Steady-state tracer dynamics in a lattice-automaton model of bioturbation

The intensity of biogenic sediment mixing is often expressed as a “biodiffusion coefficient” (D_b), quantified by fitting a diffusive model of bioturbation to vertical profiles of particle-bound radioisotopes. The biodiffusion coefficient often exhibits a dependence on tracer half-life: short-lived radioisotopes (e.g. ²³⁴Th) tend to yield notably larger D_b values than longer-lived radioisotopes (e.g. ²¹⁰Pb). It has been hypothesized that this is a result of differential mixing of tracers by particle-selective benthos. This study employs a lattice-automaton model of bioturbation to explore how steady-state tracers with different half-lives are mixed in typical marine settings. Every particle in the model is tagged with the same array of radioisotopes, so that all tracers experienced exactly the same degree of mixing. Two different estimates of the mixing intensity are calculated: a tracer-derived D_b, obtained in the standard way by fitting the biodiffusion model to resulting tracer profiles, and a particle-tracking D_b, derived from the statistics of particle movements. The latter provides a tracer-independent measure of mixing for use as a reference. Our simulations demonstrate that an apparent D_b tracer-dependence results from violating the underlying assumptions of the biodiffusion model. Breakdown of the model is rarely apparent from tracer profiles, emphasizing the need to evaluate the model’s criteria from biological and ecological parameters, rather than relying on obvious indications of model breakdown, e.g., subsurface maxima. Simulations of various marine environments (coastal, slope, abyssal) suggest that the time scales of short-lived radioisotopes, such as ²³⁴Th and ⁷Be, are insufficient for the tracers to be used with the biodiffusion model. ²¹⁰Pb appears an appropriate tracer for abyssal sediments, while ²¹⁰Pb and ²²⁸Th are suitable for slope and coastal sediments.