Estimating the duration of geologic intervals from a small number of age determinations: A challenge common to petrology and paleobiology

The duration of a geologic interval, such as the time over which a given volume of magma accumulated to form a pluton, or the lifespan of a large igneous province, is commonly determined from a relatively small number of geochronologic determinations (e.g., 4-10) within that interval. Such sample sets can underestimate the true length of the interval by a significant amount. For example, the average interval determined from a sample of size n = 5, drawn from a uniform random distribution, will underestimate the true interval by 50%. Even for n = 10, the average sample only captures similar to 80% of the interval. If the underlying distribution is known then a correction factor can be determined from theory or Monte Carlo analysis; for a uniform random distribution, this factor is n+1/n-1. Systematic undersampling of interval lengths can have a large effect on calculated magma fluxes in plutonic systems. The problem is analogous to determining the duration of an extinct species from its fossil occurrences. Confidence interval statistics developed for species origination and extinction times are applicable to the onset and cessation of magmatic events.