The movement of organisms can be described with different modelling frameworks. On the large spatial scales, we often prefer advection-diffusion descriptions which describe how animals move on average and how they spread. On smaller scales, the detailed patterns of movements become visible. Bacteria may display run-tumble motion, where they move with constant direction until they abruptly reorient themselves. Also larger organisms may display similar behaviour. When we use different descriptions to describe motion at different scales, we need to make sure that our descriptions are consistent. Stated differently, if we have observed the small-scale movements of an organism, we may ask what is the corresponding advection-diffusion model which describes the motion on larger scales? This paper uses theory from stochastic processes to approximation run-tumble motion with an advection-diffusion model. Compared to previous methods, the resulting approximation is simpler to compute, also in situations where the bias is strong. This happens for example when chemotactic bacteria experience strong chemical cues around sinking marine snow.
Read the paper here.
Reference:
Thygesen, Uffe Høgsbro (2016) A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run–Tumble Motion. Bulletin of Mathematical Biology, in press, available online. DOI: 10.1007/s11538-016-0155-3