Link Acquisition Rate
Natural link acquisition can in most cases take a very long time, short of content going ‘viral’.
For websites actively marketing their content it’s reasonable they might gain somewhere between 0 and say 100 links per month. In my experience, a site that gains 100 natural links per month is doing really well.
In specific genres there will probably be different average natural acquisition speeds.
For example, a blog site dedicated to discussing baby’s health may have a very high engagement rate from new mothers. Websites like that might gain backlinks very quickly, because their audience wants to share great information with friends and family.
A plumber’s website on the other hand, would unlikely have anything like that amount of interest and probably not many reasons to share the content either (based on most plumber’s sites I have seen). And that would be considered ‘normal’.
If your website gains links much faster that other sites in the genre, it may gain special attention from the Google Penguin algorithm as being a ‘deviant’ from the norm or it might even get individual attention from an actual human at Google.
Based on the quality profile of those links, the algorithm (or the human) may make a negative or positive judgement on the value of those links.
When a human intervenes with algorithmic judgement and acts to penalize a site, this is called a ‘manual action’ and it’s reported in Google Search Console.
It’s possible that a website might gain a large number of links very rapidly if they run certain kinds of promotions or have other marketing or perhaps even have a viral element that gets shared very quickly.
A negative judgement by Google Penguin could be considered then if the other elements of the backlink profile do not match an expected norm.