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The amount of ultimately recoverable resources and/or timing of peak production have been the central purpose of numerous studies. One broadly applied method is Hubbert modeling, subsequently extended as multicyclic Hubbert modeling. This paper explores a modification to conventional multicyclic Hubbert modeling that we term "cycle-jumping" wherein the overlap of multiple curves is limited and explicitly accounted for. The model is designed in a way that each curve is described by the same three parameters as a multicyclic Hubbert model, and every two curves are connected through an explicit transition. The transition width indicates the time of the shift from one curve to the next and is controlled by a weighting parameter for the respective curves. Cycle-jumping provides a superior data fit compared to the conventional cycle-addition model and, more important, reflects historical production data more realistically as socioeconomic and political factors important to resource production vary in time.

The U.S. state of Missouri contains seven major and numerous lesser Fe oxide deposits within the 1.47 Ga St. Francois Mountains terrane. These deposits have been previously described as iron oxide-apatite (IOA) and iron oxide-copper-gold (IOCG) deposits and are speculated to contain significant resources of critical minerals, most notably rare earth elements and cobalt. One of the less-studied deposits in the region is the 1.455 Ga Kratz Spring deposit. The deposit consists of two steeply dipping magnetite bodies beneath 450 m of sedimentary cover. The genesis of the Kratz Spring deposit and its relationship to nearby IOA-IOCG deposits remains poorly constrained. To better understand the formation of the Kratz Spring deposit, we integrated stratigraphic, petrographic, and bulk rock studies with in situ trace element and Fe isotope chemistry of magnetite and hematite. Our data show that the Kratz Spring deposit is hydrothermal in origin but is divided into two subdeposits according to different fluid sources and formation conditions: (1) a deep but cooler hydrothermal Kratz Spring South deposit with a juvenile fluid source and (2) a shallow but hotter magmatic-hydrothermal Kratz Spring North deposit with variable fluid sources. Our genetic model suggests the two Kratz Spring deposits are local expressions of the same mineralization system; i.e., the Kratz Spring South deposit is a distal, lower-temperature offshoot of the feeder system that formed the Kratz Spring North deposit. Understanding the magmatic-hydrothermal plumbing system that formed Missouri’s IOA-IOCG deposits is important to guide critical mineral exploration efforts in the region.