Monogamy is a general mating system in birds. But extra-pair copulations were found to exist in many monogamy birds, especially in small Passeriformes birds. The Saxaul Sparrow（Passer ammodendri）is a monogamy and cavity-nesting bird species. Based on parenthood identification in the Saxaul Sparrow, we designed to figure out its proportion of extra-pair copulations, clarify the mechanism of extra-pair copulations and disscuss the influence factors of females engaged in EPC. We collected 837 samples from 175 broods at An'xi Extra-arid Desert National Nature Reserve from April to July in 2014. We drawed several conclusions through analyzing the data.
1. The Saxaul Sparrow was a social monogamy bird which had extra-pair copulations behavior. 29.71%（52 of 175）broods had at least one extra-pair offspring, 11.06%（72 of 651）offsprings were extra-pair offsprings. There were no significant difference on proportion of extra-pair copulations between the Saxaul Sparrow，the tree sparrow and the house sparrow. The result supported phylogenetic distribution hypothesis.
2. The mechanism of EPC in the Saxaul Sparrow supported the good genes hypothesis and fertility insurance hypothesis, but didn't support genetic compatibility hypothesis.
（1）Our result supported the good genes hypothesis. Reproduction parameters including clutch size, nestling, fledgling and the number of offsprings in EPC nests were significantly higher than non-EPC nests. Growth state including age of growth fastest and instantaneous maximum growth rate about wing length and tarsus length of EPO were significantly higher than WPO. To extra-pair offsprings, body condition index and maximum breadth of the crown of their genetic father were significantly higher than their social father. Female culmen length in non-EPC nests were significantly higher than EPC nests. It suggested that shorter culmen length females were more likely to engaged in EPC. Female engaged in EPC were more likely to choose males as their extra-pair mate which crown more breadth or body condition index more higher. Thus it could ehhance the possibility of reproductive success of themselves and offsprings fitness.
（2）Our result support fertility insurance hypothesis. Nesting rate, number of fertilized eggs and fertility rate in EPC nests were significantly higher than non-EPC nests. Females engaged in EPC in order to prevent infertility of their social mate.
（3）Our result didn't support genetic compatibility hypothesis. Our result shows that genetic heterozygosity of female and cucked males didn’t affect female to engage in EPC. Female engaged in EPC were not to obtain heterozygosity genes for offsprings. And genetic similarity between social mate didn’t affect the occurance of EPC. Female engaged in EPC didn’t rely on the genetic similarity between extra-pair mate and females. Also, there were no significant correlation between genetic heterozygosity of offsprings, the number of EPO, the rate of EPO and genetic similarity of their parents. Our result didn't support genetic compatibility hypothesis. Females engaged in EPC were not to obtain complementary genes, to maximize compatibility between males and themselves or improve the heterozygosity of offsprings were not suitable for the Saxaul Saprrow.
3. Female engaged in EPC were influenced by ambient temperature during egg production, laying date and male body condition index, but didn't affected by nest density and male badge size.
（1）When ambient temperature during egg production was higher, females were more likely to engaged in EPC.
（2）When laying date was earlier, females were more likely to engaged in EPC.
（3）When male body condition index was lower, females were more likely to engaged in EPC.
（4）Nest density didn’t affect the occurance and proportion of extra-pair copulations in the Saxaul Sparrow. There were no significant difference on nest density between EPC nests and non-EPC nests. Nest density had no significant effect on female engaged in EPC. There were no significant correlation between the number of EPO, rate of EPO and nest density.
（5）Male badge size didn’t affect the occurance and proportion of extra-pair copulations in the Saxaul Sparrow. Maximum breadth of the crown and rictus length had a significant positive effect on male badge size. There were no significant difference on male badge size between EPC nests and non-EPC nests. To extra-pair offsprings, there were no significant difference on male badge size between social father and genetic father. And there were no significant correlation between rate of extra-pair offsprings and male badge size.