Determining selection across heterogeneous landscapes: a perturbation-based method and its application to modeling evolution in space

Spatial structure can decisively influence the way evolutionary processes unfold. Several methods have thus far been used to study evolution in spatial systems, including population genetics, quantitative genetics, momentclosure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply in both continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very effi- cient, and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations

Multi-nutrient, multi-group model of present and future oceanic phytoplankton communities

International audiencePhytoplankton community composition profoundly affects patterns of nutrient cycling and the dynamics of marine food webs; therefore predicting present and future phytoplankton community structure is crucial to understand how ocean ecosystems respond to physical forcing and nutrient limitations. We develop a mechanistic model of phytoplankton communities that includes multiple taxonomic groups (diatoms, coccolithophores and prasinophytes), nutrients (nitrate, ammonium, phosphate, silicate and iron), light, and a generalist zooplankton grazer. Each taxonomic group was parameterized based on an extensive literature survey. We test the model at two contrasting sites in the modern ocean, the North Atlantic (North Atlantic Bloom Experiment, NABE) and subarctic North Pacific (ocean station Papa, OSP). The model successfully predicts general patterns of community composition and succession at both sites: In the North Atlantic, the model predicts a spring diatom bloom, followed by coccolithophore and prasinophyte blooms later in the season. In the North Pacific, the model reproduces the low chlorophyll community dominated by prasinophytes and coccolithophores, with low total biomass variability and high nutrient concentrations throughout the year. Sensitivity analysis revealed that the identity of the most sensitive parameters and the range of acceptable parameters differed between the two sites. We then use the model to predict community reorganization under different global change scenarios: a later onset and extended duration of stratification, with shallower mixed layer depths due to increased greenhouse gas concentrations; increase in deep water nitrogen; decrease in deep water phosphorus and increase or decrease in iron concentration. To estimate uncertainty in our predictions, we used a Monte Carlo sampling of the parameter space where future scenarios were run using parameter combinations that produced acceptable modern day outcomes and the robustness of the predictions was determined. Change in the onset and duration of stratification altered the timing and the magnitude of the spring diatom bloom in the North Atlantic and increased total phytoplankton and zooplankton biomass in the North Pacific. Changes in nutrient concentrations in some cases changed dominance patterns of major groups, as well as total chlorophyll and zooplankton biomass. Based on these scenarios, our model suggests that global environmental change will inevitably alter phytoplankton community structure and potentially impact global biogeochemical cycles

Multi-nutrient, multi-group model of present and future oceanic phytoplankton communities

Phytoplankton community composition profoundly affects patterns of nutrient cycling and the dynamics of marine food webs; therefore predicting present and future phytoplankton community structure is crucial to understand how ocean ecosystems respond to physical forcing and nutrient limitations. We develop a mechanistic model of phytoplankton communities that includes multiple taxonomic groups (diatoms, coccolithophores and prasinophytes), nutrients (nitrate, ammonium, phosphate, silicate and iron), light, and a generalist zooplankton grazer. Each taxonomic group was parameterized based on an extensive literature survey. We test the model at two contrasting sites in the modern ocean, the North Atlantic (North Atlantic Bloom Experiment, NABE) and subarctic North Pacific (ocean station Papa, OSP). The model successfully predicts general patterns of community composition and succession at both sites: In the North Atlantic, the model predicts a spring diatom bloom, followed by coccolithophore and prasinophyte blooms later in the season. In the North Pacific, the model reproduces the low chlorophyll community dominated by prasinophytes and coccolithophores, with low total biomass variability and high nutrient concentrations throughout the year. Sensitivity analysis revealed that the identity of the most sensitive parameters and the range of acceptable parameters differed between the two sites. We then use the model to predict community reorganization under different global change scenarios: a later onset and extended duration of stratification, with shallower mixed layer depths due to increased greenhouse gas concentrations; increase in deep water nitrogen; decrease in deep water phosphorus and increase or decrease in iron concentration. To estimate uncertainty in our predictions, we used a Monte Carlo sampling of the parameter space where future scenarios were run using parameter combinations that produced acceptable modern day outcomes and the robustness of the predictions was determined. Change in the onset and duration of stratification altered the timing and the magnitude of the spring diatom bloom in the North Atlantic and increased total phytoplankton and zooplankton biomass in the North Pacific. Changes in nutrient concentrations in some cases changed dominance patterns of major groups, as well as total chlorophyll and zooplankton biomass. Based on these scenarios, our model suggests that global environmental change will inevitably alter phytoplankton community structure and potentially impact global biogeochemical cycles

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Modeling the clonal heterogeneity of stem cells

Recent experimental studies suggest that tissue stem cell pools are composed of functionally diverse clones. Metapopulation models in ecology concentrate on collections of populations and their role in stabilizing coexistence and maintaining selected genetic or epigenetic variation. Such models are characterized by expansion and extinction of spatially distributed populations. We develop a mathematical framework derived from the multispecies metapopulation model of Tilman et al (1994) to study the dynamics of heterogeneous stem cell metapopulations. In addition to normal stem cells, the model can be applied to cancer cell populations and their response to treatment. In our model disturbances may lead to expansion or contraction of cells with distinct properties, reflecting proliferation, apoptosis, and clonal competition. We first present closed-form expressions for the basic model which defines clonal dynamics in the presence of exogenous global disturbances. We then extend the model to include disturbances which are periodic and which may affect clones differently. Within the model framework, we propose a method to devise an optimal strategy of treatments to regulate expansion, contraction, or mutual maintenance of cells with specific properties

Interactions between growth-dependent changes in cell size, nutrient supply and cellular elemental stoichiometry of marine Synechococcus

The factors that control elemental ratios within phytoplankton, like carbon:nitrogen:phosphorus (C:N:P), are key to biogeochemical cycles. Previous studies have identified relationships between nutrient-limited growth and elemental ratios in large eukaryotes, but little is known about these interactions in small marine phytoplankton like the globally important Cyanobacteria. To improve our understanding of these interactions in picophytoplankton, we asked how cellular elemental stoichiometry varies as a function of steady-state, N- and P-limited growth in laboratory chemostat cultures of Synechococcus WH8102. By combining empirical data and theoretical modeling, we identified a previously unrecognized factor (growth-dependent variability in cell size) that controls the relationship between nutrient-limited growth and cellular elemental stoichiometry. To predict the cellular elemental stoichiometry of phytoplankton, previous theoretical models rely on the traditional Droop model, which purports that the acquisition of a single limiting nutrient suffices to explain the relationship between a cellular nutrient quota and growth rate. Our study, however, indicates that growth-dependent changes in cell size have an important role in regulating cell nutrient quotas. This key ingredient, along with nutrient-uptake protein regulation, enables our model to predict the cellular elemental stoichiometry of Synechococcus across a range of nutrient-limited conditions. Our analysis also adds to the growth rate hypothesis, suggesting that P-rich biomolecules other than nucleic acids are important drivers of stoichiometric variability in Synechococcus. Lastly, by comparing our data with field observations, our study has important ecological relevance as it provides a framework for understanding and predicting elemental ratios in ocean regions where small phytoplankton like Synechococcus dominates

Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed into an external cavity leads to the formation of temporal vectorial dissipative solitons. These solitons arise as cycles in the polarization orientation, leaving the total intensity constant. When the cavity round-trip is much longer than their duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solutions coexist together and with the background solution, i.e. the solution with zero soliton. The theoretical proof of localization is given by the analysis of the Floquet exponents. Finally, we reduce the dynamics to a single delayed equation for the polarization orientation allowing interpreting the vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure