of the driving Brownian motion, and , which describes the strength of its attraction to . As tends to , the process is less and less constrained by its attraction to and the process becomes a Brownian motion. Because of this, the models may be nested, and log-likelihood ratio tests discerning which of the two models is appropriate may be carried out. Stable models of continuous character evolution: though Brownian motion is appealing and tractable as a model of continuous evolution, it does not permit non-neutrality in its basic form, nor does it provide for any variation in the rate of evolution over time. Instead, one may use a stable process, one whose values at fixed times are distributed as stable distributions, to model the evolution of traits. Stable processes, roughly speaking, behave as Brownian motions that also incorporate discontinuous jumps. This allows to appropriately model scenarios in which short bursts of fast trait evolution are expected. In this setting, maximum likelihood methods are poorly suited due to a rugged likelihood surface and because the likelihood may be made arbitrarily large, so Bayesian methods are more appropriate. Applications Character evolution Ancestral reconstruction is widely used to infer the ecological, phenotypic, or biogeographic traits associated with ancestral nodes in a phylogenetic tree. All methods of ancestral trait reconstructions have pitfalls, as they use mathematical models to predict how traits have changed with large amounts of missing data. This missing data includes the states of extinct species, the relative rates of evolutionary changes, knowledge of initial character states, and the accuracy of phylogenetic trees. In all cases where ancestral trait reconstruction is used, findings should be justified with an examination of the biological data that supports model based conclusions. Griffith O.W. et al. Ancestral reconstruction allows for the study of evolutionary pathways, adaptive selection, developmental gene expression, and functional divergence of the evolutionary past. For a review of biological and computational techniques of ancestral reconstruction see Chang et al.. For criticism of ancestral reconstruction computation methods see Williams P.D. et al.. Behavior and life history evolution In horned lizards (genus Phrynosoma), viviparity (live birth) has evolved multiple times, based on ancestral reconstruction methods. Diet reconstruction in Galapagos finches Both phylogenetic and character data are available for the radiation of finches inhabiting the Galapagos Islands. These data allow testing of hypotheses concerning the timing and ordering of character state changes through time via