In this talk, we will consider the problem of bifurcating DCMs under nutrient-light co-limitation from a weakly nonlinear point of view. In particular, we will work with the plankton-nutrient model in one spatial dimension introduced in A. Zagaris's talk and investigate the weakly nonlinear stability problem for these bifurcating DCMs.
The most intriguing mathematical aspect of this problem concerns the existence of an infinite number of eigenvalues tightly clustered around the origin. Although the corresponding modes are latent (non-bifurcating), they have to be included in the analysis as they interact nonlinearly with active (bifurcating) modes.
We will present explicit asymptotic results valid both close to and far from the bifurcation point, verifying that the bifurcating DCM is stable. Then, we will see that the latent modes have a decisive impact on the dynamics, solely through nonlinear interactions and although a strictly linear point of view dictates that they should be utterly irrelevant. In fact, the bifurcating stable DCM is soon annihilated in a saddle-node bifurcation induced by these latent modes, offering its place to a secondary pattern.
Climate driven changes to the physical structure of the ocean will modify oceanic temperature, light, and nutrients, essential ingredients for the growth of ocean phytoplankton. In turn, resulting changes in phytoplankton growth and community structure will affect export production, deep ocean carbon storage, and ultimately atmospheric carbon.
The questions I work on at present are: How will changes in temperature, light and nutrients affect phytoplankton growth rates and biomass and will they impact more the small phytoplankton or the large phytoplankton? What will be the resulting consequences for biological production and the carbon cycling in the ocean?
I propose from theoretical arguments a "critical nutrient hypothesis", i.e. that in the low nutrient regions roughly corresponding to 40S – 40N, future nutrient decreases due to increasing stratification will affect more small phytoplankton biomass than diatoms, with consequences for export production and the carbon cycle. I expect the opposite behavior in the high nutrient high latitudes, with future nutrient decreases affecting more diatoms than small phytoplankton. More broadly, I propose an analytical framework linking changes in nutrients, light and temperature with changes in phytoplankton biomass and assess these theoretical considerations against coupled model projections (1980-2100) from one of the leading US IPCC-class Earth System models, the NCAR CCSM3.1.
The vulnerability of polar bears to climate warming is well-established, and most polar bear populations are expected to decline substantially under expected climatic scenarios. However, until recently, only qualitative expectations were phrased in the literature (along with actual observations of declines in body condition, survival, reproduction and abundance); quantitative predictions of future abundances under climate change scenarios were missing. Such predictions are difficult to achieve because population models, and by extension population viability analyses, require knowledge of how reproduction and survival will change under future environmental conditions. For polar bears, this cannot be measured directly because past and predicted conditions differ substantially. Here, I will outline a framework that circumvents this problem: Most climate warming effects on polar bears can be understood as changes in their energy budget, either through increased movement costs or through decreased energy intake. Dynamic energy budget models can capture these effects and predict changes to reproduction and survival as a function of changes in energy expenditure and/or intake. Because energy budget models focus on physiological processes, they can be developed and tested under current environmental conditions. The output of these models can then serve as input to traditional population models that synthesize predictions of reproduction and survival into predictions of abundance. I will illustrate this approach with two examples, using data from western Hudson Bay to derive predictions for certain components of survival and reproductive success. I will then outline challenges that need to be addressed to advance the framework, including the need to develop a full energy budget model for polar bears (to address all components of survival and reproduction), the need to incorporate prey dynamics into the single-species framework (to more accurately quantify changes to the energy intake and expenditure of polar bears), and the need for sea ice models that operate on a regional rather than global scale (to more accurately link biological processes to future environmental conditions). The generality of the framework and its applicability to other species will also be discussed.
The Arctic environment is experiencing a rapid change due to the ongoing climate warming, with an especially high rate of temperature increase in the Arctic. The core of this change is the cryosphere destruction: an abrupt decrease in sea ice extent and volume, intensified glacier melting, and degradation of the permafrost. These processes profoundly affect the entire Arctic natural system including cascading effects on the Arctic Ocean food web. Recent years have witnessed changes in biogeochemical cycling and primary production patterns in various parts of the Arctic Ocean and intrusions of low-latitude biota into the high Arctic. For a proper evaluation of these changes and their future projection, they need to be considered in the context of long-term development of the Arctic environments beyond the scope of historical observations. Sediments from the Arctic Ocean floor hold the long-time archive of the history of sea ice, oceanic circulation, and related biological conditions. Investigation of sediment cores collected from multiple sites across the Arctic Ocean provide insights into paleoceanographic variations during the last several 100,000 years, with a yet longer-time record now available from a central Arctic Ocean site. In this talk I will give an overview of these geological studies with a focus on implications for the development of sea ice and effects on the Arctic Ocean biota.
Pelagic copepods are the dominant mesozooplankton in much of the world's oceans. They form a crucial link in the transfer of energy from primary production to upper trophic levels, and they are a significant contributor to vertical carbon flux through migration and fecal pellets. Much effort has gone into studying the effects of climate change on individual species. The effects of changing conditions on communities and assemblages are not as well understood. Answering this kind of question requires the development of a more general mathematical framework. Copepod morphologies are very similar across species. Differences between species are better described by how life history strategies are parameterized. By formulating these strategies with mechanistic equations, we can build a copepod model that is general enough to describe a wide range of species. Each species is represented by a digital chromosome of parameters, so that different sets of parameter values map to different species. This framework allows us to span scales from individually-based processes to system level properties such as biodiversity and size spectra. We can explore how temperature, resource availability, and mortality regimes structure modeled copepod communities.
During the 1990s the Gulf of Maine (GOM) underwent an ecosystem regime shift associated with an increase in freshwater inputs. This freshening has been linked to increased phytoplankton abundance, which in turn positively affected the growth of zooplankton and, consequently, many pelagic fish populations. Calanus finmarchicus is one of the most abundant species of zooplankton in the GOM and so is an important prey source for many species higher up the food chain such as herring and the North Atlantic right whale. While reproduction for C. finmarchicus was high during this period, abundance of the later stages of the surface population was paradoxically low. Adult herring preferentially feed on the later copepodid stages; it is therefore possible that increased herring presence exerted top-down control on C. finmarchicus. An alternative hypothesis is that the changes in phytoplankton abundance during the 1990s impacted recruitment of C. finmarchicus into the later stages. Specifically, phytoplankton variability may impact whether C. finmarchicus remain at the surface to reproduce or enter into a resting state until the following year, emerging to take advantage of the spring bloom. Using three simple differential equation models, we examined the interplay of top-down verses bottom-up processes on the observed changes in seasonal patterns of surface populations of late-stage C. finmarchicus.
The polar oceans have already experienced significant ecosystem shifts associated with sea ice retreat. Earth system models suggest that major changes in marine ecosystems and biogeochemistry will keep on going through the 21st century. However, future projections of the polar oceans are subject to some of the largest uncertainties. Among the sources of uncertainty is the role of sea ice: Earth system models consider sea ice as biologically inert, while observations indicate active biogeochemistry in sea ice. Hence, developing a realistic sea ice biogechemistry model component seems necessary.
The fact that sea ice is so prone to microbial life is due to the fact that compared to freshwater ice, sea ice is highly porous. Practically, sea ice can be viewed as a matrix of solid ice with liquid inclusions of brine. Depending on permeability, brine inclusions are connected or not with the underlying ocean. The brine network is ventilated by brine drainage mechanisms, supplying or flushing out nutrients.
In this presentation, based on observations and models, I will contextualize, explain and show how to model one fundamental aspect of biogeochemistry in sea ice, namely how biogeochemistry in sea ice is coupled with liquid brine dynamics.
The size of phytoplankton cells determines their competitive ability, sinking rate, and potential to export carbon to the deep ocean. Observations suggest that small phytoplankton species dominate the equatorial and subtropical oceans while larger species are more abundant in subpolar regions. To understand this pattern, we have developed an allometric model for the evolution of phytoplankton cell size. The model shows that increasing body size can be a successful adaptation, even in the absence of temporal variability or predation. The evolutionarily stable strategy is set by the allometric relationships for nutrient uptake kinetics and by metabolism. In a simple chemostat model, fluctuations in resource supply increase the optimal cell size. I will discuss the organization of phytoplankton communities along a latitudinal gradient in nutrient supply, sea surface temperature, and insolation.
In this talk, we will present analytic results concerning phytoplankton growth under nutrient-light co-limitation. The model we employ consists of two reaction-advection-diffusion PDEs for the plankton and nutrient concentrations and incorporates self-shading effects.
In the first part of this talk, we will work with a single spatial dimension (depth) and look closely into the linear stability problem for the trivial steady state (no phytoplankton). Using our results, we will identify the emergence of two distinct localized patterns: benthic layers (BLs), corresponding to the localization of plankton close to the bottom of the water column, and deep-chlorophyll maxima (DCMs), corresponding to localization in a thin region interior to the water column. This first part will close with an ecological interpretation of our findings.
In the second half, we will extend our model to account for an extra, horizontal dimension and include diffusion and (depth-dependent) advection along this new dimension. We will then investigate the corresponding linear stability problem and derive a condition for the relative sizes of horizontal diffusivity and advection, under which horizontally modulated DCMs may be expected to appear.