『Abstract
　This articles reviews the theoretical foundations for the concept of peak minerals; drawing on similarities and differences with peak oil as modelled using Hubbert style curves. Whilst several studies have applied peak modelling to selected minerals, discussion of the appropriateness of using Hubbert style curves in the minerals context remains largely unexplored. Our discussion focuses on a comparison between oil and minerals, on the key variables: rates of discovery, estimates of ultimately recoverable resources and demand and production trends. With respect to minerals, there are several obstacles which complicate the application of Hubbert style curves to the prediction of future mineral production, including the lack of accurate discovery data, the effect of uncertain reserve estimates, and varying ore quality and quantity. Another notable differences is that while oil is often combusted during use, minerals are used to make metals which are inherently recyclable. Notwithstanding, by using a range of estimates of resources and/or reserves, a period of time can be identified which indicates when a peak in minerals production may occur. This information may then be used to plan for a transition from using a potentially constrained resource, to using substitutes if available, or to reducing demand for that mineral in society.

Key Words: economic; environmental; Hubbert; mining; minerals; peak oil; resource depletion; sustainable』

Introduction
Peak oil and assumptions for Hubberts curve
　Discovery and reserves
　Demand and production rates
　Application of Hubbert style curves
Mineral depletion and availability
Models for forecasting mineral availability
Obstacles to modelling peak minerals with Hubbert curves
　Lack of discovery data
　Uncertain reserves
　Production effects of varying ore grades and resource quality
　Comparisons of data for peak oil and peak minerals modelling
　Applying Hubbert curves to mineral production
Peak minerals practical applications
Conclusions
Acknowledgments
References