Background: The three chick wing digits represent a classical example of a pattern specified by a morphogen gradient. Here we have investigated whether a mathematical model of a Shh gradient can describe the specification of the identities of the three chick wing digits and if it can be applied to limbs with more digits. Results: We have produced a mathematical model for specification of chick wing digit identities by a Shh gradient that can be extended to the four digits of the chick leg with Shh-producing cells forming a digit. This model cannot be extended to specify the five digits of the mouse limb. Conclusions: Our data suggest that the parameters of a classical-type morphogen gradient are sufficient to specify the identities of three different digits. However, to specify more digit identities, this core mechanism has to be coupled to alternative processes, one being that in the chick leg and mouse limb, Shh-producing cells give rise to digits; another that in the mouse limb, the cellular response to the Shh gradient adapts over time so that digit specification does not depend simply on Shh concentration. Developmental Dynamics 243:290-298, 2014. © 2013 Wiley Periodicals, Inc.