A joint research effort of u/sc127 and u/lemonsaltwater
Throughout Seasons 2 and 3, swans are a recurring theme in Colin and Pen’s story, both in terms of explicit imagery/sound and allusions to swan behavior and stories. There are so many allusions that it is clear the showrunners, and Julia Quinn,* want us to make these associations, as every detail is intentional.
(\while neither of us have read the books, but based on character names, as well as references to the books on this sub, we can assume this. If you've read the books, please comment with more swan references! We do not present this as something hidden/new but rather for the fun of finding all of the references.)*
The biggest allusion to swans is how swans mate for life and form into bonding pairs quite young, well before mating age. Trumpeter swans bond as young as 20 months — but then wait several years and don’t mate until at least the age of 4-7. Colin and Pen meet at a young age and form a friendship but it then takes several years for it to become romantic.
Let’s plunge our beaks underwater and dive into how these associations play out for Colin and Pen individually and then as a couple.

Colin’s character as a swan

Colin has always been a swan, even if he didn’t lean into it. It shows up in a variety of character traits throughout the seasons.
Male swans are fiercely protective of their partners. We see Colin’s protectiveness over Pen show up multiple times. I did a longer post on the evolution of Colin's protectiveness a few weeks ago, but here are some scene highlights:

• Ep 1x01: After Penelope beams at how happy she is to be wearing a pink dress, Cressida then spills her drink on her. Colin feels defensive of her, and rejects Cressida's bid to dance (big social no-no!) and dances with Penelope instead
• Ep 2x07, 2x08 (Cousin Jack’s scam): He not only gets angry at Mondrich for insulting the Featherington family, but also at Cousin Jack for taking advantage of the Featherington women

https://i.redd.it/3fwzxihqji5d1.gif

• Season 3 has multiple examples of Colin protecting Pen: after his dating help is revealed, balloon, protecting her from a mistake. It is notable that the few times we see Colin angry, they are all related to Pen’s feelings.

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We'll likely see more of this in Part 2 (and various book spoilers indicate this as well).
Male swans are also one of the few species of waterfowl that take an active role in rearing children. Male swans will sit on the eggs and protect them, unlike other waterfowl. In Seasons 1 and 2, Colin is often seen playing with his younger siblings. We see the male swan’s interest in child rearing most obviously in 2x02 when Eloise recoils from Daphne’s baby and Colin swoops in to tenderly and lovingly hold him.
https://i.redd.it/vce8xkfeli5d1.gif
Swans are known for mating for life and for being dedicated partners, unlike other species of waterfowl. Colin “My Wife” Bridgerton, hello. But even before Season 3, we see this in Season 2 when Colin is the only one in the front row who appears happy at Anthony and Edwina’s wedding, and according to Luke, Colin is actually crying because he loves love so much. He delights in love.
https://i.redd.it/xgsjjbu1mi5d1.gif
Afterwards, Colin finds himself somewhat depressed and “searching for answers at the bottom of his flask” after their “bungled nuptials.” For someone who sees love as "the one thing in life that holds genuine meaning," to see an engagement broken off at that point is deeply distressing. (We'll return to Anthony's wedding later.)
His recurring appearance changes after his extended travels: Swans shed all of their feathers during their annual summer migration period. After his travels between S1 and S2, he returns with facial hair. After his travels between S2 and S3, he returns with new clothing.

Penelope: Duck => Swan

Penelope, meanwhile, needs to go through a transformation in order to become a swan.
(There are a lot of motifs used for Penelope throughout the show: butterflies, cake, etc, but here we’re going to focus on ducks and swans.)
Let’s start with her name. To get all Colin-season-2 for a moment, “Penelope” is believed to derive from the Ancient Greek word penelops, which means “duck.” In modern language, “pen” is the official name for a female swan. And her last name is Featherington.
Something that starts as a duck and becomes a swan… that sounds a lot like the HC Andersen short story The Ugly Duckling, which is about a duck who is cast aside by society for being ugly, only to later learn that the reason it looked different was because it was actually a swan.
While Colin and Pen are more likely to quote Byron than Danish fairy tales, the allusions to The Ugly Duckling are quite strong throughout Penelope’s character arc. (And indeed, fantasy plays a huge role in their worldviews.)
This is directly referenced in the book:

“I thought you believed in me," she said, "that you saw beyond the ugly duckling.”

For a brief refresher on The Ugly Duckling, let’s take Wikipedia’s summary and annotate it:

After a mother duck's eggs hatch, one of the ducklings takes longer to hatch and is bigger and perceived by the other animals as an ugly little creature. It suffers much verbal and physical abuse from its mother and siblings, and has an absent father.

Penelope is the youngest of three children. From the first episode, it is clear that her mother regards her as less desirable and less beautiful than her sisters. Her father is neglectful and largely absent. She is repeatedly subject to unkind comments and treatment by her mother and sisters. To take just one example, when suitors come over to meet Marina, and her mother closes courting hour, she says “Please feel free to bid farewell to Phillipa or Prudence, or even Penelope.” (Colin is the only one to take her up on this.)
Portia also insists that Penelope wear bright yellow dresses even though she herself prefers pink. Yellow is the color of baby ducks. Portia tends towards green, often in iridescent fabrics, which roughly maps to the coloring of several types of adult ducks (even females). (In the Ugly Duckling, the ugly duckling is gray rather than yellow like it’s siblings. However, they’ve taken a bit of artistic license here to reinforce the duck imagery.)

It wanders from the barnyard and lives with wild ducks and geese until hunters slaughter the flocks. It finds a home with an old woman, but her cat and hen tease and taunt him mercilessly, and once again he sets off alone.

We don’t have a direct literal correlation to the cats and hens, but we can interpret “leaving the barnyard” as Penelope being too early presented in society, and the “cats and hens” being the multitude of catty comments and “clucking hens” (judgmental, gossipy mothers) of society.
It’s also interesting how Cousin Jack is presented quite clearly as a hunter in Season 2, and the gun rack on the wall clearly makes Portia uncomfortable. There aren’t direct references to duck hunting, yet that was a common hobby. (We admittedly don’t know anything about rifles and can’t figure out if any of them he displays on the wall are specifically for duck hunting, but would love it if someone knew!) Cousin Jack, of course, nearly destroys their family.

The duckling sees a flock of migrating wild swans. It is delighted and excited but cannot join them because he is too young, ugly, and unable to fly. When winter arrives, a farmer finds and carries the freezing duckling home but he is frightened by the farmer's noisy children and flees the house. The duckling spends a miserable winter alone outdoors, mostly hiding in a cave on the lake that partly freezes over.

We can read this as being when Pen watches Colin leave for Greece, and when she looks at the happy Bridgerton household. She is also too young and immature to fervently declare her feelings as she states one should. Nicola plays her as immature (the little hop when she speaks, high voice), and she is trapped in her mother’s house.
The allusion of the migrating swans is also interesting as one could see all of the Bridgertons as swans who glide gracefully on the surface of society (“pretty Bridgertons”). While not all of the Bridgertons exhibit swan-like behavior, Violet and Edmund do (but more on that below). Note how in 3x02 Penelope says the place she feels the most comfortable is/was the Bridgerton Drawing Room at Sunday tea -- surrounded by the flock of swans.
We could be a bit literal with our interpretation here and say that Colin’s protection of Pen with the Ruby scam is equivalent to the farmer’s care, and then is scared off not by children but his own friends. But I think we can look at it more broadly to say that Penelope goes from thinking she will be cared for — as Colin says during their dance in 2x08 — but then feels cast aside.
She then spends a miserable summer alone, without Eloise or Colin. We know she was miserable by how she is dressed and carries herself in the beginning of 301: hunched over and back in an old gown with her protective helmet of curls.

The duckling, now having fully grown and matured, cannot endure a life of solitude and hardship anymore. It decides to throw himself at a flock of swans, feeling that it is better to be killed by such beautiful birds than to live a life of ugliness.

When we first meet her in 3x01, it is clear she has had an awful, lonely summer. She is shown in her old clothing -- notably more pink but still yellow, a sign of the impending transition -- and looking shy and hunched over.
https://i.redd.it/b1fn60pwqi5d1.gif
But she resolves to fully break free of her family and marry. Her first dress is iridescent emerald green — the color of peacocks, which is likely the most direct motif given she hides behind a peacock in the garden, but it is also the color of adult mallards and several other duck species.
She throws herself into the fray at great personal risk rather than having to continue to live with her family of ducks that reject her. However, she is still awkward and unsure of herself. While she walks down the stairs with confidence, once she's on the floor, she's isn't fully carrying herself with confidence, and sort of slides her feet along the floor in a slouchy manner. She then proceeds to bungle her conversation with the lords who approach her. In other words, she still sees herself as an ugly duckling -- or perhaps ugly duck since she's grown. But Colin is able to see beyond that and has the first glimmers of starting to notice her as something different than everyone else.
https://i.redd.it/i2dcbfb1qi5d1.gif
Part 2 speculation:

The Ugly Duckling is shocked when the swans welcome and accept it, only to realize by looking at his reflection in the water that it had been not a duckling but a swan all this time. The flock takes to the air, and it spreads its wings to take flight with the rest of its new family.

Penelope is shocked when Colin has feelings for her, and according to the trailer, is welcomed with open arms by Violet and the rest of the swan’s family (except Eloise, who does not exhibit swan-like behaviors herself, but that's a different topic). Given the focus on mirrors so far this season, perhaps this combined mirrougly duckling/swan theme will reappear. Penelope will then integrate herself into the Bridgerton family and identify more with them, rather than her family of birth. She thus gets both self-acceptance, a husband, a loving family, and freedom all at the same time.
Given the use of mirrors this season, I expect Colin will literally and figuratively help Penelope see herself in the mirror the way he sees her, in a parallel to what Colin says in S2 E2 about her letters:

Your letters were so encouraging. I thought, if Penelope can see me this way, then surely I can too.

A brief note on Penelope's clothing
We can see hints of this in her clothing. Over Season 3 Part 1, Penelope’s clothing changes from Featherington green to Bridgerton blue. Yet in the kiss scene and Colin’s dream, she’s wearing dresses that are such light blue/green that they almost appear to be white, and she doesn't seem to wear these dresses in other scenes. (The dream one is similar to the market scene, but the sleeve detailing is different -- it's much more feathery. Hmmm.) While white dresses can imply wedding, perhaps another thread to pull here is their swan-like whiteness. The moment when they kiss is the first time it occurs to him to see her romantically, and it is also the first time he sees her in a white dress. That she is in white in his dream reinforces the idea that he sees her a swan.
(Yet they aren't fully white — so there is still evolution to happen.)
https://i.redd.it/498qr6joqi5d1.gif
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Colin calling her Pen — "swan" — from the very beginning
And lastly, back to her nickname. The first time we ever see Colin talk to Penelope is in S1 E1 after Colin visits the Featherington house during courting hour for Marina, he refers to her as Pen. He refers to her again as Pen when they dance later in that episode. The viewer thus sees her transition from Penelope, a duck, and then becomes Pen, a swan. Colin has thus always seen her as a swan, even if he didn’t realize it.
(We have not done a full analysis of the times he calls her Penelope vs the times he calls her Pen, nor of other people using her nickname.)

Audio and visual swan motifs

So, Colin is always a swan, and Pen transitions from duck to swan. Several times throughout the seasons, we see direct and indirect nods to swans in terms of imagery, dialogue, and other scene elements when Colin and Pen are together.
It’s notable that, as far as we can tell, swans and swan noises largely only show up when Colin and Pen are together. (There is one exception, discussed in the next section.)
The most obvious is in 2x05:

COLIN: After all, everyone else is finding some purpose to their lives. Anthony is to be married. Benedict has his artistic pursuits. And, well, here I am... feeding the ducks. [Looks at a swan as he says this]
PENELOPE: I am sure the ducks are most grateful.

https://i.redd.it/53fkdvblui5d1.gif
https://i.redd.it/0lqr6dxnui5d1.gif
The implication being, of course, is that Colin does not realize he's not looking at a duck but at a swan. His feelings for her aren't romantic yet. But he is really looking at a swan — Pen. And that she, not the ducks, is grateful for his company and conversation.
Interestingly, quacking is heard in the background. It’s hard to say whether it’s ducks or swans — perhaps it’s intentionally ambiguous.
Singing swans = courting activities? Or a shift in feelings for Colin?
But let’s pull that thread a bit, as swans singing comes up several more times. Swan songs have historically had an association with death, yet “their sounds are more distinguishable during courting rituals and not correlated with death.” We could then interpret hearing swan songs as times that are courting-esque, or perhaps moments when Colin’s perspective on Penelope is starting to shift.
In 2x06, Penelope has a heated conversation with Eloise about Eloise’s feelings about Theo. Eloise asks her if she’s ever felt the torment of feelings for someone, and Penelope says she could only imagine it. She then looks over at Colin and swans are heard in the background.
A few moments later, when Penelope walks over to Colin for the “purpose” conversation, swans are again heard in the background. (Listen very closely as she walks over to him.)
In 3x01, when Colin and Penelope talk in the garden after the presentation, swans are heard in the background as Colin looks at her while she looks away. In this scene, Colin is wearing his beautiful embroidered vest, which features a duck near the collar. It also features a parrot. (Shout out to u/EverEarthling for this amazing deep dive on the vest!) Perhaps when Colin bought this vest in Paris, he still viewed Penelope as a duck, and himself as a parrot (i.e. one who parrots the behaviors of what society expects). Given this, we might not see this vest again, as gorgeous as it is.
https://preview.redd.it/9r4qb648wi5d1.jpg?width=1920&format=pjpg&auto=webp&s=facbf720d29560adad66b31923c1646ab7fc66c8
While we might think these were coincidences because they happened to be near water, it seems unlikely, as there are a lot of garden/park/outdoor scenes where no swans are seen or heard.
In 303, at the end of the Willow scene, swans are heard in the background as Penelope leaves. Swans then re-appear the Hawkins Balloon Fair. There is a giant wicker statue of a swan, decked in lilacs and light pink roses, off to the side of the balloon. (Lilacs being the favorite flower of the Bridgertons and light pink being the Bridgerton color of first love.) While we don’t get an obvious camera angle of this, based on body positions, Penelope would have been looking at this swan statue the entire time while talking to Debling.
https://preview.redd.it/x25logl1wi5d1.jpg?width=1920&format=pjpg&auto=webp&s=3e95b51b6a6cf37cfb0010ea699158f5bfd12b86
Here's Nicola goofing around with said swan statue.
https://preview.redd.it/j1n4t28svi5d1.jpg?width=1125&format=pjpg&auto=webp&s=75bfa6f3a86aa6890d9ee9f8afc296b1762b77e2
In 3x04, the Queen has dancing swans in her wig. And, this is the first time in the season when Colin and Penelope dance together.
https://preview.redd.it/kmvtrgniki5d1.jpg?width=1920&format=pjpg&auto=webp&s=6caac598ac9992cd65b278059a1da22caa214e23
We also have a small wink in terms of grass. Swans who have not yet begun mating, even if they are paired, will gather in flocks in fields of grass. Paired swans who are too young to mate will move throughout the flock socially yet still be paired — much like the environment of a ball. In 2x03, Colin mentions how he once spent meditating for hours on a single blade of grass, and in 3x03, when trying to impress Debling and looking directly at a swan, Penelope says how she likes grass.
(Perhaps we can also interpret this to mean that Eloise is not a swan: she says she’d rather watch grass grow than talk to other debutantes. But, again, that’s for another post on Eloise being different than her siblings.)
Interestingly, at these swan social gatherings, “some individuals will have several courtships with other members of the flock, whilst others, tend to stay away from densely populated parts of the herd and do their own thing.” Sounds like Colin and Pen!
From the book, there's a mention of a "swan song:" (credit to u/leadwithlovealways)
https://preview.redd.it/4rui2ve22j5d1.png?width=3405&format=png&auto=webp&s=e0b63ac184f171f44735d9e58d2e43aff311383f

Colin + Pen = Swans

Let’s talk for a moment about the behaviors of bonded swan pairs and their mating behaviors, as there are a lot of parallels.
One important part of the beginning of the swan courting ritual is that both will drop their wings completely to their sides, and not puff themselves up at all. We can see this literally in terms of Colin and Pen in the carriage (both have their arms down at their sides), but also metaphorically: they are both at their most vulnerable, their least puffed-up, in the entire season.
https://preview.redd.it/2jmk55zcxi5d1.jpg?width=1920&format=pjpg&auto=webp&s=2c3d3ce9c8046d8dacadf0254090ba5b2d6db57b
When swans are bonded, they will press their chests together and bend their necks together and rest their foreheads against one another, forming a heart shape. In their first kiss, we see Colin rest his forehead against Penelope’s ever so slightly — somewhat tentatively, almost, and his chest is not pressed to hers. (It is in his dream, though.). We see the forehead-resting and chests pressed together more times in the carriage scene.
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Mating dances
First, watch this video of swans doing a mating dance. (Or read, if you prefer.) Note how look away from each other and then back with intense eye contact.

They will stare at each other during the up and down motions of the necks and will sometimes raise both heads together at the same time to look at each other with sideways glances as they turn their heads from side to side.

Now, let's pivot back to Bridgerton -- and to another couple. In 2x05, Anthony and Kate’s pivotal dance when they can no longer ignore their feelings for one another resembles the courting dance of swans, with their arms interconnected and circling around another. While one could say that’s true of most dancing, this one is particularly striking, and perhaps it's when Anthony drops his rakishness or ability to think about others and starts to accept his committed, swan nature (though it takes him some time). You can also see echoes of the swan mating dance in how they pass one another side-by-side in Simon & Daphne's dance when they're truly in love, though the Kate/Anthony dance is much clearer.
The closest we’ve seen to Colin and Pen dance like this is 2x08, yet that dance is much more tentative than Kate and Anthony’s, and only bears a very faint resemblance to the swan mating dance. They make eye contact, but it is not intense or focused. Colin also refers to her as "Penelope", not "Pen," during that dance, and they barely touch. Distance is implied in multiple ways. But back to the topic of this post, one has to wonder whether we’ll see Colin and Pen dance in a way similar to a swan mating dance in Part 2.
Swan mating rituals
Now we're going to dive a bit deep in terms of parallels between swans and intimacy. Yes, this is completely fucking unhinged on an already unhinged post. I’m sorry if you will never be able to look at swans the same again.

• Swans will keep intense eye contact during courting and mating. Yup, check.
• While mating for most birds lasts only a few seconds, for swans it can be at least 20 minutes if not up to an hour. Seems fitting given the mentions of a 10-minute long intimacy scene in Episode 5!
• Right before swans engage in the act, the male swan will drape his neck over the female swan’s. We seem to be getting hints of this in the trailer, with Colin standing behind her in the mirror.
• We're going to skip over specifics of swan sex positions. That would simply be too unhinged.
• Right after mating, swans stay close together and echo the head turning/tilting of the courting ritual. We get a glimpse of this after the carriage scene is interrupted, and one can hope this means we get lots of after-sex cuddling. If not, it’s totally in headcanon now.
• After mating, swans will clean one another. We can see this in how Colin lovingly puts Pen’s dress and hair back in place before straightening his own clothes in the carriage scene.
• Swans also tend to mate many more times than is necessary in order to fertilize eggs. Based on this, and based on what we’ve heard about Part 2, we’re probably going to see this parallel, too.
• Male swans eagerly build a nest once they’ve decided to mate. This matches what we’ve heard about Colin quickly buying a house for him and Pen.
• Swan couples that are new to a territory/nest usually don’t lay any eggs for the first year, so maybe they’ll wait a bit before having children. But that seems unlikely with these two given that birth control didn’t exist…

Looking forward

Given that swans mate for life, we can be guaranteed a happy ending here.
As the show goes on, one can predict that swans will represent the two of them in various ways, and that we might expect to see swan motifs in the decoration of their new home. (In the Part 2 trailer, in the wedding scene, the walls are decorated with a swan motif.)
https://preview.redd.it/yhtphnem1j5d1.png?width=2436&format=png&auto=webp&s=3dab8825cccd5db6cd6c8f35c1f9f8605a4e68b1
In terms of children, swans keep their children close to them during their early life. We therefore might be able to predict that both Colin and Pen will likely be very attached to their children, and we will be unlikely to see them without their children once their children are in the picture. Even though Colin loves to travel, we could also predict he’ll quickly want to settle down and delight in being at home with their children, just like a swan.
Since male swans actively participate in child rearing, we also hope we’ll get to see lots of heart-warmingly adorable scenes of Colin bouncing their babies on his knees and taking care of them in future seasons. Maybe we’ll be lucky and even get a Regency-ified version of baby wearing with Colin wearing their baby wrapped around him with a shawl!

Bonus: Press tour Easter eggs!

In the Netflix India Bollywood/Bridgerton video, Luke wore a duck sweater. u/sc127's read on this:

Black Swan theory regarding Nicola's outfit: Do you think it's alluding to Colin and Pen getting married? In the eyes of the Ton, they would consider the Polin relationship as a Black Swan. It fits the criteria of being a surprise, having a major effect, and can be rationalized in hindsight.
Pink Ducks on Luke: I think the symbolism is more straight forward compared to Nicola's outfit. Pink is Pen's favorite color and it is the Bridgerton color of first love. Colin is in love with a duck named Pen :)

https://preview.redd.it/mrxy2a7v1j5d1.png?width=1200&format=png&auto=webp&s=2c4d919cbd7c18dab681e5516098c540e7d79b12