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Abstract
The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra, advection induced, dispersal factor. We designed and assembled a dedicated microfluidic device to control and quantify the expansion of populations of E. coli bacteria under both co-flowing and counter-flowing conditions, measuring the front speed at varying intensity of the imposed flow. At variance with respect to the case of classic advective-reactive-diffusive chemical fronts, we measure that almost irrespective of the counter-flow velocity, the front speed remains finite at a constant positive value. A simple model incorporating growth, dispersion and drift on finite-size hard beads allows to explain this finding as due to a finite volume effect of the bacteria. This indicates that models based on the Fisher-Kolmogorov-Petrovsky-Piscounov equation (FKPP) that ignore the finite size of organisms may be inaccurate to describe the physics of spatial growth dynamics of bacteria.
Highlights
The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth
The study of the expansion of biological species in these environments is relevant for ecology, for example to understand algae blooms or the spread of invasive species[5], and, in conservation biology, for the reintroduction and persistence of populations under difficult environmental conditions, like for instance organisms living in the silt of a river[6]
The complete flow field has been solved with a numerical simulation by a Lattice Boltzmann Method (LBM) and verified in the device with Particle Tracking Velocimetry measurements on polystyrene beads diluted in water
Summary
The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In all cases the complexity of these systems is challenging because of the interplay between living species, with their motility behaviours and their active strategies to persist under difficult conditions and the role of the flow, which is usually both a vehicle for nutrient and the cause of transport of organisms out of their initial environments[7] Phenomena such as the spatial spreading of populations in new territories and the invasion of new species can dramatically change due to a streaming flow. The natural generalisation of classic spatial models of growth in liquid environments is formulated in terms of reaction-diffusion-advection equations of the density of organisms, c(x, t)[8,9] In these ecosystems, the spatial dynamics of a population is given by the combination of growth, individual own dispersion, and the transport by the flow as an extra biased migration factor10:. For sharp enough initial conditions, like the ones relevant in biology, it admits traveling wave solutions with www.nature.com/scientificreports/
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