Partial Differential Equations in Ecology

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots

The stability of model ecosystems

Ecologists would like to understand how complexity persists in nature. In this thesis I have taken two fundamentally different routes to study ecosystem stability of model ecosystems: classical community ecology and classical population ecology. In community ecology models, we can study the mathematical mechanisms of stability in general, large model ecosystems. In population ecology models, fewer species are studied but greater detail of species interactions can be incorporated. Within these alternative contexts, this thesis contributes to two consuming issues concerning the stability of ecological systems: the ecosystem stability-complexity debate; and the causes of cyclic population dynamics. One of the major unresolved issues in community ecology is the relationship between ecosystem stability and complexity. In 1958 Charles Elton made the conjecture that the stability of an ecological system was coupled to its complexity and this could be a “wise principle of co-existence between man and nature” with which ecologists could argue the case for the conservation of nature for all species, including man. The earliest and simplest model systems were randomly constructed and exhibited a negative association between stability and complexity. This finding sparked the stability-complexity debate and initiated the search for organising principles that enhanced stability in real ecosystems. One of the universal laws of ecology is that ecosystems contain many rare and few common species. In this thesis, I present analytical arguments and numerical results to show that the stability of an ecosystem can increase with complexity when the abundance distribution is characterized by a skew towards many rare species. This work adds to the growing number of conditions under which the negative stability - complexity relationship can been inverted in theoretical studies. While there is growing evidence that the stability-complexity debate is progressing towards a resolution, community ecology has become increasingly subject to major criticism. A long-standing criticism is the reliance on local stability analysis. There is growing recognition that a global property called permanence is a more satisfactory definition of ecosystem stability because it tests only whether species can coexist. Here I identify and explain a positive correlation between the probability of local stability and permanence, which suggests local stability is a better measure of species coexistence than previously thought. While this offers some relief, remaining issues cause the stability-complexity debate to evade clear resolution and leave community ecology in a poor position to argue for the conservation of natural diversity for the benefit of all species. In classical population ecology, a major unresolved issue is the cause of non-equilibrium population dynamics. In this thesis, I use models to study the drivers of cyclic dynamics in Scottish populations of mountain hares (Lepus timidus), for the first time in this system. Field studies currently favour the hypothesis that parasitism by a nematode Trichostrongylus retortaeformis drives the hare cycles, and theory predicts that the interaction should induce cycling. Initially I used a simple, strategic host-parasite model parameterised using available empirical data to test the superficial concordance between theory and observation. I find that parasitism could not account for hare cycles. This verdict leaves three options: either the parameterisation was inadequate, there were missing important biological details or simply that parasites do not drive host cycles. Regarding the first option, reliable information for some hare-parasite model parameters was lacking. Using a rejection-sampling approach motivated by Bayesian methods, I identify the most likely parameter set to predict observed dynamics. The results imply that the current formulation of the hare-parasite model can only generate realistic dynamics when parasite effects are significantly larger than current empirical estimates, and I conclude it is likely that the model contains an inadequate level of detail. The simple strategic model was mathematically elegant and allowed mathematical concepts to be employed in analysis, but the model was biologically naïve. The second model is the antipode of the first, an individual based model (IBM) steeped in biological reality that can only be studied by simulation. Whilst most highly detailed tactical models are developed as a predictive tool, I instead structurally perturb the IBM to study the ecological processes that may drive population cycles in mountain hares. The model allows delayed responses to life history by linking maternal body size and parasite infection to the future survival and fecundity of offspring. By systematically removing model structure I show that these delayed life history effects are weakly destabilising and allow parameters to lie closer to empirical estimates to generate observed hare population cycles. In a third model I structurally modify the simple strategic host-parasite model to make it spatially explicit by including diffusion of mountain hares and corresponding advection of parasites (transportation with host). From initial simulations I show that the spatially extended host-parasite equations are able to generate periodic travelling waves (PTWs) of hare and parasite abundance. This is a newly documented behaviour in these widely used host-parasite equations. While PTWs are a new potential scenario under which cyclic hare dynamics could be explained, further mathematical development is required to determine whether adding space can generate realistic dynamics with parameters that lie closer to empirical estimates. In the general thesis discussion I deliberate on whether a hare-parasite model has been identified which can be considered the right balance between abstraction and relevant detail for this system

Predictability studies of coastal marine ecosystem behavior

The study presented in this thesis is principally meant to analyze the genericity of a deterministic, comprehensive marine ecosystem model in combination with various refined representations of hydrodynamical processes, and to evaluate the potential predictability skills of this combined modelling system with specific applications in two rather different coastal basins. This objective has been realized by first developing a modular coupling interface between the Princeton Ocean Model (POM) and the European Regional Seas Ecosystem Model (ERSEM), called High-Resolution OpenSESAME POM ERSEM (HiROPE). Secondly, this model framework, embedding a composite of 'complex' conceptual principles of the functioning of the main biogeochemical processes, has been applied to substantially different marine systems, the Baltic proper and the northern Adriatic Sea. The generic biological first principles of the ERSEM ecosystem model have been throughly controlled for consistency, and a suitable mathematical syntax has been defined in order to accomodate the various biogeochemical cycles of the resolved elements. The model has been specifically applied in the chosen basins with different temporal and spatial resolutions: a one-dimensional (vertical, 1D-V), climatological implementation in the northern Adriatic Sea; a 1D-V implementation in the Baltic proper with realistic forcing functions in the period 1979-1991 and a fully three-dimensional, high-frequency realistic implementation in the northern Adriatic Sea (October 1995). General conclusions are that the representation of hydrodynamical variability, the definition and resolution of boundary processes, the introduction of new source terms or the implementation of new biological state variables, affect the predictability of the system behavior more than the utilization of incomplete initial conditions of biological variables in a complex comprehensive ecosystem model

Predictability studies of coastal marine ecosystem behavior

The study presented in this thesis is principally meant to analyze the genericity of a deterministic, comprehensive marine ecosystem model in combination with various refined representations of hydrodynamical processes, and to evaluate the potential predictability skills of this combined modelling system with specific applications in two rather different coastal basins. This objective has been realized by first developing a modular coupling interface between the Princeton Ocean Model (POM) and the European Regional Seas Ecosystem Model (ERSEM), called High-Resolution OpenSESAME POM ERSEM (HiROPE). Secondly, this model framework, embedding a composite of 'complex' conceptual principles of the functioning of the main biogeochemical processes, has been applied to substantially different marine systems, the Baltic proper and the northern Adriatic Sea. The generic biological first principles of the ERSEM ecosystem model have been throughly controlled for consistency, and a suitable mathematical syntax has been defined in order to accomodate the various biogeochemical cycles of the resolved elements. The model has been specifically applied in the chosen basins with different temporal and spatial resolutions: a one-dimensional (vertical, 1D-V), climatological implementation in the northern Adriatic Sea; a 1D-V implementation in the Baltic proper with realistic forcing functions in the period 1979-1991 and a fully three-dimensional, high-frequency realistic implementation in the northern Adriatic Sea (October 1995). General conclusions are that the representation of hydrodynamical variability, the definition and resolution of boundary processes, the introduction of new source terms or the implementation of new biological state variables, affect the predictability of the system behavior more than the utilization of incomplete initial conditions of biological variables in a complex comprehensive ecosystem model

Human-elephant interactions: from past to present

korrigierter Nachdruck, nur Änderungen im ImpressumIn recent decades, a significant number of Pleistocene (ca. 2.6 million years–10,000 years ago) open-air and cave sites yielding elephant or mammoth bones in direct association with hominin remains and/or lithic artifacts have been discovered in Eurasia, Africa and America. Many of them show strong evidence of acquisition and processing of proboscidean carcasses by early humans, leading scientists to interpret them as “elephant butchering sites”. Indeed, proboscidean exploitation by early Homo has been proposed to have been critical for Palaeolithic human lifeways, influencing not only their subsistence, but also other aspects of early human evolution and adaptations. The nature and degree of interactions between humans and elephants comprises an important field in palaeoanthropological studies since decades, but many questions remain still unanswered or partially explored. By bringing together research papers from the fields of Palaeolithic Archaeology, Palaeoanthropology, Palaeontology, Zooarchaeology, Geology, Ethnography and Nutrition Studies, the book systematically covers a diverse array of perspectives on elephant-human interactions across the world from the Pleistocene times until today. The volume includes 19 contributions and is organized into four thematic sections: 1) The Palaeolithic record, 2) A view of the evidence, 3) Elephants in past human nutrition, and 4) Ethnography – Human-elephant interactions in recent Africa. Collectively, the volume not only showcases the current state of knowledge, but also intends to provoke renewed interest for current and further research, and build an interdisciplinary and synthetic understanding of the significance of proboscideans throughout human evolution

Human-elephant interactions: from past to present

In recent decades, a significant number of Pleistocene (ca. 2.6 million years–10,000 years ago) open-air and cave sites yielding elephant or mammoth bones in direct association with hominin remains and/or lithic artifacts have been discovered in Eurasia, Africa and America. Many of them show strong evidence of acquisition and processing of proboscidean carcasses by early humans, leading scientists to interpret them as “elephant butchering sites”. Indeed, proboscidean exploitation by early Homo has been proposed to have been critical for Palaeolithic human lifeways, influencing not only their subsistence, but also other aspects of early human evolution and adaptations. The nature and degree of interactions between humans and elephants comprises an important field in palaeoanthropological studies since decades, but many questions remain still unanswered or partially explored. By bringing together research papers from the fields of Palaeolithic Archaeology, Palaeoanthropology, Palaeontology, Zooarchaeology, Geology, Ethnography and Nutrition Studies, the book systematically covers a diverse array of perspectives on elephant-human interactions across the world from the Pleistocene times until today. The volume includes 19 contributions and is organized into four thematic sections: 1) The Palaeolithic record, 2) A view of the evidence, 3) Elephants in past human nutrition, and 4) Ethnography – Human-elephant interactions in recent Africa. Collectively, the volume not only showcases the current state of knowledge, but also intends to provoke renewed interest for current and further research, and build an interdisciplinary and synthetic understanding of the significance of proboscideans throughout human evolution.The symposium and the volume "Human-elephant interactions: from past to present" were funded by the Volkswagen Foundation