What happened to the expected -ε- thematic vowel in present active indicative 1 p sg and 3 p pl?

Question

I am trying to understand how Greek verbs are formed, having just begun learning their formation in present active indicative. The model verb used is λύω, which I understand to be formed as such:

singularis			dualis		pluralis
1st	2nd	3rd	2nd	3rd	1st	2nd	3rd
λύ-∅-ω	λύ-ε-ις	λύ-ε-ι	λύ-ε-τον	λύ-ε-τον	λύ-ο-μεν	λύ-ε-τε	λυ-ο-υσι

The explanations I have found for the thematic vowel include:

796. The thematic verbs are so named because in a majority of their forms the personal ending (819–821) is preceded by ^ο⁄_ε (ο before μ or ν, or in the optative mode, otherwise ε), which is called the thematic vowel. Thus, λυ^ο⁄_ε (λύω) is called the theme, to which the personal endings (819–821) are attached.
―Wright/Pharr: Homeric Greek

Further, in Shelmerdine:

You’ll notice that all the present active verb forms contain some form of an o or e vowel:

Singular				Plural
1st	(I)	-ω	o	(we)	-ο-μεν	o
2nd	(you)	-εις	e	(you)	-ε-τε	e
3rd	(he)	-ει	e	(they)	-ουσῐ	o

This is the thematic vowel, which regularly appears in certain forms as an e, in others as an o. We can describe a thematic verb like λύω as consisting of three parts: stem, thematic vowel, and personal ending.
―Shelmerdine, C. W.: L. A. Wilding’s Greek for Beginners, Focus Publishing / R. Pullins Co., Newburyport, 2001, pp. 6f.

In the following table, she lists the verb forms as λύ-ω, λύ-εις, λύ-ει, λύ-ο-μεν, λύ-ε-τε, λύ-ουσῐ(ν), only using a hyphen to show the thematic vowel for the plurals. None of these explanations therefore leave me with a proper understanding of what is going on. Based off of Wright/Pharr, I would have expected 1st person singular to be -ε-ω and 3rd person plural to be -ε-υσῐ(ν), as their explanation specifies that it is -ε- except before -μ and -ν (which yields an -ο-). Is there a (historical) linguistic explanation for why these two forms apparently do not follow the rules explained by Wright and Pharr? Or am I missing something obvious? (In which case I apologise!)

Answer 1

In Proto-Indo-European, an alternation between *e and *o is common (sometimes also including lengthened *ē and *ō, or zero (the vowel disappearing)). This alternation is commonly called "ablaut", though some people prefer the Greek equivalent "apophony", and happens in both roots and suffixes.

For example, compare πατέρα, ἀπάτορα, πατήρ, ἀπάτωρ, and πατρός. All of these come from the same root, but the vowel appearing in that root changes depending on the form. Similarly, λέγω~λόγος, λείπειν~λέλοιπα~λιπεῖν, γένος~γόνος~γίγνομαι, and so on. Greek has a lot of reflexes of this.

The exact details aren't completely understood, but for whatever reason, the 1S (maybe), 1P, and 3P forms take *o as their thematic vowel, while the others take *e. Pharr suggests a phonetic motivation, which makes sense to me: the ancestor of the 3P form has an *n in it (compare Latin -nt), and *ons regularly becomes ουσ in Attic but οισ in Aeolic (compare second declension acc pl)—which is exactly what we see in the 3P ending (Sappho 2 αἰ δ' ἄηται / μέλλιχα πνέοισιν "and the breezes gently blow").

The important part to remember, though, is that by Classical times, that's just how it is. Synchronically, there's no n in the 3P ending in Attic, and Greek-speakers in general almost certainly didn't think in terms of ablaut grades. They just knew those were the forms they'd inherited, and thus what they used.

Answer 2

This is a basic Indo-European phenomenon called “ablaut”: the fluctuation between e and o in parallel forms. We have it also in legō (with e) vs logos (with o in the root syllable). In the personal endings of the present paradigm of the thematic verbs we have e in lueis, luei, luete, and the dual forms, but o in lu-ō, lu-o-men and lu-o-nsi > luousi.