and McCauley utilized a computer simulation model to observe the effects of deviations from the assumptions listed above. Errors resulted from the finite number of samples, as well as random evolutionary history. When dealing with non-diploid genetics, alterations need to be made to the FST equation to account for differences from diploid genetics, including sex ratio of dispersers and haploid examples.

Whitlock and McCauley concluded with suggestions for future studies of gene flow and dispersal:
* Do not translate FST into a measure of Nm when FST is truly intended to measure genetic differences between populations;
* Explore which additional ecological features cause a departure from the assumptions in the island model;
* Use genetic data to examine other possible demographic processes, in addition to source-sink dynamics and extinction/colonization;
* Estimates of Nm should always be accompanied by confidence limits.

It was also noted that FST might give reasonable estimates of NEm in cases that meet certain requirements, but if we know through direct means that these requirements are met, then we probably already know more about the studied population than an indirect measure of gene flow would offer.