Planktonic communities and chaotic advection in dynamical models of Langmuir circulation

A deterministic mechanism for the production of plankton patches within a typical medium scale oceanic structure is proposed and investigated. By direct numerical simulation of a simple model of Langmuir circulation we quantify the effects of unsteady flows on planktonic communities and demonstrate their importance. Two qualitatively different zones within the flow are identified: chaotic regions that help to spread plankton and locally coherent regions, that do not mix with the chaotic regions and which persist for long periods of time. The relative importance of these regions to both phytoplankton and zooplankton is investigated, taking into account variations in plankton buoyancy. In particular, species-specific retention zone structure is discussed in relation to variations in environmental forcing

The orientation of swimming bi-flagellates in shear flows

Biflagellated algae swim in mean directions that are governed by their environments. For example, many algae can swim upward on average (gravitaxis) and toward downwelling fluid (gyrotaxis) via a variety of mechanisms. Accumulations of cells within the fluid can induce hydrodynamic instabilities leading to patterns and flow, termed bioconvection, which may be of particular relevance to algal bioreactors and plankton dynamics. Furthermore, knowledge of the behavior of an individual swimming cell subject to imposed flow is prerequisite to a full understanding of the scaled-up bulk behavior and population dynamics of cells in oceans and lakes; swimming behavior and patchiness will impact opportunities for interactions, which are at the heart of population models. Hence, better estimates of population level parameters necessitate a detailed understanding of cell swimming bias. Using the method of regularized Stokeslets, numerical computations are developed to investigate the swimming behavior of and fluid flow around gyrotactic prolate spheroidal biflagellates with five distinct flagellar beats. In particular, we explore cell reorientation mechanisms associated with bottom-heaviness and sedimentation and find that they are commensurate and complementary. Furthermore, using an experimentally measured flagellar beat for Chlamydomonas reinhardtii, we reveal that the effective cell eccentricity of the swimming cell is much smaller than for the inanimate body alone, suggesting that the cells may be modeled satisfactorily as self-propelled spheres. Finally, we propose a method to estimate the effective cell eccentricity of any biflagellate when flagellar beat images are obtained haphazardly

Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent

The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens

The rate of expansion of bacterial colonies of S. liquefaciens is investigated in terms of a mathematical model that combines biological as well as hydrodynamic processes. The relative importance of cell differentiation and production of an extracellular wetting agent to bacterial swarming is explored using a continuum representation. The model incorporates aspects of thin film flow with variable suspension viscosity, wetting, and cell differentiation. Experimental evidence suggests that the bacterial colony is highly sensitive to its environment and that a variety of mechanisms are exploited in order to proliferate on a variety of surfaces. It is found that a combination of effects are required to reproduce the variation of bacterial colony motility over a large range of nutrient availability and medium hardness

Synthetizing hydrodynamic turbulence from noise: formalism and applications to plankton dynamics

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian 2D turbulent flows by using linear stochastic partial differential equations, where the noise term acts as a random force of well-prescribed statistics. This methodology leads to a divergence-free, isotropic, stationary and homogeneous velocity field, whose characteristic parameters are well reproduced, in particular the kinematic viscosity and energy spectrum. This practical approach to tailor a turbulent flow is justified by its versatility when analizing different physical processes occurring in advectely mixed systems. Here, we focuss on an application to study the dynamics of Planktonic populations in the ocean

Quantitative effects of medium hardness and nutrient availability on the swarming motility of <i>Serratia liquefaciens</i>

We report the first controlled measurements of expansion rates for swarming colonies of Serratia liquefaciens under different growth conditions, combined with qualitative observations of the organization of the colony into regions of differentiated cell types. Significantly, the results reveal that swarming colonies of S. liquefaciens can have an increasing expansion rate with time. We compare and contrast the expansion rate results with predictions from a recent mathematical model which coupled key hydrodynamical and biological mechanisms. Furthermore, we investigate whether the swarming colonies grow according to a power law or exponentially (for large times), as suggested by recent theoretical results

Theory of periodic swarming of bacteria: application to Proteus mirabilis

The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common species exhibiting this type of growth) a series of concentric rings are developed as the bacteria multiply and swarm following a scenario periodically repeating itself. We have developed a theoretical description for this process in order to get a deeper insight into some of the typical processes governing the phenomena in systems of many interacting living units. All of our theoretical results are in excellent quantitative agreement with the complete set of available observations.Comment: 11 pages, 8 figure

Synchrony &#38; chaos in patchy ecosystems

The apparent synchronisation of spatially discrete populations is a well documented phenomenon. However, it is not clear what the governing mechanisms are for this synchrony, and whether they are robust over a range of environmental conditions and patch specific population dynamic behaviours. In this paper, we explore two (possibly interacting) modes of coupling, and investigate their theoretically discernible, and perhaps even experimentally measurable, signatures. To aid us in this investigation we employ a planktonic example system, with direct application to plankton patchiness. Furthermore, we address the role of chaos in complex spatio-temporal dynamics; we find that chaos associated with funnel attractors can play a distinguished role, over dynamics less sensitive to small variations, in being more susceptible to generalised synchronisation (such as phase synchronisation) in the presence of small local parameter variation. This is in contrast to the case for coupled systems with identical dynamics, and suggests that non-identically coupled systems are more vulnerable to global extinction events when exhibiting funnel-type chaotic dynamics

Wavelengths of bioconvection patterns

Bioconvection occurs as the result of the collective behaviour of many micro-organisms swimming in a fluid and is realised as patterns similar to those of thermal convection which occur when a layer of water is heated from below. A methodology is developed to record the bioconvection patterns that are formed by aqueous cultures of the single-celled alga Chlamydomonas nivalis. The analysis that is used to quantify the patterns as a function of cell concentration, suspension depth and time is described and experimental results are presented

The role of time delays in a non-autonomous host–parasitoid model of slug biocontrol with nematodes

Motivated by the difficulty in designing efficacious biocontrol strategies for dominant, agriculturally damaging slug species using naturally occurring parasitic nematodes, we investigate theory for the significant impact of stage structured delays on a non-autonomous host–parasitoid system. Initially, we mathematically strengthen existing stability results for a general class of autonomous system with delays at different trophic levels using analytical and numerical continuation methods. These results are employed to guide theoretical analyses of the effect of delays in a particular, seasonally forced, host–parasitoid system that can model aspects of slug–nematode biocontrol dynamics. Significantly, the model reveals a log-dose response consistent with experiments, and suggests that the optimal timing and frequency of applications is highly dependent on the form of the control required. We find that short-term high-level as well as less dramatic but sustained control are both possible by varying the timing of application. Moreover, we establish that resonance can occur between application and slug life-cycle frequencies inducing potentially undesirable large amplitude fluctuations in slug numbers. Finally, we assess the practicality of planning a crop protection response in the field