Rabbi Akiva teaches based on the verse: "in beauty and glory (hadar) You are adorned "(Psalm 104:1).
Etrog--this is the Holy One;
Lulav--this is the Holy One;
Myrtle--this is also the Holy One; Willow--is the Holy One.
Etrog--this is Abraham our father whom God beautified with old age;
Lulav--this is Isaac our father who was bound up on the altar;
Myrtle--this is Jacob our father: just as myrtle is crowded by its leaves, so too was Jacob crowded by his children;
Willow--this is Joseph: just as the willow dries out and crumbles before the other species, so too Joseph died before his brothers.
Etrog--this is Sarah our mother whom the Holy One beautified with old age;
Lulav--this is Rebecca our mother, just as the palm tree has fruit and thorns so too Rebecca established the righteous and wicked;
Myrtle--this is Leah our mother: just as the myrte is crowded by its leaves, so too Leah was crowded by her children; Willow--is Rachel our mother, just as the willow dries out before the other three species, so too Rachel died before her sister.
4 species--this is the Jewish people
Etrog has both smell and taste, so it is that some people are learned in Torah and fill their lives with good actions;
Lulav--has taste but no smell, so it is that some people are learned in Torah but do not fill their lives with good actions;
Myrtle--has smell but no taste as both smell and taste, some people fill their lives with good actions but do not learn Torah;
Willow--has neither taste nor smell, so too do some Jews know no Torah nor do they fill their lives with good actions.
The Holy One said, "We should be sure not to lose any of them. Rather, let's bind all of them together and their will atone for each other."
This is why Moses said, "On the first day you shall take the product of hadar trees, branches of palm trees, boughs of leafy trees, and willows of the brook, and you shall rejoice before the Holy One your God seven days." (Lev. 23:40)