Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).

Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

Evaluating the Performance of a Regional-Scale Photochemical Modelling System: Part I Ozone Predictions

We present a detailed evaluation of the seasonal performance of the Community Multiscale Air Quality (CMAQ) modelling system and the PSU/NCAR meteorological model coupled to a new Numerical Emission Model for Air Quality (MNEQA). The combined system simulates air quality at a fine resolution (3 km as horizontal resolution and 1 h as temporal resolution) in north-eastern Spain, where problems of ozone pollution are frequent. An extensive database compiled over two periods, from May to September 2009 and 2010, is used to evaluate meteorological simulations and chemical outputs. Our results indicate that the model accurately reproduces hourly and 1-h and 8-h maximum ozone surface concentrations measured at the air quality stations, as statistical values fall within the EPA and EU recommendations. However, to further improve forecast accuracy, three simple bias-adjustment techniques mean subtraction (MS), ratio adjustment (RA), and hybrid forecast (HF) based on 10 days of available comparisons are applied. The results show that the MS technique performed better than RA or HF, although all the bias-adjustment techniques significantly reduce the systematic errors in ozone forecasts.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

Locations and Relocations:Modelling, Determinants, and Interrelations

Empirical studies on industrial location do not typically distinguish between new and relocated establishments. This paper addresses this shortcoming using data on the frequency of these events in municipalities of the same economic-administrative region. This enables us to test not only for differences in their determinants but also for interrelations between start-ups and relocations. Estimates from count regression models for cross-section and panel data show that, although partial effects differ, common patterns arise in “institutional” and “neoclassical” explanatory factors. Also, start-ups and relocations are positive but asymmetrically related. JEL classification: C25, R30, R10. Keywords: cities, count data models, industrial location

Improving the effort concept: a revision of the traditional approach in the context of controlled Dynamic Stochastic Environments

The objective of this paper is to re-evaluate the attitude to effort of a risk-averse decision-maker in an evolving environment. In the classic analysis, the space of efforts is generally discretized. More realistic, this new approach emploies a continuum of effort levels. The presence of multiple possible efforts and performance levels provides a better basis for explaining real economic phenomena. The traditional approach (see, Laffont, J. J. & Tirole, J., 1993, Salanie, B., 1997, Laffont, J.J. and Martimort, D, 2002, among others) does not take into account the potential effect of the system dynamics on the agent's behavior to effort over time. In the context of a Principal-agent relationship, not only the incentives of the Principal can determine the private agent to allocate a good effort, but also the evolution of the dynamic system. The incentives can be ineffective when the environment does not incite the agent to invest a good effort. This explains why, some effici

Individual-based modelling of bacterial cultures to study the lag ohase

Els bacteris són la forma dominant de vida del planeta: poden sobreviure en medis molt adversos, i en alguns casos poden generar substàncies que quan les ingerim ens són tòxiques. La seva presència en els aliments fa que la microbiologia predictiva sigui un camp imprescindible en la microbiologia dels aliments per garantir la seguretat alimentària. Un cultiu bacterià pot passar per quatre fases de creixement: latència, exponencial, estacionària i de mort. En aquest treball s’ha avançat en la comprensió dels fenòmens intrínsecs a la fase de latència, que és de gran interès en l’àmbit de la microbiologia predictiva. Aquest estudi, realitzat al llarg de quatre anys, s’ha abordat des de la metodologia Individual-based Modelling (IbM) amb el simulador INDISIM (INDividual DIScrete SIMulation), que ha estat millorat per poder fer-ho. INDISIM ha permès estudiar dues causes de la fase de latència de forma separada, i abordar l’estudi del comportament del cultiu des d’una perspectiva mesoscòpica. S’ha vist que la fase de latència ha de ser estudiada com un procés dinàmic, i no definida per un paràmetre. L’estudi de l’evolució de variables com la distribució de propietats individuals entre la població (per exemple, la distribució de masses) o la velocitat de creixement, han permès distingir dues etapes en la fase de latència, inicial i de transició, i aprofundir en la comprensió del que passa a nivell cel•lular. S’han observat experimentalment amb citometria de flux diversos resultats previstos per les simulacions. La coincidència entre simulacions i experiments no és trivial ni casual: el sistema estudiat és un sistema complex, i per tant la coincidència del comportament al llarg del temps de diversos paràmetres interrelacionats és un aval a la metodologia emprada en les simulacions. Es pot afirmar, doncs, que s’ha verificat experimentalment la bondat de la metodologia INDISIM.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.