Replacement for ‘at the example of ’

I’m currently searching for the title of my research thesis and I can’t find a good phrase.

I did a “Systematic Analysis of fruit growth” in a generic way and additionally applied the analysis to apples.

Regarding the content I thought of the following title:

• “Systematic Analysis of the fruit growth at the example of apples”
• “Systematic Analysis of the fruit growth exemplify by apples”

Both sound awkward and might even be not correct (they sound incorrect to me)

I came up with the following other possibilities:

• “Systematic Analysis of the fruit growth demonstrated on apples”
• “Systematic Analysis of the fruit growth taking the example of apples”
• “Systematic Analysis of the fruit growth applied on apples”
• “Systematic Analysis of the fruit growth using apples as a case study”
• “Systematic Analysis of the fruit growth demonstrated on apples as a case study”

None of these really fits what I wanted to say. I would go for the first one, but I’m not sure whether “demonstrate” might be to informal and one might think of a “demonstration” (show on a stage).

Is there another correct phrase for “at the example of ”?

Systematic analysis of fruit growth exemplified by apples

sounds good.

Though @Will came up with the right word to directly replace "at the example of", I like your "Systematic Analysis of fruit growth using apples as a case study" (minus the "the"), since it says exactly what it is, a case study (assuming you actually did one).

Two options using case study, depending on the primary focus:

Systematic Analysis of fruit growth: a case study

Apples: a case study of systemic analysis of fruit growth

I'm not an academic, but the papers I encounter at technical conferences often use "case study" and rarely use "example".

You shouldn’t say “at the example of” – don’t use “at”. Maybe “using the example of”. But in any case, for a title this is rather long-winded and awkward, even for the normally long-winded and awkward titles of academic papers.

Without knowing anything about your paper, I’d be more likely to choose something like, “Systematic Analysis of Fruit Growth: A Case Study on Apples”.

I’m hard-pressed to state a rule to justify this, but I think the word “example” is rarely appropriate in a title in the way you’re trying to use it. Maybe a case like, “Economic Devastation of Civil War: The Liberian Example”. But if you’re creating the example, then you tend to call it a “case study”. And even in my Liberian example, it would be at least as good to say, “Economic Devastation of Civil War: A Liberian Case Study”.

For a non-title, i.e. text within the body of a discussion, I might say something like, “We performed a systematic analysis of fruit growth using apples as an example.”