Pinhasi and Pluciennik (2004) analyzed the crania of Mesolithic and Neolithic populations and found no biological relationship between the Natufians and the later West Asian groups who spread farming to Europe:
Analysis of morphological variability in the Near East and Europe suggests that the Epipalaeolithic populations from the Natufian Levant were noticeably different to the Mesolithic populations described from the Danube Gorge, the western Mediterranean, and central Europe. No close similarities were observed between Early Neolithic and Mesolithic European groups in any of the regions studied, with the possible exception of Mediterranean Europe. However, neither were clear affinities observed between Epipalaeolithic Near Eastern groups [Natufians] and any other Neolithic or Mesolithic groups. These results support a third scenario — that the Epipalaeolithic population from which the first Anatolian farmers descended has yet to be discovered.... There is therefore no unequivocal evidence from biological morphometrics for local continuity between Natufian specimens and any of those from the Anatolian or Levantine PPN [Pre-Pottery Neolithic] cultures. Statistical analysis of the Levantine populations indicates no obvious biological continuity between Natufian groups and their successors — either the first Neolithic cultures of the PPNA or subsequently between the PPNA and the PPNB.
Pinhasi and von Cramon-Taubadel (2009) confirm the previous findings, and as a result don't involve the Natufians at all in any of the possible dispersal models of migration from West Asia to Europe:
Figure 3 plots the first two principal co-ordinates of the craniometric distance matrix. The OTUs [operational taxonomic units] do not group according to any particular geographic or temporal pattern on the first or second principal co-ordinates. However, the first principal co-ordinate separates the archaeologically defined Neolithic OTUs from OTUs designated as Mesolithic plus the Natufian. Therefore, the principal co-ordinate analysis suggests that Neolithic and Mesolithic populations are biologically differentiated.