Mathematical modelling reveals potential acceleration of the supercontinent cycle

Abstract

Abstract The supercontinent cycle has been the focus of researchers for many years, but the parameters of its cyclicity remain a central debate; thus, prediction of the occurrence of the next supercontinent remains elusive. In this research, a mathematical point of view is adopted, based on the assumption that the supercontinent Columbia assembled at – 2000 Myr $$\left( {X\left( { - 2} \right)} \right)$$ X - 2 and the supercontinent Rodinia assembled at – 1000 Myr $$\left( {X\left( { - 1} \right)} \right)$$ X - 1 . The younger supercontinents are calculated following this mathematical equation: $$X\left( n \right) = 2*X\left( {n - 1} \right) - X\left( {n - 2} \right) - \left( {\frac{540}{{3^{n} }}} \right)$$ X n = 2 ∗ X n - 1 - X n - 2 - 540 3 n , where $$X\left( n \right)$$ X n represents the assembly and n is the position of the supercontinent in the sequence. Therefore, Gondwana $$\left( {X\left( 0 \right)} \right)$$ X 0 amalgamated at -540 Myr, Pangea $$\left( {X\left( 1 \right)} \right)$$ X 1 at – 260 Myr, Eurasia $$\left( {X\left( 2 \right)} \right)$$ X 2 at – 40 Myr and Pangea Proxima $$\left( {X\left( 3 \right)} \right)$$ X 3 might form at + 160 Myr. Moreover, two logarithmic regressions give fairly similar results, confirming that a constant acceleration of the supercontinent cycle is probable. The detrital zircon, metamorphic and hafnium isotope records support the assemblies’ hypotheses that produce the mathematical equation. However, a recent supercontinent or “megacontinent” called Eurasia lacks strong geological evidence in the three datasets. These findings might reconcile the paradox brought about by the closer ages in time for the Earth’s more recent supercontinental assemblies and the assumed constant cyclicity of the cycle.