Another way to avoid effects of population stratification is to use population isolates. With a small number of founders and long isolation, population isolates have long been exceptional resources for genetic studies of simple genetic diseases. Researchers have also argued that population isolates provide advantages for mapping complex traits [Wright et al., 1999; Peltonen et al., 2000; Peltonen, 2000; Shifman and Darvasi, 2001; Escamilla, 2001; Venken and Del-Favero, 2007]. In addition to reducing genetic heterogeneity, such isolates have more homogeneous environmental backgrounds than are typical in larger heterogeneous populations [Peltonen, 2000; Shifman and Darvasi, 2001]. With less population stratification, Hardy-Weinberg Equilibrium (HWE) is more likely to hold in population isolates. [Peltonen et al., 2000]. These factors increase the validity of testing for differences in allele frequencies between cases and controls. However, a challenge to the use of population isolates is that classical statistical methods for ideal population data, which consist of independent individuals, may not be applicable: an important feature of population isolates is that the relatedness of two random individuals may be non-negligible [Bourgain and Genin, 2005]. Such cryptic
