Quadratic perturbations of a quadratic reversible Lotka-Volterra System

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The period function of the generalized Lotka-Volterra centers

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Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Acción de algunos acaricidas sobre los fítoseídos y la araña roja Panonychus ulmi (Koch) en manzano

Se han realizado 5 ensayos en manzanos para evaluar la acción de algunos acarici­das sobre la araña roja Panonychus ulmi (Koch) y sus depredadores los fitoseidos. En 4 ensayos la especie era Amblyseius andersoni (Chant) y en la otra A. californicus (McGregor). En total se han ensayado 14 materias activas. Se observa una mayor toxicidad de los productos sobre A. californicus que sobre A. andersoni, y en esta última especie la toxicidad suele ser mayor cuando el nivel de P. ulmi es más elevado. Las materias activas que son mas tóxicas para los fitoseidos son: amitraz, bifentrin y fenpropatrin. En el caso del amitraz se observa incluso una proliferación de P. ulmi. Los productos que son menos tóxicos para los fitoseidos y que dan una mayor relación depredador/presa, a pesar de su baja eficacia sobre P. ulmi, son: benzoximato, dioctil-sulfosuccinato-sodico y fenbutestan. Los acaricidas: cihexaestan, dinobuton, hexitiazox y propargita son medianamente tóxicos para los fitoseidos, pero su poca eficacia sobre P. ulmi provoca como resultado una relación depredador/ presa más baja que el testigo. Los que dan una mayor eficacia sobre P. ulmi, pero son más tóxicos para los fi­toseidos que los productos anteriores, por lo que dan como resultado unas relaciones de­ predador/presa más irregulares son: fenazaquin, fenpiroximato, piridaben y tebufenpirad. Deben realizarse más estudios sobre las dosis, mezclas y momentos de aplicación de todos estos productos para su utilización en el control integrado de la araña roja.

Ten years after the Prestige Oil Spill: seabird trophic ecology as indicator of long-term effects on the coastal marine ecosystem

Major oil spills can have long-term impacts since oil pollution does not only result in acute mortality of marine organisms, but also affects productivity levels, predator-prey dynamics, and damages habitats that support marine communities. However, despite the conservation implications of oil accidents, the monitoring and assessment of its lasting impacts still remains a difficult and daunting task. Here, we used European shags to evaluate the overall, lasting effects of the Prestige oil spill (2002) on the affected marine ecosystem. Using δ15N and Hg analysis, we trace temporal changes in feeding ecology potentially related to alterations of the food web due to the spill. Using climatic and oceanic data, we also investigate the influence of North Atlantic Oscillation (NAO) index, the sea surface temperature (SST) and the chlorophyll a (Chl a) on the observed changes. Analysis of δ15N and Hg concentrations revealed that after the Prestige oil spill, shag chicks abruptly switched their trophic level from a diet based on a high percentage of demersal-benthic fish to a higher proportion of pelagic/semi-pelagic species. There was no evidence that Chl a, SST and NAO reflected any particular changes or severity in environmental conditions for any year or season that may explain the sudden change observed in trophic level. Thus, this study highlighted an impact on the marine food web for at least three years. Our results provide the best evidence to date of the long-term consequences of the Prestige oil spill. They also show how, regardless of wider oceanographic variability, lasting impacts on predator-prey dynamics can be assessed using biochemical markers. This is particularly useful if larger scale and longer term monitoring of all trophic levels is unfeasible due to limited funding or high ecosystem complexity.

Experimental assessment of the effects of a Neotropical nocturnal piscivore on juvenile native and invasive fishes

We experimentally examined the predator-prey relationships between juvenile spotted sorubim Pseudoplastystoma corruscans and young-of-the-year invasive and native fish species of the Paraná River basin, Brazil. Three invasive (peacock bass Cichla piquiti, Nile tilapia Oreochromis niloticus, and channel catfish Ictalurus punctatus) and two native (yellowtail tetra Astyanax altiparanae and streaked prochilod Prochilodus lineatus) fish species were offered as prey to P. corruscans in 300 L aquaria with three habitat complexity treatments (0%, 50% and 100% structure-covered). Prey survival was variable through time and among species (C. piquiti < O. niloticus < A. altiparanae < P. lineatus < I. punctatus), depending largely on species-specific prey behavior but also on prey size and morphological defenses. Habitat complexity did not directly affect P. corruscans piscivory but some prey species changed their microhabitat use and shoaling behavior among habitat treatments in predator’s presence. Pseudoplatystoma corruscans preyed preferentially on smaller individuals of those invasive species with weak morphological defensive features that persisted in a non-shoaling behavior. Overall, our results contrast with those in a companion experiment using a diurnal predator, suggesting that nocturnal piscivores preferentially prey on different (rather diurnal) fish species and are less affected by habitat complexity. Our findings suggest that recovering the native populations of P. corruscans might help controling some fish species introduced to the Paraná River basin, particularly C. piquiti and O. niloticus, whose parental care is expected to be weak or null at night

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.

On the stability of periodic orbits in Rn

We consider an autonomous differential system in Rn with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the transversal intersection of n ¡ 1 codimension one hypersurfaces and is an alternative to the use of the first order variational equations. We apply it to study the stability of the periodic orbits in several examples, including a periodic solution found by Steklov studying the rigid body dynamics.

Periodic Solutions in Low-Dimensional Climatic Models

Classic climatic models use constitutive laws without any response time. A more realistic approach to the natural processes governing climate dynamics must introduce response time for heat and radiation fluxes. Extended irreversible thermodynamics (EIT) is a good thermodynamical framework for introducing nonclassical constitutive laws. In the present study EIT has been used to analyze a Budyko–Sellers one-dimensional energybalance model developed by G. R. North. The results present self-sustained periodic oscillations when the response time is greater than a critical value. The high-frequency (few kiloyears) damped and nondamped oscillations obtained can be related to abrupt climatic changes without any variation in the external forcing of the system

Noise and periodic modulations in neural excitable medium

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. For this purpose, we have considered two types of modulations, namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is present, irrespective of whether the system is monostable or bistable.

Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Multi-scale effects of nestling diet on breeding performance in a terrestrial top predator inferred from stable isotope analysis

Inter-individual diet variation within populations is likely to have important ecological and evolutionary implications. The diet-fitness relationships at the individual level and the emerging population processes are, however, poorly understood for most avian predators inhabiting complex terrestrial ecosystems. In this study, we use an isotopic approach to assess the trophic ecology of nestlings in a long-lived raptor, the Bonelli"s eagle Aquila fasciata, and investigate whether nestling dietary breath and main prey consumption can affect the species" reproductive performance at two spatial scales: territories within populations and populations over a large geographic area. At the territory level, those breeding pairs whose nestlings consumed similar diets to the overall population (i.e. moderate consumption of preferred prey, but complemented by alternative prey categories) or those disproportionally consuming preferred prey were more likely to fledge two chicks. An increase in the diet diversity, however, related negatively with productivity. The age and replacements of breeding pair members had also an influence on productivity, with more fledglings associated to adult pairs with few replacements, as expected in long-lived species. At the population level, mean productivity was higher in those population-years with lower dietary breadth and higher diet similarity among territories, which was related to an overall higher consumption of preferred prey. Thus, we revealed a correspondence in diet-fitness relationships at two spatial scales: territories and populations. We suggest that stable isotope analyses may be a powerful tool to monitor the diet of terrestrial avian predators on large spatio-temporal scales, which could serve to detect potential changes in the availability of those prey on which predators depend for breeding. We encourage ecologists and evolutionary and conservation biologists concerned with the multi-scale fitness consequences of inter-individual variation in resource use to employ similar stable isotope-based approaches, which can be successfully applied to complex ecosystems such as the Mediterranean.