Depth of the biomass maximum affects the rules of resource competition in a water column.

The theory of resource competition in spatially extended systems with resources and biomass fluxes is far from trivial. Here, we analyze the competition between two phytoplankton species for light and a nutrient in a weakly mixed water column. We develop a general framework for such an analysis and show that the competition outcome can be largely understood from a single parameter, the slope of the invasion threshold in the plane of resources. Using this approach, we show that the competition outcome crucially depends on the depth of the biomass maximum. Under eutrophic conditions, when the phytoplankton production peaks on the surface, species composition depends on the ratio of resource supplies, and the competition outcome follows the "classic" rule: coexistence is possible if each competitor has the greatest effect on its most limiting resource. By contrast, in oligotrophic systems, characterized by deep biomass maxima, the absolute level of resource supplies drives species composition, and coexistence becomes more feasible if each competitor mostly consumes its least limiting resource. Finally, when the production peaks in the subsurface, good nutrient competitors are favored. Our findings are supported by empirical data.

Depth of the biomass maximum affects the rules of resource competition in a water column.

The theory of resource competition in spatially extended systems with resources and biomass fluxes is far from trivial. Here, we analyze the competition between two phytoplankton species for light and a nutrient in a weakly mixed water column. We develop a general framework for such an analysis and show that the competition outcome can be largely understood from a single parameter, the slope of the invasion threshold in the plane of resources. Using this approach, we show that the competition outcome crucially depends on the depth of the biomass maximum. Under eutrophic conditions, when the phytoplankton production peaks on the surface, species composition depends on the ratio of resource supplies, and the competition outcome follows the "classic" rule: coexistence is possible if each competitor has the greatest effect on its most limiting resource. By contrast, in oligotrophic systems, characterized by deep biomass maxima, the absolute level of resource supplies drives species composition, and coexistence becomes more feasible if each competitor mostly consumes its least limiting resource. Finally, when the production peaks in the subsurface, good nutrient competitors are favored. Our findings are supported by empirical data.

Complex transient dynamics of stage-structured populations in response to environmental changes.

Stage structures of populations can have a profound influence on their dynamics. However, not much is known about the transient dynamics that follow a disturbance in such systems. Here we combined chemostat experiments with dynamical modeling to study the response of the phytoplankton species Chlorella vulgaris to press perturbations. From an initially stable steady state, we altered either the concentration or dilution rate of a growth-limiting resource. This disturbance induced a complex transient response-characterized by the possible onset of oscillations-before population numbers relaxed to a new steady state. Thus, cell numbers could initially change in the opposite direction of the long-term change. We present quantitative indexes to characterize the transients and to show that the dynamic response is dependent on the degree of synchronization among life stages, which itself depends on the state of the population before perturbation. That is, we show how identical future steady states can be approached via different transients depending on the initial population structure. Our experimental results are supported by a size-structured model that accounts for interplay between cell-cycle and population-level processes and that includes resource-dependent variability in cell size. Our results should be relevant to other populations with a stage structure including organisms of higher order.

The role of dissipation in time-dependent non-integrable focusing billiards.

In this study, we compare the dynamical properties of chaotic and nearly integrable time-dependent focusing billiards with elastic and dissipative boundaries. We show that in the system without dissipation the average velocity of particles scales with the number of collisions as ̅V∝n(α). In the fully chaotic case, this scaling corresponds to a diffusion process with α≈1/2, whereas in the nearly integrable case, this dependence has a crossover; slow particles accelerate in a slow subdiffusive manner with α<1/2, while acceleration of fast particles is much stronger and their average velocity grows super-diffusively, i.e., α>1/2. Assuming ̅V∝n(α) for a non-dissipative system, we obtain that in its dissipative counterpart the average velocity approaches to ̅V(fin)∝1/δ(α), where δ is the damping coefficient. So that ̅V(fin)∝√1/δ in the fully chaotic billiards, and the characteristics exponents α changes with δ from α(1)>1/2 to α(2)<1/2 in the nearly integrable systems. We conjecture that in the limit of moderate dissipation the chaotic time-depended billiards can accelerate the particles more efficiently. By contrast, in the limit of small dissipations, the nearly integrable billiards can become the most efficient accelerator. Furthermore, due to the presence of attractors in this system, the particles trajectories will be focused in narrow beams with a discrete velocity spectrum.

A graphical theory of competition on spatial resource gradients.

Resource competition is a fundamental interaction in natural communities. However, little remains known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyse the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations, which lead to coexistence in a uniform environment, may favour alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes.

Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer.

The vertical distribution of phytoplankton is of fundamental importance for the dynamics and structure of aquatic communities. Here, using an advection-reaction-diffusion model, we investigate the distribution and competition of phytoplankton species in a water column, in which inverse resource gradients of light and a nutrient can limit growth of the biomass. This problem poses a challenge for ecologists, as the location of a production layer is not fixed, but rather depends on many internal parameters and environmental factors. In particular, we study the influence of an upper mixed layer (UML) in this system and show that it leads to a variety of dynamic effects: (i) Our model predicts alternative density profiles with a maximum of biomass either within or below the UML, thereby the system may be bistable or the relaxation from an unstable state may require a long-lasting transition. (ii) Reduced mixing in the deep layer can induce oscillations of the biomass; we show that a UML can sustain these oscillations even if the diffusivity is less than the critical mixing for a sinking phytoplankton population. (iii) A UML can strongly modify the outcome of competition between different phytoplankton species, yielding bistability both in the spatial distribution and in the species composition. (iv) A light limited species can obtain a competitive advantage if the diffusivity in the deep layers is reduced below a critical value. This yields a subtle competitive exclusion effect, where the oscillatory states in the deep layers are displaced by steady solutions in the UML. Finally, we present a novel graphical approach for deducing the competition outcome and for the analysis of the role of a UML in aquatic systems.