It really comes down to, what keeps the theory simple while still explaining all the data?
In (Kenyan) Swahili, for example, there are affricates
/d͡ʒ/. We could just as easily call them clusters
/dʒ/. But is there any advantage to having them be individual? We never find a
/ʒ/ on its own, and there are places in the syllable structure where you can either have a single consonant or one of these affricates.
The theory becomes much simpler if you treat the affricates as single consonants instead of pairs: in this case you don't have to explain why
/ʒ/ can never stand on its own, or why the specific pairs
/dʒ/ can be in positions that normally only allow a single consonant.
(In fact, I prefer to call those sounds
/ɟ/, palatal plosives, because it makes some of the symmetry nicer. But as always, the naming comes down to whatever is most useful and clear:
/c/ doesn't tell you its most common pronunciation, while
This is basically the meaning of the tie-marker. If you write [d͡z], you are explicitly claiming that it is a single consonant (commonly known as an affricate); if you write [dz], you're not saying that explicitly, so you might be saying that it is a cluster (or, you're just not bothering with the diacritic). There are a few cases where there is a contrast in the language, such as Polish trzy "three" with a cluster and czy "whether" with an affricate. Since such contrasts are rare, it is rarely necessary to use the diacritic.
There is no clear boundary between an affricate and a sequence of a stop and fricative of the same place of articulation. So the distinction most often comes down to the purpose of the analysis.
For instance, English /ts, dz, tr, dr, tθ, dð, pf, bv/ are phonetically realized like affricates in many environments, but these combinations are usually not considered distinct phonemes because their distribution is restricted to one or two of word-initial, word-medial, and word-final positions. /tʃ/ and /dʒ/, however, can appear in any of the three and appear to be morphologically inseparable, unless in the middle of a compound (e.g. lightship). For a more thorough reasoning, see Cruttenden (2014: 186–8).
But if you're making a phonetic (as opposed to phonological) observation, it is well within reason to treat affricated realizations of English /ts, dz, tr, dr, tθ, dð, pf, bv/ as affricates and transcribe them with tie bars.
Ladefoged & Maddieson (1996: 90) said:
Affricates are an intermediate category between simple stops and a sequence of a stop and a fricative. It is not always easy to say how much frication should be regarded as an automatic property of a release; some places of articulation seem to be often accompanied by considerable frication ... At the other extreme, a combination of a stop and fricative that both happen to have the same place of articulation do not necessarily form an affricate. Phonological considerations must play a part in any decision as to whether a stop and a following homorganic fricative is to be regarded as an affricate which is a single unit, or as two segments (or two timing slots), forming a sequence of a stop and a fricative.