Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics

The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that the combined effects of migration and noise cannot account for the stabilization. The missing ingredient is the dependence of the oscillations' frequency upon their amplitude; with that, noise-induced differences between patches are amplified due to the frequency gradient. Migration among desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the functional dependence of the desynchronization upon diffusion strength and frequency differences. The oscillations' amplitude is shown to be (almost) noise independent. The results are compared with a numerical integration of the marginally stable Lotka-Volterra equations. An unstable system is extinction-prone for small noise, but stabilizes at larger noise intensity

Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient of the growth rate is due to abiotic factors only, and (ii) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin of Mathematical Biolog

08-02 "Ecological Macroeconomics: Consumption, Investment, and Climate Change"

The challenge of reducing global carbon emissions by 50-85 per cent by the year 2050, which is suggested by the Intergovernmental Panel on Climate Change (2007a) as a target compatible with limiting the risk of a more-than-2ºC temperature increase, clearly conflicts with existing patterns of economic growth, which are heavily dependent on increased use of fossil fuel energy. While it is theoretically possible to conceive of economic growth being “delinked” from fossil fuel consumption, any such delinking would represent a drastic change from economic patterns of the last 150 years. Current macroeconomic theory is heavily oriented towards an assumption of continuous, exponential growth in GDP. The historical record shows GDP growth is strongly correlated with a parallel record of increasing fossil energy use and CO2 emissions. A path of reduced carbon emissions would require major modifications in economic growth patterns. Climate change is part of an inter-related group of environmental issues associated with growth limits. These include population growth, agricultural production, water supplies, and species loss. To achieve a low-carbon path requires population stabilization, limited consumption, and major investments in environmental protection and social priorities such as public health, nutrition, and education. Macroeconomic theory must be adapted to reflect these new realities. A reclassification of macroeconomic aggregates is proposed to distinguish between those categories of goods and services that can expand over time, and those that must be limited to reduce carbon emissions. This reformulation makes it clear that there are many possibilities for environmentally beneficial economic expansion. New forms of Keynesian policy oriented towards ecological sustainability, provision of basic social needs such as education and health care, and distributional equity can provide a basis for a rapid reduction in carbon emissions while promoting investment in human and natural capital.

Induced Technological Change in a Limited Foresight Optimization Model

The threat of global warming calls for a major transformation of the energy system the coming century. Modeling technological change is an important factor in energy systems modeling. Technological change may be treated as induced by climate policy or as exogenous. We investigate the importance of induced technological change (ITC) in GET-LFL, an iterative optimization model with limited foresight that includes learning-by-doing. Scenarios for stabilization of atmospheric CO2 concentrations at 400, 450, 500 and 550 ppm are studied. We find that the introduction of ITC reduces the total net present value of the abatement cost over this century by 3-9% compared to a case where technological learning is exogenous. Technology specific polices which force the introduction of fuel cell cars and solar PV in combination with ITC reduce the costs further by 4-7% and lead to significantly different technological solutions in different sectors, primarily in the transport sector.Energy system model, Limited foresight, Climate policy, Endougenous learning, Technological lock-in

Analysis of Technological Portfolios for CO2 stabilizations and Effects of Technological Changes

In this study, cost-effective technological options to stabilize CO2 concentrations at 550, 500, and 450 ppmv are evaluated using a world energy systems model of linear programming with a high regional resolution. This model treats technological change endogenously for wind power, photovoltaics, and fuel-cell vehicles, which are technologies of mass production and are considered to follow the “learning by doing” process. Technological changes induced by climate policies are evaluated by maintaining the technological changes at the levels of the base case wherein there is no climate policy. The results achieved through model analyses include 1) cost-effective technological portfolios, including carbon capture and storage, marginal CO2 reduction costs, and increases in energy system cost for three levels of stabilization and 2) the effect of the induced technological change on the above mentioned factors. A sensitivity analysis is conducted with respect to the learning rate.Energy systems model, Global warming, Technological portfolios, Technological changes