It is well recognized that models in the life sciences can be sensitive to small variations in their model functions, a phenomenon known as 'structural sensitivity'. Conventionally, modellers test for sensitivity by varying parameters for a specific formulation of the model functions, but models can show structural sensitivity to the choice of functional representations used: a particularly concerning problem when system processes are too complex, or insufficiently understood, to theoretically justify specific parameterizations. Here we propose a rigorous test for the detection of structural sensitivity in a system with respect to the local stability of equilibria, the main idea being to project infinite dimensional function space onto a finite dimensional space by considering the local properties of the model functions. As an illustrative example, we use our test to demonstrate structural sensitivity in the seminal Rosenzweig-MacArthur predator-prey model, and show that the conventional parameterbased approach can fail to do so. We also consider some implications that structural sensitivity has for ecological modelling: we argue that when the model exhibits structural sensitivity but experimental results remain consistent it may indicate that there is a problem with the model construction, and that in some cases trying to find an 'optimal' parameterization of a model function may simply be impossible when the model exhibits structural sensitivity. Finally, we suggest that the phenomenon of structural sensitivity in biological models may help explain the irregular oscillations often observed in real ecosystems.
One of the most crucial tasks faced by biologists today is revealing the mechanisms which account for biodiversity, yet we are still far from a full understanding of these mechanisms, and in particular the role of spatially heterogeneous population distributions. Recently, the spatially heterogeneous coexistence seen in cyclic competition models--in which species compete as in the game rock-paper-scissors--has brought them to the fore as a paradigm for biodiversity. Research into cyclic competition has so far been focused almost exclusively on stochastic lattice models with discrete space, which ignore several key dynamical aspects. In particular, such models usually assume that species disperse at the same speed. This paper aims to extend our understanding of cyclic competition by applying a reaction-diffusion Lotka-Volterra scheme to the problem, which allows us to vary the mobility of each species, and lets us take into account cyclic competition with more complex underlying mechanisms. In this paper we reveal an entirely new kind of cyclic competition-'conditional' cyclic competition, with a different underlying mechanism to 'classic' cyclic competition-and we show that biodiversity in communities with cyclic competition in fact depends heavily on the ratios between the species mobilities. Furthermore, we show that this dependence can be completely different for conditional and classic cyclic competition. We also present a wide range of spatiotemporal patterns which are formed in the system, including spiral and target waves, spiralling patches, and irregular chaotic patches. We show that the previously unknown case of conditional cyclic competition is host to a scenario of patchy co-invasion, where the spread of the population front takes place via the formation, splitting and propagation of patches of high species density. This is also an example of invasional meltdown because one competitor facilitates the invasion of the other, but unlike well-known cases of invasional meltdown the co-invaders in this system are not mutualists but antagonistic competitors, and the overall result mitigates, rather than amplifies, the damage done to the native ecosystem.
Background: There has been an increased interest in donation after circulatory death (DCD) to expand donor pool for cardiac transplantation. Normothermic regional perfusion (NRP) allows in situ assessment of DCD hearts, allowing only acceptable organs to be procured. We sought to determine if extended cold storage was possible for DCD hearts following NRP and to compare hearts stored using standard cold storage with a novel cardioprotective solution designed for room temperature storage. Methods and Results: Donor pigs underwent hypoxic cardiac arrest (DCD) followed by 15 minutes of warm ischemia and resuscitation on NRP. They were then randomly assigned to static storage with histidine-tryptophan-ketoglutarate (HTK) at 4°C (HTK group, n=5) or SOM-TRN-001 at 21°C (SOM group, n=5). Conventional beating-heart donations were used as controls (n=4). Fourteen transplants were successfully performed. HTK hearts showed initial dysfunction following reperfusion; however, they demonstrated significant recovery up to 3 hours post-transplant. No significant differences were seen between HTK and control hearts post-transplantation (cardiac index: control 49.5±6% and HTK 48.5±5% of baseline). SOM improved myocardial preservation; hearts showed stable contractility after transplantation (cardiac index: 113.0±43% of NRP function) and improved diastolic function compared with HTK. Preservation in SOM also significantly reduced proinflammatory cytokine production and release following transplantation and partially prevented endothelial dysfunction. Conclusions: DCD hearts stored using a standard preservation solution demonstrated comparable post-transplantation myocardial function to standard controls. Thus, short periods of cold storage following successful NRP and documented adequate function is an acceptable strategy for DCD hearts. Preservation in SOM at room temperature is feasible and can improve cardiac recovery by minimizing endothelial dysfunction and tissue injury.
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