Methods for genomic integration for

1. A method of modifying a target site in a Kluyveromyces host cell genome, the method comprising:

(a) contacting the host cell, which has reduced non-homologous end joining (NHEJ) activity, wherein the NHEJ activity is reduced by integrating a nucleic acid at YKU70 or YKU80 loci. with:

(i) a first linear nucleic acid capable of homologous recombination with itself or with one or more additional linear nucleic acids contacted with the host cell, whereby homologous recombination in the host cell results in formation of a circular extrachromosomal nucleic acid comprising a coding sequence for a selectable marker and a stability element comprising a centromere sequence (CEN) sequence at least 95% identical to SEQ ID NO: 2 and an autonomously replicating sequence (ARS) consensus sequence at least 90% identical to SEQ ID NO: 3;

(ii) a nuclease capable of cleaving the target site, wherein the nuclease is an RNA guided endonuclease or a meganuclease; and

(iii) a donor DNA molecule capable of homologous recombination at the cleaved target site, whereby homologous recombination in the host cell results in integration of the donor linear nucleic acid at the target site; and

(b) selecting a transformed host cell expressing the selectable marker.

2. The method of claim 1 , wherein the stability element is at least 95% identical to SEQ ID NO: 1.

3. The method of claim 1 , wherein the host cell is K marxianus.

4. The method of claim 1 , wherein the nuclease is an RNA-guided DNA endonuclease.

5. The method of claim 1 , wherein the nucleic acid integrated at YKU70 or YKU80 loci encodes the RNA guided endonuclease.

6. The method of claim 1 , wherein the stability element comprises SEQ ID NO: 1.

7. The method of claim 1 , wherein CEN sequence comprises SEQ ID NO: 2 and the ARS consensus sequence comprises SEQ ID NO: 3.