Gemara

138b (Mishnah): One is exempt from sending a Tamei bird, even if it is on Tahor eggs, or a Tahor bird sitting on Tamei eggs.

R. Eliezer obligates sending a male Korei sitting on eggs;

Chachamim exempt.

140b - Question (R. Zeira): If a dove sits on eggs of a Tasil (a similar species), or vice-versa, what is the law?

Answer (Abaye - Mishnah): One is exempt from sending a Tamei bird on Tahor eggs or a Tahor bird on Tamei eggs;

Inference: One must send a Tahor bird on Tahor eggs of a different species.

Rejection: Perhaps that refers to a Korei (partridge. It often sits on eggs of other species.)

(Mishnah - R. Eliezer): One must send a male Korei sitting on eggs;

Chachamim exempt.

(R. Elazar): The Tana'im argue only about a male Korei, but all obligate sending a female Korei (on eggs of another species).

One might have thought that Chachamim exempt even a female Korei, and the Mishnah discusses a male Korei to show the extremity of R. Eliezer's opinion. R. Elazar teaches that this is not so.

(R. Elazar): The Tana'im argue only about a male Korei, but all exempt males of other species.

One might have thought that R. Eliezer obligates even males of other species, and the Mishnah discusses a male Korei to show the extremity of Chachamim's opinion. R. Elazar teaches that this is not so.

Support (Beraisa): There is no Mitzvah to send males of other species;

R. Eliezer obligates sending a male Korei,

Chachamim exempt.

Rishonim

Rif (48a): R. Elazar taught that the Tana'im argue only about a male Korei, but all exempt males of other species. A Beraisa supports this. All agree that there is no Mitzvah to send males of other species. R. Eliezer obligates sending a male Korei, and Chachamim exempt.

Rosh (3): Why did the Rif omit R. Elazar's first teaching? It seems that the Halachah follows both of them. They do not argue with each other. The latter teaching is not relevant to Halachah. I brought it only due to the Rif. It seems that his text said 'some say that R. Elazar said...', i.e. R. Elazar taught only one of them; they argue with each other. According to Version #1, the Beraisa mentions a male Korei due to Rabanan. R. Elazar obligates all males. According to Version #2, the Beraisa mentions a male Korei due to R. Elazar. Rabanan exempt even a female Korei. He rules like Version #2, for a Beraisa supports it. I disagree. Our texts do not say 'some say...' Also, it seems that they do not argue with each other. It says 'a male Korei' to teach that Rabanan agree about a female Korei. This is why it did not say Stam 'Korei'. 'Korei' was taught to teach about R. Elazar, that he exempts other males.

Ran (DH Rebbi): The Gemara mentioned a Korei because even Chachamim obligate a female Korei, since it normally lies on eggs of other species. The Gemara never resolved the question about other species.

Beis Yosef (YD 292 DH veha'Ran): It is astounding that the Ran did not derive the Rif's opinion the way the Rosh did to explain why he omitted R. Zeira's question.

Rambam (Hilchos Shechitah 13:10): If a male hovers over a nest, or a Tamei bird over Tahor eggs or vice-versa, one is exempt from Shilu'ach ha'Kan.

Rambam (11): If it was hovering on eggs of another Tahor species, one must send it. If he did not, he is not lashed.

Poskim

Shulchan Aruch (YD 292:7): If a male hovers over a nest, or a Tamei bird over Tahor eggs or vice-versa, one is exempt from Shilu'ach ha'Kan.

Beis Yosef (DH u'Mah she'Chasav Oh): Korei is a Tahor bird that often lies on eggs of other species. Rashi explains that they argue only about a male Korei, but all obligate a female Korei even on eggs of other species, since it normally does so. All exempt males of other species, for it says "the mother hoves".

Beis Yosef (DH u'Mah she'Chasav Rabeinu b'Shem): The Tur says that the Rambam learns from Abaye's answer about Tasil. We cannot derive that a Tahor bird on eggs of a different Tahor species is liable, for perhaps it discusses Korei, but other species are exempt, for it is abnormal for them. The question was not resolved. It is a Torah Safek whether one must send it, so we are stringent. We are lenient about lashes, for this is a Safek about a mortal issue. It seems that the Rambam had the Rif's text, that the two versions argue with each other, and he rules like Version #2. However, he obligates all Tahor females, because the question was not resolved. It seems that the Rif exempts, for he omitted this Safek (other Tahor females). Why is he lenient about a Safek mid'Oraisa? It seems that indeed, he obligates. He omitted the question, for what he wrote about R. Elazar's teaching sufficed. He brought the Beraisa in which Tana'im argue about a male Korei. This implies that all obligate all Tahor females. He holds that the two versions argue about this. In version #1, Chachamim obligate a female Korei and exempt other females. R. Zeira asked whether we explain the Mishnah like Version #1 or Version #2. The one who tried to prove that it is like Version #1 had not heard the Beraisa. We rely on the Beraisa, which is like Version #2.

Beis Yosef (DH u'Mihu): We cannot explain the Rambam this way. If so, one should be lashed! Rather, the Rambam was unsure whether R. Zeira asked about only because he had not heard the Beraisa. Or, perhaps he heard it; he was unsure if Chachamim exempt other females. Therefore, the Rambam exempts from lashes. However, if so he should obligate lashes for a female Korei! Rather, the Rambam explains that the rejection 'perhaps it discusses a Korei' is not according to Chachamim, like Rashi explained. Rather, it is according to R. Eliezer. It is unclear whether Chachamim obligate any species, even a Korei.

Beis Yosef (DH v'Rabbeinu): The Tur sides with the Rambam. This is because even if the two versions of R. Elazar do not argue, and surely Chachamim exempt for females other than Korei, like the Rosh said, since R. Zeira's question was not settled, we are stringent like the Rosh. Since R. Elazar was sure, we follow him, without concern for the Safek of R. Zeira.

Bach (5): The Rif omitted R. Zeira's question. We hold like Chachamim, who exempt even a female Korei, and all the more so (even) a (female) dove or Tasil. R. Zeira asked only according to R. Eliezer, according to Version #2. Since he obligates a male Korei, perhaps all the more so he obligates females of other species. Or, perhaps only Korei is liable, and even males, but even females of other species are exempt. Alternatively, R. Zeira asked according to Version #1, according to Chachamim. They agree that a female Korei is liable. Do they agree about about other species? A Beraisa supports Version #2, that Chachamim exempt even a female Korei. All the more so they exempt other species. This is why the Rif omitted R. Zeira's question.

Bach (DH Aval): The Rosh holds that the Tana'im argue only about a male Korei. The Halachah follows Chacham who exempt. The Rosh omitted R. Zeira's question. The Beraisa taught about a male Korei to teach also about Chachamim, that they obligate a female Korei. This implies that even females of other species are exempt. If they were liable, the Beraisa should have taught this Chidush. Rather, R. Zeira asked according to R. Eliezer, who obligates a male Korei. This is difficult. The Gemara said that a Beraisa supports the latter teaching. This shows that there is an argument, even according to the texts that do not say 'some say...' Also, what is the relevance of the Beraisa like Version #2? The Halachah follows Chachamim who exempt even a male Korei, and all the more so other males. This is good for the Rif. The Beraisa teaches that the Halachah follows Version #2, and Chachamim exempt even a female Korei.

Bach (DH veha'Rambam): The Rambam holds that the versions argue, and the Halachah follows Version #2, for the Beraisa supports it. It teaches that R. Eliezer obligates a male Korei, even though other males are exempt. We do not know whether Chachamim obligate a female Korei. Perhaps the Beraisa mentioned a male Korei only to teach about R. Elazar's opinion. This is why R. Zeira asked about this. This is unlike the Rif, who holds that Version #2 surely exempts even a male Korei according to R. Eliezer. We rejected the proof from the Mishnah; perhaps it is like R. Eliezer, and it discusses a Korei, even a male Korei. The question was not settled. Likewise, we do not know what Chachamim hold about a female Korei. The Tur did not bring the Rif's Perush. He brought the Rosh, for it is closer to Rashi's Perush.

Gra (12) and Shach (12): Even a male Korei is exempt, like Chachamim.