Physiologists have long appreciated that environmental conditions and their variability have an influence on phenotypic plasticity (see Section 4). It is widely thought that acclimatization is more likely in species from temperate than those from less variable tropical and polar environments (Spicer and Gaston, 1999; Ghalambor et al., 2006), and less likely in stenothermal (narrow temperature tolerance) species (Somero et al., 1996; Pörtner et al., 2000), although tropical species might be more eurythermal (wide temperature tolerance) than their polar counterparts (Somero, 2005). More generally, the environmental circumstances under which adaptive population differentiation, phenotypic plasticity, or some combination thereof arise form the subject of a large and growing theoretical field (e.g. West-Eberhard, 2003; Berrigan and Scheiner, 2004; Pigliucci, 2005). Somewhat surprisingly, this field and work examining the evolution of thermal physiology remain reasonably distinct (though see Lynch and Gabriel, 1987; Gilchrist, 1995), even though the physiological models often struggle to explain the high frequency of eurythermic strategies (see reviews in Angilletta et al., 2002, 2003, 2006). Hence, we focus on the former plasticity models, noting parallels with the thermal physiology models where appropriate. Many investigations have shown that greater environmental variability tends to favour phenotypic plasticity within populations, as long as cue reliability and accuracy of the response (which is a function of environmental lability and unpredictability, and of the extent to which the response lags behind the environmental change) is high, and the cost of plasticity is low (Lively, 1986; Moran, 1992; Scheiner, 1993; Tufto, 2000). This conclusion holds for both optimality and quantitative genetic (environmental threshold) models (Hazel et al., 2004). Recent modelling work has also shown that the likelihood of this outcome is affected strongly by migration between different populations (Tufto, 2000; Sultan and Spencer, 2002). With little or no migration, and different environments, adaptive differentiation between populations in each of these environments readily evolves. Increases in migration rate, by contrast, lead to fixation of the plastic phenotype even though it might not be the best type anywhere (i.e. relative to adaptively differentiated habitat specialists) (Tufto, 2000; Sultan and Spencer, 2002). Nonetheless, if response accuracy is low (i.e. no better than random for at least one environmental state), the specialist phenotype is favoured, and the same is likely to be true if the global cost of plasticity is high (though evidence for the latter is scarce) (Van Tienderen 1991, 1997; Moran 1992; Sultan and Spencer, 2002, but see also Relyea 2002; van Kleunen and Fischer, 2005). In addition, environmental-threshold models show that with low cue reliability and low frequency of benign patches, a reversed (counter-intuitive) conditional, but unstable, strategy is favoured (Hazel et al. 2004).