The rhythmic and sequential subdivision of segments of the vertebrate body axis during embryonic development is controlled by an oscillating multicellular genetic network termed the segmentation clock. We have proposed a theory representing the cellular oscillators of this process as phase oscillators coupled with a time delay. We can determine uniquely from experiments on zebrafish the parameters of our theory, except for the time delay. An infinite number of different values of the delay parameter are consistent with the experimental data, although only a small number of them are compatible with the known biochemistry of intercellular communication. To discriminate between those, we use an evolutionary argument: that the biological time delay has to be such as to make the segmentation process robust. All the delay values that we consider, except one, would result in setting the dynamical segmentation process in a multistable region of parameter space, where fluctuations could make the process shift to non-biological behavior. We propose that the only delay value that places the system in a uniquely stable behavior is the one likely to occur in biological systems, and therefore chose this value for the delay of the zebrafish segmentation clock. Finally, we apply our theory to four different vertebrate species (zebrafish, snake, mouse and chick) and show that the spatial regulation of the genetic oscillations is quantitatively different in these species.