1. In the context of ongoing climatic warming, forest landscapes face increasing risk of conversion to non-forest vegetation through alteration of their fire regimes and their post-fire recovery dynamics. However, this pressure could be amplified or dampened, depending on how fire-driven changes to vegetation feed back to alter the extent or behaviour of subsequent fires. 2.Here we develop a mathematical model to formalize understanding of how firevegetation feedbacks and the time to forest recovery following high-severity (i.e. stand-replacing) fire affect the extent and stability of forest cover across landscapes facing altered fire regimes. We evaluate responses to increasing burn rates while varying the direction (negative vs. positive) of fire-vegetation feedbacks under a continuum of values for feedback strength and post-fire recovery time. In doing so, we determine how interactions among these variables produce thresholds and tipping points in landscape responses to changing fire regimes.3. Where the early-seral vegetation was less fire-prone than older forests, negative feedbacks limited the reductions in forest cover in response to higher fire frequency or slower forest recovery. By contrast, positive feedbacks (more flammable early-seral vegetation) produced a tipping point beyond which increases in burn rates or a slowing of forest recovery drove extensive forest loss.4. With negative feedbacks, the rates of forest loss and expansion in response to variation in fire frequency were similar. However, where feedbacks were positive, the conversion from predominantly forested to non-forested conditions in response to increasing fire frequency was faster than the re-expansion of forest cover following a return to the initial burn rate. Strengthening the positive feedbacks increased this asymmetry. 5.Synthesis. Our analyses elucidate how fire-vegetation feedbacks and post-fire recovery rates interact to affect the trajectories and rates of landscape response to altered fire regimes. We illustrate the vulnerability of ecosystems with positive firevegetation feedbacks to climate change-driven increases in fire activity, especially 1926 | Journal of Ecology TEPLEY ET aL.

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Abstract. A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A functional analytic framework is also developed which partially connects stochastic iterations and certain Picard iterates. Some local existence and uniqueness results are also obtained by contractive mapping conditions on the Picard iteration.

We establish the existence, uniqueness and attraction properties of an ergodic invariant measure for the Boussinesq Equations in the presence of a degenerate stochastic forcing acting only in the temperature equation and only at the largest spatial scales. The central challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. Towards this aim we encounter a Lie bracket structure in the associated vector fields with a complicated dependence on solutions. This leads us to develop a novel Hörmander-type condition for infinite-dimensional systems. Demonstrating the sufficiency of this condition requires new techniques for the spectral analysis of the Malliavin covariance matrix.

This paper concerns the Taylor-Aris dispersion of a dilute solute concentration immersed in a highly heterogeneous fluid flow having possibly sharp interfaces (discontinuities) in the diffusion coefficient and flow velocity. The focus is twofold: (i) Calculation of the longitudinal effective dispersion coefficient, and (ii) sample path analysis of the underlying stochastic process governing the motion of solute particles. Essentially complete solutions are obtained for both problems.