Abstract
Phenylketonuric and hyperphenylalaninaemic patients in the population of the Republic of Ireland were screened for mutations at the human phenylalanine hydroxylase (PAH) locus. A composite data set for the island of Ireland was generated by merging the findings of this study with extant data for Northern Ireland. Analysis of this data on the basis of the four historic provinces (Munster, Leinster, Connacht and Ulster) revealed genetic diversity that is informative in terms of demographic forces that shaped the Irish population. R408W, the predominant Irish PAH mutation associated with haplotype 1.8, reached its highest relative frequency in the most westerly province, Connacht. This suggests that the gradient of R408W-1.8 observed across north-western Europe continues into Ireland and peaks in Connacht. Spatial autocorrelation analysis demonstrated that the gradient is consistent with a localised cline of R408W-1.8 likely to have been established by human migration. This and parallel allele frequency clines may represent the genetic traces of the Palaeolithic colonisation of Europe, a pattern not substantially altered in north-western Europe by subsequent Neolithic migrations. An analysis of mutant allele distributions in Ulster, Scotland and the rest of Ireland confirmed that Ulster has been a zone of considerable admixture between the Irish and Scottish populations, indicating a proportion of Scottish admixture in Ulster approaching 46%. Mutations primarily associated with Scandinavia accounted for 6.1% of mutations overall, illustrating the influence of Viking incursions on Irish population history.
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Acknowledgements
We thank our colleagues Dr Donncha Dunican, Dr Peter McWilliam, Professor Stanley Monkhouse, Dr Daniel Bradley (Smurfit Institute of Genetics, Trinity College Dublin), Dr Barra O Donnabhain (Department of Archaeology, University College Cork) and Dr Linda Tyfield (University of Bristol, UK) for helpful discussions and for critical reading of the manuscript. We gratefully acknowledge financial support from the Research Committee of the Royal College of Surgeons in Ireland and from the Royal Irish Academy Millennium Project on ‘Irish Origins: the genetic history and geography of Ireland’ jointly funded with the National Millennium Committee of Ireland.
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Appendix
Assume that the overall mutant allele frequencies q1 and q2 can be estimated in the parental populations 1 and 2, for example from the square root of the disease incidence in these populations assuming Hardy–Weinberg equilibrium. The incidence of the disease in the hybrid group, however, is not known and the overall mutant allele frequency qh cannot be estimated. Assume also that the relative frequency of a specific mutant, ie the frequency of that allele within a sample of mutants, is known for the parental populations (r1 and r2) and for the hybrid population (rh). The Berstein model27 suggests that the frequency of an allele in the hybrid population (rhqh in our case) is a linear combination of the frequencies of the allele in the parental populations (r1q1 and r2q2), that is:

where m and (1-m) are the relative contributions of parental population 1 and parental population 2 into the hybrid respectively. In our case, however, qh is unknown and m thus cannot be estimated directly from equation 1. A possible solution is to assume that the incidence of the disease in the hybrid group, and therefore qh, is also a linear combination of the incidences observed in the parental populations. That is:

Combining equations (1) and (2) we obtain the following estimate of m:

As suggested for other estimators of a ratio28, we propose to combine the information from different mutants averaging first the numerator and the denominator of (3) across mutations, and taking then the ratio of these averages. The estimate of m can be finally used to compute back an estimate of qh from equation (2).
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O'Donnell, K., O'Neill, C., Tighe, O. et al. The mutation spectrum of hyperphenylalaninaemia in the Republic of Ireland: the population history of the Irish revisited. Eur J Hum Genet 10, 530–538 (2002). https://doi.org/10.1038/sj.ejhg.5200841
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DOI: https://doi.org/10.1038/sj.ejhg.5200841
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