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AbstractMarine plankton play a crucial role in carbon storage, global climate, and ecosystem function. Planktonic ecosystems are embedded in patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework that accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The theory resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the time evolution of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary in size up to six times. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

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. 20 pages, 8 figures

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time. 5 pages, 3 figures

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-- diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically , the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Flooded rice production is crucial to global food security, but there are associated environmental concerns. In particular, it is a significant source of methane (CH4) and nitrous oxide (N2O) emissions and a large consumer of water resources, while arsenic levels in the grain are a serious health concern. There is also a tendency to use more organic fertilisers to close nutrient cycles, posing a threat of even higher GHG emissions and grain arsenic levels. It has been shown that alternate wetting and drying (AWD) water management reduces both water use and GHG emissions, but success at maintaining yields varies. This study tested the effect of early AWD (e-AWD) versus continuous flooding (CF) water management practices on grain yields, GHG emissions and grain arsenic levels in a split-plot field experiment with organic fertilisers under organic management. The treatments included: i) farmyard manure, ii) compost, and iii) biogas digestate, alone or in combination with mineral fertiliser. The e-AWD water regime showed no difference in yield for the organic treatments. Yields significantly increased by 5–16 % in the combination treatments. Root biomass and length increased in the e-AWD treatments up to 72 and 41 %, respectively. The e-AWD water regime reduced seasonal CH4 emissions by 71–85 % for organic treatments and by 51–76 % for combination treatments; this was linked to a 15–47 % reduction in dissolved organic carbon (DOC), thereby reducing methanogenesis. N2O emissions increased by 23–305 % but accounted for <20 % of global warming potential (GWP). Area and yield-scaled GWPs were reduced by 67–83 %. The e–AWD regime altered soil redox potentials, resulting in a reduction in grain arsenic and lead concentrations of up to 66 % and 73 % respectively. Grain cadmium levels were also reduced up to 33 % in organic treatments. Structural equation modelling showed that DOC, redox, ammonium and root biomass were the key traits that regulated emissions and maintained yield. Despite the fact that the experiment was conducted in the dry-season when soil moisture conditions can be relatively well-controlled, our findings should be confirmed in multi-year studies in farmers’ fields. These results suggest that in flooded rice systems receiving organic amendments or organic management, the e-AWD water regime can achieve multiple environmental and food safety objectives without compromising yield.

While the global economy continues to grow, ecosystem services tend to stagnate or decline. Economic theory has shown how such shifts in relative scarcities can be reflected in project appraisal and accounting, but empirical evidence has been sparse to put theory into practice. To estimate relative price changes in ecosystem services to be used for making such adjustments, we perform a global meta-analysis of contingent valuation studies to derive income elasticities of marginal willingness to pay (WTP) for ecosystem services to proxy the degree of limited substitutability. Based on 735 income-WTP pairs from 396 studies, we find an income elasticity of WTP of around 0.6. Combined with good-specific growth rates, we estimate relative price change of ecosystem services of around 1.7 percent per year. In an application to natural capital valuation of forest ecosystem services by the World Bank, we show that natural capital should be uplifted by around 40 percent. Our assessment of aggregate public natural capital yields a larger value adjustment of between 58 and 97 percent, depending on the discount rate. We discuss implications for policy appraisal and for estimates of natural capital in comprehensive wealth accounts.