We can see that the に particle is directly attached to the だ copula. The だ copula really just being である, doesn't this mean the に particle and で particle have been attached? I was under the assumption that 格助詞 (or logical particles for Cure Dolly students) cannot attach to each other- which is why we can do には (Since は is a 副助詞 or non-logical particle) and we can't do にが for example.
I know Cure Dolly teaches this, but to be honest, this can fall into the big bucket of wrong things Cure Dolly teaches. There is a bit to unpack here. Firstly “〜だ" can attach to about anything. You won't find say “あなたにだ。” very often, but one can say it to mean “It's for you.” It'll sooner arise as “あなたにです” because there at least the polite version has a function of making it polite “あなたに” on itself is usually used, but for instance as a more practical example something like “心配しているよ、君のことをだ。” is perfectly grammatical, removing the “〜だ” in no way changes the meaning. Adding it simply makes the sentence sound more firm and assertive. “〜だ” is also not even a “格助詞” I believe in Japanese grammar but I know Cure Dolly teaches that it can only follow nouns and na-adjectives. Cure Dolly is wrong. All these sentences are grammatical:
- なんでだよ?
- そうだ。
- 行かなくちゃだけど。
- 分かりませんでした。
- 私がですか?いいえ、食べたことはありません。
- 私はですね、そういう音楽がかなり好きです。
Also, “〜の” is evidently a “格助詞” and can of course follow many other particles. “お母さんへの手紙” or “お母さんからの金” are both perfectly fine.
Then we get into whether “〜だって” is actually a form of “〜だ” to begin with. In theory it's the “〜たって” form of “〜だ” the same way “〜でも” is the “〜ても” form of “〜だ” but in practice it doesn't always work that way and both are just a more emphatic version of “〜も” so it depends on how it's used.
- 私だって食べたことあるよ。
- 人は大人だって自由じゃない。
In both cases we can replace “〜だって” with “〜でも” for essentially the same effect but only in the first case can we replace it with “〜も” for something similar. In the first case it's a binding particle that occupies the same space as “〜も" and “〜は” and follows other particles but replaces “〜が” and “〜を”. In the second case it's indeed a form of “〜だ” and it simply means “Being an adult still doesn't make a man free.” or I guess more literally and awkward “A man, even if he be an adult, is not free.”
So in your example the meaning is fairly close to “〜も” and leads to ”I think even birds and fish have feelings.” I wouldn't treat it as a form of “〜だ”. It just so happens that “〜だ” can also follow other particles which is a different unrelated discussion.