As it is late (and I have to get up early for work (joy)) I am going to paste below an answer I recently wrote about barbarian recruitment. That said, I will quickly clarify a few points. Italians ceased to provide significant numbers of recruits following the first century A.D. As the army was stationed along the frontiers, it rapidly "provincialized", drawing the vast majority of it's recruits from the provinces. Specifically, more rural and poorer provinces like Illyria and Pannonia provided a disproportiate number of recruits. Over the course of the Principate, in terms of equipment and tactical role, legionary and auxilliary forces gradually became more similar. During the third century, and it is unclear precisely when, given the lack of source material, the distinction between legionaries and auxiliaries dissapears. It is therefore not possible to speak of Late Antique "auxiliaries", even though "auxilia" remains as a classification for newly-raised field army regiments (the auxilia palatina) during the early fourth century. The military reforms of Diocletian and Constantine reform the army into two "corps"- the regiments stationed along the frontiers (classified as limitanei) and the interior (and initially, imperial-centric) field armies (the units of which are classified as comitatenses). In regards to non-Romans:

Remember that the Late Antique army was divided into two distinct "corps"- the troops stationed along the frontiers (classified as limitanei, though there is a debate about the precise definition of that term), and those that formed the regional field armies (classified as comitatenses). Elton's analysis is only examining the field armies, the smaller "corps" of the Late Antique army (as the majority of the army remained stationed along the frontiers, thus classified as limitanei). He is referring to a third of recruits for the field armies, not a third of recruits in general.

Determining the numbers of recruits needed to sustain the army in peacetime is problematic, as we suffer from a lack of documentation (this is true also for the Principate, though to a slightly lesser extent). Domestic recruits were, naturally, drawn only from the male population, and more particularly from males twenty to forty-five years of age. If we assume a pan-imperial population of 54 million and an army size of 445,000, Carrié estimates the army required between 27,000 and 45,000 recruits annually (the variance arising from differing assumptions about mortality rates). These figures are cited by Lee, and similar numbers confirmed by Whitby. By comparison, Walter Scheidel estimates the (smaller) army of the Principate required about 15,000 recruits per annum. The army of Late Antiquity thus needed more recruits than that of the Principate. This is unsurprising, as all scholars agree the army increased in size.

27,000 represented one out of every twenty-three men aged between twenty and forty-five (the "military demographic"). 45,000 represented one out of every nineteen men aged between twenty and forty-five. In general peacetime, this figure would not have imposed an excessive burden on the Empire's manpower resources. Remember that Elton's analysis of barbarian recruitment examined only the field armies. The exact proportion of comitatenses vis-a-vis limitanei is unclear, though the limitanei were by far the larger corps. As barbarian recruitment differed in form from domestic recruits (for reasons detailed below), we really cannot break down the above figures further. However, they are illustrative of the fact that barbarian recruitment was not driven by manpower shortages, as annual recruitment levels were clearly demographically sustainable. All the above numbers can and are debated. But they illustrate the order of magnitude, which is more important than precise figures.

It is important to properly contextualize the recruitment of barbarians in Late Antiquity within the broader history of foreign recruitment. During the Principate, the Romans deliberately targeted foreign groups for auxiliary service that were deemed to possess specific skills (like mounted archery) or strong martial cultures that consistently produced high-quality recruits (like the Batavians along the Rhine).These traditions were built upon in Late Antiquity. New regiments for the Tetrarchic and Constantinian field armies (classified as auxilia palatina) were drawn primarily from Frankish and Alemannic groups. In the fifth and sixth centuries, regiments of Hunnic and Avar cavalry appear in the Eastern field armies as mounted archers. As part of an agreement to be resettled inside the Empire, barbarian groups agreed to supply recruits. These recruits (and the communities they came from) were known as laeti (though other terms were used, such as gentiles, dediticii, and tributarii), though there is no evidence for specific laetic units. Non-Romans tended to be concentrated into specific units, rather than dispersed evenly, with these regiments themselves concentrated in the field armies. While the "ethnic" character of these regiments doubtless reinforced unit cohesion, it would have dissipated over time, as losses were replaced by domestic recruits, eventually leaving only the regimental name to indicate the identity of it's original company. The principal difference in Late Antiquity is the increase in number of non-Romans within the army.

Centuries of interaction with non-Romans profoundly affected Roman military culture, equipment, dress, and slang over the course of the Principate and Late Antiquity. Yet there is absolutely no reason to view negatively the increased presence of barbarians in the Later army, especially as standards of training and discipline (and, indeed, combat effectiveness) remained high throughout the period. The "Romanizing" ability of the army cannot be understated, especially when we consider that the army had for centuries successfully integrated recruits drawn from the poorer, more rural areas of the Empire, where the penetration of Roman culture was far weaker. Over the course of their term of service, most non-Romans would have been imbued with a sense of Romanitas, although one with a distinctly martial character. Non-Romans were drawn to military service in part for cultural reasons, but also for the economic benefits of service, such as pay and food security.

In Late Antiquity, the vast majority of recruits were born inside the Empire. In times of stability, the annual number of necessary recruits did not strain Rome's manpower resources. Barbarians were targeted for recruitment not out of necessity, but out of desire. Barbarians were viewed as quality recruits, either because of their cultural background (the highly martial culture of the Germanic peoples) or because of specific skills (like Hunnic horse-archers). It is only in the turmoil of the mid fifth century that the Western Empire begins the wholesale recruitment of barbarian groups, as the gradual loss of territory (especially North Africa to the Vandals) greatly strained it's ability to financially support the army.

I again apologize for not giving you a more focused response. Please feel free to ask any clarifications; I can address them tomorrow morning.