<PAGE>   1

                                                                   EXHIBIT 10.13

                 FIRST AMENDMENT TO JOINT DEVELOPMENT AGREEMENT

This first amendment ("First Amendment"), entered into as of March 27, 2001,
("First Amendment Date"), is by and between ILLUMINA, INC., a Delaware
corporation located at 9390 Towne Centre Drive, Suite 200, San Diego, CA
92121-3015 ("Illumina"), and PE CORPORATION (NY), a New York corporation,
through its PE Biosystems Group, now known as its Applied Biosystems Group,
located at 850 Lincoln Centre Drive, Foster City, CA 94404 ("PEB").


                                    RECITALS

        The parties have entered into a Joint Development Agreement ("Original
Agreement") having an Effective Date of November 8, 1999.

        This First Amendment, entered into pursuant to Section 13.7 of the
Original Agreement, serves to amend the Original Agreement by providing for the
development and commercialization of Tag Sequence technology.

        NOW, THEREFORE, in consideration of the mutual obligations in this First
Amendment and in the Original Agreement, and for other good and valuable
consideration, the receipt and sufficiency of which are acknowledged, the
parties to this First Amendment agree as follows:


                                    AMENDMENT

1.      Definitions: Any words with initial capitalization that are used and not
        defined in this First Amendment will have the meanings set forth in the
        Original Agreement.

2.      ADD new Section 1.33 immediately after Section 1.32 of the Original
        Agreement as follows:

"Tag Sequence" means                ***

                                    ***

                                    ***

***  Portions of this page have been omitted pursuant to a request for
     Confidential Treatment and filed separately with the Commission.



<PAGE>   2

3.      ADD the following to Section 3.1 of the Original Agreement immediately
        before the last sentence of Section 3.1:

                The Parties will share responsibility for defining and
                developing Tag Sequences for the Collaboration Product which
                will attempt to avoid third party intellectual property rights
                or other encumbrances.

4.      ADD new Sections 4.1.5 and 4.1.6 immediately after Section 4.1.4 of the
        Original Agreement as follows:

        4.1.5   Manufacture of Tag Sequences.    ***
                                   ***
                                   ***


        4.1.6   Use of Tag Sequences. The Parties agree that Tag Sequences will
                be used in the Collaboration Field by the Parties and purchasers
                of Collaboration Product. Tag Sequences may not be used by third
                parties outside the Collaboration Field unless the use is
                approved by the Joint Steering Committee.

5.      ADD new Section 6.1.4 immediately after Section 6.1.3 of the Original
        Agreement as follows:

        6.1.4.  The Parties agree that any Intellectual Property Rights
                concerning Tag Sequences conceived after the Effective Date of
                the Original Agreement, whether Collaboration PEB Intellectual
                Property, Collaboration Joint Intellectual Property, or
                Collaboration Illumina Intellectual Property, including the
                methods by which such Tag Sequences are designed, selected or
                made, as well as any compositions directed to such Tag
                Sequences, shall be deemed Collaboration Joint Intellectual
                Property.

6.      Continued Effect of Original Agreement. All provisions of the Original
        Agreement except as modified by this First Amendment, shall remain in
        full force and effect and are hereby reaffirmed. Other than as stated in
        this First Amendment, this First Amendment will not operate as a waiver
        of any condition or obligation imposed on the Parties under the Original
        Agreement.

7.      Interpretation of Amendment. In the event of any conflict,
        inconsistency, or incongruity between any provision of this First
        Amendment and any provision of


***  Portions of this page have been omitted pursuant to a request for
     Confidential Treatment and filed separately with the Commission.



                                       2
<PAGE>   3

        the Original Agreement, the provisions of this First Amendment will
        govern and control.

8.      Entire Agreement. This First Amendment, along with the Original
        Agreement constitute the sole agreements between the Parties relating to
        the subject matter hereof and supersede all previous writings and
        understandings. Confidential disclosures made under previously executed
        Confidentiality Agreements between the Parties will remain subject to
        the terms of those Confidentiality Agreements. No Party has been induced
        to enter into this Agreement by, nor is any Party relying on, any
        representation or warranty outside those expressly set forth in this
        Agreement.

9.      Counterparts. This First Amendment may be executed in any number of
        counterparts, and each counterpart will deemed an original instrument,
        but all counterparts together will constitute one agreement.

[Signature page follows.]



                                       3
<PAGE>   4

The Parties, through their authorized officers, have executed this First
Amendment as of the First Amendment Date.

ILLUMINA, INC.                              PE CORPORATION, THROUGH
                                            ITS APPLIED BIOSYSTEMS GROUP

By:   /s/ John R. Stuelpnagel               By: Elaine J. Heron
   ----------------------------------          ---------------------------------

Name: John R. Stuelpnagel                   Name: /s/ Elaine J. Heron
     --------------------------------            -------------------------------

<TABLE>
<S>                                         <C>
Title: Vice President, Business Development Title: Vice President, Applera Corporation
      -------------------------------------       ------------------------------------
                                                   General Manager, Molecular Biology Division
                                                   Applied Biosystems
</TABLE>

Date:  4/2/01                               Date:  3/29/01
     --------------------------------            -------------------------------



                                       4