The 1.4 claim probably comes from the assertion made by L&K that "Accordingly, P=0.01 should bbe required to declare confirmation at the 5% level. Note that this correction is equivalent to a multiple testing (or Bonferroni) correction for 5 markers." If you check figure 1, a P value of 0.01 will approximately line up with a LOD score of 1.4.
That said, think about the conditions L&K place on that calculation: they assume that you have done a linkage analysis with sparse markers, probably in an animal model, and that the 95% confidence interval for your region is about 20 cM and includes five markers. That's where the 0.01 comes from. Using this framework, if you test only one marker, in theory, the replication P value could be higher; if you test more, the required replication P value should be lower. In practice, the required threshold for credible replication depends on your effect size and the size of the replication population. If you were doing a classical sort of experiment (e.g. scanning for a QTL for rice grain size, then doing a follow-up experiment to test your best candidate) then this advice would probably still be good. These days, though, many people are testing many phenotypes at once (e.g. eQTL studies) so in my opinion you need stronger evidence of replication because the multiple-testing challenge is greater.
For recommendations on whether an association study is credible your go-to quote usually comes from John Ioannidis. I recommend Validating, augmenting and refining genome-wide association signals (Ioannidis NRG 2009) as a place to start.
There is a great write-up of this issue on the genomesunzipped blog. They reference a review by Visscher et al which is also worth reading.
In which species are you interested? The value is rather different for human and in-bred mice, for example. In which trait(s) are you interested? The LOD scores for something like hypertension is vastly different than for differences in gene expression, where LOD scores of 20 and up are routine. Actually, this is a genetics question and not strictly bioinformatics. Nonetheless, if you can provide a few more details, I or others may be able to help.
Thanks for the response Larry. I am interested in quantitative traits in humans, bone mineral density in particular.
You're welcome. Just a reminder that if you find a response useful, you're encouraged to vote it up so that others who have a similar question are guided to potential solution(s).
Thanks for the update Larry and reading suggestion. As I am focusing on complex traits in humans, the 2.5-3.0 range would be more suitable. Still getting used to the BioStar platform!