Natural spikes are perhaps more likely to be accompanied by online buzz from independent sources. Artificial link sources and artificial buzz are generally coordinated and I think are more easily spotted on a social web graph.
Common sense suggests that link building which proceeds faster than probable traffic would also show as unnatural spikes and raise flags.
In its Historical Data Patent, Google noted that signs of coordination accompany synthetic web graphs and intent to spam. At the time of the data patent, Google probably needed to rely on "spiky" anchor text patterns more than it does now. But to think of that merely as word matching is probably simplistic. Patterns of coordination on many levels can be spotted statistically.
For discussion of some broader natural patterns, see jmccormac's excellent post on normal link acquisition patterns in this thread... and also my reference to the Google Historical Data patent....