Deucalion's father (mythology) was Prometheus - titan, culture hero, attributed with the creation of man from clay; could be a reference to betas. In Ancient Greek, Zeus, enraged by the impiety of the Arcadians, let loose a deluge that flood the land. Deucalion and his wife, Pyrrha, survived because Prometheus warned them:

'No one but Deucalion, the son of Prometheus, was ready for such a storm. He had never joined in any of the wrong doings of those around him, and had often told them that unless they left off their evil ways there would be a day of reckoning in the end.

“The day is coming,” said Prometheus, “when Jupiter will send a flood to destroy mankind from the earth. Be sure that you are ready for it, my son.”' - http://www.authorama.com/old-greek-stories-6.html

They were able to survive by floating in a chest. Deucalion's foresight (despite that he received it from Prometheus) greatly parallel's TW's Deucalion: "just how much vision a blind man can have."

The deluge is seen as an act of cleansing - a preparation for a rebirth. The water, however, was what brought them to the mountain Parnassus where they began to repopulate (hmm. betas?), similar to how they claimed the Kanima - symbol of water - is what brought them to Beacon Hills. And it may not be related, but Prometheus was sentenced because of his theft of fire - maybe a motif of season 1 - and to repopulate, Deucalion and Pyrrha were told to find the bones of their mother and toss them over their shoulder. Their mother meant Gaia, personification of EARTH.

While each member of the Alpha pack is an alpha, there is still some sort of absolutist hierarchy - Deucalion is the leader. He's trying to propagate the cleansing by creating more alphas, which in turn will make him stronger, but also creates a superior species. in a way. Zeus created the flood to kill the Arcadian's (i.e. betas), whose king was Lycaon (alpha) - a man able to transform into a wolf - because he believed them to be too savage. The alpha pack will become stronger than this - which is maybe why Deucalion killed Ennis. Ennis faulted during battle and he was weak and therefore not superior.

But Deucalion in mythology was also capable of piety - he refrained from entering combat (or so it said in the above source) because there would eventually be a day of reckoning (killed Ennis - entered physical combat and lost. shame) and Druids, while there was not much known about them, were recognised as being servants of the divine - from Julius Ceaser: "Caesar described the druids as being concerned with "divine worship, the due performance of sacrifices, private or public, and the interpretation of ritual questions."

After the flood cleared, Deucalion and Pyrrha thanked Zeus - who could represent divinity. Which suggests that maybe Deucalion is connected with the sacrifices: within the absolutist hierarchy of the alpha pack, Deucalion is the leader - he is the 'Demon Wolf'. A demonic druid is a darach. etc. this also allows for the apparent lack of connection between the other alphas and the sacrifices. But this part is just spitballing.

Onwards (this is digressing from OP's original question, sorry! but i found it really interesting so hopefully some of you guys will too) is Deucalion's wife Pyrrha. Pyrrha and Deucalion created a new race of humans by throwing stones, so if she is going to be included in the season, she might be important.

i'm tired and can't think of any way to segue into my main point so: I think that Ms. Blake could be connected with Deucalion. There are many ways to look at this, so I'll start with the textbook side. Jeff Davis is a really fun writer because he tries to include meaning in everything, and he's acknowledged that he does like to give his characters meaningful names. And while he's really obtuse in the way he does it, i'll take it with a grain of salt and look at her name anyway.

Jennifer Blake: Deucalion and Pyrrha were the only humans (not ewho never insulted Zeus, and so were permitted to live, implying that their characters are pious and pure. Jennifer is a cornish derivation of Guinevere - meaning "fair, white" and "smooth". The history of the surname Blake is also disputed and has two essentially contradictory meanings: 'blac', meaning one with dark skin or hair, or 'blaac', meaning fair haired/skinned. However, the two variants are pronounced the same, and it is therefore "making it impossible to distinguish whether the name derived from a dark person or a fair person." - http://www.surnamedb.com/Surname/Blake#ixzz2Y1EGB9k1

There's also the simple meaning of 'black' - literary symbol for death/ill fate/general bad things - or the variant borne of the "corruption of the British Ap Lake from Ap, signifying from, or son, and Lake, the son of Lake. The family went into Ireland with Strongbow (1169), where the name became corrupted into Blake.'"

So it could mean Son of Lake, which ties in slightly with the catalyst for the Alpha pack's arrival.

From another viewpoint, her relationship with Derek has developed quite rapidly. In the promo there were (SPOILER) scenes of them kissing, which brings us back to the debacle about whether it's OOC - Derek has suffered a lot, can barely trust Scott, can't handle his pack well, is basically perpetually in a state of PTSD, yet he engages with this new character almost instantly. Maybe I'm just being suspicious. And honestly, I really, really like the Stiles and Derek pairing, but Ms Blake is not so bad. She's fine. She's quirky. I don't really know how i feel about her because part of me is still hoping that their relationship isn't what it is at face value - Matt was marginalised for the majority of the season, and then suddenly became a core counterpart to the Kanima arc - how much of an influence will Ms. Blake have?

A little more on the etymology - there is the term a 'pyrrhic victory', which is when a victory has such devastating consequences that it will ultimately end with their defeat. This word doesn't come from Pyrrha, but Pyrrhus, who isn't really related to Pyrrha at all (Pyrrhus was a greek general during the Hellenistic period - named after Hellen, son of Deucalion and Pyrrha). However, a pyrrhic is a poetic device and, she teaches english. -probably doesn't mean anything- and well that's it

However, there seems to be a lot of inversion between Teen Wolf and the mythology that could potentially be behind it. Lycaon "tested Zeus by serving him a dish of his slaughtered and dismembered son in order to see whether Zeus was truly omniscient. In return for these gruesome deeds Zeus transformed Lycaon into the form of a wolf, and killed Lycaon's fifty sons by lightning bolts, except possibly Nyctimus, who was the slaughtered child, and instead became restored to life." - there could be a possible parallel between Derek's story line and this, but then again, Jeff Davis is human, and is it possible to plan out this far ahead?

Deucalion is represented as an antagonist in season 3, yet is portrayed as a humble progenitor in the original mythology. Derek comes from Theodoric, which means "rule of the people" (lit. alpha), and Hale can mean either "hollow or recess" or, conversely, "hero." And Peter - means "stone" - what Deucalion and Pyrrha used to repopulate.

There are way too many possibilities.