A method for producing eukaryotic host cells that express an immunoglobulin of interest, comprising: (a) providing host cells that include a first nucleic acid molecule encoding (i) a signal peptide and (ii) a capture moiety comprising a cell surface anchoring protein selected from the group consisting of α-agglutinin, Cwp1p, Cwp2p, Gas1p, Yap3p, Flolp, Crh2p, Pir1p, Pir4p, Sed1p, Tip1p, Wpip, 5 Hpwp1p, Als3p, and Rbt5p fused to a binding moiety that is capable of specifically binding an immunoglobulin which is expressed in the same host cell, wherein the binding moiety binds the Fc region of the immunoglobulin and is selected from the group consisting of protein A, protein A ZZ domain, protein G and protein L, and wherein the first nucleic acid molecule is operably linked to a first regulatable promoter; (b) transfecting the host cells with a plurality of nucleic acid molecules encoding a genetically diverse population of heavy chains of an immunoglobulin and a plurality of nucleic acid molecules encoding a genetically diverse population of light chains of an immunoglobulin wherein each of the nucleic acid molecules is operably linked to a second regulatable promoter to produce a plurality of genetically diverse host cells capable of displaying an immunoglobulin on the surface thereof; (c) inducing expression of the nucleic acid molecule encoding the capture moiety for a time sufficient to produce the capture moiety on the surface of the host cell; (d) inhibiting expression of the nucleic acid molecule encoding the capture moiety and inducing expression of the nucleic acid molecules encoding the immunoglobulins in the host cells to produce the host cells that express the immunoglobulin of interest displayed; (e) contacting the host cells with a detection means that specifically binds to the immunoglobulin of interest displayed on the cell surface of the host cells; and (f) isolating host cells expressing the immunoglobulin of interest, which bind the detection means, wherein the first regulatable promoter is a promoter that is inducible without inducing expression of the second regulatable promoter and wherein the second regulatable promoter is a promoter that is inducible without inducing the expression of the first regulatable promoter. (a) providing host cells that include a first nucleic acid molecule encoding (i) a signal peptide and (ii) a capture moiety comprising a cell surface anchoring protein selected from the group consisting of α-agglutinin, Cwp1p, Cwp2p, Gas1p, Yap3p, Flolp, Crh2p, Pir1p, Pir4p, Sed1p, Tip1p, Wpip, 5 Hpwp1p, Als3p, and Rbt5p fused to a binding moiety that is capable of specifically binding an immunoglobulin which is expressed in the same host cell, wherein the binding moiety binds the Fc region of the immunoglobulin and is selected from the group consisting of protein A, protein A ZZ domain, protein G and protein L, and wherein the first nucleic acid molecule is operably linked to a first regulatable promoter; (b) transfecting the host cells with a plurality of nucleic acid molecules encoding a genetically diverse population of heavy chains of an immunoglobulin and a plurality of nucleic acid molecules encoding a genetically diverse population of light chains of an immunoglobulin wherein each of the nucleic acid molecules is operably linked to a second regulatable promoter to produce a plurality of genetically diverse host cells capable of displaying an immunoglobulin on the surface thereof; (c) inducing expression of the nucleic acid molecule encoding the capture moiety for a time sufficient to produce the capture moiety on the surface of the host cell; (d) inhibiting expression of the nucleic acid molecule encoding the capture moiety and inducing expression of the nucleic acid molecules encoding the immunoglobulins in the host cells to produce the host cells that express the immunoglobulin of interest displayed; (e) contacting the host cells with a detection means that specifically binds to the immunoglobulin of interest displayed on the cell surface of the host cells; and (f) isolating host cells expressing the immunoglobulin of interest, which bind the detection means,