Human islet amyloid polypeptide (hIAPP), also known as amylin, is a 37-amino-acid peptide, co-secreted with insulin, and widely found in fibril form in type-2 diabetes patients. By using all-atom molecular dynamics simulations, we study hIAPP fibril segments (i.e., fibrillar oligomers) formed with sequences of naturally occurring variants from cat, rat, and pig, presenting different aggregation propensities. We characterize the effect of mutations on the structural dynamics of solution-formed hIAPP fibril models built from solid-state NMR data. Results from this study are in agreement with experimental observations regarding their respective relative aggregation propensities. We analyze in detail the specific structural characteristics and infer mechanisms that modulate the conformational stability of amylin fibrils. Results provide a platform for further studies and the design of new drugs that could interfere with amylin aggregation and its cytotoxicity. One particular mutation, N31K, has fibril-destabilizing properties, and could potentially improve the solubility of therapeutic amylin analogs.